Flow condition prediction method for carbon capture and storage pipeline conveying network

Abstract

The invention discloses a method for predicting the flow condition of a carbon capture and storage pipeline conveying network. The method comprises the following steps: step 1, establishing a steady-state multi-component flow model; 2, processing nodes in the pipeline network; 3, numerical solution is carried out; and 4, calculating thermodynamics and transmission properties. According to the method, the flow condition in the whole pipeline network can be accurately predicted, and the height change of the pipeline and the periodic change of the flow at the source end which are ignored in the existing model are considered; secondly, the model of the invention can process different impurities and levels thereof in carbon dioxide flows from different sources, which is crucial to accurate prediction of the composition of finally conveyed carbon dioxide and fluid conditions, and is helpful to avoid the physical and chemical reaction problem of the pipeline caused by the impurities. Meanwhile, the problems of capacity loss and injectivity in the storage process are reduced, and the economical efficiency and feasibility of the CCS technology can be improved.

Description

Technical Field

[0001] The present invention relates to the field of carbon capture and storage (CCS). Background Art

[0002] Carbon capture and storage (CCS) technology is seen as one of the important means to mitigate climate change. In this context, CCS technology has become one of the key tools to mitigate greenhouse gas emissions. The importance of CCS lies in its ability to reduce carbon dioxide emissions while allowing us to continue to use existing energy infrastructure, thereby buying time for the transition to a cleaner energy system. With the advancement of technology and the gradual reduction of costs, CCS is becoming more and more economically attractive. In particular, the importance of this technology is further highlighted when considering the depletion of fossil fuels and the resulting changes in demand for CCS.

[0003] Currently, the use of an integrated pipeline transportation network is likely to be the most practical and economical way to transport captured CO2 for storage from various emission sources (such as power plants and cement manufacturing) by reducing capital costs and permitting issues compared to individual pipelines. The application of different types of CO2 capture technologies (pre-combustion, post-combustion and oxy-fuel) to different CO2 sources (coal, natural gas power generation as well as industrial) has the potential to result in CO2 streams of varying quality being injected into the transportation network. This represents a practical dilemma given the established impacts of various impurities on many aspects of CCS performance.

[0004] However, current work either assumes that the stream is pure CO2 or that the stream contains impurities but is identical in composition from each source. As discussed above, both of these assumptions are likely to underestimate the amount of compression required across the network and therefore fail to accurately predict delivery conditions and composition. Furthermore, the amount of CO produced by each source will vary over time, depending on the economics of its production. Transitions between these different source conditions will change the flow behavior, i.e. the pressure drop in the system, and result in changes in the composition of the delivered CO2 stream. Therefore, a multi-source flow model for CCS is needed that predicts flow conditions throughout the network and delivery to storage sites. Summary of the invention

[0005] In order to accurately predict the final transport components and fluid conditions, the present invention proposes a CCS pipeline transport network flow condition prediction method.

[0006] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a method for predicting flow conditions of a carbon capture and storage pipeline transportation network, comprising the following steps:

[0007] Step 1: Establish a steady-state multi-component flow model. Based on the conservation equations of mass, momentum, and energy, introduce the Darcy friction factor and heat transfer equation to deal with the friction loss of the fluid in the pipeline and the heat exchange with the surrounding environment to ensure a comprehensive simulation of the actual flow conditions.

[0008] Mathematical model of non-adiabatic steady flow based on conservation equations of mass, momentum and energy:

[0009]

[0010] Where x, D, ρ, and h are the local coordinates of the pipe, the pipe diameter, and the density and enthalpy of the fluid; u, P, f, and q are w and θ represent flow velocity, fluid pressure, Darcy friction coefficient, wall heat flux, and the inclination angle of the pipe to the horizontal axis, respectively; the conservation equation also applies to each component i of the n-component mixture:

[0011]

[0012] Assuming that the fluid is a homogeneous mixture of all components, i.e. it is well mixed, for turbulent flow in a straight pipe, the Darcy friction coefficient can be calculated as a function of the Reynolds number and the relative roughness of the pipe wall using the Colebrook-White equation:

[0013]

[0014] Where ε is the wall roughness, Re = ρuD / μ is the flow Reynolds number, and is the dynamic viscosity of the fluid;

[0015] Heat flux density at the tube wall q w Defined by the heat transfer equation:

[0016] q w =α·(T amb -T f )

[0017] Where T amb and T f are the temperature of the medium around the pipeline and the temperature of the fluid in the pipeline respectively; α is the total heat transfer coefficient; for the section of the buried pipeline, D0, δ ins d soil They are the outer diameter of the pipeline from the ground, the thickness of the insulation layer and the radius depth;

[0018] For buried insulation layer pipe, the total heat transfer coefficient is defined as:

[0019]

[0020] Where λ w , ins ,soil are the thermal conductivity of the pipe wall, the thermal conductivity of the insulation layer and the thermal conductivity of the soil respectively; α f and α0 are the heat transfer coefficients on the inner and outer sides of the tube wall respectively;

[0021] Step 2: Processing of nodes in the pipeline network,

[0022] Assuming that the pressure, energy and momentum losses at the nodes are negligible, the flow conditions in different pipe sections are connected only by the conservation equations of mass, energy and momentum;

[0023] Step 3: Numerical solution;

[0024] Step 4: Calculation of thermodynamic and transport properties.

[0025] In step 2, for the case of a Y-joint, assuming that pressure, energy and momentum losses are negligible, the mass, momentum and energy balances can be expressed as:

[0026] ρ1u1A1+ρ2u2A2=ρ3u3A3

[0027] p1=p2=p3

[0028]

[0029] ρ1u1z 1,i +ρ2u2z 2,i =ρ3u3z 3,i ,i=1,...,n

[0030] The above equation can be generalized to describe the conditions at the junctions of k pipes:

[0031]

[0032] p j =p k ,j=1,...,k-1

[0033]

[0034] In step 3, given the flow rate and temperature of each source inlet, the solution method for the flow in the pipe network is as follows:

[0035] 1) Estimate the feed pressure at the network source based on the inlet flow and temperature;

[0036] 2) Using a set of conservation equations for mass, momentum, and energy, the equilibrium equations at the inlet of the segment are solved. For the connection point, the inlet pressure is assumed to be p1, that is, the pressure junction at the end of one of the pipes. In this way, the inlet flow, composition, and temperature conditions are provided. The steady-state flow is calculated in each individual segment along the network one by one, and solved using an implicit Euler method with a constant step size along each segment;

[0037] 3) The pressure at the network source is iterated until each node satisfies the constraints, using the differential algebraic solver DASS.

[0038] In step 4, the volume-adjusted Peng-Robinson equation mixing rule is used to describe the phase behavior of the mixture at different temperatures and pressures and determine the phase state of the fluid; the transport properties are calculated based on the density, temperature and composition of the fluid using data from the NIST Thermophysical database.

[0039] The present invention provides a multi-source flow model that can accurately predict the flow conditions in the entire pipeline network, including pressure, temperature, fluid phase and carbon dioxide composition, until it is transported to the storage point. The model takes into account the height changes of the pipeline and the periodic changes in the source flow that are ignored in the existing model, such as the impact of production adjustments of coal-fired power plants on the flow; secondly, the model of the present invention can handle different impurities and their levels in carbon dioxide flows from different sources, which is crucial for accurately predicting the final carbon dioxide composition and fluid conditions, and helps to avoid physical and chemical reaction problems of pipelines caused by impurities, such as ductile fracture, brittle fracture and corrosion, while reducing capacity loss and injectivity problems during storage, which helps to improve the economy and feasibility of CCS technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a cross-sectional view of the buried thermal insulation pipeline in the present invention;

[0041] Figure 2 A schematic diagram of a Y-shaped joint connecting three pipe sections in a pipe network in the present invention;

[0042] Figure 3 This is a schematic diagram of a simulated pipe network of the present invention;

[0043] Figure 4 It is a curve diagram of the fluid pressure change in the main trunk line of the present invention;

[0044] Figure 5 It is a curve diagram of the temperature change of the fluid in the main trunk line of the present invention;

[0045] In the picture: 1. Soil, 2. Steel pipe, 3. Insulation layer. DETAILED DESCRIPTION

[0046] A method for predicting flow conditions of a carbon capture and storage pipeline transportation network of the present invention comprises the following steps:

[0047] Step 1: Establish a steady-state multicomponent flow model

[0048] A steady-state multi-component flow model is proposed. Based on the conservation equations of mass, momentum and energy, the flow behavior of CO2 in a complex pipeline network is described in detail. Not only the pure flow characteristics of CO2 are considered, but also the impurities and their content changes in CO2 flows from different sources are incorporated, so as to accurately predict the pressure, temperature, fluid phase and CO2 composition in the entire network. By introducing the Darcy friction factor and heat transfer equation, the friction loss of the fluid in the pipeline and the heat exchange with the surrounding environment are handled to ensure a comprehensive simulation of the actual flow conditions. The mathematical model is as follows:

[0049]

[0050] Where x, D, ρ, and h are the local coordinates of the pipe, the pipe diameter, and the density and enthalpy of the fluid, respectively. u, P, f, q w and θ represent flow velocity, fluid pressure, Darcy friction coefficient, wall heat flux, and the inclination angle of the pipe to the horizontal axis, respectively. The conservation equations also apply to each component i of an n-component mixture:

[0051]

[0052] The fluid is assumed to be a homogeneous mixture of all components, i.e. it is well mixed. For turbulent flow in a straight pipe, the Darcy friction coefficient can be calculated as a function of the Reynolds number and the relative roughness of the pipe wall using the Colebrook-White equation:

[0053]

[0054] Where ε is the wall roughness, Re = ρuD / μ is the flow Reynolds number, and is the dynamic viscosity of the fluid. The heat flux density at the pipe wall q w Defined by the heat transfer equation:

[0055] q w =α·(T amb -T f )

[0056] Where T amb and T f are the temperature of the medium around the pipe and the temperature of the fluid in the pipe respectively. α is the total heat transfer coefficient. Figure 1 is the cross-sectional view of the buried pipeline, where D0, δ ins d soilare the outer diameter of the pipeline from the ground, the thickness of the insulation layer and the radius depth. For buried insulation layer pipelines, the total heat transfer coefficient is defined as:

[0057]

[0058] Where λ w , ins , soil are the thermal conductivity of the pipe wall, the thermal conductivity of the insulation layer and the thermal conductivity of the soil respectively. f and α0 are the heat transfer coefficients for the inner and outer sides of the tube wall, respectively. Both values ​​are calculated using standard correlations for forced and natural convection heat transfer.

[0059] Step 2: Processing of nodes in the pipeline network

[0060] When dealing with nodes in a pipeline network, the model assumes that the pressure, energy, and momentum losses at the nodes are negligible, and only uses the mass, energy, and momentum conservation equations to connect the flow conditions of different pipeline segments. For Y-joints, the model solves these conservation equations to ensure that the combined pipeline segments meet the flow, pressure, and energy balance at the nodes, thereby achieving continuous and accurate prediction of the flow conditions of the entire network.

[0061] Applying the above flow model to a network requires a method to predict flow conditions at nodes. At such junctions, different flows from several pipe segments may merge into a single pipe for further transport. Figure 2 A schematic diagram of a Y-junction is shown for the simplest case. For the Y-junction case, the pressure, energy, and momentum losses are assumed to be negligible, the first of which is reasonable since these losses are likely to be at least two orders of magnitude smaller than the pressure drop along the pipe section. The mass, momentum, and energy balances can be written as:

[0062] ρ1u1A1+ρ2u2A2=ρ3u3A3

[0063] p1=p2=p3

[0064]

[0065] ρ1u1z 1,i +ρ2u2z 2,i =ρ3u3z 3,i ,i=1,…,n

[0066] The above equation can be generalized to describe the conditions at the junctions of k pipes:

[0067]

[0068] p j =p k,j=1,…,k-1

[0069]

[0070] Step 3: Numerical solution method

[0071] The steady-state flow equations are numerically solved using the implicit Euler method and the differential algebraic solver DASSL. First, the pressure at each source of the network is guessed based on the inlet flow and temperature; then, the steady-state flow of each pipeline segment is calculated one by one along the network sequence, and the source pressure is adjusted iteratively until the pressure conditions at all nodes and end points are met. This method not only improves the accuracy of the solution, but also ensures the continuity and consistency of the flow conditions at different pipeline segments and nodes.

[0072] Given the inlet flow and temperature of each source, the solution process for the flow in the pipe network is as follows:

[0073] 1) First guess the feed pressure at the network source;

[0074] 2) The steady-state flow is calculated sequentially in each individual segment along the network using a set of mass, momentum and energy conservation equations, which are solved using an implicit Euler method using a constant step size along each segment. Prior to this, the equilibrium equations at the inlet of the segment are solved, and for the connection point, the inlet pressure is assumed to be p1, i.e. the pressure junction entering the end of one of the pipes. In this way, the inlet flow, composition and temperature conditions are provided;

[0075] 3) In addition to the pressures at the specified delivery points, the pressures at the network sources are iterated until the constraints are satisfied at each node, for which the differential algebraic solver DASS is used.

[0076] Step 4: Calculation of thermodynamic and transport properties

[0077] In order to accurately calculate the thermodynamic and transport properties of the mixture, the present invention uses the volume-adjusted Peng-Robinson equation mixing rules. These equations and rules can accurately describe the phase behavior of the mixture at different temperatures and pressures and determine the phase state of the fluid. At the same time, using data from the NIST Thermophysical database, transport properties such as viscosity, thermal conductivity, etc. are calculated based on the density, temperature and composition of the fluid. These calculations provide the necessary physical parameters for the model, ensuring the accuracy and reliability of the flow simulation.

[0078] The relevant thermodynamic properties of the mixtures at various temperatures and pressures are determined using the volume adjusted Peng-Robinson (MPR) EoS, where the mixing rules of Nishiumi et al. (1988) are applied to explain the behavior of the relevant mixtures. As part of these calculations, the position of the thermodynamic state relative to the phase envelope is determined to determine the phase of the fluid. Transport properties are calculated as a function of fluid density, temperature, and composition using the NIST Thermophysics Database.

[0079] It is worth noting that if CCS technology is widely deployed, the efficiencies offered by CO2 capture and transmission networks will make it more likely to be used, as opposed to many single source-to-sink connections. Furthermore, as intermittent renewable generation increasingly penetrates our energy landscape, the characteristics of CO2 entering these networks are likely to be transient and exacerbated by the operation of capture plants to maximize profitability. The need to understand the behavior of these networks under realistic conditions is the main motivation for this study, as accurate predictions of steady-state flows are essential prior to any transient analysis.

[0080] To better understand the behavior of these networks under realistic conditions, accurate predictions of steady-state flows, Figure 3 A detailed schematic diagram of the CO2 pipeline network considered in the invention is shown. The pipeline segments are numbered consecutively from 1 to 7 starting from the storage location. For simplicity, this study only considers the inflow from power stations A and B, with CO2 flow rates of 4.847 and 20.153 Mt y, respectively. -1 . It is assumed that the remaining sources have no contribution.

[0081] There are four hypothetical scenarios:

[0082] 1) Both A and B use post-combustion capture technology (representing the least amount of impurities)

[0083] 2) Both A and B use oxy-fuel capture technology (with most impurities).

[0084] 3) B uses oxy-fuel capture technology and A uses post-combustion capture technology.

[0085] 4) A uses oxy-fuel capture technology and B uses post-combustion capture technology.

[0086] Table 1 lists the representative feed mass flow rates and compositions for power stations A and B under the above four scenarios.

[0087] Table 1 Feed flow and composition for scenarios 1-4

[0088]

[0089] Table 2 gives the predicted feed pressures required for plants A and B, and the delivery temperature for C. The composition of the CO2 stream delivered by C is also shown.

[0090] Table 2 Predicted feed pressure and conveying components required for Schemes 1-4

[0091]

[0092] Figure 4 and Figure 5 The pressure and temperature profiles along the length of the main pipeline for each of the four simulated scenarios are shown. Figure 4 , the following observations can be made:

[0093] 1. The rate of pressure drop from the feed to the delivery point is almost linear.

[0094] 2. The additional supply flow from the B power station to the main line at the intersection of pipeline 5 and pipeline 3 using the tie line (pipeline 4) results in an increase in the downstream pressure drop rate.

[0095] 3. In general, an increase in the amount of impurities leads to an increase in the pressure drop along the pipeline. Scenario 1 and Scenario 4 produce almost identical pressure profiles, even though the feed composition of Power Plant A is significantly different in both cases. This is due to the much higher feed flow rate at Power Plant B compared to Power Plant A, which masks the latter’s effect.

[0096] Go to Figure 5 , the following observations can be made:

[0097] 1. With Figure 4 Similar to the pressure profile in , the rate of temperature drop from the feed to the delivery point is almost linear.

[0098] 2. At the entry point of pipeline 3 (about 69 km), an increase in temperature is observed in all cases. This is due to the warm feeder entering from power station B.

[0099] 3. The higher the impurity content, the greater the temperature drop. It can also be observed that the temperature drop rates of scenario 1 and scenario 4 are similar. The explanation for this is Figure 4 Same as point 3.

[0100] The present invention is described by way of embodiments, and those skilled in the art will appreciate that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application belong to the protection scope of the present invention.

Claims

1. A method for predicting flow conditions of a carbon capture and storage pipeline transportation network, characterized in that: The following steps are involved: Step 1: Establish a steady-state multi-component flow model. Based on the conservation equations of mass, momentum, and energy, introduce the Darcy friction factor and heat transfer equation to deal with the friction loss of the fluid in the pipeline and the heat exchange with the surrounding environment to ensure a comprehensive simulation of the actual flow conditions. Mathematical model of non-adiabatic steady flow based on conservation equations of mass, momentum and energy: Where x, D, ρ, and h are the local coordinates of the pipe, the pipe diameter, and the density and enthalpy of the fluid; u, P, f, and q are w and θ represent flow velocity, fluid pressure, Darcy friction coefficient, wall heat flux, and the inclination angle of the pipe to the horizontal axis, respectively; the conservation equation also applies to each component i of the n-component mixture: Assuming that the fluid is a homogeneous mixture of all components, i.e. it is well mixed, for turbulent flow in a straight pipe, the Darcy friction coefficient can be calculated as a function of the Reynolds number and the relative roughness of the pipe wall using the Colebrook-White equation: Where ε is the wall roughness, Re = ρuD / μ is the flow Reynolds number, and is the dynamic viscosity of the fluid; Heat flux density at the tube wall q w Defined by the heat transfer equation: q w =α·(T amb -T f ) Where T amb and T f are the temperature of the medium around the pipeline and the temperature of the fluid in the pipeline respectively; α is the total heat transfer coefficient; for the section of the buried pipeline, D0, δ ins ,d soil They are the outer diameter of the pipeline from the ground, the thickness of the insulation layer and the radius depth; For buried insulation layer pipe, the total heat transfer coefficient is defined as: Where λ w , ins , soil are the thermal conductivity of the pipe wall, the thermal conductivity of the insulation layer and the thermal conductivity of the soil respectively; α f and α0 are the heat transfer coefficients on the inner and outer sides of the tube wall respectively; Step 2: Processing of nodes in the pipeline network, Assuming that the pressure, energy and momentum losses at the nodes are negligible, the flow conditions in different pipe sections are connected only by the conservation equations of mass, energy and momentum; Step 3: Numerical solution; Step 4: Calculation of thermodynamic and transport properties.

2. A method for predicting flow conditions of a carbon capture and storage pipeline transportation network according to claim 1, characterized in that: In step 2, for the case of a Y-joint, assuming that pressure, energy and momentum losses are negligible, the mass, momentum and energy balances can be expressed as: ρ1u1A1+ρ2u2A2=ρ3u3A3 p1=p2=p3 p1u1z 1,i +p2u2z 2,i =ρ3u3z 3,i ,i=1,...,n The above equation can be generalized to describe the conditions at the junctions of k pipes: p j =p k ,j=1,...,k-1 3. A method for predicting flow conditions of a carbon capture and storage pipeline transportation network according to claim 1, characterized in that: In step 3, given the flow rate and temperature of each source inlet, the solution method for the flow in the pipe network is as follows: 1) Estimate the feed pressure at the network source based on the inlet flow and temperature; 2) Using a set of conservation equations for mass, momentum, and energy, the equilibrium equations at the inlet of the segment are solved. For the connection point, the inlet pressure is assumed to be p1, that is, the pressure junction at the end of one of the pipes. In this way, the inlet flow, composition, and temperature conditions are provided. The steady-state flow is calculated in each individual segment along the network one by one, and solved using an implicit Euler method with a constant step size along each segment; 3) The pressure at the network source is iterated until each node satisfies the constraints, using the differential algebraic solver DASS.

4. A method for predicting flow conditions of a carbon capture and storage pipeline transportation network according to claim 1, characterized in that: In step 4, the volume-adjusted Peng-Robinson equation mixing rule is used to describe the phase behavior of the mixture at different temperatures and pressures and determine the phase state of the fluid; the transport properties are calculated based on the density, temperature and composition of the fluid using data from the NIST Thermophysical database.

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