A method for predicting flow conditions in a carbon capture and storage pipeline transportation network

Abstract

A kind of carbon capture and storage pipeline transportation network flow condition prediction method, comprising the following steps: step 1: establishing steady-state multicomponent flow model;Step 2: processing of nodes in pipeline network;Step 3: numerical solution;Step 4: calculation of thermodynamic and transport properties.The present application can accurately predict the flow conditions in the entire pipeline network, taking into account the height variation of the pipeline and the periodic variation of the source flow which are ignored in existing models;Secondly, the model can handle different impurities and their levels in the carbon dioxide stream from different sources, which is crucial for accurately predicting the composition and fluid conditions of the final transported carbon dioxide, helping to avoid the problem of physical and chemical reactions in the pipeline caused by impurities, while reducing the capacity loss and injection problems during storage, helping to improve the economic and feasibility of CCS technology.

Description

TECHNICAL FIELD

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

[0002] With the increasing severity of global climate change, carbon capture and storage (CCS) technology is considered as one of the important means to mitigate climate change. Climate change not only threatens the natural ecosystem, but also has a profound impact on human society, including decreased agricultural production, rising sea levels, and frequent extreme weather events. In this context, CCS technology has become one of the key tools to reduce 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 gaining time for the transition to a cleaner energy system. With the advancement of technology and the gradual reduction of costs, CCS is becoming increasingly economically attractive. In particular, when considering the depletion of fossil fuels and the resulting changes in demand for CCS, the importance of this technology is further highlighted.

[0003] Currently, using an integrated pipeline transportation network can be the most practical and economical way to transport captured CO2 compared to a single pipeline, by reducing capital costs and reducing licensing issues for sequestration from various emission sources such as power plants and cement manufacturing. The application of different types of CO2 capture technologies (pre-combustion, post-combustion, and oxy-combustion) to different CO2 sources (coal, natural gas power generation, and industry) has the potential to result in different quality CO2 streams being injected into the transportation network. Considering the established impact of various impurities on many aspects of CCS performance, this represents a practical dilemma.

[0004] However, current work either assumes that the stream is pure CO2 or that the stream contains impurities, but the composition of each source is the same. As mentioned above, both of these assumptions can underestimate the amount of compression required for the entire network, thus failing to accurately predict the transmission conditions and composition. In addition, the amount of CO2 produced by each source will vary over time, depending on the economics of its production. The transition 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 CO2 stream being transported. Therefore, a multi-source flow model for CCS is needed to predict the overall flow conditions of the entire pipeline network and the entire flow conditions of the CO2 stream being transported to the storage site. SUMMARY

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

[0006] The technical scheme adopted by the present invention to achieve the above-mentioned purposes is: a carbon capture and storage pipeline transportation network flow condition prediction method, comprising the following steps:

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

[0008] Non-adiabatic steady-state flow mathematical model based on mass, momentum and energy conservation equations:

[0009]

[0010] In the formula, x, D, p, h are the local coordinates of the pipeline, the diameter of the pipeline, the density and the enthalpy of the fluid; u, P, f, q w and θ respectively represent the flow velocity, the fluid pressure, the Darcy friction factor, the heat flux density of the pipe wall and the inclination angle of the pipeline with the horizontal axis, and g represents the acceleration of gravity; the conservation equation is also applicable to each component zi of the n-component mixture:

[0011]

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

[0013]

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

[0015] The heat flux density q w at the pipe wall is 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 surrounding the pipeline and the temperature of the fluid inside the pipeline, respectively; α is the overall heat transfer coefficient; for the cross section of the buried pipeline, D0, δ ins , d soil are the outer diameter of the pipeline from the ground, the thickness of the insulation layer and the radius depth, respectively;

[0018] For a buried insulated pipeline, the overall heat transfer coefficient is defined as:

[0019]

[0020] In the formula, λw , λ ins , λ soil are the thermal conductivities of the pipe wall, the insulation layer and the soil, respectively; α f and α0are the heat transfer coefficients on the inner and outer sides of the pipe wall, respectively;

[0021] Step 2: Treatment of nodes in the pipe network,

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

[0023] Step 3: Numerical solution;

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

[0025] In Step 2, for the case of a Y-junction, assuming that the pressure, energy and momentum losses are negligible, the mass, momentum and energy balances can be respectively:

[0026] ρ1u1A1+ρ2u2A2=ρ3u3A3

[0027] p1=p2=p3

[0028]

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

[0030] where A1, A2, A3 represent the cross-sectional areas of pipe 1, pipe 2 and pipe 3 of the Y-junction, respectively, p1, p2, p3 represent the fluid pressures at the connection point of pipe 1, pipe 2 and pipe 3, respectively, u1, u2, u3 represent the fluid flow rates at the connection point of pipe 1, pipe 2 and pipe 3, respectively, h1, h2, h3 represent the fluid specific enthalpies at the connection point of pipe 1, pipe 2 and pipe 3, respectively, z 1,i ,z 2,i ,z 3,i : represent the mass fractions of component i in the fluids of pipe 1, pipe 2 and pipe 3, and subscript i indicates the i-th component in the mixture.

[0031] The above equations can be extended to describe the conditions at the junction of k pipes:

[0032]

[0033] p j =p k ,j=1,…,k-1

[0034]

[0035] In step 3, given the inlet flow rate and temperature, the solution method of the flow in the pipe network is as follows:

[0036] 1) Guess the feed pressure at the network source according to the inlet flow rate and temperature;

[0037] 2) Use the set of mass, momentum and energy conservation equations to solve the balance equations at the section inlet, and for the connection points, assume the inlet pressure as p1, i.e. the pressure interface into one of the pipe ends, in this way, provide the inlet flow rate, composition and temperature conditions, calculate the steady-state flow in each individual section along the network in turn, and use the implicit Euler method with constant step along each section to solve;

[0038] 3) Iteratively solve the pressure at the network source until each node meets the constraints, using the differential algebraic solver DASS.

[0039] In step 4, the Peng-Robinson equation mixing rule with volume adjustment is used to describe the phase behavior of the mixture at different temperatures and pressures, and to determine the phase state of the fluid; the data in the NIST Thermophysical database are used to calculate the transport properties according to the density, temperature and composition of the fluid.

[0040] The present application provides a multi-source flow model which can accurately predict the flow conditions in the entire pipe network, including pressure, temperature, fluid phase state and carbon dioxide composition, until the delivery to the storage point. The present application considers the height variation of the pipe and the periodic variation of the source flow which are ignored in the existing models, such as the influence of the production adjustment of the coal-fired power plant on the flow; secondly, the present application model can handle different impurities and their levels in the carbon dioxide flow from different sources, which is crucial for accurately predicting the composition and fluid conditions of the final delivered carbon dioxide, and helps to avoid the problems of physical and chemical reactions in the pipe caused by impurities, such as ductile fracture, brittle fracture and corrosion, while reducing the capacity loss and injection problems during storage, and helps to improve the economy and feasibility of the CCS technology. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is a buried heat preservation pipe sectional view in the present application;

[0042] Figure 2 is a Y-shaped joint schematic diagram connecting three pipe sections in the pipe network in the present application;

[0043] Figure 3 is a pipe network simulation schematic diagram in the present application;

[0044] Figure 4A graph of fluid pressure variation in the main trunk road of the application;

[0045] Figure 5 A graph of fluid temperature variation in the main trunk road of the application;

[0046] In the figure: 1, soil, 2, steel pipe, 3, thermal insulation layer. DETAILED DESCRIPTION

[0047] The carbon capture and storage pipeline transportation network flow condition prediction method of the application comprises the following steps:

[0048] Step 1: Establish a steady-state multi-component flow model

[0049] A steady-state multi-component flow model is proposed, which describes the flow behavior of CO2 in a complex pipeline network based on mass, momentum and energy conservation equations. Not only the pure flow characteristics of CO2 are considered, but also the impurities in the CO2 flow from different sources and their content changes are taken into account, so as to accurately predict the pressure, temperature, fluid phase state and CO2 composition in the entire network. By introducing Darcy friction factor and heat transfer equation, the friction loss of fluid in the pipeline and the heat exchange with the surrounding environment are handled, ensuring comprehensive simulation of actual flow conditions. The mathematical model is as follows:

[0050]

[0051] In the formula, x, D, ρ, h are the local coordinates of the pipeline, the diameter of the pipeline, the density and enthalpy of the fluid respectively. u, P, f, q w and θ respectively represent the flow velocity, fluid pressure, Darcy friction coefficient, pipe wall heat flux density and the inclination angle of the pipeline with the horizontal axis, and g is the acceleration of gravity. The conservation equation is also applicable to each component zi of the n-component mixture:

[0052]

[0053] It is assumed that the fluid is a homogeneous mixture of all components, i.e. it is fully mixed. For turbulent flow in a straight pipe, the Darcy friction factor can be calculated as a function of Reynolds number and pipe wall relative roughness using the Colebrook-White equation:

[0054]

[0055] In the formula, ε is the wall roughness, Re = ρuD / μ is the flow Reynolds number, and μ is the dynamic viscosity of the fluid. The heat flux density q w at the pipe wall is defined by the heat transfer equation:

[0056] q w = α·(T amb -T f )

[0057] where T amb and T f are the temperature of the surrounding medium and the temperature of the fluid inside the pipe, respectively. a is the overall heat transfer coefficient. Figure 1 is a cross-sectional view of a buried pipe, where D0, δ ins , d soil are the outer diameter of the pipe, the thickness of the insulation layer and the radius depth, respectively. For a buried insulated pipe, the overall heat transfer coefficient is defined as:

[0058]

[0059] where λ w , λ ins , λ soil are the thermal conductivity of the pipe wall, the thermal conductivity of the insulation layer and the thermal conductivity of the soil, respectively. a f and a0are the heat transfer coefficients on the inside and outside of the pipe wall, respectively. Both of these values are calculated using standard correlations for forced and natural convection heat transfer.

[0060] Step 2: Treatment of nodes in the pipe network

[0061] In treating the nodes in the pipe network, the model assumes that the pressure, energy and momentum losses at the nodes are negligible, and the flow conditions of different pipe segments are connected only through mass, energy and momentum conservation equations. For Y-junctions, the model ensures that the merged pipe segments satisfy the flow, pressure and energy balance at the nodes by solving these conservation equations, thus achieving continuous and accurate prediction of the flow conditions throughout the network.

[0062] Applying the above flow model to a network requires a method to predict the flow conditions at a junction. At such a junction, different water flows from several pipe segments can merge into one pipe for further conveyance. Figure 2 A schematic of a Y-junction, which shows the simplest case, is shown for the case of a Y-junction, where it is assumed that the pressure, energy and momentum losses are negligible, with the first being reasonable since these losses can be at least two orders of magnitude smaller than the pressure drop along the pipe segments. The mass, momentum and energy balances can be written as:

[0063] ρ1u1A1+ρ2u2A2=ρ3u3A3

[0064] p1=p2=p3

[0065]

[0066] ρ1u1z 1,i +ρ2u2z 2,i =ρ3u3z 3,i ,i=1,…,n

[0067] where A1, A2, A3 represent the cross-sectional area of the Y-junction pipe 1, pipe 2 and pipe 3, respectively, pi, p2, p3 represent the fluid pressure at the junction point of pipe 1, pipe 2 and pipe 3, respectively, ui, u2, u3 represent the fluid flow rate at the junction point of pipe 1, pipe 2 and pipe 3, respectively, hi, h2, h3 represent the fluid specific enthalpy at the junction point of pipe 1, pipe 2 and pipe 3, respectively, z 1,i ,z 2,i ,z 3,i : represents the mass fraction of component i in the fluid of pipe 1, pipe 2 and pipe 3, subscript i indicates the i-th component in the mixture.

[0068] The above equations can be extended to describe the conditions at the junction of k pipes:

[0069]

[0070] p j = p k , j = 1,..., k - 1

[0071]

[0072] Step 3: Numerical solution method

[0073] The implicit Euler method and the differential algebraic solver DASSL are used to numerically solve the steady-state flow equations. First, the source pressures of the network are guessed based on the inlet flow rates and temperatures; then, the steady-state flow of each pipe segment is calculated sequentially along the network, and the source pressures are adjusted iteratively until the pressure conditions at all nodes and endpoints are satisfied. This method not only improves the accuracy of the solution, but also ensures the continuity and consistency of the flow conditions at different pipe segments and nodes.

[0074] Given the inlet flow rates and temperatures of each source, the solution process of the flow in the network is as follows:

[0075] 1) First, guess the inlet pressure of the network source;

[0076] 2) Use the set of mass, momentum and energy conservation equations to calculate the steady-state flow in each individual segment along the network, which are solved using the implicit Euler method with a constant step size along each segment. Before that, solve the balance equations at the segment inlet, and for the junction points, assume the inlet pressure pi as the pressure at the end of one of the pipes. In this way, the inlet flow rate, composition and temperature conditions are provided;

[0077] 3) In addition to the specified delivery point pressure, the pressure at the network source is iterated until each node satisfies the constraints, for which the differential algebraic solver DASSL is used.

[0078] Step 4: Calculation of thermodynamic and transport properties

[0079] To accurately calculate the thermodynamic and transport properties of the mixtures, the present invention employs volume-scaled Peng-Robinson equation mixing rules. These equations and rules are capable of accurately describing the phase behavior of mixtures at different temperatures and pressures and determining 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 as a function of fluid density, temperature, and composition. These calculations provide the necessary physical parameters for the model, ensuring the accuracy and reliability of the flow simulation.

[0080] At different temperatures and pressures, the relevant thermodynamic properties of the mixture are determined using the volume-scaled Peng-Robinson (MPR) EoS, where the mixing rules of Nishiumi et al. (1988) are applied to account for the behavior of the relevant mixtures. As part of these calculations, the thermodynamic state is located with respect to the phase envelope to determine the phase of the fluid. Transport properties are calculated as a function of fluid density, temperature, and composition using the NIST Thermophysical database.

[0081] It is worth noting that if CCS technology is widely deployed, the efficiency provided by CO2 capture and transportation networks will make it more likely to be used, unlike many single source-to-sink connections. Furthermore, as intermittent renewable energy generation penetrates our energy landscape more and more, the characteristics of CO2 entering these networks can be transient and exacerbated by the operation of the capture plant to maximize profitability. Understanding the behavior of these networks under realistic conditions is the main motivation for this study, as accurate predictions of steady-state flow are essential before any transient analysis.

[0082] To better understand the behavior of these networks under realistic conditions, accurate predictions of steady-state flow, Figure 3 A detailed schematic of the CO2 pipeline network considered in the invention is shown. The pipeline sections are numbered consecutively from 1 to 7 starting from the storage site. For simplicity, this study only considers inflows from power plants A and B with carbon dioxide flow rates of 4.847 and 20.153 Mt y -1 , respectively. It is assumed that the remaining sources do not contribute.

[0083] Four scenarios are assumed:

[0084] 1) Both A and B use post-combustion capture technology (representing the least amount of impurities)

[0085] 2) Both A and B use oxy-fuel capture technology (with the most impurities).

[0086] 3) B uses oxyfuel capture technology, A uses post-combustion capture technology.

[0087] 4) A uses oxyfuel capture technology, B uses post-combustion capture technology.

[0088] Table 1 lists representative feed mass flow rates and compositions for A and B power stations in the four scenarios described above.

[0089] Table 1 Feed flow rates and compositions for scenarios 1-4

[0090]

[0091]

[0092] Table 2 gives the predicted feed pressures required for A and B power stations, and the delivery temperatures for C. Also shown is the composition of the CO2 stream delivered by C.

[0093] Table 2 Feed pressures and delivery compositions required for predicted scenarios 1-4

[0094]

[0095] Figure 4 and Figure 5 show the pressure and temperature profiles along the length of the main pipe for each of the four simulated scenarios, respectively. Reference is made to Figure 4 The following observations can be made:

[0096] 1. The rate of pressure drop from the feed to the delivery point is almost linear.

[0097] 2. The additional feed flow from B power station to the main line at the junction of pipe 5 and pipe 3 using the interconnector (pipe 4) results in an increased rate of pressure drop downstream.

[0098] 3. Generally, an increase in the amount of impurities results in an increase in the pressure drop along the pipe. Scenarios 1 and 4 produce almost identical pressure profiles, despite the fact that the feed composition for A power station is very different in both cases. This is due to the fact that the feed flow from B power station is much higher than that from A power station, thus masking the effect of the latter.

[0099] Turning to Figure 5 The following observations can be made:

[0100] 1. Similar to the pressure profiles in Figure 4 , the rate of temperature drop from the feed to the delivery point is almost linear.

[0101] 2. At the point of entry to pipe 3 (approximately 69 km), a temperature rise is observed in all cases. This is due to the warm feed flow from B power station.

[0102] 3. The higher the impurity content, the greater the temperature drop. It can also be observed that the temperature drop rate is similar for scenarios 1 and 4. The explanation for this is the same as point 3 of Figure 4 .

[0103] The application is described by way of examples, and those skilled in the art will recognize various changes and modifications or equivalent alternatives that can be made to these features and examples without departing from the spirit and scope of the application. In addition, modifications can be made to these features and examples to adapt them to specific situations and materials without departing from the spirit and scope of the application. The application is therefore not limited to the specific examples disclosed herein, and all examples falling within the scope of the claims of this application are intended to be covered by the application.

Claims

1. A method for predicting flow conditions in a carbon capture and storage pipeline network, characterized by: 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, the density and enthalpy of the fluid, respectively; u, P, f, and q are w and θ represent flow velocity, fluid pressure, Darcy friction coefficient, pipe wall heat flux, and the inclination angle of the pipe to the horizontal axis, respectively; g is the acceleration of gravity; the conservation equation also applies to each component z of the n-component mixture i : Assuming 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 μ is the flow viscosity of the fluid; Heat flux density q at the tube wall 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 cross section of the buried pipeline, D0, δ ins d soil are the outer diameter of the pipeline from the ground, the thickness of the insulation layer and the radius depth; For buried insulated pipes, the total heat transfer coefficient is defined as: Where λ w ,λ ins ,λ 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. The method for predicting flow conditions in a carbon capture and storage pipeline network according to claim 1, characterized in that: In step 2, for the case of the Y-joint, assuming that pressure, energy, and momentum losses are negligible, the mass, momentum, energy, and component balances can be expressed as follows: ρ1u1A1+ρ2u2A2=ρ3u3A3 p1=p2=p3 p1u1z 1,i +p2u2z 2,i =ρ3u3z 3,i ,i=1,…,n Where A1, A2, A3 represent the cross-sectional areas of the Y-joint pipe 1, pipe 2, and pipe 3, respectively; p1, p2, p3 represent the fluid pressures of pipe 1, pipe 2, and pipe 3 at the connection points, respectively; u1, u2, u3 represent the fluid flow rates of pipe 1, pipe 2, and pipe 3 at the connection points, respectively; h1, h2, h3 represent the specific enthalpy of the fluids of pipe 1, pipe 2, and pipe 3 at the connection points, respectively; z 1,i ,z 2,i ,z 3,i : represents the mass fraction of component i in the fluids of pipelines 1, 2, and 3, and the subscript i represents the i-th component in the mixture; The above equation can be generalized to describe the conditions at the junction of k pipes: p j =p k ,j=1,…,k-1 3. The method for predicting flow conditions in 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 for the flow in the pipe network is as follows: 1) Estimate the feed pressure at the network source based on the inlet flow rate and temperature; 2) Using a set of conservation equations for mass, momentum, and energy, the equilibrium equations at the segment inlet 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, and the solution is solved using an implicit Euler method with a constant step size along each segment. 3) The pressure at the network source is iterated until the constraints are satisfied at each node, using the differential algebraic solver DASS.

4. The method for predicting flow conditions in 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 to 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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