A supercritical gas injection simulation method, medium, and apparatus for deep geothermal energy engineering

Abstract

This invention discloses a supercritical gas injection simulation method for deep-earth energy storage projects. This method constructs a computational framework for supercritical gas-salt two-phase flow based on the lattice Boltzmann method, utilizes the Shan-Chen two-component model to characterize the interaction between supercritical gas and water, and introduces a continuous surface force model equation to controllably couple interfacial tension, thereby achieving numerical simulation of supercritical gas injection under high density ratio and high surface tension conditions. Through an improved force term discretization scheme and independent adjustment of the surface tension term, high-precision recovery of force balance at the interface is achieved, significantly improving simulation stability and physical consistency. This invention fills the gap in the lattice Boltzmann method for simulating the displacement, migration, and storage behavior of various supercritical gases in porous aquifers or fractured grids, and can provide technical support for the design, operation, and safety assessment of deep-earth energy storage projects.

Description

Technical Field

[0001] This invention relates to the field of deep underground energy storage and multiphase flow numerical simulation technology, specifically to a multiphysics coupled numerical simulation method, medium, and equipment for supercritical gas injection, displacement, and storage processes in deep underground energy storage projects. More specifically, it is a dynamic simulation method for supercritical gas-salt water two-phase flow based on the Lattice Boltzmann method (LBM), which is particularly suitable for simulating gas injection processes in deep underground energy storage projects such as hydrogen, helium, air, or carbon dioxide storage in aquifers. Background Technology

[0002] With the increasing proportion of new energy power generation, energy systems are placing higher demands on large-scale, long-cycle, and reusable energy storage technologies. Compared to surface energy storage facilities, utilizing underground space for energy storage projects offers significant advantages such as large capacity, smaller footprint, higher safety, and less environmental impact, making it an important development direction in the current energy engineering field. Typical deep-ground energy storage projects include compressed air energy storage, underground hydrogen storage, salt cavern energy storage, and carbon dioxide geological sequestration.

[0003] In the aforementioned deep-earth energy storage projects, the working medium is typically injected into the underground space in gaseous form and exhibits a supercritical or near-supercritical state under high pressure and high temperature conditions. For example, hydrogen, air, and carbon dioxide often exhibit low viscosity, high compressibility, and significant density variations under underground energy storage operating conditions. When supercritical gas is injected into an underground medium that was originally filled with water or brine, a gas-liquid two-phase displacement process will inevitably occur, and its migration behavior directly affects energy storage efficiency, operational safety, and structural stability.

[0004] The flow mechanism of supercritical gas injection exhibits significant complexity. On the one hand, the large density and viscosity ratios between gas and liquid can easily induce instability in numerical calculations. On the other hand, underground media often possess complex geometries, such as porous media, fractured rock masses, or irregular artificial chambers, with interface morphology constantly evolving over time. Furthermore, at deep-earth scales, gravity and buoyancy effects are not negligible, and supercritical gases often exhibit a pronounced tendency to rise, further exacerbating interface instability. If compression, expansion, and heat exchange behaviors during the injection process are considered simultaneously, the problem evolves into a typical multiphase, multiphysics coupling problem. Due to limitations in experimental conditions and observation methods, experimental studies of supercritical gas injection and gas-liquid displacement processes in deep-earth energy storage projects are typically costly, and it is difficult to directly obtain key physical quantities such as gas-liquid interface morphology, velocity field, and pressure field within the underground space. Therefore, employing high-precision numerical simulation methods to study this process has become an important technical approach for understanding its underlying mechanisms and optimizing engineering design.

[0005] In the field of numerical simulation, traditional finite element method, finite volume method, and commercial computational fluid dynamics software have been widely used in the study of gas-liquid two-phase flow problems. However, these methods still have certain limitations when dealing with the specific engineering scenario of supercritical gas injection. For example, under conditions of high density ratio and low viscosity ratio, the accuracy of interface capture is easily affected by numerical dissipation; under conditions of complex fractures or rough walls, mesh generation and interface tracking are costly, and numerical stability is difficult to guarantee. To improve the ability to describe multiphase flow interfaces, researchers have proposed various interface capture or tracking methods, such as the volume fraction method, level set method, and phase field method. These methods can describe the interface evolution process to a certain extent, but they usually rely on explicit interface functions or artificially set interface thickness parameters, the physical meaning of which is not clear under supercritical fluid conditions. When fluid properties change significantly with pressure and temperature, there is a lack of unified standards for the selection of relevant parameters, thus limiting their applicability in engineering-scale simulations.

[0006] In general, existing numerical simulation methods still struggle to simultaneously consider interface stability, engineering-scale applicability, and computational efficiency under complex geometric conditions when simulating supercritical gas injection and gas-liquid displacement processes in deep-earth energy storage projects. Therefore, there is an urgent need for a numerical simulation method that is suitable for deep-earth energy storage engineering applications, can explicitly couple multiphase interaction forces and interfacial tension models within a unified computational framework, and can stably simulate the entire supercritical gas injection process to meet the practical needs of engineering design and operational evaluation. Summary of the Invention

[0007] The purpose of this invention is to address the common problems of insufficient interface stability, difficulty in independently controlling interface tension, and limited applicability to engineering scale in existing numerical simulation methods for simulating supercritical gas injection and gas-liquid displacement processes in deep underground energy storage projects. This invention provides a supercritical gas injection simulation method, medium, and equipment for deep underground energy storage projects.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A simulation method for supercritical gas injection in deep-earth energy storage projects is proposed. Based on the multi-component lattice Boltzmann method, a computational model of supercritical gas-liquid two-phase flow is constructed to simulate the entire process of supercritical gas injection, migration, and liquid displacement in deep-earth energy storage projects. The method includes the following steps: A computational domain corresponding to a deep-earth energy storage project is constructed. A supercritical gas injection velocity inlet and a liquid phase pressure outlet are set in the computational domain. The computational domain is discretized using a regular lattice. A lattice Boltzmann computational framework for supercritical gas-liquid two-phase flow based on the lattice Boltzmann method is established. Within the lattice Boltzmann computational framework, the distribution function evolution equations (i.e., lattice Boltzmann evolution equations) for the supercritical gas phase and liquid phase are established respectively to describe the flow and transport behavior of each phase of the supercritical gas phase and liquid phase in the computational domain. The Shan-Chen pseudopotential multiphase model is introduced. By constructing a pseudopotential function based on local density, interaction forces are applied between different fluid components, thereby driving phase separation between the gas phase and the liquid phase and forming a diffusion interface at the mesoscale. A phase field indicator function is introduced to characterize the position of the interface between the gas phase and the liquid phase (referred to as the gas-liquid interface). The phase field gradient is obtained through the definition of the phase field. Then, a continuous surface force model is introduced to introduce the interfacial tension between the gas phase and the liquid phase into the momentum equation in the form of a body force term, which is used to characterize the curvature effect and surface tension of the interface between the gas phase and the liquid phase. The Shan-Chen pseudopotential multiphase model is explicitly coupled with the continuous surface force model, so that the interface normal and curvature information participate in the surface tension calculation, and the coupled interface tension is uniformly introduced into the distribution function evolution equation. A gravity term is introduced into the distribution function evolution equation to simulate the stratification, convection, and interfacial instability behavior of supercritical gas under the influence of gravity and buoyancy in deep-earth energy storage projects. By running the computational model over time, data on pressure field, velocity field, phase distribution, and interface evolution during supercritical gas injection and gas-liquid displacement processes are obtained.

[0009] Furthermore, the supercritical gas includes any one or more of supercritical hydrogen, supercritical helium, supercritical air, or supercritical carbon dioxide, and the liquid is water or salt water.

[0010] Preferably, in this invention, the interface curvature in the continuous surface force model is obtained by density gradient calculation, and the interface normal vector is determined by the spatial gradient of the gas-liquid two-phase density field.

[0011] Preferably, in the three-dimensional computational domain, the interface curvature is discretized using a second-order finite difference scheme to improve the accuracy of interface tension calculation and reduce spurious flow.

[0012] Preferably, the solid wall boundary adopts a wettability boundary condition, and different contact angle parameters are set to reflect the wetting characteristics of different rock masses or lining materials to supercritical gas.

[0013] Preferably, the gas injection boundary can be set as constant pressure injection, constant mass flow rate injection, or periodic injection and production conditions that vary with time, to simulate different operating modes of deep-earth energy storage projects.

[0014] Furthermore, the lattice Boltzmann computational framework uses a three-dimensional 18-velocity lattice model, meaning the values ​​in the following formula range from 0 to 18. , In the formula, k=1, 2, representing different fluid phases, such as k =1 represents supercritical gas. k =2 represents the liquid phase; For in position and time Place, No. Phase fluid along the first Particle distribution function in discrete velocity directions; For the first Distribution function of the phase fluid under local equilibrium state; It is a discrete velocity vector; It is the time step, usually taken as 1; For the first The dimensionless relaxation time of a phase is related to the fluid dynamic viscosity; To act on the first The total external force term of the phase fluid in the velocity direction Projection onto the surface, and the volume forces in the calculation. ; The interaction forces between different phases in the Shan-Chen pseudopotential multiphase model; To simulate the wetting relationship between the gas and liquid phase interfaces and the rock mass or lining material.

[0015] Furthermore, the phase field indication function The expression is as follows: , In the formula, and denoted by x, representing the densities of the supercritical gas phase and the liquid phase at position x, respectively. This phase field indicator function takes +1 in the supercritical gas phase region, -1 in the liquid phase region, and exhibits continuous variation in the interface region.

[0016] Furthermore, after obtaining the phase field indicator function, the unnormalized form of the interface normal vector is calculated using its spatial gradient: , Where: spatial derivatives in each direction (x, y, and z directions in the coordinate system) , and The calculation is performed on a discrete lattice using a second-order central difference scheme. The unnormalized interface normal vector is normalized to obtain the interface unit normal vector. , in For small positive numbers used to avoid dividing by zero.

[0017] Furthermore, the interface curvature k is calculated using the divergence of the interface unit normal vector, and discretized at the lattice nodes using a second-order central difference scheme, the expression of which is: , Once the unit normal vector and the curvature of the interface are determined, the continuous surface force model will incorporate the interface tension. Represented as a physical force term distributed across the interface region, its form is: , In the formula, is the interfacial tension coefficient between the gas phase and the liquid phase.

[0018] Furthermore, for fluids of different phases, , It represents the interfacial tension of a phase. This represents the interfacial tension of another phase.

[0019] Furthermore, the interfacial tensions of the gas and liquid phases are linearly superimposed in physical space. If other volume forces are considered, they are also superimposed to construct a unified volume force term: = The unified volume force term is introduced as a source term into the evolution equation of the distribution function, where... For volume forces, For the interaction forces of different phases, For different phase interfaces, G represents the interfacial tension, and G represents gravity.

[0020] A computer-readable storage medium comprising a stored program that, when executed by a processor, implements the supercritical gas injection simulation method for deep-earth energy storage engineering as described above.

[0021] An electronic device includes at least one processor and at least one memory connected to the processor; wherein the processor is configured to call program instructions in the memory to execute the supercritical gas injection simulation method for deep underground energy storage projects as described above.

[0022] Compared with existing technologies, the beneficial effects of this invention are as follows: 1. This simulation method achieves numerical simulation of supercritical gas injection under high density ratio and high surface tension conditions by explicitly coupling a pseudo-potential multiphase model and a continuous surface force model within a lattice Boltzmann computational framework; through an improved force term discretization scheme and independent adjustment of the surface tension term, it achieves high-precision recovery of force balance at the interface, significantly improving simulation stability and physical consistency; 2. Through the above-mentioned steps, this simulation method can also stably simulate the problems of high density ratio and low viscosity ratio in supercritical gas and liquid systems, reducing non-physical spurious flows; 3. It is naturally applicable to complex porous media, fractured rock masses, and artificial chambers and other engineering geometries; 4. It simultaneously considers gravity, wettability, and optional thermal effects, making it highly applicable to deep-earth energy storage projects; 5. It also features high computational efficiency, making it suitable for parameter analysis and operational evaluation of the supercritical gas injection process in deep-earth energy storage projects. Attached Figure Description

[0023] Figure 1 This is a schematic flowchart of a supercritical gas injection simulation method for deep underground energy storage projects according to the present invention. Figure 2 This is a schematic diagram illustrating different contact angles of the present invention; Figure 3 This invention describes a two-phase displacement process without coupled CSF during supercritical carbon dioxide displacement of brine. Figure 4 This invention relates to the coupling of CSF during the supercritical carbon dioxide displacement of brine process. Two-phase fluid displacement process; Figure 5 This invention relates to the coupling of CSF during the supercritical carbon dioxide displacement of brine process. Two-phase fluid displacement process. Detailed Implementation

[0024] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] The lattice Boltzmann method, a numerical approach based on mesoscopic statistical theory, has been increasingly adopted in multiphase flow and underground engineering simulations in recent years due to its simple algorithm structure, inherent parallelism, and ease of handling complex geometric boundaries. Within the lattice Boltzmann framework, researchers have developed various multiphase models. Among them, the Shan-Chen pseudopotential model can achieve phase separation by constructing interaction forces, eliminating the need for explicit interface tracking and exhibiting good geometric adaptability. However, existing research indicates that when using the Shan-Chen pseudopotential model (SC model) alone, the interfacial tension magnitude is often coupled with the interfacial thickness, making independent control difficult. Under conditions of high surface tension or engineering scale, it is prone to generating non-physical spurious flows, affecting the stability and reliability of the computational results. On the other hand, the continuous surface force model can introduce interfacial tension into the momentum equation in the form of volume forces, theoretically enabling independent control of interfacial tension. However, it typically relies on explicit interface functions and has not yet formed a unified and stable coupled computational framework with the pseudopotential model. Effective coupling of the CSF model with the Shan-Chen model can simultaneously achieve independent control of interfacial tension and a continuous description of the fluid phase field gradient.

[0026] Based on this, this embodiment provides a supercritical gas injection simulation method for deep underground energy storage projects. A supercritical gas-liquid two-phase flow calculation model is constructed based on the multi-component lattice Boltzmann method to simulate the entire process of supercritical gas injection, migration, and liquid displacement in deep underground energy storage projects. Figure 1 As shown, it includes the following steps: Step 1: Construct the computational domain corresponding to the deep-earth energy storage project. Set up a supercritical gas injection velocity inlet and a liquid phase pressure outlet in the computational domain. The computational domain is discretized using a regular lattice. Establish a lattice Boltzmann computational framework for supercritical gas-liquid two-phase flow based on the lattice Boltzmann method to adapt the solution of the lattice Boltzmann method in two-dimensional or three-dimensional space. Step 2: Under the lattice Boltzmann computational framework, establish the distribution function evolution equations (i.e., lattice Boltzmann evolution equations) for the supercritical gas phase and liquid phase respectively, to describe the flow and transport behavior of each phase of the supercritical gas phase and liquid phase in the computational domain. Step 3: Introduce the Shan-Chen pseudo-potential multiphase model into the computational model. By constructing a pseudo-potential function based on local density, interaction forces are applied between different fluid components, thereby driving phase separation between the gas phase and liquid phase and forming a diffusion interface at the mesoscale. Step 4: Introduce a phase field indicator function into the calculation model to characterize the position of the interface between the gas phase and the liquid phase (referred to as the gas-liquid interface). Obtain the phase field gradient through the definition of the phase field. Then introduce a continuous surface force model to introduce the interfacial tension between the gas phase and the liquid phase into the momentum equation in the form of a body force term to characterize the curvature effect and surface tension of the interface between the gas phase and the liquid phase. Step 5: Explicitly couple the Shan-Chen pseudopotential multiphase model with the continuous surface force model, so that the interface normal and curvature information participate in the surface tension calculation, and uniformly introduce the coupled interface tension into the distribution function evolution equation. Step 6: Introduce a gravity force term into the distribution function evolution equation to simulate the stratification, convection, and interfacial instability behavior of supercritical gas under the influence of gravity and buoyancy in deep-earth energy storage projects. Step 7: Run the computational model over time to obtain data on pressure field, velocity field, phase distribution, and interface evolution during supercritical gas injection and gas-liquid displacement.

[0027] This invention presents a supercritical gas injection simulation method for deep-earth energy storage projects. Based on the Lattice Boltzmann Method (LBM), it constructs a computational framework for supercritical gas-liquid two-phase flow. The Shan-Chen pseudopotential multiphase model characterizes the interaction between supercritical gas and liquid, and a Continuum Surface Force (CSF) equation is introduced to allow for adjustable coupling of interfacial tension, thereby enabling numerical simulation of supercritical gas injection under high density ratio and high surface tension conditions. Through an improved force term discretization scheme and independent adjustment of the surface tension term, high-precision recovery of force balance at the interface is achieved, significantly improving simulation stability and physical consistency. This invention fills the gap in the Lattice Boltzmann Method for simulating the displacement, migration, and storage behavior of various supercritical gases in porous aquifers or fractured grids, and can provide technical support for the design, operation, and safety assessment of deep-earth energy storage projects.

[0028] This simulation method achieves independent control of the interfacial tension magnitude by explicitly coupling a pseudo-potential multiphase model and a continuous surface force model within a lattice Boltzmann computational framework, thereby improving the numerical stability of the gas-liquid interface.

[0029] This simulation method, through the above-mentioned steps, can stably simulate the high density ratio and low viscosity ratio problems existing in supercritical gas and liquid systems, reducing non-physical spurious flows; it is naturally applicable to engineering geometries such as complex porous media, fractured rock masses, and artificial chambers; it can simultaneously consider gravity, wettability, and optional thermal effects, making it highly applicable to deep-earth energy storage projects; moreover, it has high computational efficiency and is suitable for parameter analysis and operational evaluation of supercritical gas injection processes in deep-earth energy storage projects.

[0030] Furthermore, the supercritical gas includes any one or more of supercritical hydrogen, supercritical helium, supercritical air, or supercritical carbon dioxide, and the liquid is water or salt water. This calculation model is preferably applicable to the high density ratio pseudopotential model.

[0031] The two components are immiscible, and their interface evolution is controlled by both interaction forces and surface tension. In the numerical implementation, a computational domain is first constructed based on the actual structure of the deep-earth energy storage project. This domain can be an artificial chamber, salt cavern, or aquifer pore-fracture structure. A supercritical gas injection port, a liquid discharge port, and solid wall boundaries are set within the computational domain. The solid wall boundaries are non-slip or periodic boundaries used to characterize the rock mass or lining structure.

[0032] The evolution of the distribution functions of each phase is performed using the lattice Boltzmann evolution equation with a volume force term, and the relaxation time is determined by the dynamic viscosity of the corresponding fluid. To achieve phase separation between the gas and liquid phases, the Shan-Chen pseudo-potential multiphase model is introduced into the model. This model constructs a pseudo-potential function based on local density to apply interaction forces between different fluid components, thereby driving phase separation between the gas and liquid phases and forming a diffusion interface at the mesoscale.

[0033] The above method allows for the description of the flow behavior of different fluid components within a unified framework. In this embodiment, the lattice Boltzmann computational framework uses a three-dimensional 18-velocity (D3Q18) lattice model, where the values ​​in the following formula range from 0 to 18, as implemented below: , In the formula, k=1, 2, representing different fluid phases, such as k =1 represents supercritical gas. k =2 represents the liquid phase; For in position and time Place, No. Phase fluid along the first Particle distribution function in discrete velocity directions; For the first Distribution function of the phase fluid under local equilibrium state; It is a discrete velocity vector; It is the time step, usually taken as 1; For the first The dimensionless relaxation time of a phase is related to the fluid dynamic viscosity; To act on the first The total external force term of the phase fluid in the velocity direction Projection onto the surface, and the volume forces in the calculation. ; The interaction forces between different phases in the Shan-Chen pseudopotential multiphase model; To simulate the wetting relationship between the gas and liquid phase interfaces and the rock mass or lining material, Indicates external force.

[0034] like Figure 2 As shown, this model can effectively achieve different contact avoidance angles. , In the formula, This is the fluid-solid interaction strength coefficient, whose sign and magnitude control wettability. Indicates the solid wall surface to the first The phase fluid is affinity (e.g., hydrophilic), while Indicates rejection; For the first Phase fluid at position and time The local density is obtained by summing the distribution functions: ; Corresponding discrete velocity direction The lattice weight coefficients have fixed values ​​in the D3Q18 model; For indicator functions, in If the element is a fluid, take 0; if it is a solid, take 1.

[0035] In this embodiment, considering the large density difference between the gas and liquid phases, a preferred method is to use... The strength of the SC pseudopotential interaction force is determined by the interaction parameters. control.

[0036] The original model implicitly depends on the surface tension of the two-phase fluid. This means that as the interface thickness and grid size change, numerous calculations are required when adjusting for specific operating conditions, and in some cases, it is impossible to guarantee that the requirements of the operating conditions will be fully met. Based on this, to achieve independent control of interfacial tension, the method of this invention introduces a continuous surface force model (CSF) to supplement the description of the interfacial mechanical behavior. The introduction of the CSF is not independent of the Shan-Chen pseudo-potential multiphase model, but rather a natural connection based on the gas-liquid interface formed by the pseudo-potential multiphase model, thereby achieving synergy between interface generation and interfacial tension control within a unified framework. Since the Shan-Chen pseudo-potential multiphase model forms a continuous diffusion interface between the gas phase and the liquid phase through density differences, the spatial distribution of the gas-liquid interface can be uniquely determined by the local density field.

[0037] Based on this, at each time step, the phase field indication function is first constructed. or The expression is as follows: , In the formula, and denoted by x, representing the densities of the supercritical gas phase and the liquid phase at position x, respectively. This phase field indicator function takes +1 in the supercritical gas phase region, -1 in the liquid phase region, and exhibits continuous variation in the interface region.

[0038] Furthermore, after obtaining the phase field indicator function, the unnormalized form of the interface normal vector is calculated using its spatial gradient: , Where: spatial derivatives in each direction (x, y, and z directions in the coordinate system) , and The calculation is performed on a discrete lattice using a second-order central difference scheme. The unnormalized interface normal vector is normalized to obtain the interface unit normal vector. , in To avoid dividing small positive numbers by zero, in this embodiment... Take 10 -12 .

[0039] Furthermore, the interface curvature k is calculated using the divergence of the interface unit normal vector. A second-order central difference scheme is used for discretization at the lattice nodes to ensure the numerical accuracy and stability of the interface curvature calculation. Its expression is: , Once the unit normal vector and the curvature of the interface are determined, the continuous surface force model will incorporate the interface tension. Represented as a physical force term distributed across the interface region, its form is: , In the formula, Let be the interfacial tension coefficient between the gas and liquid phases. The magnitude of the interfacial tension can be determined using this expression. It can be independently controlled, and is not related to the interface thickness or density ratio.

[0040] Furthermore, for fluids of different phases, , It represents the interfacial tension of a phase. This represents the interfacial tension of another phase, ensuring global momentum conservation.

[0041] Furthermore, the interfacial tensions of the gas and liquid phases are linearly superimposed in physical space. If other volume forces are considered, they are also superimposed to construct a unified volume force term: = The unified volume force term is introduced as a source term into the evolution equation of the distribution function, where... For volume forces, For the interaction forces of different phases, For different phase interfaces, G represents the interfacial tension, and G represents gravity.

[0042] Through the above processing method, the Shan-Chen pseudopotential multiphase model is responsible for the formation and maintenance of the gas-liquid interface, while the continuous surface force model is responsible for the quantitative application of interfacial tension. The two work together within a unified mechanical framework, thereby improving both interfacial stability and physical consistency in the simulation of high density ratio supercritical gas injection.

[0043] like Figure 3 As shown, without the coupled continuous surface force (CSF) model, the evolution of the gas-liquid interface is mainly controlled by the interaction forces in the Shan-Chen pseudopotential multiphase model. It can be observed that supercritical carbon dioxide exhibits a relatively flat and continuously advancing interface front during the displacement of brine, demonstrating a stable and complete displacement process overall, without the incomplete displacement or interface instability commonly seen in two-phase flow experiments. This phenomenon indicates that, given the current mesh resolution and pseudopotential interaction strength... Under these conditions, the equivalent surface tension implied in the model is insufficient to accurately reflect the physical surface tension level of the supercritical carbon dioxide-salt water system. Theoretically, by further increasing the strength of the pseudo-potential interaction... This can increase the equivalent surface tension in the model, thereby enhancing the constraint of capillary effects on the interface morphology. However, simply relying on increasing this level often significantly amplifies the gradient of the pseudopotential in the interface region, causing numerical oscillations or even computational divergence, making it difficult to steadily advance the simulation process. Therefore, the traditional Shan-Chen pseudopotential model, without introducing an additional interface tension control mechanism, struggles to simultaneously achieve both numerical stability and a true physical representation of surface tension.

[0044] Figure 4 and Figure 5 Introduce CSF into the model and set the interfacial tension coefficient to 1. and The results indicate that the evolutionary characteristics of the gas-liquid interface have changed significantly. From Figure 4 It is evident that when the continuous surface force model explicitly applies interfacial tension as a volume force to the interfacial region, although the interfacial tension coefficient is only... The interface is no longer smoothly displacing; it begins to exhibit certain degree of interface undulation and fluctuation, indicating that the explicit introduction of interface tension has a substantial impact on the displacing process. Furthermore, as the interface tension coefficient increases... At this stage, the amplitude and spatial inhomogeneity of interfacial fluctuations significantly increase, exhibiting typical interfacial instability evolution behavior. Under these conditions, the interfacial morphology is no longer dominated by numerical diffusion, but is jointly determined by the competitive relationship between interfacial tension, density difference, and viscosity effect. The displacement behavior at this stage is closer to the flow characteristics under low capillary conditions in actual supercritical carbon dioxide-salt water systems.

[0045] comprehensive Figure 3 The comparison results in Figure 5 show that the introduction of CSF significantly improved the interfacial stability during the supercritical carbon dioxide displacement of brine process, while the interfacial tension coefficient... This becomes a key parameter for regulating the displacement morphology. Without CSF coupling, the interface behavior is mainly constrained by the intrinsic parameters of the pseudopotential model, and the degree of freedom of regulation is limited. However, after CSF coupling, the interface generation mechanism and the interface tension control mechanism are decoupled, enabling the model to simulate the displacement process under different capillary dominance levels while maintaining the stability of a large density ratio.

[0046] The above results further illustrate that explicit CSF coupling is of great significance for accurately characterizing the gas-liquid interface evolution, displacement efficiency and flow stability in supercritical gas injection simulations related to deep underground energy storage projects. It also provides a basis for selecting reasonable interfacial tension values ​​in combination with actual engineering parameters.

[0047] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A supercritical gas injection simulation method for deep geothermal energy engineering, characterized by, A computational model for supercritical gas-liquid two-phase flow was constructed based on the multi-component lattice Boltzmann method to simulate the entire process of supercritical gas injection, migration, and liquid displacement in deep-earth energy storage projects, including the following steps: A computational domain corresponding to a deep-earth energy storage project is constructed. A supercritical gas injection velocity inlet and a liquid phase pressure outlet are set in the computational domain. The computational domain is discretized using a regular lattice. A lattice Boltzmann computational framework for supercritical gas-liquid two-phase flow based on the lattice Boltzmann method is established. Within the lattice Boltzmann computational framework, distribution function evolution equations for the supercritical gas phase and liquid phase are established to describe the flow and transport behavior of each phase of the supercritical gas and liquid phases in the computational domain. The Shan-Chen pseudopotential multiphase model is introduced. By constructing a pseudopotential function based on local density, interaction forces are applied between different fluid components, thereby driving phase separation between the gas phase and the liquid phase and forming a diffusion interface at the mesoscale. A phase field indicator function is introduced to characterize the position of the interface between the gas phase and the liquid phase. The phase field gradient is obtained through the definition of the phase field. Then, a continuous surface force model is introduced to introduce the interfacial tension between the gas phase and the liquid phase into the momentum equation in the form of a body force term, which is used to characterize the curvature effect and surface tension of the interface between the gas phase and the liquid phase. The Shan-Chen pseudopotential multiphase model is explicitly coupled with the continuous surface force model, so that the interface normal and curvature information participate in the surface tension calculation, and the coupled interface tension is uniformly introduced into the distribution function evolution equation. A gravity term is introduced into the distribution function evolution equation to simulate the stratification, convection, and interfacial instability behavior of supercritical gas under the influence of gravity and buoyancy in deep-earth energy storage projects. By running the computational model over time, data on pressure field, velocity field, phase distribution, and interface evolution during supercritical gas injection and gas-liquid displacement processes are obtained.

2. The supercritical gas injection simulation method for deep underground energy storage projects according to claim 1, characterized in that, The supercritical gas includes any one or more of supercritical hydrogen, supercritical helium, supercritical air, or supercritical carbon dioxide, and the liquid is water or salt water.

3. The supercritical gas injection simulation method for deep underground energy storage projects according to claim 1, characterized in that, The lattice Boltzmann computational framework uses a three-dimensional 18-velocity lattice model, meaning the values ​​in the following formula range from 0 to 18. ， In the formula, k =1 and 2 represent different fluid phases; For in position and time Place, No. Phase fluid along the first Particle distribution function in discrete velocity directions; For the first Distribution function of the phase fluid under local equilibrium state; It is a discrete velocity vector; It is the time step; For the first The dimensionless relaxation time of a phase is related to the fluid dynamic viscosity; To act on the first The total external force term of the phase fluid in the velocity direction Projection onto the surface, and the volume forces in the calculation. ; The interaction forces between different phases in the Shan-Chen pseudopotential multiphase model; To simulate the wetting relationship between the gas and liquid phase interfaces and the rock mass or lining material.

4. The supercritical gas injection simulation method for deep underground energy storage projects according to claim 1, characterized in that, The phase field indication function The expression is as follows: ， In the formula, and denoted by x, representing the densities of the supercritical gas phase and the liquid phase at position x, respectively. This phase field indicator function takes +1 in the supercritical gas phase region, -1 in the liquid phase region, and exhibits continuous variation in the interface region.

5. The supercritical gas injection simulation method for deep underground energy storage projects according to claim 1, characterized in that, After obtaining the phase field indicator function, the unnormalized form of the interface normal vector is calculated using its spatial gradient: , In the formula: the spatial derivatives in the x, y, and z directions are calculated using a second-order central difference scheme on the discrete lattice. The unnormalized interface normal vector is normalized to obtain the interface unit normal vector. , in For small positive numbers used to avoid dividing by zero.

6. The supercritical gas injection simulation method for deep underground energy storage projects according to claim 5, characterized in that, The interface curvature k is calculated using the divergence of the unit normal vector of the interface, and discretized on the grid nodes using a second-order central difference scheme. Its expression is: ， Once the unit normal vector and the curvature of the interface are determined, the continuous surface force model will incorporate the interface tension. Represented as a physical force term distributed across the interface region, its form is: ， In the formula, is the interfacial tension coefficient between the gas phase and the liquid phase.

7. The supercritical gas injection simulation method for deep underground energy storage projects according to claim 6, characterized in that, For fluids of different phases, , It represents the interfacial tension of a phase. This represents the interfacial tension of another phase.

8. The supercritical gas injection simulation method for deep underground energy storage projects according to claim 6, characterized in that, The interfacial tensions of the gas and liquid phases are linearly superimposed in physical space. If other volume forces are considered, they are also superimposed to construct a unified volume force term: = The unified volume force term is introduced as a source term into the evolution equation of the distribution function, where... For volume forces, For the interaction forces of different phases, For different phase interfaces, G represents the interfacial tension, and G represents gravity.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program that, when executed by a processor, implements the supercritical gas injection simulation method for deep-earth energy storage engineering as described in any one of claims 1 to 8.

10. An electronic device, characterized in that, The electronic device includes at least one processor and at least one memory connected to the processor; wherein the processor is used to call program instructions in the memory to execute the supercritical gas injection simulation method for deep underground energy storage projects as described in any one of claims 1 to 8.

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