Methods and systems for designing and evaluating the performance of hollow fiber membrane contactors, MBCs, in natural gas sweetening processes

Abstract

A computer-implemented method of designing and evaluating performance of a hollow fiber membrane contactor (MBC) in a natural gas sweetening process using a MBC model is described in embodiments. The MBC model includes model parameters, model equations, and boundary conditions for calculating data associated with the natural gas sweetening process. The natural gas sweetening process includes removal of acid gases from natural gas using a solvent including at least one component. The method includes: (i) forming a regression model using empirical data; (ii) determining a Henry's constant for CO2 in the solvent using the regression model; (iii) inputting the determined Henry's constant for CO2 as one of the model parameters in the MBC model; and (iv) determining CO2 absorption in the solvent using the MBC model to design and evaluate performance of the MBC.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to methods and systems for designing and evaluating the performance of a membrane-based contactor (MBC) in a natural gas sweetening process, particularly by using a hollow fiber membrane contactor (MBC) model. BACKGROUND

[0002] Natural gas (NG) is currently the third most commonly used form of fossil fuel energy and is widely used for both power generation and transportation. NG comprises a mixture of combustible hydrocarbon gases (typically methane (CH4), ethane (C2H6), propane (C3H8), butane (C4H10), and pentane (C5H12)) and impurities (e.g., carbon dioxide (CO2)). Removing CO2 from NG is important for several reasons: (i) to meet sales gas standards for NG, which typically force CO2 content to be less than 2-3%, (ii) to avoid freezing in cryogenic chillers, (iii) to avoid catalyst poisoning in ammonia plants, (iv) to reduce corrosion risk in processing equipment and pipelines, (v) to reduce the heating value of NG, and (vi) to meet <50 ppmv in liquefied natural gas plants to avoid freezing in cryogenic chillers. 10 12 ) and pentane (C5H

[0003] In the past decade, membrane contactors (MBCs) for CO2 absorption have gained wide recognition for their large intensification potential compared to conventional absorption columns. MBC technology uses microporous hollow fiber membranes (HFM) to achieve efficient gas and liquid mass transfer without the two phases being dispersed into each other. Encapsulating microporous hollow fiber membranes as HFM modules provides higher mass transfer area compared to conventional packed columns, which in turn endows MBCs with high intensification potential. This modularity also allows for more flexible design and scale-up.

[0004] Mathematical models provide an effective tool to help understand the CO2 removal mechanism in MBCs, thereby enabling better evaluation and optimization of their performance. However, most models to date are flawed and do not take into account various factors or influences that can especially impact the accuracy of the simulated output of a MBC, such as CO2 absorption rate. Moreover, most commercial process simulators do not include models or tools associated with the use of HFM in MBC technology. The lack of HFM mathematical tools poses a problem for end users to design and optimize HFM systems, particularly for HFM systems used in natural gas sweetening processes.

[0005] Accordingly, it is desirable to provide methods and systems for evaluating the performance of a membrane-based contactor (MBC) in a natural gas sweetening process using a MBC model that takes into account various factors and influences in a MBC to address the above problems and / or to provide useful alternatives for the public.​

[0006] Further features and advantages will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, and upon examination of the claims. SUMMARY

[0007] Aspects of the present application relate to methods and systems for designing and evaluating performance of a hollow fiber membrane contactor (MBC) in a natural gas sweetening process using a MBC model.

[0008] According to a first aspect, there is provided a computer-implemented method for designing and evaluating performance of a hollow fiber membrane contactor (MBC) in a natural gas sweetening process using a MBC model. The MBC model comprises model parameters, model equations and boundary conditions for calculating data associated with the natural gas sweetening process, and the natural gas sweetening process comprises removal of acid gases from natural gas using a solvent comprising at least one component. The method comprises: (i) forming a regression model using empirical data; (ii) determining a Henry’s constant for CO2 in the solvent using the regression model; (iii) inputting the determined Henry’s constant for CO2 in the MBC model as one of the model parameters; and (iv) determining CO2 absorption in the solvent using the MBC model to design and evaluate performance of the MBC.

[0009] By forming a regression model using empirical data, a Henry’s constant for CO2 in the solvent can be determined, which advantageously accounts for the CO2 loading in the solvent. This is important because the CO2 loading in the solvent affects the rate of CO2 absorption in the solvent, which in turn affects the performance of the MBC. Furthermore, forming a regression model using empirical data improves the accuracy of the model predictions, for example, as compared to using analytical equations alone. Moreover, by not using a large number of analytical equations that would otherwise be required to simulate the Henry’s constant for CO2, the above-described method shortens the simulation time required to determine CO2 absorption in the solvent using the MBC model for designing and evaluating performance of the MBC. The regression model can be formed for the Henry’s constant for CO2 using empirical data associated with solubility of CO2 in the solvent. In an embodiment, the regression model can be formed for the Henry’s constant for nitrous oxide as described below.

[0010] The method can include forming a regression model of the Henry's constant of N2O using empirical data of solubility of N2O in the solvent; determining the Henry's constant of N2O using the regression model of the Henry's constant of N2O; and determining the Henry's constant of CO2 in the solvent using the Henry's constant of N2O to account for the CO2 loading in the solvent. N2O is chosen because it has similar properties to CO2 and does not react with the solvent. Therefore, experiments conducted to obtain solubility of N2O in the solvent are simple and their data are reliable.

[0011] The method can include forming a regression model of the Henry's constant of a hydrocarbon in the solvent using empirical data of solubility of the hydrocarbon in the solvent to account for the loss of the hydrocarbon from the natural gas to the solvent; and determining the Henry's constant of the hydrocarbon in the solvent using the regression model of the Henry's constant of the hydrocarbon.

[0012] Similar to the above, the accuracy of the model prediction is improved due to forming the regression model of the Henry's constant of the hydrocarbon using empirical data. Furthermore, the above method improves the simulation time required to determine the Henry's constant of the hydrocarbon, which in turn is used to determine the loss rate of the hydrocarbon, by not using a large number of analytical equations that are otherwise required to simulate the Henry's constant of the hydrocarbon, as described below.

[0013] The method can include determining the loss rate of the hydrocarbon in the solvent using the Henry's constant of the hydrocarbon in an equation of hydrocarbon rate loss, wherein the loss rate of the hydrocarbon is a function of the concentration of the hydrocarbon, and wherein the concentration of the hydrocarbon is inversely proportional to the Henry's constant of the hydrocarbon in the solvent. By considering the loss rate of the hydrocarbon in the solvent, the above method advantageously considers the issue of physical absorption of the hydrocarbon from the NG into the solvent (e.g., amine solvent) which is significant when the pressure is increased to 60 bar (increased by 10-30 times when compared to near atmospheric pressure). Furthermore, any hydrocarbon (HC) that is not recovered by the solvent absorption will end up in the waste acid gas stream, thus representing product loss, and the presence of hydrocarbons in the acid gas stream also causes issues downstream of the MBC treatment, such as catalyst fouling in the Clause reactor. By having an effective method of simulating the loss rate of the hydrocarbon, various parameters of the natural gas desulfurization treatment can be adjusted to minimize product loss and mitigate issues such as catalyst fouling as described above.

[0014] The method can include including the equation of hydrocarbon rate loss as one of the model equations of the MBC model.

[0015] The method can comprise determining a mole fraction of the at least one component of the solvent in the gas outlet using Raoult’s Law; and using the mole fraction in a solvent rate loss equation to determine a solvent loss rate, wherein the solvent loss rate is proportional to the determined mole fraction. By determining the mole fraction of the at least one component of the solvent in the gas outlet, the solvent loss rate can be determined. This advantageously accounts for the effect of solvent evaporation on the performance of the MBC process. In practice, the gradual loss of solvent in the MBC to the treated gas can change the CO2absorption rate. Furthermore, the amount of water evaporated from the solvent causes a drop in the temperature of the solvent. This drop in the temperature of the solvent can affect the mass transfer performance in the MBC. For example, important factors such as the CO2capture capacity and the corrosion rate directly depend on the temperature of the MBC column.

[0016] The method can comprise including the solvent rate loss equation as one of the model equations of the MBC model.

[0017] The method can comprise using the solvent loss rate to determine the energy consumed by the solvent evaporation and the liquid temperature of the solvent at the liquid inlet of the MBC.

[0018] The method can comprise determining the change in liquid temperature by balancing the energy consumed by the solvent evaporation with the exothermic CO2absorption reaction along the length of the MBC under adiabatic conditions. By determining the change in liquid temperature, the mass transfer performance in the MBC can be assessed, as described above. Other important factors of the performance of the MBC, such as the CO2capture capacity, can also depend on the temperature of the MBC column.

[0019] According to a second aspect, a computer-implemented method for assessing the performance of a natural gas sweetening process is described. The natural gas sweetening process comprises an absorption operation and a desorption operation, wherein the absorption operation is associated with an acid gas absorption using a hollow fiber membrane contactor, MBC, and the desorption operation is associated with a solvent regeneration using a solvent regenerator, and wherein the absorption operation is modeled based on the MBC model using the computer-implemented method described above.

[0020] The method for assessing the performance of a natural gas sweetening process can comprise calculating an optimized flow rate for achieving a predetermined CO2purity in the natural gas, the optimized flow rate being associated with a lean operation and a semi-lean operation each, the lean operation being an operation associated with the use of a lean solvent having a CO2loading of less than 0.02 mol mol -1 of CO2, and the semi-lean operation being an operation associated with the use of a semi-lean solvent having a CO2loading of greater than 0.2 mol mol -1a semi-lean solvent associated operation of the CO2 loading; and determining a total processing load of the natural gas sweetening process associated with the absorption operation and the desorption operation under the lean operation and the semi-lean operation.

[0021] The method for evaluating performance of a natural gas sweetening process can include calculating a pressure for operating a rich solution flash drum associated with each of the lean operation and the semi-lean operation to achieve a predetermined lower heating value of a fuel gas, the fuel gas being a gas recovered from hydrocarbon loss in the solvent during the natural gas sweetening process.

[0022] According to a third aspect, there is provided a computer-implemented method for designing and evaluating performance of a membrane-based contactor (MBC) in a natural gas sweetening process using a MBC model, wherein the MBC model comprises model parameters, model equations and boundary conditions for calculating data associated with the natural gas sweetening process, and the natural gas sweetening process comprises removal of acid gases from natural gas using a solvent comprising at least one component, the method comprising: (i) using empirical data of solubility of a hydrocarbon in the solvent to form a regression model of Henry’s constant of the hydrocarbon in the solvent to account for hydrocarbon loss from the natural gas to the solvent, wherein the regression model is a function of temperature of the solvent, pressure of the solvent and mass fraction of the at least one component in the solvent; (ii) determining Henry’s constant of the hydrocarbon in the solvent; (iii) using Henry’s constant of the hydrocarbon in a hydrocarbon rate loss equation to determine a rate of loss of the hydrocarbon in the solvent to account for hydrocarbon loss from the natural gas to the solvent, wherein the rate of loss of the hydrocarbon is a function of concentration of the hydrocarbon, and wherein the concentration of the hydrocarbon is inversely proportional to Henry’s constant of the hydrocarbon; and (iv) using the MBC model to determine CO2 absorption in the solvent to design and evaluate performance of the membrane-based contactor, wherein the hydrocarbon rate loss equation is included as one of the model equations of the MBC model.

[0023] According to a fourth aspect, there is provided a computer readable medium having stored thereon processor-executable instructions that, when executed on a processor, cause the processor to perform a method as described above.

[0024] According to a fifth aspect, there is provided a hollow fiber membrane contactor data processing system, MBC data processing system, for designing and evaluating performance of a hollow fiber membrane contactor, MBC, in a natural gas sweetening process using a MBC model. The MBC model comprises model parameters, model equations and boundary conditions for calculating data associated with the natural gas sweetening process, and the natural gas sweetening process comprises removal of acid gases from natural gas using a solvent comprising at least one component. The MBC data processing system comprises a processor and a data storage device having stored thereon computer program instructions operable to cause the processor to: form a regression model using empirical data; determine a Henry's constant for CO2 in the solvent using the regression model; input the determined Henry's constant for CO2 in the MBC model as one of the model parameters; and determine CO2 absorption in the solvent using the MBC model to design and evaluate MBC performance.

[0025] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to: form a regression model for a Henry's constant for N2O using empirical data for solubility of nitrous oxide, N2O, in the solvent; determine the Henry's constant for N2O using the regression model for the Henry's constant for N2O; and determine the Henry's constant for CO2 in the solvent using the Henry's constant for N2O to account for CO2 loading in the solvent.

[0026] The regression model for the Henry's constant for nitrous oxide, N2O, can be a function of CO2 loading in the solvent and liquid temperature.

[0027] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to: form a regression model for a Henry's constant for a hydrocarbon in the solvent using empirical data for solubility of the hydrocarbon in the solvent to account for hydrocarbon loss from the natural gas to the solvent; and determine the Henry's constant for the hydrocarbon in the solvent using the regression model for the Henry's constant for the hydrocarbon.

[0028] The regression model for the Henry's constant for the hydrocarbon can be a function of liquid temperature of the solvent, liquid pressure of the solvent and mass fraction of the at least one component in the solvent.

[0029] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to: determine a loss rate of the hydrocarbon in the solvent using the Henry's constant for the hydrocarbon in a hydrocarbon loss rate equation, wherein the loss rate of the hydrocarbon is a function of a concentration of the hydrocarbon, and wherein the concentration of the hydrocarbon is inversely proportional to the Henry's constant for the hydrocarbon.

[0030] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to include the solvent rate loss equation as one of the model equations of the MBC model.

[0031] The solvent can be hydrocarbon saturated at the liquid outlet of the MBC.

[0032] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to: determine a mole fraction of the at least one component of the solvent in the gas outlet using Raoult's law; and use the mole fraction in a solvent rate loss equation to determine a solvent loss rate, wherein the solvent loss rate is proportional to the determined mole fraction.

[0033] The treated gas at the gas outlet of the MBC can be solvent saturated, and the natural gas and the solvent can be in equilibrium at the gas outlet.

[0034] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to include the solvent rate loss equation as one of the model equations of the MBC model.

[0035] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to use the solvent loss rate to determine an energy consumed by solvent evaporation at the liquid inlet of the MBC and a liquid temperature of the solvent.

[0036] Solvent evaporation can occur at the liquid inlet before the solvent reacts with the CO2 in the natural gas along the length of the MBC.

[0037] The data storage device of the MBC data processing system can store computer program instructions operable to cause the processor to determine a change in the liquid temperature by balancing the energy consumed by solvent evaporation with the exothermic CO2 absorption reaction along the length of the MBC under adiabatic conditions.

[0038] Thermal diffusion along a radial axis can be neglected, and the liquid temperature can be considered uniform in the radial direction.

[0039] wherein the solvent includes 50% by weight of methyldiethanolamine (MDEA), a regression model of the Henry's constant of nitrous oxide (N2O) is modeled as:

[0040]

[0041] wherein, is associated with an inlet CO2 loading in the solvent, and T l is a liquid temperature of the solvent.

[0042] The regression model of the Henry's constant of the hydrocarbon is modeled as:

[0043] H i，l = a0 + a1C + a2T l + a3P l + a4CT l + a5CP l + a6T l P l

[0044] wherein, T l is a liquid temperature of the solvent, P l is a liquid pressure of the solvent, C is a mass fraction of the at least one component in the solvent, and coefficients a1 to a6 are parameters of the regression model of the Henry's constant of the hydrocarbon.

[0045] According to a sixth aspect, a natural gas sweetening treatment operation system is described. The natural gas sweetening treatment operation system comprises the MBC data processing system and the solvent regeneration data processing system described above, the MBC data processing system is associated with an absorption operation for absorbing acid gases using the hollow fiber membrane contactor (MBC), and the solvent regeneration data processing system is associated with a desorption operation for regenerating a solvent using a solvent regenerator.

[0046] The natural gas sweetening treatment operation system can comprise a processor and a data storage device storing computer program instructions operable to cause the processor to: calculate an optimized flow rate for achieving a predetermined CO2 purity in the natural gas, the optimized flow rate being associated with each of a lean operation and a semi-lean operation, the lean operation being an operation associated with using a lean solvent having a CO2 loading less than 0.02 mol mol -1 of the hydrocarbon, and the semi-lean operation being an operation associated with using a semi-lean solvent having a CO2 loading greater than 0.2 mol mol -1 of the hydrocarbon; and determine a total treatment load of the natural gas sweetening treatment associated with the absorption operation and the desorption operation under the lean operation and the semi-lean operation.

[0047] The data storage device of the natural gas sweetening treatment operation system can store computer program instructions operable to cause the processor to: calculate a pressure for operating a rich solution flash drum associated with each of the lean operation and the semi-lean operation to achieve a predetermined lower heating value of a fuel gas, the fuel gas being a gas recovered from a hydrocarbon loss in the solvent during the natural gas sweetening treatment.

[0048] It will be appreciated that features relating to one aspect can be applicable to other aspects. Thus, embodiments provide methods and systems for designing and evaluating performance of a hollow fiber membrane contactor (MBC) in a natural gas sweetening treatment using a MBC model. By forming a regression model using empirical data, a Henry’s constant for CO2 can be determined, which advantageously accounts for CO2 loading in the solvent. The regression model is formed based on empirical data, thereby improving accuracy of model predictions. Further, the above-described method improves simulation time required to determine CO2 absorption in the solvent using a MBC model for evaluating performance of the MBC, by not using a large number of analytical equations otherwise required to simulate the Henry’s constant for CO2. Embodiments can also provide a regression model of a Henry’s constant for hydrocarbons formed using empirical data, which improves accuracy of model predictions. Further, embodiments also improve simulation time required to determine a loss rate of hydrocarbons as described, by not using a large number of analytical equations otherwise required to simulate the Henry’s constant for hydrocarbons. In turn, by accounting for the loss rate of hydrocarbons in the solvent, embodiments advantageously account for issues of physical absorption of hydrocarbons from NG into amine solvent, which is significant when pressure in the MBC is increased to, for example, 60 bar. BRIEF DESCRIPTION OF DRAWINGS

[0049] Embodiments will now be described, by way of example only, with reference to the following drawings:

[0050] Figure 1A and Figure 1B shows a schematic diagram of a modeling framework for a counter-current hollow fiber MBC module according to an embodiment, wherein Figure 1A shows a schematic diagram illustrating a cylindrical approximation around individual fibers of a MBC, and Figure 1B shows a schematic diagram of a single hollow fiber of a MBC, which illustrates counter-current flow of gas and solvent in the MBC;

[0051] Figure 2 shows a schematic diagram of a spatial domain for modeling a MBC according to an embodiment;

[0052] Figure 3 shows a graph comparing a cumulative pore area ratio distribution based on a simulated lognormal pore size distribution to manufacturer data according to an embodiment;

[0053] Figure 4a plot showing the analytical wetting ratio representation compared to the fitted alternative representation in terms of critical hole radius according to an embodiment;

[0054] Figure 5A and Figure 5B a plot showing the plot lines associated with different membrane areas of hollow fiber MBCs according to an embodiment, wherein Figure 5A a plot showing the required outer radius of steel tubes inserts of different membrane areas and the predicted total number of fibers in the MBC module to maintain a packing density of 0.55, and Figure 5B a plot showing the predicted CO2absorption flux and CO2outlet gas purity for different membrane areas;

[0055] Figure 6A , Figure 6B and Figure 6C a plot showing the predicted and measured Henry’s constants for water and different hydrocarbons in 50 wt% aqueous MDEA according to an embodiment, wherein Figure 6A a plot showing the predicted and measured Henry’s constants for methane (CH4), Figure 6B a plot showing the predicted and measured Henry’s constants for ethane (C2H6), and Figure 6C a plot showing the predicted and measured Henry’s constants for propane (C3H8);

[0056] Figure 7A and Figure 7B a plot showing the predicted Henry’s constants for nitrous oxide (N2O) according to an embodiment, wherein Figure 7A a plot showing the experimental data for the Henry’s constant of N2O compared to the predicted Henry’s constant for N2O, and Figure 7B a plot showing the predicted Henry’s constants for N2O at various CO2loadings for lean amine and semi-lean amine operation;

[0057] Figure 8 a schematic diagram of a laboratory scale setup for removal of carbon dioxide (CO2) in natural gas sweetening treatment using horizontal MBCs according to an embodiment;

[0058] Figure 9 is a schematic diagram of a pilot natural gas (pilot NG) plant setup for removal of carbon dioxide (CO2) in natural gas sweetening treatment using hollow fiber membrane contactors (MBCs) according to an embodiment;

[0059] Figure 10A , Figure 10B and Figure 10C are block diagrams of a natural gas sweetening treatment operation system, a hollow fiber membrane contactor (MBC) data processing system, and a solvent regeneration data processing system, respectively, according to an embodiment;

[0060] Figure 11 This illustrates, according to an embodiment, a method for using including... Figure 10B The flowchart illustrates a method for designing and evaluating the performance of hollow fiber membrane contactors (MBCs) in natural gas desulfurization processes, using a hollow fiber membrane contactor (MBC) model in the system.

[0061] Figure 12 This is a flowchart illustrating the steps of a method for determining the rate of hydrocarbon loss in a solvent of an MBC according to an embodiment;

[0062] Figure 13 This is a flowchart illustrating a method for determining the solvent loss rate and liquid temperature change of the solvent in an MBC according to an embodiment;

[0063] Figure 14 This is a flowchart illustrating the steps of a method for determining the total processing load of natural gas desulfurization under lean operation and semi-lean operation, according to an embodiment.

[0064] Figure 15A , Figure 15B , Figure 15C , Figure 15D and Figure 15E This illustrates a laboratory-scale MBC setup according to an embodiment. Figures 15A-15C ) and for pilot-scale NG plant setup ( Figure 15D and Figure 15E The graph is equivalent to the predicted CO2 absorption flux from experimental data, where Figure 15A The graphs show the CO2 absorption flux and predicted wetting ratio for laboratory-scale MBC settings with different CO2 loadings. Figure 15B The graphs show the CO2 absorption flux and predicted wetting ratio for different total gas flow rates in a laboratory-scale MBC setup. Figure 15C The graphs show the CO2 absorption flux and predicted wetting ratio for different total liquid flow rates in a laboratory-scale MBC setup. Figure 15D The graphs show the CO2 absorption flux and predicted wetting ratio for different CO2 loadings at the pilot-scale NG plant setup, and... Figure 15E The graph shows the CO2 absorption flux and predicted wetting ratio for different CO2 inlet concentrations in the natural gas mixture at the pilot NG plant setup;

[0065] Figure 16 The graphs show the predicted and experimental solvent temperatures and CO2 absorption at different axial positions along the length of the MBC according to the embodiment.

[0066] Figure 17Figure showing predicted and experimental hydrocarbon molar flow rates in the flash gas for the pilot NG plant at different liquid flow rates according to embodiments;

[0067] Figure 18 Figure showing plot of predicted vapour pressures of water, MDEA and PZ against different solvent temperatures from 293 K to 353 K according to embodiments;

[0068] Figure 19 Figure showing schematic of the gML compliant MBC unit operation model for modelling natural gas sweetening in gPROMS ProcessBuilder according to embodiments;

[0069] Figure 20 Figure showing schematic of the MBC based natural gas sweetening process flow in gPROMS ProcessBuilder according to embodiments;

[0070] Figure 21A and Figure 21B Figure showing plot of predicted and experimental CO2 purity, CO2 removal efficiency and total process duty at the MBC outlet for different CO2 loadings in the amine solvent according to embodiments, wherein Figure 21A Figure showing plot of predicted and experimental CO2 purity and CO2 removal efficiency for different CO2 loadings in the amine solvent, and Figure 21B Figure showing plot of predicted and experimental total process duty for different CO2 loadings in the amine solvent;

[0071] Figure 22A and Figure 22B Figure showing plot of predicted and experimental CO2 absorption flux and CO2 loading for different solvent regeneration temperatures according to embodiments, wherein Figure 22A Figure showing plot of predicted and experimental CO2 absorption flux for different solvent regeneration temperatures, and Figure 22B Figure showing plot of predicted and experimental CO2 loading for different solvent regeneration temperatures;

[0072] Figure 23 Figure showing schematic of the MBC pilot scale semi-lean operation process flow in gPROMS ProcessBuilder according to embodiments;

[0073] Figure 24A and Figure 24B Figure showing pie chart of the breakdown of the equipment process duty according to embodiments, wherein Figure 24A Figure showing pie chart of the breakdown of the equipment process duty for lean amine operation, and Figure 24B Figure showing pie chart of the breakdown of the equipment process duty for semi-lean amine operation;

[0074] Figure 25A andFigure 25B Graphs showing predicted hydrocarbon recovery and low heating value (LHV) of natural gas against rich solution drum pressure according to embodiments, wherein Figure 25A Graphs showing predicted hydrocarbon recovery and LHV of natural gas against rich solution drum pressure under lean amine operation, and Figure 25B Graphs showing predicted hydrocarbon recovery and LHV of natural gas against rich solution drum pressure under semi-lean amine operation;

[0075] Figure 26A and Figure 26B Graphs showing the effect of solvent temperature at the MBC inlet on the evaporation loss of different components of the solvent (i.e. water, MDEA, and PZ) in natural gas sweetening according to embodiments, wherein Figure 26A Graphs showing the evaporation loss of water, MDEA, and PZ at different solvent temperatures, and Figure 26B Graphs showing the ratio of evaporation loss in the acid gas to the loss in the treated gas for water and MDEA+PZ at different solvent temperatures; and

[0076] Figure 27 A schematic diagram showing a cross-section of a commercial MBC module according to embodiments. DETAILED DESCRIPTION

[0077] The present disclosure relates to the use of methods and systems for designing and evaluating the performance of a membrane-based contactor (MBC) in natural gas sweetening using a MBC model. The MBC model includes model parameters, model equations, and boundary conditions for calculating data associated with natural gas sweetening, and the natural gas sweetening includes removing acid gases from natural gas using a solvent comprising at least one component. The solvent can include water, methylethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), and / or piperazine (PZ). The solvent can also be referred to as an amine solvent, which is used interchangeably in the specification below.

[0078] In developing a MBC-based process NG plant-wide model for NG sweetening, the solvent evaporation rate, mass and energy balance, solubility of hydrocarbons in the amine solvent, and CO2 loading in the amine solvent must be considered. The MBC model of the present disclosure for high pressure MBC is formulated and experimentally validated as described below with respect to FIGS. 1 to Figure 18 The MBC model of the present disclosure for high pressure MBC is formulated and experimentally validated as described below with respect to FIGS. 1 to Figures 19 through 27 CO2 absorption and desorption operations in full-scale MBC processes for NG sweetening are described. Although the MBC model has been applied to high pressure conditions (e.g. greater than 5 bar), it can also be applied to low pressure conditions. For example, the MBC model can be used to capture carbon from flue gas at atmospheric pressure (e.g. 1 bar).

[0079] Figure 1A and 1B schematic diagram 100, 110 for modeling a counter-current hollow fiber MBC module according to an embodiment is shown, wherein Figure 1A schematic diagram 100 showing a cylindrical approximation around individual fibers of the MBC is shown, and Figure 1B schematic diagram 110 of a single hollow fiber of the MBC is shown, which demonstrates the counter-current flow of gas and solvent in the MBC.

[0080] As Figure 1A shown, a hollow fiber MBC module 102 comprises a plurality of hollow fibers 104. The hollow fibers 104 are packed closely together, and their shells are each approximated using a circle as shown. As Figure 1B shown, in a counter-current configuration, a NG gas mixture containing CO2 flows through the hollow fibers 104 in the tube via a gas inlet 112 at z = L, while the solvent flows inside the shells of the hollow fibers 104 via a liquid / solvent inlet 114 at z = 0. The gas mixture diffuses from the tube side through the walls of the hollow fibers 104 into the shells, where the CO2 is chemically absorbed by the solvent to increase the removal rate.

[0081] Figure 2 schematic diagram 200 for modeling a MBC in a spatial domain according to an embodiment is shown. The schematic diagram 200 shows a half cross-section of a hollow fiber membrane (HFM) comprising a hollow 202 through which a natural gas mixture flows, a tube 204 of the HFM, a membrane 206 of the HFM, and a shell 208 of the HFM through which a solvent flows to the natural gas mixture in a counter-current arrangement. Exchange of hydrocarbons and CO2 occurs on the membrane 206 of the HFM.

[0082] A complete description of the membrane wetting modeling and underlying assumptions are given in the previous work “Modeling for Design and Operation of High-Pressure Membrane Contactors in Natural Gas Sweetening” in Chemical Engineering Research and Design 132, 1005-1019 (2018), and its entirety is incorporated herein by reference. A concept variable called wetting radius r w [m] is introduced to represent the average fraction of the membrane pores filled with liquid to describe the degree of membrane wetting. The non-wetting and fully wetting modes of operation correspond to r w = r2 and r w = r1, respectively, where r1 and r2 are as Figure 2The inner and outer radii of the fiber are shown. When symmetry is exploited, the spatial domain for modeling the hollow fiber can be considered as (r,z)∈[0,r3]×[0,L], which is further partitioned into four subdomains as shown: (i) tube 204, 0≤r≤r1; (ii) membrane-dry, r1≤r≤r Figure 2 w (z); (iii) membrane-wet, r w (z)≤r≤r2; and (iv) shell 208, r2≤r≤r3. The geometry of the wet and non-wet membrane subdomains becomes complex due to the dependence of the wetting radius on the axial position z. Many factors are known to influence the degree of wetting, including the membrane-solvent combination, membrane properties such as contact angle, and various operating parameters. In principle, membrane wetting can be prevented by keeping the transmembrane pressure below the critical breakthrough pressure.

[0083] The mass conservation equations in the tube 204, membrane 206, and shell 208 sections of the HFM, along with the associated boundary conditions and underlying assumptions, are shown in Table 1 below as a reference. These equations consider steady-state and isothermal operation for all phases and were previously described in the prior work “Modeling for Design and Operation of High-Pressure Membrane Contactors in Natural Gas Sweetening” in Chemical Engineering Research and Design 132, 1005-1019 (2018).

[0084] Table 1: Summary of mass conservation equations and boundary conditions.

[0085]

[0086]

[0087] The following sections detail the modeling of hydrocarbon absorption in the solvent and solvent evaporation losses according to embodiments, as well as the energy balance used to describe the temperature variations inside the MBC.

[0088] Modeling hydrocarbon loss

[0089] As a first approximation, the solvent is assumed to be saturated with hydrocarbons (HC) at the MBC liquid outlet (z=L), and Henry’s law is used to estimate the concentration of hydrocarbons using Equation 1 below:

[0090]

[0091] where P g [Pa] is the gas pressure,​ [-] is the inlet mole fraction of hydrocarbons, and H i,l [m 3 Pa mol -1 ] is the Henry’s constant for hydrocarbons (corresponding to outlet solvent temperature, pressure, and composition). Since the solvent inlet stream of the MBC does not contain any hydrocarbons, the loss rate of hydrocarbons to the solvent is considered at the total mass balance level (lumped). Thus, this means that the loss rate of hydrocarbons to the solvent is not calculated along the length of the MBC, but only at the outlet of the MBC. This reduces the computational time required for the loss rate calculation. The loss rate of hydrocarbons to the solvent is obtained using the following Equation 2:

[0092]

[0093] where F l is the liquid flow rate of the solvent. The loss rate as shown in Equation 2 above provides the worst-case scenario in estimating the amount of HC potentially lost if the HC was not recovered in the downstream flash drum. This can be used to benchmark the HC loss compared to other conventional CO2 removal techniques. The prediction of H i,l is described in detail later with respect to Equation 13 below.

[0094] Modeling solvent evaporation in treated gas

[0095] As with the previous hydrocarbon loss, it is assumed here that the treated gas at the MBC outlet (z = 0) is saturated with solvent, and the solvent evaporation rate is considered at the total mass balance level (lumped). This assumption can over-predict the solvent evaporation rate since the gas residence time is shorter than the time required to reach its equilibrium. However, it is interesting to model the worst-case scenario of the solvent evaporation rate to study the solvent loss in the treated gas versus the solvent circulation rate, and to benchmark the solvent rate loss in the MBC system with a conventional packed column system (see Equations 13 and 14 described below). Figure 26A and Figure 26B ).

[0096] For the vapor-liquid equilibrium at z = 0, Raoult’s law can be used to approximate the mole fraction of solvent in the gas outlet using the following Equation 3

[0097]

[0098] where the terms P i vap,in [kPa] and are the mole fraction, vapor pressure of species i e {H2O, MDEA, PZ} at the liquid inlet, and gas outlet pressure, respectively.

[0099] Since the gas inlet in the counter-current MBC does not contain solvent, the following equation 4 is used to calculate the solvent loss rate

[0100]

[0101] where N is the number of fibers in the MBC module, r1[m] is the inner radius of the fiber, is the average velocity of the gas phase, [-] is the compressibility factor, and R = 8.3145 J mol -1 K -1 is the ideal gas constant.

[0102] Modeling solvent temperature

[0103] Instead of using a simple temperature correction based on a lumped energy balance, a spatial distribution of the solvent temperature is modeled according to the embodiments. This modeling takes into account the heat loss due to solvent evaporation as described above, as well as the exothermic reaction between CO2 and the amine under adiabatic conditions. For simplicity, it is assumed that solvent evaporation occurs at the liquid inlet (z = 0) before the solvent reacts with CO2 along the fiber length. It should be noted that while solvent evaporation decreases the solvent temperature, CO2 absorption increases the solvent temperature. Therefore, the modeling of the solvent temperature will provide insights on the relative contribution of each effect on the solvent temperature. Experimental validation will confirm the validity of the modeling assumptions later.

[0104] Based on the solvent evaporation rate determined in equation 4 above, the energy consumed by solvent evaporation, Q vap [J s -1 ] and the solvent temperature at the shell inlet can be determined as shown in equation 5.

[0105]

[0106] where ρ l [kg m -3 ], C p [J kg -1 K -1 ], P i vap,in and are the solvent inlet volumetric flow rate, density, specific heat capacity, inlet temperature, inlet vapor pressure and latent heat of evaporation of the substance i e {H2O, MDEA, PZ}, respectively. The specific heat capacity and the latent heat of evaporation of the amine solvent are set to C p = 3600 J kg -1 K -1 and and

[0107] The diffusive heat transfer in the shell is fast enough so that the heat diffusion along the axis can be neglected. Furthermore, it is assumed that the solvent temperature is uniform in the radial direction. This leads to the following energy balance, as shown in equation 6, for quantifying the solvent temperature rise T l (z) :

[0108]

[0109] where is the average concentration of CO2 along the fiber length, and the reaction enthalpy is set to AH r = -60000 J mol -1 .

[0110] Note that according to the embodiments, the above equation 6 is now refined to a spatial profile modeling, thus advantageously introducing a spatial dimension for the solvent temperature variation along the fiber length of the MBC. The predicted value of T l (0) in equation 5 provides the boundary condition at z = 0 for equation 6.

[0111] Membrane properties

[0112] The high-pressure MBC module is filled with hydrophobic polytetrafluoroethylene (PTFE) hollow fibers. The following Table 2 shows the main characteristics and geometrical properties of the MBCs used for the laboratory and pilot scale tests. The laboratory scale setup and the pilot scale NG plant are described below with respect to Figure 8 and Figure 9 respectively. The data can be obtained from the manufacturer (e.g. PRSB, 2016 - “Module D - Hollow Fiber Membrane (HFM) Quality Check and Characterization”, PETRONAS Research Sdn Bhd.) or calculated by the analysis equations based on the obtained data.

[0113] Table 2: Specifications of the laboratory and pilot scale membranes.

[0114]

[0115] A first approximation of the membrane tortuosity can be obtained using the following equation 7:

[0116]

[0117] The pore size distribution (PSD) data from the manufacturer (PRSB, 2016) was used to fit the following lognormal distribution in the following equation 8,

[0118]

[0119] in σ and σ represent the average hole radius and the relative hole standard deviation, respectively.

[0120] Figure 3 A graph 300 showing the cumulative pore area ratio distribution based on simulated log-normal pore size distribution 302 and manufacturer data 304 according to an embodiment is shown. Figure 4 The graph 400 shows a comparison of the analytical wetting ratio representation 402 with the fitted alternative representation 404 in terms of critical pore radius. The fitting is performed using Equation 8 above. Figure 3 and Figure 4 The graph.

[0121] Figure 3 The least-squares fit obtained in the above table 2 shows excellent agreement with the data. And the corresponding estimate of σ. Furthermore, the wetting ratio can be obtained in the following form. As this range [0,δ max The critical hole radius δ within the range w The substitution relationship of functions:

[0122]

[0123] Where a0 = 9.029, a1 = -17.209, a2 = 11.222, and a3 = -2.938. Assuming the wetting orifice is completely filled with liquid, the wetting ratio can be calculated using Equation 10:

[0124]

[0125] For a given pore size distribution (PSD) function and maximum pore radius δ max [m], in Figure 4 The diagram shows a comparison between the actual wetting ratio 402 calculated using Equation 10 above and the fitted alternative 404 using Equation 9 above.

[0126] Pilot scale module design

[0127] HFM and the properties of the woven fabric are expected to provide large pilot-scale gas handling capacity, due to the fact that... The packing density is relatively high, and the specific surface area is approximately 2300 m². -1 However, due to limitations in other parts of the plant, the pilot plant could not operate at temperatures above 75 kg / hr. -1The operation is carried out at a certain gas flow rate. Therefore, the pilot plant is operated at the designed capacity, where the new membrane in horizontal operation will enable CO2 removal efficiency close to 100% in most experiments. Therefore, a new pilot module is needed to achieve a CO2 purity of 50 ppmv at full capacity. To maintain a packing density close to 0.55 in the new module, the module cross-sectional area is scaled down by inserting a steel tube (e.g., a tube insert) into the center of the module. Packing density and membrane area A m It is given by the following formula:

[0128]

[0129] A m =2πr²LN, (12)

[0130] Where N is the number of fibers in the MBC module, R m [m] and R t [m] represents the inner radius of the module and the outer radius of the steel pipe insert, respectively, and L is the fiber length.

[0131] Figure 5A and Figure 5B The graphs 500 and 510, according to embodiments, correlate different membrane areas with hollow fiber MBCs, wherein... Figure 5A The graph 500 shows the required outer radius 502 for steel tube inserts with different membrane areas and the predicted total number of fibers 504 in the MBC module in order to maintain a fill density of 0.55. Figure 5B This shows the maximum pilot-scale capacity (i.e. Predicted CO2 absorption flux for different membrane areas at mol%) 512Ф [mol m -2 s -1 ] and CO2 outlet gas purity The graph is 510. These predictions were calculated using the membrane properties shown in Table 2.

[0132] like Figure 5B As shown, the model predicts that when the total membrane area is higher than 80m², 2 In cases where the CO2 outlet gas purity is 514 ppmv or less, wetting is negligible in all cases due to the horizontal operation of MBC. From Figure 5B It was also observed that, considering the membrane area was large enough to keep the CO2 outlet purity at the ppm level, the CO2 absorption flux 512 decreased with increasing membrane area.

[0133] However, due to the rigid steel tubing and braided structure of HFM, only 8,400 fibers can actually be used, compared to the required approximately 11,000 fibers, with a radius R. t= 0.08 m tube insert was successfully installed. This configuration resulted in a packing density of only 0.38 and a reduced surface area of 68 m 2 i,l

[0134] Prediction of hydrocarbon solubility in amine solvents

[0135] Methane, ethane, and propane solubilities in water and in aqueous amine solutions of 50 wt% MDEA were collected from solubility charts reported from previous work. These charts were derived from a combination of thermodynamic modeling (i.e., Peng-Robinson equation of state and Henry’s law) and experimental data.

[0136] For a temperature range of 300-345 K and a pressure range of 48-72 bar, the following polynomial regression model for the Henry’s constant of a hydrocarbon in an amine solvent H i,l i e {CH4, C2H6, C3H8} was fit to this data set. The regression model was developed using Design-Expert version 11 and is shown in equation 13 below:

[0137] H i，1 = a0+ a1C + a2T l + a3P l + a4CT l + a5Cp l + a6T l P l (13)

[0138] where T l [K], P l [Pa], and C [-] are the liquid temperature, liquid pressure, and mass fraction of MDEA in the aqueous amine solvent, respectively. It should be understood that although the regression model was developed using Design-Expert version 11, other suitable software for forming regression models can be used.

[0139] The coefficients a1through a6and the absolute average deviation for each Henry’s constant are given in Table 3 below.

[0140] Figure 6A , Figure 6B and Figure 6C show plots 600, 610, 620 of the predicted and measured Henry’s constants for different hydrocarbons in water and in 50 wt% aqueous MDEA according to the embodiments, where Figure 6A plot 600 shows the predicted and measured Henry’s constants for methane (CH4), Figure 6B plot 620 shows the predicted and measured Henry’s constants for propane (C3H8), and Figure 6CA plot showing the predicted and measured Henry's constants for propane (C3H8). Figure 6A , Figure 6B and Figure 6C Data points 602, 612, and 622 are respectively associated with experimental data for the Henry's constants of different hydrocarbons in water, while Figure 6A , Figure 6B and Figure 6C Data points 604, 614, and 624 are respectively associated with experimental data for the Henry's constants of different hydrocarbons in 50 wt% aqueous MDEA.

[0141] The comparison between the experimental Henry's constants and the predicted Henry's constants as shown in Figure 6A , Figure 6B and Figure 6C shows excellent agreement, with most of the predicted deviations being within ±5%. The resulting Henry's constant replacement equation 13 will be used to predict hydrocarbon worst-case loss.

[0142] Table 3: Coefficients and absolute average deviations of H i,l

[0143]

[0144]

[0145] Prediction of Henry's constants in semi-lean amine solvents

[0146] To determine the Henry's constant for CO2to account for the effect of CO2loading in a solvent (e.g., an amine solution), a regression model is developed using empirical data. In an embodiment, a regression model can be formed for the Henry's constant for CO2using empirical data associated with the solubility of CO2in a solvent. Direct empirical data associated with the solubility of CO2in a solvent can not be readily available. In the present embodiment as described below, the Henry's constant for CO2is determined using a regression model formed for the Henry's constant of nitrous oxide (N2O). N2O is chosen because N2O has similar properties as CO2and does not react with the solvent. Therefore, experiments conducted to obtain the solubility of N2O in a solvent are simple, and their data are reliable. In the present embodiment, a regression model is developed based on empirical data for the solubility of N2O in a 50 wt% aqueous MDEA solution for CO2loading and temperature ranges of 0-0.5 mol-mol -1 and 295-353 K, respectively. It should be understood that although the regression model is developed using data for a 50 wt% aqueous MDEA solution, data from other suitable solvents can also be used. Here, the effect of pressure on the Henry's constant is neglected, and it is assumed that PZ behaves like MDEA. The regression Henry's constant for N2O is given in the following equation 14:

[0147] ​

[0148] where and T l are the inlet CO2 loading and liquid temperature in the amine, respectively.

[0149] Figure 7A and Figure 7B Plots 700, 710 show the predicted and measured Henry's constants for nitrous oxide (N2O). Figure 7A Plot 700 shows the experimental data for the Henry's constant of N2O compared to the predicted Henry's constant of N2O. As Figure 7A The dashed line 702 shown represents the regression model of equation 14 above with a 5% spread. Figure 7B Plot 710 shows the predicted Henry's constants of N2O at various CO2 loadings for lean and semi-lean amine operation. The dashed line 712 shows the plot of the predicted Henry's constant of N2O for lean amine operation, while line 714 shows the plot of the predicted Henry's constant of N2O for semi-lean amine operation.

[0150] Figure 7A experimental and alternative predictions based on equation 14 in show excellent agreement. In Figure 7B it can be seen that for all CO2 loadings, the regression model developed for lean amine solvents predicts lower The regression model for the lean amine solvents used is shown in equations 15 and 16 below:

[0151]

[0152] where φ i the volume fraction of species i; and the solubility of N2O in pure amine solvent i e {MDEA, PZ} is considered to be:

[0153]

[0154] Using the Henry's constants for N2O determined above, the Henry's constants for CO2 can be estimated at various temperatures based on the analogy of N2O using equations 17 to 19 below.

[0155]

[0156] The Henry's constants for N2O and CO2 in water and are:

[0157]

[0158]

[0159] Higher values result in higher which in turn indicates lower CO2 solubility in the solvent. Furthermore, the gradient of increases higher compared to equation 14, which confirms the adverse effect of higher CO2 loading on the CO2 absorption flux.

[0160] For completeness, the equations, models and boundary conditions used in the MBC model are summarized in Table 4 below. Table 4 has been updated in consideration of the models and equations as mentioned above compared to Table 3.

[0161] Table 4 Summary of model equations and boundary conditions used in the MBC model

[0162]

[0163]

[0164]

[0165] Table 5: Model parameters used in the laboratory and pilot plant MBC simulations.

[0166]

[0167]

[0168] Experimental setup

[0169] Figure 8 A schematic diagram 800 showing a laboratory scale setup for removal of carbon dioxide (CO2) in natural gas sweetening treatment using a horizontal MBC module 802 according to an embodiment.

[0170] Feed gas 804 comprising a mixture of CH4 / CO2or N2 / CO2is provided by a pressurized gas cylinder 806 to the tube side of the lab-scale MBC module 802, while lean solvent 807 (typically lean amine solvent) is pumped through the shell side of the MBC module 802 from a lean amine tank 808 via an amine pump 810 in a counter-current configuration to the feed gas 804. The feed gas flow rate and the solvent flow rate are controlled using a mass flow controller (MFC) and a pump stroke (not shown), respectively. The treated gas 812 from the MBC module 802 is analyzed. After the setup reaches a steady state indicated by a constant CO2composition in the outlet gas stream of the module 802, the compositions of the feed gas 804 and the treated gas 812 are analyzed and recorded using a gas chromatograph (e.g., GC7900, Shanghai Tech-Comp Instruments Co., Ltd). The treated gas 812 from the MBC module 802 is then depressurized and vented to a safe location. A trans-membrane pressure of ΔPTMPD = 30 kPa is maintained at any point along the fibers of the MBC module 802 to prevent gas bubbling. The amine solvent that has been used in the MBC module 802 for CO2absorption is referred to as rich solvent, and is collected using a rich amine tank 814.

[0171] Separately, an experimental setup for pilot-scale testing is arranged as shown in Figure 9 Figure 9 is a schematic diagram 900 of a pilot natural gas (NG) plant setup for removing carbon dioxide (CO2) using a horizontal hollow fiber membrane contactor (MBC) module 902 in natural gas desulfurization treatment according to an embodiment.

[0172] ​The NG plant setup includes an absorption section 904 and a regeneration section 906. At the absorption section 904, a feed gas 908 containing C02-rich natural gas is fed to the tube side of the MBC 902 while lean amine 909 is pressurized to about 54 bar into an amine tank 912 and fed to the shell side of the MBC module 902 using an amine pump 912 via an amine chiller 914 in a counter-current configuration with the feed gas 908. The feed gas flow rate and liquid flow rate are controlled using mass flow controllers and pump strokes (not shown), respectively. The flow rate of the treated gas 916 at the MBC outlet is measured with a mass flow meter before sending the treated gas 916 to a flare header (not shown). The rich amine solvent 917 collected from the MBC shell outlet is directed to a flash drum 918 to degas any volatile and dissolved hydrocarbons. After the setup reaches a steady state, the gas composition in the MBC feed and outlet and the flash outlet is analyzed and recorded using a gas chromatograph (e.g., PGC1000 gas chromatograph, ABB). The flash gas 920 is then discharged from the flash drum 918 while the output flash liquid outlet stream 921 is heated by cross-exchange with hot lean solvent in a lean-rich exchanger 922 before being fed to a solvent regenerator 924 where the acid gas 926 is stripped by the ascending flow vapor generated by a reboiler 928. On the other hand, a column is provided with a reflux liquid stream by a column overhead condenser 927 to ensure that the top product stream, also known as the acid gas stream, is as pure as possible. The top product stream leaving the top of the regenerator is cooled and sent to a reflux drum 930 to separate the condensed water from the acid gas 926. The condensed water is then returned to the top of the solvent regenerator 924 via a reflux pump 932 while the acid gas 926 is sent to a flare header. Finally, a solvent makeup 936 from the reboiler 928 is fed to the amine tank 910 via a lean solution cooler 938 using a low pressure amine pump 934 to make up for the solvent evaporated in the MBC module 902, the flash drum 918, and the solvent regenerator 924. The solvent regeneration process is operated at a low pressure to recover HC and lower the solvent boiling point to reduce energy consumption. The lower boiling point also benefits in keeping the solvent below its degradation temperature.

[0173] In this example, laboratory scale setup experiments were performed with a binary feed gas mixture of N2 / CO2 at 54 bar. A pilot scale setup was also operated at 54 bar in a natural gas treatment plant in Malaysia under industrially relevant operating conditions. In both cases, an aqueous mixture of methyldiethanolamine (MDEA) and piperazine (PZ) was used as the chemical solvent. The corresponding operating and design conditions in the laboratory and pilot plant are summarized in Table 6.

[0174] Table 6: Operating and design conditions in the laboratory and pilot plant

[0175]

[0176] Starting with lean operation, the CO2 loading gradually increased over the course of the experiment (where MBC inlet CO2 loading in solvent ) was reduced to achieve higher CO2 loading in the solvent. Once the plant reached steady state at a particular reboiler energy load, the lean amine was sampled and analyzed for CO2 content and loading before further reboiler energy load reduction. During the experiment, parameters such as CO2 inlet, feed gas, and amine flow rates were held constant after the setup reached steady state, and gas composition in the MBC feed, outlet, and flash gas were analyzed and recorded every 6 minutes using a gas chromatograph (e.g., PGC1000 gas chromatograph, ABB). Additionally, pure CO2 from a set of cylinders was mixed into the feed gas line to achieve high CO2 loading experiments (up to 18%). The fluid flow rates and gas composition values were averaged every hour and compared to model predictions.

[0177] Figure 10A 、 10B and 10C illustrate block diagrams of a natural gas sweetening treatment operation system 1000, a hollow fiber membrane contactor (MBC) data processing system 1010, and a solvent regeneration data processing system 1011, in accordance with an embodiment.

[0178] As shown in Figure 10A , the natural gas sweetening treatment operation system 1000 includes the MBC data processing system 1010 and the solvent regeneration data processing system 1011, where the MBC data processing system 1010 is associated with an absorption operation using, for example, a hollow fiber membrane contactor (MBC) 902 for acid gas absorption, and the solvent regeneration data processing system 1011 is associated with a desorption operation using, for example, a solvent regenerator 924 for solvent regeneration. As will be appreciated by those skilled in the art, the natural gas sweetening treatment operation system 1000 can include additional components, such as processes, storage devices, input / output interfaces, so that an operator can evaluate data from and / or control various components of the natural gas sweetening treatment operation system 1000. For clarity and brevity, these components are not shown.

[0179] Figure 10Bis a block diagram illustrating an MBC data processing system 1010 according to an embodiment. The MBC data processing system 1010 is a computer system having a memory that stores computer program modules that implement a computer-implemented method for evaluating performance of MBC for natural gas sweetening treatment according to embodiments as described above with respect to FIGS. 1-9. The MBC data processing system 1010 includes a processor 1012, a working memory 1014, an input module 1016, an output module 1018, a user interface 1020, a program storage 1022, and a data storage 1024. The processor 1012 can be implemented as one or more central processing unit (CPU) chips. The program storage 1022 is a non-volatile storage such as a hard disk drive that stores computer program modules such as MBC computer modules 1026. The computer program modules are loaded into the working memory 1014 for execution by the processor 1012. The input module 1016 is an interface that allows the MBC data processing system 1010 to receive data (e.g., liquid flow rate of solvent, gas flow rate of natural gas, etc.). The output module 1018 is an output device that allows data and results of the analysis of the computed model parameters by the MBC data processing system 1010 to be output to, for example, the natural gas sweetening treatment operating system 1000. The output module 1018 can be coupled to a display device or a printer. The user interface 1020 allows a user of the MBC data processing system 1010 to input selections and commands, and can be implemented as a graphical user interface.

[0180] The program storage 1022 stores MBC computer modules 1026. The MBC computer program modules 1026 cause the processor 1012 to perform various MBC data processing described in more detail below. In some contexts, the program storage 1022 can be referred to as a computer readable storage medium and / or a non-transitory computer readable medium. As Figure 10B illustrated, the MBC computer modules 1026 are different modules that perform respective functions implemented by the MBC data processing system 1010. It should be understood that the MBC computer modules 1026 can be broken down into sub-modules, executed as multiple computer processes, and optionally executed on multiple computers. Further, alternative embodiments can combine multiple instances of a particular module or sub-module. It should also be understood that while software implementations of computer program modules are described herein, these can alternatively be implemented as one or more hardware modules (such as a field programmable gate array(s) or an application specific integrated circuit(s)) that include circuitry that implements functionality equivalent to that implemented in software.

[0181] The data storage 1024 stores various models, model data, and computed and empirical model parameters. As Figure 10BAs shown, the data storage device 1024 has storage for an MBC model 1028. In the present embodiment, the MBC model 1028 includes a regression model 1030 for the Henry’s constant (H N2O,l ) of N2O (discussed above with respect to Figure 7A and 7B ), a regression model 1032 for the Henry’s constant (H i,l ) of hydrocarbons (discussed above with respect to Figure 6A , Figure 6B and Figure 6C ), a hydrocarbon loss rate model 1034 (discussed above with respect to Equations 1 and 2), an MBC space model 1036 (discussed above with respect to Figure 1A , Figure 1B and Figure 2 ), a mass conservation model 1038 (e.g., as shown in Table 4 above), a material balance model 1040 (e.g., as shown in Table 4 above), boundary conditions 1042 (e.g., as shown in Table 4 above), transport and reaction kinetics model 1044 (as exemplified in the prior work “Modeling for Design and Operation of High-Pressure Membrane Contactors in Natural Gas Sweetening” in Chemical Engineering Research and Design 132, 1005-1019 (2018)), other physical models 1046, and model parameters 1048 (e.g., as shown in Table 5 above). In embodiments, the MBC model 1028 can include a regression model 1050 for the Henry’s constant (H CO2,l ) of CO2. In this case, the Henry’s constant for CO2 can be determined directly from the regression model 1050 to account for CO2 absorption in the solvent. This is described below with respect to Figure 11 .

[0182] Figure 10Cis a block diagram illustrating a solvent regeneration data processing system 1011 according to an embodiment. The solvent regeneration data processing system 1011 is associated with other modules involved in a plant-wide natural gas sweetening process (to be discussed in more detail below). Similar to the MBC data processing system 1010 as described above, the solvent regeneration data processing system 1011 is a computer system having a memory storing computer program modules. The solvent regeneration data processing system 1011 includes a processor 1052, a working memory 1054, an input module 1056, an output module 1058, a user interface 1060, a program storage 1062, and a data storage 1064. The processor 1052 can be implemented as one or more central processing unit (CPU) chips. The program storage 1062 is a non-volatile storage such as a hard disk drive that stores computer program modules. The computer program modules are loaded into the working memory 1054 for execution by the processor 1052. The input module 1056 is an interface that allows data (e.g., pressure in the rich solution flash drum) to be received by the solvent regeneration data processing system 1011. The output module 1058 is an output device that allows data and results of the analysis of the model parameters computed by the solvent regeneration data processing system 1011 to be output to, for example, the natural gas sweetening process operating system 1000. The output module 1058 can be coupled to a display device or a printer. The user interface 1060 allows a user of the solvent regeneration data processing system 1011 to input selections and commands, and can be implemented as a graphical user interface.

[0183] The program storage 1062 stores a rich solution flash drum module 1066, a heat exchanger module 1068, a pump module 1070, a solvent regenerator module 1072, and a solvent make-up module 1074. These computer program modules cause the processor 1052 to perform various solvent regeneration data processing described in more detail below. In some contexts, the program storage 1062 can be referred to as a computer readable storage medium and / or a non-transitory computer readable medium. As Figure 10C As depicted, the computer program modules are distinct modules that perform the respective functions implemented by the solvent regeneration data processing system 1011. It should be understood that the boundaries between these modules are merely illustrative and alternative embodiments can merge modules or impose alternative decompositions of module functionality. For example, the modules discussed herein can be decomposed into sub-modules, executed as multiple computer processes, and optionally executed on multiple computers. Furthermore, alternative embodiments can combine multiple instances of a particular module or sub-module. It should also be understood that while software implementations of the computer program modules are described herein, these can alternatively be implemented as one or more hardware modules (such as a field programmable gate array or an application specific integrated circuit) that include circuitry to implement functionality equivalent to that implemented in software.

[0184] Data storage device 1064 stores various model data and model parameters. For example... Figure 10C As shown, data storage device 1064 has storage for mass and energy balance model 1076, transport and thermophysics model 1078, other physical models 1080, and model parameters 1082 (e.g., as shown later in Tables 8 and 9). In embodiments, mass and energy balance model 1076, transport and thermophysics model 1078, other physical models 1080, and model parameters 1082 can be obtained by interacting with property packages such as Advanced PengRobinson, UNIQUAC-RK, and RSKA from Multiflash v6.1 for the gas and liquid phases in absorption and regeneration units, respectively. Data storage device 1064 includes a rich solution flash drum model 1084, a heat exchanger model 1086, a pump model 1088, a solvent regenerator model 1090, and a solvent replenishment model 1092 for use with their respective modules. The following is about Figure 23 Describe these models.

[0185] Figures 11 through 13 This is a flowchart illustrating methods 1100, 1200, and 1300 that can be performed by the MBC data processing system 1010 according to an embodiment, while Figure 14 This is a flowchart illustrating a method 1400 that can be performed by a natural gas desulfurization operating system 1000 according to an embodiment.

[0186] Referring to method 1100, in step 1102, a regression model is formed using empirical data. The regression model for the Henry's constant of CO2 can be formed using empirical data relating to the solubility of CO2 in a solvent. In this embodiment, a regression model for the Henry's constant of N2O is formed using empirical data on the solubility of nitrous oxide (N2O) in a solvent. In this case, the regression model is a function of the carbon dioxide (CO2) loading and the liquid temperature of the solvent. This is described above with respect to Equation 14. The solvent may include various percentages of H2O, MEDA, and / or PZ. Examples of solvents include 50% aqueous MEDA.

[0187] In step 1104, the Henry's constant for CO2 is determined using the regression model. In the case where the regression model is formed from empirical data associated with solubility of CO2 in the solvent according to an embodiment, the Henry's constant for CO2 can be determined directly from the regression model. In the present embodiment where the regression model for the Henry's constant of N2O is formed, the Henry's constant for CO2 is determined using the Henry's constant for N2O. In this case, the Henry's constant for N2O is first determined using the regression model. The Henry's constant for CO2 in the solvent is then calculated using the Henry's constant for N2O to account for the CO2 loading in the solvent. The Henry's constant for CO2 can be determined using the N2O analogy as shown by Equations 17 to 19 described above.

[0188] In step 1106, the determined Henry's constant for CO2 is inputted in the MBC model 1028 as one of the model parameters 1048. The MBC model 1028 can include other models, for example, as shown by Figure 10B .

[0189] In step 1108, the CO2 absorption in the solvent is determined using the MBC model 1028 to design and evaluate the MBC performance.

[0190] Figure 12 is a flowchart showing steps of a method 1200 for determining a loss rate of hydrocarbons in a solvent of an MBC according to an embodiment.

[0191] In step 1202, a regression model for the Henry's constant of hydrocarbons in the solvent is formed using empirical data of solubility of hydrocarbons in the solvent to account for the loss of hydrocarbons from the natural gas to the solvent. This is described above with respect to Equations 13, Table 3, and Figure 6A , Figure 6B and Figure 6C above. As described in Equation 13, the regression model is a function of the liquid temperature, the liquid pressure, and the mass fraction of at least one component in the solvent of the solvent.

[0192] In step 1204, the Henry's constant for hydrocarbons in the solvent is determined using the regression model for the Henry's constant of hydrocarbons.

[0193] In step 1206, the loss rate of hydrocarbons in the solvent is determined using the Henry's constant for hydrocarbons in the hydrocarbon rate loss equation. The hydrocarbon rate loss equation is described above with respect to Equation 2. As shown in Equation 2, the loss rate of hydrocarbons is a function of the concentration of hydrocarbons. As shown and described above with respect to Equation 1, the concentration of hydrocarbons is in turn inversely proportional to the Henry's constant for hydrocarbons in the solvent.

[0194] Figure 13 is a flowchart showing a method 1300 for solvent loss rate and liquid temperature change of a solvent for an MBC according to an embodiment.

[0195] In step 1302, Raoult's law is used to determine the mole fraction of at least one component of the solvent in the gas outlet. This is described in Equation 3 above.

[0196] In step 1304, the solvent loss rate is determined using a mole fraction in the solvent rate loss equation. This is described in Equation 4 above. As shown in Equation 4, the solvent loss rate is proportional to the determined mole fraction.

[0197] In step 1306, the solvent loss rate determined in step 1304 is used to determine the energy consumed by solvent evaporation at the liquid inlet of the MBC and the liquid temperature of the solvent. The consumed energy and the liquid / solvent temperature can be determined, for example, using equations 5 and 6 as described above.

[0198] In step 1308, the change in liquid temperature is determined by balancing the energy consumed by solvent evaporation with the exothermic CO2 absorption reaction along the length of the MBC under adiabatic conditions. This is described in Equation 6 above. Equation 6 above is now refined into a spatial distribution model, thus advantageously incorporating the spatial dimension of the solvent temperature change along the fiber length of the MBC.

[0199] Figure 14 This is a flowchart illustrating the steps of a method 1400 for determining the total processing load of natural gas desulfurization under lean and semi-lean operation, according to an embodiment. Method 1400 can be performed by the natural gas desulfurization operating system 1000 as described above, and its modeling will be described in more detail below.

[0200] In step 1402, optimized flow rates associated with lean and semi-lean operations are calculated to achieve the desired CO2 purity in the natural gas. The lean operation is associated with using flow rates less than 0.02 mol / L. -1 The operation is associated with a lean solvent with a CO2 loading, and the semi-lean operation is associated with using a solvent with a CO2 loading greater than 0.2 mol / L. -1 The operation is associated with a semi-lean solvent and CO2 loading. This is described in Table 11 below.

[0201] In step 1404, the total processing load of the natural gas desulfurization treatment associated with the absorption and desorption operations is determined under both lean and semi-lean operations. This is discussed below regarding... Figure 24A and Figure 24B Describe it.

[0202] Figure 15A , Figure 15B , Figure 15C , Figure 15D and Figure 15E This illustrates a laboratory-scale MBC setup according to an embodiment. Figures 15A-15C) and pilot-scale NG plant setup ( Figure 15D and Figure 15E The graphs of predicted CO2 uptake flux based on experimental data are shown at 1500, 1510, 1520, 1540, and 1550. Figure 15A The graph 1500 shows the CO2 absorption flux 1502, 1504, 1506 and the predicted wetting ratio 1508 for different CO2 loads in a laboratory-scale MBC setting. Figure 15B The graph 1510 shows the CO2 absorption flux 1512, 1514, 1516 and the predicted wetting ratio 1518 for different total gas flow rates in a laboratory-scale MBC setting. Figure 15C The graph 1520 shows the CO2 absorption flux 1522, 1524, 1526 and the predicted wetting ratio 1528 for different total liquid flow rates in a laboratory-scale MBC setting. Figure 15D The graph 1540 shows the CO2 absorption flux 1542, 1544, 1546 and predicted wetting ratio 1548 for different CO2 loadings in a pilot NG plant setting; and Figure 15E The graph 1550 shows the CO2 absorption fluxes 1552, 1554, 1556 and the predicted wetting ratio 1558 for different CO2 inlet concentrations in the natural gas mixture for a pilot-scale NG plant setting. Specifically, the CO2 absorption fluxes 1502, 1512, 1522, 1542, and 1552 are correlated with the predicted fluxes simulated under lean solvent conditions, the CO2 absorption fluxes 1504, 1514, 1524, 1544, and 1554 are correlated with the predicted fluxes simulated under semi-lean solvent conditions, and the CO2 absorption fluxes 1506, 1516, 1526, 1546, and 1556 are correlated with the fluxes obtained from experimental data.

[0203] Figure 15A , Figure 15B and Figure 15C Below is about such Figure 8 The "laboratory-scale MBC setting" discussed is used to describe this, and Figure 15D and Figure 15E Below is about such Figure 9 The “pilot-scale MBC setup” section will be used to describe this.

[0204] In particular, Figure 15A Showing for fixed and The effect. Figure 15B Showing for fixed and The effect.Figure 15C Showing for fixed and The effect. Figure 15D Showing for fixed and The effect. Figure 15E This shows that for 0.01 mol mol -1 , Fixed The effect. Regarding the above terms, This refers to the CO2 loading of the solvent at the inlet. This refers to the mass flow rate of the inlet gas. This refers to the solvent flow rate at the inlet volume, and This refers to the CO2 mole fraction of the inlet gas.

[0205] Laboratory scale MBC setup

[0206] As mentioned above, using the Henry's constant from equation 14, which regresses in both lean and semi-lean solvents, in Figure 15A , Figure 15B and Figure 15C The figure presents the measured and predicted CO2 absorption flux Ф [mol m -2 s -1 Comparisons were made between [the two groups]. The predictions from Equation 15 were also used for comparison. Experimental data were presented for different CO2 loadings in the solvent (0.01–0.24 mol / mol). -1 The model predictions using Equation 14 and different gas and amine flow rates are shown in Table 6. It can be seen that the model predictions using Equation 14 are in close agreement with the experimental CO2 flux. The predictions using Equation 15 are found to still agree relatively well with the measurements, but show a larger and more systematic error of up to 10% overestimation, especially under higher CO2 loading experiments. This systematic deviation between prediction and measurement is due to Equation 15 only considering lean amines, thus overestimating the solubility of CO2 in a semi-lean solvent. Although Equation 14 predicts a higher value of approximately 25% for lean amines. (see Figure 7B ), but with Figure 15A Compared to the higher CO2 loading conditions shown, the effect on CO2 absorption flux is less significant. A possible explanation is that diffusion mass transfer in the amine-poor solution exceeds CO2 dissolution at the gas-liquid interface.

[0207] like Figure 15AAs shown, the MBC model 1028 correctly predicts that a larger CO2 loading in the solvent feed reduces the CO2 absorption flux. An increase in the liquid CO2 loading essentially leads to a reduction in the free amine available for reaction with CO2. Also, from a thermodynamic point of view, the solubility of CO2 in the liquid decreases with an increase in the liquid CO2 loading, which is due to a higher value, and thus a higher (see also Figure 7B ). The model 1028 predicts that the average wetting lies in the range between 2% and 6% as the CO2 loading varies. In particular, according to the Young-Laplace equation, an increase in the CO2 loading increases the membrane wetting due to a reduction in the liquid surface tension, which leads to a reduction in the CO2 flux through the membrane.

[0208] As can be seen, the MBC model 1028 also correctly predicts an increase in the CO2 absorption flux at larger inlet gas flow rates (driven by a larger amount of CO2 in the gas feed). Note that the effect of increasing the inlet gas flow rate on the wetting rate is minimal (here only an increase of 0.2% wetting) since the pressure drop in the tube is negligible. Figure 15B

[0209] As shown, the MBC model 1028 correctly captures the improvement in the CO2 absorption flux when increasing the solvent flow rate, with a corresponding small reduction in the membrane wetting. An increase in the liquid / solvent flow rate leads to a higher pressure drop, trans-membrane pressure, and membrane wetting. But at higher liquid flow rates, the temperature increase in the solvent due to the higher CO2 absorption is lower, which leads to a relatively higher liquid surface tension, and thus to a lower membrane wetting. In summary, the MBC model 1028 correctly predicts that the effect of the higher pressure drop on the membrane wetting is small compared to the increase in the liquid surface tension. The effect of the larger concentration gradient due to the increase in velocity also contributes to an increase in the overall CO2 absorption. Figure 15C

[0210] Figures 1600 show plots of predicted and experimental solvent temperature and CO2 absorption for different axial positions along the length of the MBC 802, 902 for gas and solvent flow rates and CO2 loading of 2 kg h -1 , 10 L h -2 , and 0.22 mol mol -1 , respectively, according to an embodiment. Figure 16 The plots show predicted temperature 1602, empirical temperature data obtained from experiments 1604, predicted CO2 absorption flux 1606, and experimental CO2 absorption flux 1608. Figure 16

[0211] As shown, the MBC model 1028 correctly predicts that a larger CO2 loading in the solvent feed reduces the CO2 absorption flux. An increase in the liquid CO2 loading essentially leads to a reduction in the free amine available for reaction with CO2. Also, from a thermodynamic point of view, the solubility of CO2 in the liquid decreases with an increase in the liquid CO2 loading, which is due to a higher Figure 16 ​​As shown, the predicted solvent temperature profile 1602 along the fiber length agrees excellently with the measured solvent temperature 1604, providing a first verification of the assumptions made in the energy balance as described above with respect to equations 5 and 6. In this experiment, there appears to be no significant temperature bulge in the MBC module 802, 902. The model 1028 can be used to identify potential temperature bulges along the MBC length under different operating conditions. Note also that the temperature rise (about 20 K) in the MBC module 802, 902 is significant, where the L / G ratio (about 0.86 m 3 kmol -1 ) is comparable to the values of 0.6-1.1 m 3 kmol -1 typically encountered in conventional packed columns.

[0212] Figure 16 The predicted cumulative CO2absorption flux 1606 in the MBC module 802, 902 is zero at the gas inlet (z = 2.3 m) and increases along the fiber axis. The CO2absorption flux exhibits a slow decrease (concave shape) from the gas inlet to the gas outlet, which is expected because the higher CO2concentration near the gas inlet enhances the mass transfer of CO2through the membrane. Likewise, the temperature rise is higher near the gas inlet (convex shape) due to the release of more heat from the CO2absorption in the amine solvent.

[0213] Pilot scale MBC module

[0214] Similar comparisons between measured and predicted CO2absorption fluxes 1542, 1544, 1546, 1552, 1554, 1556 in pilot-scale MBC modules are presented in Figure 15D and Figure 15E . The experimental data are for different CO2loadings in the solvent (0.01-0.23 mol mol -1 ) and different gas and amine flow rates (see, e.g., Table 6). The model predictions using the model for CO2solubility of equation 14 agree closely with the CO2absorption fluxes in Figure 15D , while the predictions using equation 15 result in similar 10% overestimation at higher CO2loading experiments due to the neglect of the effect of CO2loading in the amine solvent.

[0215] Consistent with the laboratory-scale results, the MBC model 1028 correctly predicts that larger CO2liquid loadings decrease the CO2absorption flux due to the reduction of free amine available for reaction with CO2. This is shown, for example, in Figure 15D . In addition, the increase in CO2liquid loadings decreases the CO2solubility in the liquid (see, e.g., Figure 7B ) and the liquid surface tension, causing additional wetting and thus decreasing the CO2flux through the membrane.

[0216] In Figure 15E , experimental data corresponding to different CO2inlet concentrations in the NG mixture and lean amine are considered. The MBC model 1028 again correctly captures the improvement in the CO2absorption flux 1552, 1554 with increasing CO2inlet concentration. This improvement is driven by the higher CO2concentration gradient that increases mass transfer in the MBC. The MBC model 1028 also predicts negligible membrane wetting due to the horizontal orientation and operation with lean amine.

[0217] Estimation of hydrocarbon loss in high pressure MBC for NG desulfurization

[0218] Figure 17 Plots 1700 of experimental and predicted hydrocarbon molar flow rates in the flash gas of the pilot NG plant are shown according to an embodiment for different solvent flow rates. In particular, Figure 17 Plots of experimental flow rate of CH4 1702, experimental flow rate of C2H6 1704, experimental flow rate of C3H8 1706, predicted flow rate of CH4 1708, predicted flow rate of C2H6 1710, and predicted flow rate of C3H8 1712 are shown. The gas inlet flow rate, CO2inlet content, and solvent inlet CO2loading are 75 kg h -1 , 5 mol%, and 0.01 mol mol -1 , respectively.

[0219] Referring to Figure 17 , it can be seen that all predicted molar flows 1708, 1710 of methane and ethane are within 15% of the measured values. This validates the assumption that the solvent is approximately saturated with hydrocarbons at the MBC liquid outlet as described above with respect to equation 1. On the other hand, the predicted molar flow 1712 of propane underestimates the measured values by a factor of 2 to 3, which can be due to these flow rates being relatively small and therefore susceptible to experimental error.

[0220] Furthermore, as shown in Figure 17 , the MBC model 1028 correctly captures the increase in HC absorption with increasing solvent flow rate against experimental data as described by equation 2. The increase in HC absorption is attributed to a higher concentration gradient in the solvent, which improves mass transfer. The MBC model 1028 further predicts that methane loss is an order of magnitude higher than ethane and higher hydrocarbons. This is expected because the feed gas of the pilot plant contains 85 mol% of methane, and the solubility of methane in amine is higher than that of ethane and higher hydrocarbons (see Figure 6A , Figure 6B , and Figure 6C ). In summary, the predictions provide the correct order of magnitude of HC loss with small loss rates of about 1% for the solvent flow rates against experiments. Therefore, a similar modeling approach will be used in the techno-economic assessment discussed later.

[0221] Estimation of solvent evaporation rate in high pressure MBC for NG desulfurization

[0222] Table 7: Predicted composition flow rates of treated gas from MBC for CO2 loading, gas and solvent flow rates of 0.01 mol mol -1 , 75 kh h -1 and 275 L h -1 .

[0223]

[0224]

[0225] Figure 18 A plot 1800 showing the predicted vapor pressure of water 1802, MDEA 1804 and PZ 1806 versus different solvent temperatures from 293 K to 353 K according to an embodiment.

[0226] As shown in Table 7 above, the MBC model 1028 predicts that water evaporates mainly, while the evaporation rate of MDEA and PZ to the treated gas is negligible. This is due to the fact that at temperatures from 293-353 K, the vapor pressure of MDEA and PZ and their concentrations are much lower compared to the vapor pressure of water (see Figure 18 ).

[0227] The low solvent evaporation rate is due to the fact that at higher operating pressure (54 bar), the mole fraction of solvent in the treated gas outlet is 50 times smaller than at atmospheric pressure (see Equation 3). For MBCs operating at atmospheric pressure, such as in post-combustion CO2 capture, higher solvent evaporation losses can be expected, thus requiring a more detailed way of modeling solvent evaporation. For high-pressure MBCs used in NG desulfurization, the assumption of using Raoult’s law (see regarding Equation 3) through the overall mass balance (lumped) is reasonable, as the evaporation rate is low.

[0228] The MBC model 1028 predicts that about 0.03 wt% of the solvent flow rate fed to the MBC in the pilot plant is lost through evaporation. The corresponding energy consumed by this solvent evaporation in the MBC is less than 1% of the heat generated by CO2 absorption. This confirms that solvent evaporation has minimal effect on the solvent temperature at high pressure, and validates the approximation of considering solvent evaporation at the liquid inlet in the MBC energy balance (see regarding Equations 5 and 6). In summary, the ability to predict the solvent evaporation rate and its composition will enable quantifying the amount of solvent make-up required, and will enable a process-wide assessment of the MBC fed for NG desulfurization, as described below.

[0229] Using the MBC model 1028 (i.e., the absorption section) developed above, it can now be integrated with the solvent regeneration model / unit (i.e., the desorption section) to develop full-scale MBC-based NG desulfurization operation models, as discussed below. This integration will allow for the analysis of the impact of different conceptual designs, including various absorption / desorption design configurations and operational decisions for scale-up and full-process economic evaluation. Integrating the MBC model 1028 into the complete treatment model describing CO2 absorption and desorption operations enables model-based evaluations of full-scale MBC processes for NG desulfurization.

[0230] Full process modeling and evaluation of natural gas desulfurization using high pressure membrane contactors

[0231] Conventional NG desulfurization processes involve two operations – absorption and desorption (also known as solvent regeneration). In the absorption process, a lean or semi-lean solvent (most commonly alkanolamines) flows countercurrently with natural gas in MBC modules 802 and 902, selectively reacting with acidic gases (CO2 and H2S) from the gas phase. For high-volume CO2 removal, CO2 purity targets are typically sales gas specifications of less than 2 mol% or 6-8 mol% when the CO2 content in the feed gas is higher than 20 mol%. For advanced CO2 removal applications in liquefied natural gas (LNG) plants and ammonia plants, CO2 specifications are <50 ppmv and <100 ppmv, respectively, to avoid freezing and catalyst poisoning in cryogenic refrigerators (liquefaction processes).

[0232] The terms lean and semi-lean refer to the fraction of acidic gases present in the amine solvent. In the context of CO2 capture in the embodiments of the present invention, a "lean" solvent means a solvent containing very little or no CO2 (i.e., a CO2 loading of approximately 0.01 mol / mol). -1 The inlet solvent flow is "semi-lean," meaning the amine contains some CO2 (i.e., a CO2 loading of approximately 0.2 mol / mol). -1 The solvent stream exiting the MBC is called "rich" and requires regeneration, which consists of a combination of a flash stage and a gas-liquid contact chamber.

[0233] As previously mentioned Figure 9The solvent regeneration process, the rich amine solvent 917 from the MBC liquid outlet is first directed to a low pressure flash drum 918 to recover the flashed HC as fuel gas 920. The liquid outlet stream from the flash drum 918 is then fed to a solvent regenerator 924 where the liquid outlet stream is heated to a suitable temperature by a reboiler 928 to strip CO2from the rich solvent before the lean solvent is recycled to the MBC unit 902. On the other hand, the overhead condenser 927 provides a reflux liquid stream to the solvent regenerator 924 to ensure that the top product stream, also known as the acid gas stream, is as pure as possible. Finally, a solvent makeup is fed to the amine tank 910 to make up for the solvent evaporated in the MBC module 902, the flash drum 918 and the solvent regenerator 924. The solvent regeneration process is operated at a low pressure to recover the HC and to reduce the solvent boiling point to reduce energy consumption. The lower boiling point also helps to keep the solvent below its degradation temperature. Typically, the reboiler 928 of the solvent regeneration process is the largest contributor to the operating cost.

[0234] Some key performance indicators (KPIs) for the NG desulfurization process are: (a) the purity of CO2in the product gas; (b) the energy per ton of CO2removed; (c) the HC loss or the amount recovered as fuel gas; and (d) the amount of solvent loss required per treated gas and makeup.

[0235] Using the integrated model including the MBC model 1028 described above, the CO2removal performance and energy load of each equipment under various scenarios, including lean and semi-lean process operation, can be predicted. The amount and composition of hydrocarbon (HC) recovered in the flash drum at various pressures can also be quantified. In addition, the evaporation solvent loss in the MBC module 802, 902 and the solvent regeneration section can be predicted, such that the solvent makeup required to maintain the solvent concentration in the process can be quantified with an estimated associated cost. The predictive capability of the integrated model 1000 in terms of CO2removal performance and energy consumption will be tested against data from a pilot-scale MBC module operating at variable CO2loading in an amine solvent from an NG treatment plant in Malaysia. In this embodiment, all experiments are conducted with an aqueous mixture of MDEA and Piperazine (PZ) as the chemical solvent.

[0236] The experimental setup and corresponding model parameters for NG desulfurization treatment based on pilot-scale MBC are presented below, followed by a description of the development and implementation of the MBC full treatment model. Results of experimental validation of the full treatment model are then presented and discussed. Model-based analyses are conducted to investigate (i) the impact of optimized lean MBC operation and semi-lean MBC operation on energy duty, (ii) the impact of different operating pressures on HC recovery in the rich solution flash drum, and (iii) the impact of different inlet solvent temperatures on evaporation solvent loss. Model-based design and scale-up of industrial-scale MBC for semi-lean MBC treatment operating at industrially relevant conditions for NG desulfurization are conducted, and the potential for intensification is evaluated.

[0237] Pilot scale MBC setup

[0238] Experiments were conducted in a pilot-scale module operating at 54 bar, industrially relevant operating conditions in an NG treatment plant in Malaysia. An aqueous mixture of methyldiethanolamine (MDEA) and piperazine (PZ) was used as the chemical solvent. The experimental setup was similar to the pilot-scale described above with respect to Figure 9 , and is therefore not repeated here. The corresponding operating conditions for the absorption and desorption systems are summarized in Table 8 below. The flow and composition of the gas, regenerated solvent, and flash gas at the MBC inlet and outlet were measured and averaged every hour for comparison with model predictions. The energy consumption of all units powered by electricity was monitored. The total energy consumption or equipment referred to as treatment duty, P T [kW] is (i) the reboiler 928, (ii) the overhead condenser 927, (iii) the reflux pump 932, (iv) the LP amine pump 934, (v) the lean solution cooler 938, (vi) the HP amine pump 912, and (vii) the amine chiller 914. These equipment are modeled as described below, where each equipment forms one of the modules stored in the program storage 1062 of the solvent regeneration data processing system 1011.

[0239] Module specifications

[0240] In this example, the high-pressure MBC modules 802, 902 are filled with hydrophobic polytetrafluoroethylene (PTFE) hollow fibers, which are the same as the modules used above with respect to Table 2. According to this example, the solvent regenerator (e.g., the solvent regenerator 924 as shown in Figure 9 is filled with Super-Ring #1 material. The main characteristics and geometric properties of the MBC and solvent regeneration units are summarized in Table 8 below.

[0241] Table 8: Operating conditions in the pilot plant.

[0242]

[0243]

[0244] Table 9: MBC and solvent regeneration unit specifications.

[0245]

[0246]

[0247] Note: The above reference values are taken from (i) Honeywell UOP (2014) "Regeneration Section for PETRONAS CO2 Pilot Plant" and (ii) Billet, R. and Schultes, M. (1999) "Prediction of mass transfer columns with dumped and arranged packings", Trans IChemE, 77. pp. 501. doi: 10.1205 / 026387699526520.

[0248] Modeling of MBC based process for NG desulfurization

[0249] The modelling of the regeneration unit operations in the MBC process, i.e. the flash drum 918, heat exchanger 922, pumps 932, 934 and stripper 924 based on the MBC pilot plant setup, is now described. The integration of these with the MBC unit model 1028 developed above is carried out in the gPROMS ProcessBuilder environment of the present embodiment, although it will be appreciated that other relevant programs or software could be used for the integration. The models of the regeneration unit operations as described together with the MBC model 1028 form the NG plant-wide model of the natural gas sweetening process operation system 1000 for assessing the performance or characteristics of the natural gas sweetening process.

[0250] Figure 19 A schematic diagram 1900 showing the gML compliant MBC unit operation models in gPROMS ProcessBuilder for modelling the natural gas sweetening process according to the embodiment is shown. As described above, the models of the regeneration unit operations are integrated with the MBC model 1028 to form the NG plant-wide model of the natural gas sweetening process operation system 1000 for assessing the performance or characteristics of the natural gas sweetening process. Figure 19As shown, the MBC unit operation model includes an MBC module 1902 having a gas inlet 1904 for natural gas, a liquid inlet 1906 for solvent (e.g., amine solvent), a gas outlet 1908 for treated natural gas, and a liquid outlet 1910 for rich solvent (i.e., solvent used for CO2 absorption in the MBC module 1902). The parameters used in the gML compliant MBC unit operation model are shown in Table 10 below. The schematic 1900 shows the user interface for the MBC unit operation model compiled into a gML compliant model library.

[0251] Table 10: Parameters used in the gML compliant MBC unit operation model in gPROMS ProcessBuilder unit.

[0252] Parameters Value Units Gas inlet 2.0 kg / hour Liquid outlet 11 kg / hour mole fraction of incoming CO2 0.239000 - mole fraction of the emitted CO2 0.06128 - % CO2 removal 79.51 ％ CO2 load LA calculation 0.2252 [kmol CO2 / kmol amine] CO2_carrying_RA 0.5475 [kmol CO2 / kmol amine] Absorption of liquid into CO2 103.8 gal / lb-mol Average wet ratio 0.0472 - Average Absorbed Flux CO2 0.00198296 mol / m 2 s]] Liquid temperature at inlet 311 K Liquid temperature at outlet 330 K Liquid delta T 19.8 K Total mass in (1) 0.003328 kg / s Total mass out (1) 0.003328 kg / s Gas mass in ("mass flow rate", 1) 0.0005500 kg / s Mass of gas out ("mass flow rate", 1) 0.0004015 kg / s Mass of liquid in ("mass flow rate", 1) 0.002778 kg / s Mass of liquid out ("mass flow rate", 1) 0.002926 kg / s

[0253] Figure 20 A schematic 2000 showing an MBC based natural gas sweetening process flow in gPROMS ProcessBuilder according to an embodiment is shown. The schematic 2000 shows an MBC process flow constructed by integrating the above described MBC unit operation model into the standard unit operation library of ProcessBuilder. As shown in the schematic / flow diagram 2000, in addition to the MBC unit operation model 1900 including the MBC module 1902 having a gas inlet 1904, a liquid inlet 1906, a gas outlet 1908, and a liquid outlet 1910, the NG sweetening process flow 2000 also includes a number of other components. As shown in the schematic / flow diagram 2000, the rich solution from the liquid outlet 1910 is fed to a rich-lean exchanger 2008. The lean solvent from the lean- rich exchanger 2008 is fed to a solvent regenerator 2010. The acid gas 2012 from the solvent regenerator 2010 is fed to a reflux drum 2014 having an overhead condenser (not shown) to separate condensed water from the acid gas 2012. The condensed water is then returned to the top of the solvent regenerator 2010 via a reflux pump 2016, while the acid gas 2012 is sent to a flare header 2018. Finally, the solvent from a reboiler 2020 is pumped back into the MBC module 1902 via a lean solution cooler 2026, a high pressure amine pump 2030, and an amine chiller 2028 using a low pressure amine pump 2022 to replenish the solvent evaporated in the MBC module 1902. The process flow 2000 also provides a solvent make-up 2024 for adjusting the composition of the solvent fed to the MBC module 1902. Figure 20 As shown, the rich solvent from the liquid outlet 1910 is in fluid communication with a rich-lean solution flash drum 2002. A flash gas 2004 is discharged from the flash drum 2002, while outputting a flash liquid outlet stream 2006. The output flash liquid outlet stream 2006 is heated with hot lean solvent by a lean- rich exchanger 2008, and then fed to a solvent regenerator 2010, where acid gas 2012 is stripped. The acid gas 2012 leaving the top of the regenerator is cooled and sent to a reflux drum 2014 having an overhead condenser (not shown) to separate condensed water from the acid gas 2012. The condensed water is then returned to the top of the solvent regenerator 2010 via a reflux pump 2016, while the acid gas 2012 is sent to a flare header 2018. Finally, the solvent from a reboiler 2020 is pumped back into the MBC module 1902 via a lean solution cooler 2026, a high pressure amine pump 2030, and an amine chiller 2028 using a low pressure amine pump 2022 to replenish the solvent evaporated in the MBC module 1902. The process flow 2000 also provides a solvent make-up 2024 for adjusting the composition of the solvent fed to the MBC module 1902.

[0254] An overview of the specifications in the regeneration unit operations according to the present embodiment is provided below (see Table 8 above) along with some numerical solution details. It should be understood that although specific models / packages are used, other suitable models / packages can be suitable.

[0255] Modeling of rich solution flash drum 2002

[0256] The rich amine from the MBC shell outlet is passed through a pressure expander before entering the rich solution flash drum 2002. The outlet pressure of the expander is set to the rich solution flash drum pressure of 911 kPa (see Table 8). The rich solution drum itself is modeled as a two-phase (liquid-vapor) flash vessel, using the PSE, 2018, in gPROMS ProcessBuilder document 1.3.1, which predicts the flow rates, compositions, temperatures, and pressures of the liquid and vapor outlet streams from the rich solution flash drum 2002, described by mass and energy balances, and thermodynamic equilibria. The presence of multiple liquid phases is also considered in the model.

[0257] Modeling of heat exchangers

[0258] The heat exchangers in the process model include the lean-rich heat exchanger 2008, the lean solution cooler 2026, the amine chiller 2028, the overhead condenser and reboiler 2020. The lean-rich heat exchanger 2008, which transfers heat from the regenerated amine (hot stream) to the rich amine (cold stream), is modeled as a counter-current heat exchanger. The cold stream outlet temperature and the pressures of both outlet streams are specified in Table 8. The lean solution cooler 2026 and the amine chiller 2028, which reduce the amine temperature to 318 K and 303 K, respectively, after amine regeneration (Table 8), are modeled with standard coolers. The overhead condenser and reflux drum 2014 are modeled as a standard separator with the outlet temperature set to 333 K to separate the fluid into two phases. The reboiler is described by an evaporator kettle model with the heat specification set to 403 K (Table 8). The heat exchanger models can be used to predict the process loads required to meet the heat specifications.

[0259] Modeling of pumps

[0260] The pumps in the process model include the amine HP pump 2030, the amine LP pump 2022, and the reflux pump 2016. It is assumed that all of these pumps are mechanical with an isentropic efficiency of 85%. Using the ideal efficiency (PSE, 2018), the fluid outlet temperature is further calculated by defining the fluid compression relative to the ideal compression process. The outlet pressures of the pumps are specified according to Table 8. The pump models predict the process loads required based on the outlet pressure specifications and the efficiencies.

[0261] Modeling of solvent regenerator

[0262] For the solvent regenerator 2010, a rate-based model from the advanced model library (PSE, 2018) for gas-liquid contactors (AML:GLC) is used in this example. Mass and heat exchange between a large gas phase and a liquid phase are described via gas and liquid films, which are separated by an infinitely thin interface where the phases are in equilibrium.

[0263] The model uses the Raschig Super Ring #1 packing characteristics (see, e.g., Table 9). Inbuilt correlations in AML:GLC are used to calculate the performance of the packing. Specifically, the Onda correlation with random packing is used to predict the mass transfer coefficients and interfacial area, and the Billet holdup correlation is used to calculate the liquid holdup in the regenerator. It should be noted that in this example, the pressure drop in the column is neglected here.

[0264] The solvent regenerator model is coupled with the reboiler 2020 and the overhead condenser as described above. The full solvent regenerator model predicts the flow rates, compositions, temperatures, and pressures of the outlet gas and lean solvent streams.

[0265] Modeling of solvent make-up

[0266] The solvent make-up stream maintains the desired solvent flow rate and concentration in the MBC system. In gPROMS Process Builder, three “setpoint” elements 2032, 2034, 2036 are used to set the solvent flow rate 2032 to the MBC, MDEA mass fraction 2034, and PZ mass fraction 2036 to 275 L-h -1 , 39 wt%, and 5 wt% respectively (Table 8). These three elements feed into a mixer immediately before the MBC unit.

[0267] Thermophysical, transport, and reaction kinetics data

[0268] The temperature-dependent expressions for the macroscopic reaction rates of CO2 with MDEA and PZ and the diffusion coefficients of various species in the gas and liquid mixtures used in the MBC model 1028 are described above, while the Henry’s constant for CO2 in amine solutions is obtained as described with respect to equation 14. To reduce the computational burden, simple polynomial replacements for the diffusion coefficients D MDEA，l and D PZ，l are derived over the temperature range of 300-400 K, and will be described below for completeness. These polynomial replacements are used advantageously to speed up the simulation time while reducing the computational resources used.

[0269] The diffusivity of CO2in the liquid can be estimated based on analogy with the diffusivity of N2O in the solution, as shown in Equation 20 below:

[0270]

[0271] The diffusivity of CO2and N2O in water is given by:

[0272]

[0273]

[0274] where T l is the temperature of the liquid.

[0275] The diffusivity coefficient of N2O in the liquid amine solution is estimated using a modified Stokes-Einstein relation, as shown in Equation 23 below:

[0276]

[0277] where in this example, the viscosities of water and amine and μ l are obtained from the package "UNIQUAC-RK", respectively. Similarly, the temperature corrected diffusivity of MDEA and PZ amine in the liquid phase is correlated using a modified Stokes-Einstein relation.

[0278]

[0279]

[0280] where in this example, the diffusivity of MDEA and PZ in water and the dynamic viscosities of the liquid and water are obtained from the package "UNIQUAC-RK".

[0281] The other thermophysical and transport parameters for the gas and liquid phases in the absorption and regeneration units are obtained from gPROMS interacting with the property packages Advanced Peng Robinson, UNIQUAC-RK and RSKA according to Multiflash v6.1.

[0282] Numerical simulation

[0283] After rescaling the radial dimension of the membrane dry and wet space subdomains to be rectangular, the partial differential equations of the MBC model 1028 are discretized using a second order central finite difference scheme, as described with respect to Figure 2A coarser uniform grid consisting of 35 elements was chosen for the simulations herein, which provided solutions within <1% of the finer discretization, while reducing the computational burden. For the solvent regenerator, a first order finite difference method was used for the bulk liquid and vapor consisting of 20 elements.

[0284] Experimental model validation

[0285] According to embodiments, a comparison of the predicted CO2 removal performance, CO2 loading in the amine, and total processing load of the MBC with measured data from a pilot plant is shown in Figure 21A and Figure 21B . Figure 21A A plot 2100 showing predicted and experimental CO2 purity and CO2 removal efficiency for different CO2 loadings in the amine solvent, while Figure 21B a plot 2110 showing predicted and experimental total processing load for different CO2 loadings in the amine solvent. Experimental data was taken for different CO2 loadings in the solvent at constant gas and liquid flow rates of 75 kg h -1 and 275 L h -1 , respectively.

[0286] As shown in Figure 21A , experimental data for predicted CO2 outlet purity 2102, CO2 outlet purity 2104, predicted CO2 removal efficiency 2106, and CO2 removal efficiency 2108 for different CO2 loadings in the amine solvent were plotted. It was found that the predictions agreed well with the measurements, showing errors of less than 5% for CO2 absorption flux and CO2 removal efficiency. Note that an error of about 15% can be seen in the second experimental data point for CO2 outlet purity in Figure 21A when compared to the predicted CO2 outlet purity. This can be because the low level of CO2 outlet purity (0.73 mol%) is susceptible to large errors, which inevitably exist even with small changes in the predicted CO2 outlet purity (0.85 mol%). However, when compared in terms of CO2 absorption flux and removal efficiency, it was found that the predictions and measurements were within 5%. Furthermore, as shown in Figure 21A , the MBC model 1028 correctly predicted that a larger CO2 liquid loading decreased the CO2 removal efficiency, which in turn decreased the CO2 outlet purity. As mentioned above, an increase in liquid CO2 loading results in a decrease in the CO2 solubility and absorption capacity of the solvent due to a reduction in free amine.

[0287] As shown in Figure 21BAs shown, the predicted total treatment load 2112 and the experimental total treatment load 2114 are plotted. The full treatment model included in the natural gas desulfurization treatment operating system 1000 and illustrated as in the treatment process 2000 correctly predicts the reduction in heating and cooling loads under conditions of high CO2 loading in the solvent. Similar to... Figure 21A The results shown indicate that, as Figure 21B The overall predictions shown are in good agreement with the measurement results, indicating that the errors in CO2 load and total treatment load are less than 5%.

[0288] Figure 22A and Figure 22B Graphs 2200 and 2210 show predicted and experimental CO2 absorption flux and CO2 loading at different solvent regeneration temperatures according to embodiments. Reference Figure 22A The predicted CO2 absorption flux 2202 and the experimental CO2 absorption flux 2204 are shown for different solvent regeneration temperatures. Figure 22B The data points for the predicted inlet CO2 load 2212, experimental inlet CO2 load 2214, predicted outlet CO2 load 2216, and experimental outlet CO2 load 2218 for different solvent regeneration temperatures are shown.

[0289] The reboiler 2020 for the solvent regenerator 2010 can operate at a lower temperature in a semi-lean operation (see example). Figure 22B This reduces the energy required for solvent regeneration. For example, as previously shown, this is achieved by increasing the solvent CO2 loading to 0.23 and 0.27 mol, respectively. -1 This can significantly reduce the reboiler load. Note that the increase in regeneration temperature reduces the CO2 inlet load to the MBC 1902 (see example). Figure 22B This further improves the CO2 absorption flux (see example...). Figure 22A In addition, note that, as Figure 22B As shown, with half-depleted amine operation In comparison, amine-deficient operation The difference between the inlet and outlet CO2 loadings is greater. This is because the CO2 removal efficiency of the lean amine operation (approximately 99.9%) is higher than that of the semi-lean amine operation (approximately 80%). Figure 21A As shown.

[0290] To achieve deep CO2 removal, such as to meet LNG specifications of less than 50 ppmv CO2, the full treatment model indicates that lean solvent is necessary (e.g., CO2 loading ≈ 0.01 mol / mol). -1 On the other hand, semi-lean solvents (e.g., CO2 loading of approximately 0.23 mol / mol) -1) operation appeared to be sufficient to meet the <1.5 mol% CO2 typical sales gas specification. In this particular experiment, the semi-lean operation consumed approximately 80% less energy compared to the lean operation. Further model-based analysis and design of NG desulfurization using MBC treatment is described below.

[0291] Model-based analysis of pilot-scale MBC

[0292] A full treatment model as described above was developed for the MBC pilot plant to facilitate analysis of: (i) the treatment load of the optimized MBC lean amine and semi-lean amine treatment; (ii) the optimal pressure at the rich solution flash drum for maximum fuel gas recovery; and (iii) the amount and concentration of solvent make-up.

[0293] Optimal solvent flow rates for lean and semi-lean operation

[0294] As described above with respect to Figure 21A , Figure 21B , Figure 22A and Figure 22B , experimental validation of the full treatment model showed that both the lean and semi-lean operation were able to reduce the CO2 purity to <1.5 mol% of the sales gas specification, with the semi-lean operation consuming 80% less energy compared to the lean operation. However, these experiments were all performed at the same solvent flow rate to the MBC 1902, and therefore can correspond to sub-optimal operation. Here, the minimum liquid flow rate required to achieve a CO2 purity of 1.5 mol% for the treatment of 75 kg / h -1 of sour natural gas was determined. The lean amine operation was performed similarly to the flow diagram shown in Figure 20 , but without the excess amine being recycled back to the solvent regenerator 2010. The solvent regenerator 2010 was sized to remain the same in the pilot plant to provide a conservative reboiler treatment load compared to the semi-lean treatment.

[0295] Figure 23 A schematic diagram 2300 of the MBC pilot-scale semi-lean operation treatment flow is shown in accordance with an embodiment in gPROMS ProcessBuilder. As Figure 23 indicated, the semi-lean operation treatment flow is similar to Figure 20 , except that the reboiler 2020 and solvent regenerator 2010 are replaced by a heater 2302 and a low pressure flash drum 2304. All pressure and temperature specifications for the flow diagrams of both the lean and semi-lean operation were kept the same as described above with respect to Tables 8-10, except that the reboiler / heater temperature was adjusted to obtain the desired CO2 loading in the solvent. The results of this comparison are reported in Table 11 below.

[0296] As shown in Table 11, the optimized lean operation requires 34% lower solvent flow rate to the MBC to meet the required CO2 purity compared to the optimized semi-lean operation. This is due to the higher CO2 absorption capacity of the lean solvent, which increases the CO2 removal rate in the MBC 1902. With the lower solvent flow rate, the overall process model predicts a reduction in the process load for all pumps compared to the semi-lean operation. This corresponds to an L / G ratio of about 0.75 m 3 kmol -1 at the lower end of the range typically encountered in conventional packed columns. 3 kmol -1 .

[0297] Table 11: Optimized operating conditions and process load for lean MBC and semi-lean MBC

[0298]

[0299]

[0300] However, the overall process load under the lean operation remains 28% higher compared to the semi-lean operation due to the higher reboiler temperature required to regenerate the solvent under the lean operation. This results in a higher temperature of the regenerated solvent, which also requires a higher cooling duty in the lean solvent cooler before returning the solvent to the MBC, despite the heat integration between the inlet and outlet streams of the regenerator.

[0301] Figure 24A and Figure 24B Pies 2400, 2420 showing a breakdown of the equipment process load according to embodiments, wherein Figure 24A Pie 2400 shows a breakdown of the equipment process load in the MBC for the lean amine operation, and Figure 24B Pie 2420 shows a breakdown of the equipment process load in the MBC 1902 for the semi-lean amine operation. For each of Figure 24A and Figure 24B a breakdown of the total process load for different equipment aspects is shown.

[0302] As shown in Figure 24A under the lean operation, the reboiler contributes 50.2% (indicated by 2402) of the equipment process load, the overhead condenser contributes 3.7% (indicated by 2404) of the equipment process load, the pumps contribute 1.4% (indicated by 2406) of the equipment process load, the lean solvent cooler contributes 34.8% (indicated by 2408) of the equipment process load, and the amine chiller contributes 9.8% (indicated by 2410) of the equipment process load. On the other hand, as shown in Figure 24BAs shown, under semi-lean operation, the reboiler contributes 41.0% (represented by 2422) of the equipment handling load, the overhead condenser contributes 13.1% (represented by 2424) of the equipment handling load, the pump contributes 2.4% (represented by 2426) of the equipment handling load, the lean solution cooler contributes 26.7% (represented by 2428) of the equipment handling load, and the amine cooler contributes 16.7% (represented by 2430) of the equipment handling load.

[0303] like Figure 24A and Figure 24B These two findings indicate that the reboiler load is the largest energy consumption (approximately 40-50% of the total processing load for both operations), consistent with previous work. The lean solution cooler and amine cooler are the second and third largest, respectively (26-35% and 9-17% of the total processing load). Based on this analysis, one area for improvement could be operating the liquid above 318 K in the MBC absorption section. This operation would eliminate the requirement for an amine cooler, thus potentially reducing the footprint and processing load by a further 9-17% in both operations.

[0304] In summary, semi-lean operation exhibits greater enhancement potential with reduced energy consumption and floor space (i.e., flash drum and heater), and this should translate into reduced capital and operating expenditures compared to lean operation.

[0305] Optimal flash pressure for fuel gas recovery

[0306] Any hydrocarbons (HC) absorbed in the unrecovered solvent will eventually enter the acidic gas stream. This can represent a significant product loss and may cause problems elsewhere in the process. To maximize flash gas recovery and minimize product loss, the optimal pressure for operating the rich solution flash drum 2002 was investigated. A key constraint in practice is that the recovered flash gas should have a sufficiently high lower heating value (LHV) to meet, for example, 47.1 MJ kg⁻¹. -1 The standard fuel gas specifications. From a thermodynamic point of view, operating the rich solution flash drum 2002 at lower pressures will increase the amount of flash gas, thus increasing fuel gas recovery. However, substances with lower vapor pressures (such as CO2) will also flash away, thus reducing the fuel gas LHV. Therefore, this defines the optimal trade-off regarding the flash drum pressure.

[0307] The total HC recovered from the solvent at the rich solution flash drum 2002 was obtained from... The LHV of the recovered flash HC gas is indicated, and the LHV is... g [MJ kg -1 ]Calculated as

[0308]

[0309]

[0310] in and The molar flow rate and mass fraction i∈{CH4,C2H6,C3H8} of the flash gas from the rich solution drum; and the LHV values ​​for each LHV. i [MJ kg -1 Based on ISO 6976 (see, for example, ISO, 2016 - Natural gas - Calculation of calorific value, density, relative density and Wobbe index from components).

[0311] Figure 25A and Figure 25B The graphs 2500 and 2510 show the predicted hydrocarbon recovery and low calorific value (LHV) of natural gas for rich solution drum pressure according to the embodiments. Figure 25A This is shown in the amine-deficient operation (where =0.01) Plots of hydrocarbon recovery 2502 and low calorific value (LHV) of natural gas 2504 predicted for rich solution drum pressure 2500. For example... Figure 25A and Figure 25B The dashed line 2506 shown defines the aforementioned 47.1 MJ kg. -1 Standard fuel gas specifications. Figure 25B This shows the operation of semi-lean amines. The graph below shows the predicted hydrocarbon recovery 2512 and the low calorific value (LHV) of natural gas 2514 for the rich solution drum pressure 2510. For these two graphs 2500 and 2510, the NG gas and solvent flow rates used are 75 kg h⁻¹. -1 and 275Lh -1 .

[0312] like Figure 25A and Figure 25B As shown, by reducing the flash drum pressure of the rich solution from 1500 kPa to 700 kPa for lean and semi-lean operations respectively, the full-processing model predicts that HC recovery will increase from approximately 81% to 90% and from 77% to 88%. Note that, as Figure 25A As shown, for lean amine operation, the flash gas meets the fuel gas LHV at all operating pressures and achieves a maximum HC recovery of 90% at 700 kPa. On the other hand, as... Figure 25B As shown, except for a lower HC recovery of 77% at 1500 kPa, the predicted LHV for all operating pressures of interest under semi-lean operation does not meet fuel gas specifications. The high CO2 content in the flash gas is attributed to the CO2 loading from the rich amine from MBC module 1902 under semi-lean operation. CO2 loading in amine-deficient operation than (e.g., reference Figure 22B ). To recover more flash gas, the flash gas containing CO2 would need to be further desulfurized so that it can be used as fuel gas. Otherwise, the flash gas can be compressed and returned to the MBC gas inlet or treated gas to meet the required CO2 purity.

[0313] MBC full-process evaluation of solvent loss

[0314] The amine solvent is not consumed during the acid gas removal process, but some amine loss is inevitable due to evaporation or entrainment. Unlike conventional packed columns, solvent entrainment in the MBC 1902 is prevented by the microporous membrane that allows the liquid and gas phases to contact each other without one phase being dispersed in the other. On the other hand, solvent evaporation loss in the form of water, MDEA, or PZ can occur with the treated gas, flash gas, and acid gas streams. They depend on the type and concentration of the amine, as well as the temperature and pressure of the MBC 1902, flash drum 2002, and solvent regenerator 2010. Solvent make-up streams (e.g., represented by 2024 in the flow diagram 2000) are intended to compensate for these losses and maintain the required solvent concentration in the process. Figure 20

[0315] It is generally known that existing gas treatment plants using monoethanolamine (MEA), diethanolamine (DEA), and MDEA report average amine loss rates in the treated gas of 2 x 10 -4 kg Nm -3 . In most gas treatment systems, it is possible to reduce these losses to less than 7 x 10 -5 kg Nm -3 .

[0316] Figure 26A and Figure 26B Graphs 2600, 2610 illustrating the effect of the solvent temperature at the MBC inlet on the evaporation loss of different components of the solvent (i.e., water, MDEA, and PZ) in the process according to the present embodiment are shown. Figure 26A Graph 2600 showing the evaporation loss of water 2602, MDEA 2604, PZ 2606, and MDEA+PZ 2608 at different solvent temperatures. Figure 26B Graph 2610 showing the ratio of the evaporation loss in the acid gas to the loss in the treated gas for water 2602 and MDEA+PZ 2608 at different solvent temperatures. The graphs 2600, 2610 were simulated using NG gas and solvent flow rates of 75 kg h -1 and 275 L h -1 .

[0317] As Figure 26A ​As shown, the evaporation rates of water 2602, MDEA 2604, and PZ 2606 increase with increasing liquid temperature due to the corresponding increase in their vapor pressures. Figure 26A It is also shown that the water evaporation loss rate 2602 is the highest, followed by PZ 2606 and MDEA 2604, which is consistent with the respective vapor pressures of the components (see, e.g., Figure 18 ). In addition, the loss rates of the amines are between 0.3 and 1.1 x 10 -4 kg Nm -3 -1. The total amine loss is approximately 0.15% of the solvent circulation rate (0.4 L h -1 -1 of 275 L h -1 -1), and water accounts for more than 99 wt% of these losses. This indicates that pure water make-up should be sufficient to maintain the solvent concentration during normal operation. A small fraction of the amine solvent can be replaced by fresh amine to the process when the amine concentration decreases or the inventory of solvent in the process drops.

[0318] Figure 26B The effect of solvent temperature on the evaporation loss of acid gases versus the loss (on a mass basis) of treated gas for water 2612 and MDEA+PZ 2618, entering the MBC, is presented. These results show that significant evaporation losses also occur in the overhead solvent regenerator, which are of the same order of magnitude as the evaporation losses of the MBC treated gas. Although small, the amine losses occurring within the MBC and the regeneration section should not be neglected. This is shown in the following section.

[0319] Model-based scale-up of commercial MBC for natural gas sweetening

[0320] The objective of this section is to design a commercial MBC module (membrane area, solvent flow rates) for a semi-lean MBC operation in an industrially relevant NG sweetening application using the knowledge obtained from the laboratory scale and pilot scale studies as described above. The inlet NG has a CO2content of 24 mol% (which will be reduced to < 6.5 mol% (as shown in Table 12 below)) and a flow rate of 11,630 kmol h -1 . Note that in this simulation study, the amine chiller 2028 is removed and the overhead condenser is operated at 318 K to minimize amine loss to the acid gases. Model-based upscaling and analysis are performed to evaluate this MBC in terms of: (i) the reboiler energy required per ton of CO2removed; (ii) the potential savings in HC recovery in the rich solution flash drum; and (iii) the amount of MDEA and PZ make-up required to maintain the solvent concentration.

[0321] Table 12: Operating conditions in an industrially relevant NG sweetening application

[0322]

[0323]

[0324] The properties of the membranes were the same as those used in Table 2, with a module box inner radius R m of 0.115 m, following the pilot scale module. The following Table 13 reports the geometrical properties of the MBC used for scaling up the industrial relevant NG sweetening application.

[0325] Table 13: Specifications of the commercial scale MBC

[0326]

[0327]

[0328] Note: PRSB (2017) - “Commercial MBC Module Concept Design”, PETRONAS Research Sdn Bhd.

[0329] Solvent flow rate and membrane area A m were first derived from the L / G ratio and the CO2absorption flux obtained from the lab scale experiments (operating at similar operating conditions as outlined in Table 13 above) on Figure 16 Here, refers to the molar gas flow rate of CO2absorbed. The experimental L / G ratio (defined as the solvent flow rate per mole of CO2removed) and the CO2absorption flux were L / G = 0.86 m 3 · Kmol -1 and Ф = 7.02 x 10 -3 kmol m -2 hr -1 -1, respectively. In this context, the required solvent flow rate can thus be estimated as:

[0330]

[0331]

[0332] membrane area A m and the number of module boxes N c are determined as follows:

[0333]

[0334]

[0335] where N c is rounded to the next integer.

[0336] The total number of module boxes N cVery large, a commercial scale module with a radius of 0.8 m was considered (which contains 31 MBC cartridges, each with a radius of 0.115 m). This is shown in Figure 27 , which shows a schematic diagram 2700 of a cross-section of a commercial MBC module 2702 according to an embodiment. As shown, Figure 27 the MBC module 2702 comprises 31 MBC cartridges 2704. This design is preferred as it reduces the number of high pressure vessels, thus limiting the reduction of the physical footprint and weight of the module.

[0337] The number of MBC modules N MBC was then determined as follows:

[0338]

[0339] where N o is the number of cartridges per MBC module; and N MBC was rounded to the next integer.

[0340] A model-based scale-up of the MBC plant was then performed based on the operating conditions and MBC characteristics in Tables 12 and 13, respectively. The predicted values of the process KPIs are listed in Table 14.

[0341] Table 14: Model predictions of process KPIs.

[0342]

[0343] Compared to the lab-scale experiment in Figure 16 , this full process model predicts a CO2 purity in the treated gas that meets the target specification of < 6.5 mol%, with an increase of about 10% in the CO2 absorption flux and L / G ratio. This is attributed to the operation of the solvent inlet temperature at a higher temperature of 318 K to eliminate the requirement of an amine chiller 2028 as discussed earlier. It was also found that the increase in the solvent temperature improves the CO2 absorption flux, despite a slight increase in the average membrane wetting, whereby the increase in mass transfer due to higher reaction rate and diffusion rates of CO2 and amine outweighs the decrease in solubility of CO2 in the amine solvent.

[0344] The predicted reboiler energy per ton of removed CO2 is 2.2 GJ ton -1 , which is lower compared to the range of 2.4-4.2 GJ ton -1 typically reported for amine-based absorption processes. This can be attributed to the semi-lean operation of the MBC system as discussed with respect to Figure 24A and Figure 24B , which was shown to reduce the energy consumption. Furthermore, the full process model predicts an amine loss rate per treated gas of 1.35 x 10 -4 kg Nm -3It is lower than 2×10 in the most recent survey. -4 kg Nm -3 The average amine loss rate. Similarly, the predicted amine loss per ton of CO2 removed is 0.28 kg ton. -1 In amine-based treatments, the reported dosage is typically 0.35–2.0 kg ton. -1 The lower end of the range. For MDEA and PZ, the resulting solvent replenishments were 73 and 144 tons per yr, respectively. -1 .

[0345] Finally, a sensitivity analysis of ±5% of the Henry's constant for HC in the simulated solvent was performed to determine how the uncertainty of the Henry's constant propagates to the estimation of the amount of flash gas recovered at the rich solution flash drum and its calorific value, which is used to quantify the annual savings from HC recovery. The predicted amount of recovered flash gas is 1692–1908 kg / hr. -1 These correspond to ranges of +5% and -5% of the Henry's constant for HC in the solvent, respectively. On the other hand, the predicted calorific value (LHV) of the flash gas... g The recovery rates of HC were 30 MJ / kg. -1 And 82%. Similar to about Figure 25B The discovery of the semi-poverty operation discussed, and the predicted LHV g Below 47.1 MJ kg -1 The fuel gas specifications are due to the high CO2 content of the flash gas. Sensitivity analysis at operating pressures up to 1500 kPa for the flash drum only showed LHV. g Improved to 37 MJ kg -1 However, a lower HC recovery rate of 68% was observed. The high CO2 content in the flash gas is attributed to the CO2 loading from the rich amine derived from MBC. Compared to the CO2 loading in the previously described pilot-scale experiment Higher. Therefore, the flash gas containing CO2 will need to be desulfurized at the top of the flash drum to be used as fuel gas. Otherwise, the flash gas can be compressed and returned to the MBC gas inlet. Using the MBC model, the annual cost savings from flash gas recovery can be quantified, approaching one million US dollars.

[0346] In summary, the scaled-up MBC commercial module demonstrates promising enhancement potential, with (i) predicted reboiler energy per tonne of CO2 removed being 12-50% lower than conventional amine absorbers; (ii) lower predicted amine loss rates per tonne of treated gas and per tonne of CO2 removed compared to the typical loss rates reported in conventional amine-based treatments; and (iii) approximately US$1 million yr from HC recovery can be achieved with further desulfurization of the flash gas. -1potential savings. However, the total number of MBC modules required for this embodiment is 69, and this would require approximately 250 m 2 of floor space. This means that using MBCs can require more floor space compared to conventional absorption towers. In embodiments, further improvements in membrane properties, such as increasing the specific surface area and hydrophobicity of the membranes, are needed to improve the potential for intensification in terms of floor space. In some embodiments, commercial MBC modules can also be designed to be stacked to minimize the floor space.

[0347] As described above, experimental data and model analysis have demonstrated the advantages of semi-lean operation in terms of energy reduction and physical footprint. The results show that semi-lean operation is sufficient for bulk CO2 removal to meet sales gas specifications, while lean amine operation is required for deep CO2 removal to meet LNG specifications. The optimum operating pressure of the rich solution flash drum can also be determined to maximize HC recovery from the solvent while meeting the fuel gas LHV specifications. Furthermore, it has been predicted that the evaporation rate of the solvent is primarily water, and therefore, pure water makeup should be sufficient to maintain the amine concentration in the solvent during normal operation. In addition, the predicted amine loss rate has been found to be within the commonly reported loss rates for conventional CO2 absorption processes.

[0348] A commercial MBC has been scaled up for semi-lean MBC operation in an industrially relevant NG desulfurization application to meet a CO2 purity of <6.5 mol%. The method to predict the solvent flow rate and membrane area required for a commercial scale MBC uses the knowledge of experimental L / G ratio and CO2 absorption flux from existing lab scale experiments as a first approximation. The predicted reboiler energy per ton of CO2 removed is lower than the commonly reported range for amine-based processes, primarily due to semi-lean operation. However, the flash gas from the flash drum can need to undergo further desulfurization for use as a fuel gas due to the high CO2 loading in the rich amine. The predicted amine loss rate per processed gas and per ton of CO2 removed is lower than the commonly reported loss rates in conventional amine-based processes. These full scale MBC results can provide a base case in system model-based optimization to improve the design and operation of commercial MBC modules as part of future work.

[0349] While only certain embodiments of the application have been described, many modifications thereof can be made by those skilled in the art upon reading the preceding description with reference to the annexed drawings. For example, features described in relation to one embodiment can be incorporated into one or more other embodiments, and vice versa.

[0350] Furthermore, it should be understood that although specific procedures or software were used in the described embodiments, they should not be considered limiting. Other suitable procedures or software incorporating the above-described models, equations, and / or boundary conditions can be used to achieve the technical effects discussed.

Claims

1. A computer-implemented method for designing and evaluating the performance of a hollow fiber membrane contactor (MBC) in natural gas desulfurization using a hollow fiber membrane contactor model, i.e., an MBC model, wherein, The MBC model includes model parameters, model equations, and boundary conditions for calculating data associated with the natural gas desulfurization process, and the natural gas desulfurization process includes removing acid gases from natural gas using a solvent containing at least one component, the method comprising: A regression model was developed using empirical data correlated with the solubility of CO2 in the solvent; The regression model is used to determine the Henry's constant for CO2 in the solvent; The determined Henry's constant for CO2 is input into the MBC model as one of the model parameters; and The MBC model is used to determine CO2 absorption in the solvent in order to design and evaluate the performance of the MBC.

2. The method according to claim 1, further comprising: A regression model for the Henry's constant of N2O was developed using empirical data on the solubility of nitrous oxide (N2O) in the solvent. The Henry's constant of N2O is determined using a regression model of the Henry's constant; and The Henry's constant of N2O is used to determine the Henry's constant of CO2 in the solvent to indicate the CO2 loading in the solvent.

3. The method according to claim 1 or 2, further comprising: Empirical data on the solubility of hydrocarbons in the solvent are used to develop a regression model of the Henry's constant for hydrocarbons in the solvent to account for hydrocarbon loss from the natural gas to the solvent. as well as The Henry's constant of the hydrocarbon in the solvent is determined using a regression model of the Henry's constant of the hydrocarbon.

4. The method according to claim 3, further comprising: The rate of hydrocarbon loss in the solvent is determined using the Henry's constant of the hydrocarbon in the hydrocarbon rate loss equation, wherein the rate of hydrocarbon loss is a function of the concentration of the hydrocarbon, and wherein the concentration of the hydrocarbon is inversely proportional to the Henry's constant of the hydrocarbon in the solvent.

5. The method of claim 4, further comprising including the hydrocarbon rate loss equation as one of the model equations of the MBC model.

6. The method according to claim 4 or 5, wherein, The solvent is hydrocarbon-saturated at the liquid outlet of the MBC.

7. The method according to claim 1 or 2, further comprising: The mole fraction of at least one component of the solvent in the gas outlet is determined using Raoult's law; as well as The solvent loss rate is determined using the mole fraction in the solvent rate loss equation, wherein the solvent loss rate is proportional to the determined mole fraction.

8. The method according to claim 7, wherein, The treated gas at the gas outlet of the MBC is saturated with the solvent, and the natural gas and the solvent are in equilibrium at the gas outlet.

9. The method of claim 7, further comprising including the solvent rate loss equation as one of the model equations of the MBC model.

10. The method of claim 7, further comprising: The solvent loss rate is used to determine the energy consumed by solvent evaporation at the liquid inlet of the MBC and the liquid temperature of the solvent.

11. The method according to claim 10, wherein, Solvent evaporation occurs at the liquid inlet before the solvent reacts with CO2 in the natural gas along the length of the MBC.

12. The method of claim 11, further comprising: The change in liquid temperature is determined by balancing the energy consumed by solvent evaporation with the exothermic CO2 absorption reaction along the length of the MBC under adiabatic conditions.

13. The method according to claim 12, wherein, Thermal diffusion along the radial axis is ignored, and the liquid temperature is assumed to be uniform in the radial direction.

14. The method according to claim 2, wherein, The solvent comprises 50% by weight methyl diethanolamine (MDEA), and the regression model for the Henry's constant of nitrous oxide (N₂O) is modeled as follows: in, It is the inlet CO2 loading in the solvent, and T l It is the liquid temperature of the solvent.

15. The method according to claim 3, wherein, The regression model for the Henry's constant of the hydrocarbon is modeled as follows: H i，l =α0+α1C+α2T l +α3P l +α4CT l +α5CP l +α6T l P l Among them, T l P is the liquid temperature of the solvent. l C is the liquid pressure of the solvent, C is the mass fraction of the at least one component in the solvent, and coefficients α1 to α6 are parameters of the regression model of the Henry's constant of the hydrocarbon.

16. A computer-implemented method for evaluating the performance of a natural gas desulfurization treatment, the natural gas desulfurization treatment comprising an absorption operation and a desorption operation, wherein, The absorption operation is associated with the absorption of acidic gases using a hollow fiber membrane contactor, i.e., an MBC, and the desorption operation is associated with solvent regeneration using a solvent regenerator, wherein the absorption operation is modeled based on the MBC model using a computer-implemented method according to any one of claims 1 to 15.

17. The method of claim 16, further comprising: Calculate the optimal flow rate for achieving a predetermined CO2 purity in the natural gas, the optimal flow rate being associated with lean operation and semi-lean operation respectively, the lean operation being associated with using a CO2 purity of less than 0.02 mol / L. -1 The operation is associated with a lean solvent having a CO2 loading, and the semi-lean operation is associated with using a solvent having a CO2 loading greater than 0.2 mol / L. -1 Operations associated with CO2 loading in semi-lean solvents; as well as Determine the total processing load of the natural gas desulfurization process associated with the absorption and desorption operations under the lean and semi-lean operations.

18. The method of claim 17, further comprising: Calculate the pressure used to operate the rich solution flash drums associated with the lean operation and the semi-lean operation respectively to achieve a predetermined low calorific value for the fuel gas, which is the gas recovered from hydrocarbon losses in the solvent during the natural gas desulfurization process.

19. A computer-implemented method for designing and evaluating the performance of a hollow fiber membrane contactor (MBC) in natural gas desulfurization using a hollow fiber membrane contactor model, i.e., an MBC model, wherein, The MBC model includes model parameters, model equations, and boundary conditions for calculating data associated with the natural gas desulfurization process, and the natural gas desulfurization process includes removing acid gases from natural gas using a solvent containing at least one component, the method comprising: Empirical data on the solubility of hydrocarbons in the solvent are used to form a regression model of the Henry's constant for hydrocarbons in the solvent to account for hydrocarbon loss from the natural gas to the solvent, wherein the regression model is a function of the temperature of the solvent, the pressure of the solvent, and the mass fraction of the at least one component in the solvent; Determine the Henry's constant for the hydrocarbon in the solvent; The Henry's constant of the hydrocarbon is used in the hydrocarbon rate loss equation to determine the rate of hydrocarbon loss in the solvent, illustrating the hydrocarbon loss from the natural gas to the solvent, wherein the rate of hydrocarbon loss is a function of the hydrocarbon concentration, and wherein the hydrocarbon concentration is inversely proportional to the Henry's constant of the hydrocarbon; and The MBC model is used to determine CO2 absorption in the solvent to design and evaluate the performance of the hollow fiber membrane contactor, wherein the hydrocarbon rate loss equation is included as one of the model equations of the MBC model.

20. A computer-readable medium storing processor-executable instructions that, when executed on a processor, cause the processor to perform the method according to any one of claims 1 to 19.

21. A hollow fiber membrane contactor data processing system, namely an MBC data processing system, is used to design and evaluate the performance of hollow fiber membrane contactors (MBCs) in natural gas desulfurization processes using an MBC model, wherein... The MBC model includes model parameters, model equations, and boundary conditions for calculating data associated with the natural gas desulfurization process, and the natural gas desulfurization process includes removing acid gases from natural gas using a solvent containing at least one component. The MBC data processing system includes a processor and a data storage device, the data storage device storing computer program instructions operable to cause the processor to perform the following: A regression model was developed using empirical data correlated with the solubility of CO2 in the solvent; The regression model is used to determine the Henry's constant for CO2 in the solvent; The determined Henry's constant for CO2 is input into the MBC model as one of the model parameters; and The MBC model is used to determine CO2 absorption in the solvent in order to design and evaluate the performance of the MBC.

22. The MBC data processing system according to claim 21, wherein, The data storage device also stores computer program instructions that can be operated to cause the processor to perform the following: A regression model for the Henry's constant of N2O was developed using empirical data on the solubility of nitrous oxide (N2O) in the solvent. The Henry's constant of N2O is determined using a regression model of the Henry's constant; and The Henry's constant of N2O is used to determine the Henry's constant of CO2 in the solvent to indicate the CO2 loading in the solvent.

23. The MBC data processing system according to claim 21 or 22, wherein, The data storage device also stores computer program instructions that can be operated to cause the processor to perform the following: Empirical data on the solubility of hydrocarbons in the solvent are used to form a regression model of the Henry's constant for the hydrocarbons in the solvent to illustrate the hydrocarbon loss from the natural gas to the solvent; as well as The Henry's constant of the hydrocarbon in the solvent is determined using a regression model of the Henry's constant of the hydrocarbon.

24. The MBC data processing system according to claim 23, wherein, The data storage device also stores computer program instructions that can be operated to cause the processor to perform the following: The loss rate of the hydrocarbon in the solvent is determined using the Henry's constant of the hydrocarbon in the hydrocarbon rate loss equation, wherein the loss rate of the hydrocarbon is a function of the concentration of the hydrocarbon, and wherein the concentration of the hydrocarbon is inversely proportional to the Henry's constant of the hydrocarbon.

25. The MBC data processing system according to claim 24, wherein, The data storage device also stores computer program instructions that are operable to cause the processor to perform the following: include the hydrocarbon rate loss equation as one of the model equations of the MBC model.

26. The MBC data processing system according to claim 24 or 25, wherein, The solvent is hydrocarbon-saturated at the liquid outlet of the MBC.

27. The MBC data processing system according to claim 21 or 22, wherein, The data storage device also stores computer program instructions that can be operated to cause the processor to perform the following: The mole fraction of at least one component of the solvent in the gas outlet was determined using Raoult's law; and The solvent loss rate is determined using the mole fraction in the solvent rate loss equation, wherein the solvent loss rate is proportional to the determined mole fraction.

28. The MBC data processing system according to claim 27, wherein, The treated gas at the gas outlet of the MBC is saturated with the solvent, and the natural gas and the solvent are in equilibrium at the gas outlet.

29. The MBC data processing system according to claim 27, wherein, The data storage device also stores computer program instructions that can operate to cause the processor to perform the following: include the solvent rate loss equation as one of the model equations of the MBC model.

30. The MBC data processing system according to claim 27, wherein, The data storage device also stores computer program instructions that can operate to cause the processor to perform the following: using the solvent loss rate to determine the energy consumed by solvent evaporation at the liquid inlet of the MBC and the liquid temperature of the solvent.

31. The MBC data processing system according to claim 30, wherein, Solvent evaporation occurs at the liquid inlet before the solvent reacts with CO2 in the natural gas along the length of the MBC.

32. The MBC data processing system according to claim 31, wherein, The data storage device also stores computer program instructions that can be operated to cause the processor to perform the following: The change in liquid temperature is determined by balancing the energy consumed by solvent evaporation with the exothermic CO2 absorption reaction along the length of the MBC under adiabatic conditions.

33. The MBC data processing system according to claim 32, wherein, Thermal diffusion along the radial axis is ignored, and the liquid temperature is assumed to be uniform in the radial direction.

34. The MBC data processing system according to claim 22, wherein, The solvent comprises 50% by weight methyl diethanolamine (MDEA), and the regression model for the Henry's constant of nitrous oxide (N₂O) is modeled as follows: in, It is the inlet CO2 loading in the solvent, and T l It is the liquid temperature of the solvent.

35. The MBC data processing system according to claim 23, wherein, The regression model for the Henry's constant of the hydrocarbon is modeled as follows: H i，1 =α0+α1C+α2T l +α3P l +α4CT l +α5CP l +α6T l P l Among them, T l P is the liquid temperature of the solvent. l C is the liquid pressure of the solvent, C is the mass fraction of the at least one component in the solvent, and coefficients α1 to α6 are parameters of the regression model of the Henry's constant of the hydrocarbon.

36. A natural gas desulfurization operating system comprising an MBC data processing system and a solvent regeneration data processing system according to any one of claims 21 to 35, wherein the MBC data processing system is associated with an absorption operation for acid gas absorption using the hollow fiber membrane contactor, i.e., the MBC, and the solvent regeneration data processing system is associated with a desorption operation for solvent regeneration using a solvent regenerator.

37. The natural gas desulfurization operating system according to claim 36, comprising a processor and a data storage device, the data storage device storing computer program instructions operable to cause the processor to perform the following: Calculate the optimal flow rate for achieving a predetermined CO2 purity in the natural gas, the optimal flow rate being associated with lean operation and semi-lean operation respectively, the lean operation being associated with using a CO2 purity of less than 0.02 mol / L. -1 The operation is associated with a lean solvent having a CO2 loading, and the semi-lean operation is associated with using a solvent having a CO2 loading greater than 0.2 mol / L. -1 Operations associated with CO2 loading and semi-lean solvents; and Determine the total processing load of the natural gas desulfurization process associated with the absorption and desorption operations under the lean and semi-lean operations.

38. The natural gas desulfurization operating system according to claim 37, wherein, The data storage device also stores computer program instructions that can be operated to cause the processor to perform the following: Calculate the pressure used to operate the rich solution flash drums associated with the lean operation and the semi-lean operation respectively to achieve a predetermined low calorific value for the fuel gas, which is the gas recovered from hydrocarbon losses in the solvent during the natural gas desulfurization process.

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