A two-dimensional model construction method for simulating water-gas convection in porous media

Abstract

The present invention provides a two-dimensional model construction method for simulating the water vapor convection process in porous media, constructing a two-dimensional pore network; constructing a dynamic convection process simulation model, wherein a Two motion event is introduced in the meniscus renewal simulation, wherein the Two motion event is to introduce a transition state between the displacement process and the meniscus renewal, wherein the transition state divides the displacement process and the meniscus renewal into two simulation steps; based on the dynamic convection process simulation model, the influence of the pore size distribution of the porous media on the convection process is analyzed and obtained, wherein the influence is specifically that the more uniform the pore size distribution, the longer the air outflow path exists, and the less air is trapped in the porous media. The present invention introduces a transition state between the displacement process and the meniscus renewal, and regards the movement of the meniscus in the pores / pore throats as a "Two motion" event, thereby significantly suppressing the oscillation of the meniscus during the simulation of the water vapor convection process in the two-dimensional pore network, and can accurately describe the morphology and evolution of the convection pattern under a relatively low computational burden.

Description

Technical Field

[0001] The invention belongs to the field of hydraulics, and in particular relates to a two-dimensional model construction method for simulating a water-gas convection process in a porous medium. Background Art

[0002] According to the different flow directions, immiscible displacement can be divided into two types: co-current and convection. The former refers to the flow of the wetting phase and the non-wetting phase in the same direction, while the latter refers to the flow of the two phases in opposite directions through the same pore space. In irrigation, CO2 geological storage or shale gas production, convection often dominates, so a deep understanding of the control mechanism and process of water-gas convection at the pore scale is very important for irrigation design and enhanced recovery of gas / oil reservoirs.

[0003] Since the water-gas convection process is a highly dynamic and unstable process, there are many characteristics and uncertainties in experimental or numerical studies, so most of the current research is limited to the same-direction displacement process. In addition, some scholars have found that the convection efficiency is closely related to the pore size distribution of porous media, but the mechanism behind it is still unclear. Therefore, it is necessary to understand, simulate and predict the convection process in porous media based on physical models. The existing pore network model for simulating the convection process requires that the convection motion of the meniscus must be ignored to avoid the endless oscillation of the meniscus in the pores or pore throats, and can only simulate the same-direction displacement (i.e., moisture absorption / drainage process). Summary of the invention

[0004] In view of the defects existing in the above-mentioned prior art, the present invention provides a method for constructing a two-dimensional model for simulating a porous medium water vapor convection process, which can suppress the oscillation of the meniscus during the convection process.

[0005] The technical solution proposed by the present invention is as follows:

[0006] The present invention discloses a two-dimensional model construction method for simulating a porous medium water vapor convection process, comprising the following steps:

[0007] Constructing a two-dimensional pore network;

[0008] A dynamic convection process simulation model is constructed, wherein a Two motion event is introduced in the meniscus renewal simulation, wherein the Two motion event introduces a transition state between the displacement process and the meniscus renewal, wherein the transition state divides the displacement process and the meniscus renewal into two simulation steps;

[0009] Based on the dynamic convection process simulation model analysis, the influence of the pore size distribution of the porous medium on the convection process is obtained. Specifically, the more uniform the pore size distribution, the longer the air outflow path exists, and the less air is trapped in the porous medium.

[0010] Furthermore, the pore network is constructed based on the open source code OpenPNM, and the pore diameters are randomly assigned using the Weibull function.

[0011] Furthermore, the construction of the dynamic convection process simulation model includes the following steps:

[0012] Set initial and boundary conditions;

[0013] Set the threshold of the dynamic meniscus;

[0014] Check the pore throat;

[0015] Solve for the pressure field in the pore network;

[0016] Calculate local flow rates based on pore / pore throat pressure gradients to determine displacement processes;

[0017] The pore throats are checked until there is no dynamic meniscus in the pore network, the simulation stops, the pressure field in the pore network approaches a stable equilibrium state, and the simulation model of the dynamic convection process is completed.

[0018] Furthermore, the initial conditions and boundary conditions are specifically:

[0019] The pore network is initially filled with air, and the initial pressure field is solved;

[0020] A water inlet and an air outlet are set at the top boundary of the pore network, and the remaining boundaries are set to a sealed state.

[0021] Furthermore, the threshold of the dynamic meniscus is set to 0.

[0022] Furthermore, the pore throat inspection uses a clustering algorithm.

[0023] Furthermore, the pore throat inspection specifically includes:

[0024] Identify trapped pore throats;

[0025] Deactivate the trapped meniscus;

[0026] Identify the oscillating meniscus;

[0027] A pore throat that temporarily blocks oscillations.

[0028] Furthermore, the displacement process specifically includes:

[0029] Determine the pore throat to be operated;

[0030] Determine whether the pore throat to be operated is in a transition state;

[0031] If it is in a transition state, a simulation inspection operation is performed to control whether the meniscus of the pore throat to be operated is updated. If it is in a non-transition state, a moisture absorption / drainage operation is performed until the pore throat to be operated changes from a non-transition state to a transition state.

[0032] Furthermore, the simulation inspection operation is specifically as follows:

[0033] The original capillary pressure of the meniscus in the pore throat to be operated is modified to the minimum inlet pressure at the connected pore throat, and the meniscus pressure gradient is checked to see whether it is reversed. When the pressure gradient can overcome the sudden change of the capillary pressure, the meniscus in the pore throat to be operated is allowed to update, otherwise, the pore throat to be operated is closed and wait for the next simulation check.

[0034] The two-dimensional model construction method for simulating the water vapor convection process in porous media proposed in the present invention considers the movement of the meniscus in the pores / pore throats as a "Two motion" event by introducing a transition state between the displacement process and the meniscus renewal, compared with the traditional model that considers the movement of the meniscus in the pores / pore throats as a "One motion" event. This significantly suppresses the oscillation of the meniscus when simulating the water vapor convection process in the pore network, and can accurately describe the morphology and evolution of the convection pattern under a relatively low computational burden. The model simulation results show that as the pore size distribution becomes more uniform, the retention time of the air outflow path is longer, and the path morphology is straighter and wider. As a result, in a pore network with uniform pore size distribution, the inflow or outflow rate increases and less air is trapped under the wet front. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for describing the technical solutions. Obviously, the schematic embodiments of the present invention and their descriptions are only used to explain the present invention and do not constitute improper limitations on the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without creative work. In the drawings:

[0036] Figure 1 Schematic diagram of the steps of a method for constructing a dynamic two-dimensional model of a water vapor convection process according to an embodiment of the present invention;

[0037] Figure 2 It is a schematic diagram of the mechanism of double pore throat vibration and triple pore throat vibration caused by introducing "One motion" event and a schematic diagram of the process of simulating the convection process by introducing "Two motion" event;

[0038] Figure 3 It is a schematic diagram of the water-air convection simulation results in a two-dimensional pore network model with different pore size distributions in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] Reference Figure 1 This embodiment provides a method for constructing a two-dimensional model for simulating a water vapor convection process in a porous medium, the method comprising the following steps:

[0041] S1: construct a two-dimensional pore network;

[0042] Specifically, the open source code OpenPNM (www.openpnm.org) developed by Gostick et al. was used to construct two-dimensional pore networks with different pore size distributions. The domain size of the two-dimensional pore network is 20 mm × 20 mm, and there are 2500 pores (50 × 50) in each network. The diameters of these pores are randomly assigned using the Weibull function:

[0043]

[0044] Where: f(d; λ, k) is the probability function of pore size d; λ is the scale factor, and the average pore size increases with the increase of λ; k is the shape factor, which controls the pore size distribution of the pore network. As k increases, the pore size distribution of the network becomes more and more uneven.

[0045] S2: construct a dynamic convection pore network model;

[0046] Specifically, the dynamic convection pore network model described in this embodiment is constructed based on the Regaieg model;

[0047] S2.1: Set initial and boundary conditions;

[0048] Specifically, all pores are initially filled with air to solve the initial pressure field. In this embodiment, except for the water inlet and air outlet at the top boundary, the remaining boundaries are considered to be sealed, so when water penetrates into the pore network from top to bottom, a convective airflow is naturally formed.

[0049] S2.2: Setting the threshold of the dynamic meniscus;

[0050] Specifically, a clustering algorithm is used to identify the active air masses connected to the outlet. Since the displacement process is to be considered later, the number of dynamic menisci between the water mass and the active air mass should be greater than 0.

[0051] S2.3: When the number of dynamic menisci is greater than 0, check for “closed” pore throats;

[0052] Specifically, the trapped pore throats are first identified, the trapped meniscus is secondly deactivated, the oscillating meniscus is then identified, and finally the oscillating pore throats are temporarily blocked.

[0053] S2.4: Solve the pressure field of the pore network. When the pressure converges, proceed to step S2.5, otherwise return to step S2.3.

[0054] S2.5: Calculate local flow velocities based on pore / pore throat pressure gradients to determine displacement processes that control gas-water meniscus motion;

[0055] S2.5.1: Identify the pore throats to be operated;

[0056] S2.5.2: The model algorithm is used to determine whether the pore throat to be operated is in a transition state. If it is in a non-transition state, moisture absorption / drainage operation is performed on the pore throat to be operated until the pore throat to be operated changes from a non-transition state to a transition state. If it is in a transition state, a simulation check is performed on the pore throat to be operated to control whether the meniscus of the pore throat to be operated is updated;

[0057] Specifically, in traditional pore network models, the movement of the meniscus in the pores / pore throats is considered a "Onemotion" event (i.e., once the pores / pore throats are determined, the specified pores / pore throats will absorb moisture / drain water in this simulation step, and the position of the meniscus will be immediately updated to the next pore / pore throat in the same step), but "One motion" events usually strictly prohibit convection and only perform well in isotropic displacement simulations.

[0058] When introducing the "One motion" event to simulate the meniscus oscillation during water vapor convection, two typical situations usually occur. Figure 2 :

[0059] Case 1: Double pore throat case ( Figure 2 As shown in a), P1 is the capillary pressure of the small pore throat, P2 is the capillary pressure of the large pore throat, and P c is the capillary pressure of the meniscus, P c1 represents the capillary pressure before the displacement process, P c2 It represents the capillary pressure after the displacement process. When the displacement process is completed, the meniscus will jump from the small pore throat to the large pore throat, and the capillary pressure in the meniscus will also drop suddenly. The sudden drop in capillary pressure usually leads to a reversal of the pressure gradient. Driven by the reverse pressure gradient, the meniscus tends to immediately withdraw from the large pore throat to the small pore throat again. Therefore, when the meniscus enters a large pore throat from a small pore throat, it often oscillates violently.

[0060] Case 2: Three-throat case ( Figure 2 (b), where P1 is the capillary pressure of the left pore throat, P2 is the capillary pressure of the middle pore throat, P3 is the capillary pressure of the right pore throat, and P c is the capillary pressure of the meniscus, P c2,3 Indicates P c2 or P c3 , the oscillation mechanism of the meniscus is similar to the double pore throat case—due to the sudden change of capillary pressure and the rapid reversal of pressure gradient, the meniscus cycles between invading from the left pore throat to the middle pore throat and withdrawing from the middle pore throat to the right pore throat.

[0061] Therefore, when simulating water vapor convection, the convection motion of the meniscus must be considered. In order to avoid the oscillation of the meniscus, the traditional "One motion" event must be modified. This embodiment uses a new "Two motion" event proposed by the present invention, that is, a "transition state" (such as Figure 2 (c), where P1 is the capillary pressure of the first pore throat, P2 is the capillary pressure of the second pore throat, and P c1 represents the capillary pressure before the displacement process, P c2 represents the capillary pressure after the displacement process. After the introduction of the "transition state", the displacement process and the meniscus update are no longer performed in a single simulation step, but are divided into two simulation steps. Therefore, once the operating pore throat is determined, if the operating pore throat is not in the "transition state", it will first be humidified / drained to the "transition state", and the meniscus will be placed at the original pore throat, and the capillary pressure will remain P c1 In the next simulation step, the pressure field is updated and the capillary pressure is calculated by trying to change from P c1 Modify to P c2 To check all the pore throats in the "transition state" in the pore network model (for multiple pore throats (pore throats ≥ 2) oscillation, P c2 Set to the minimum inlet pressure at the connected pore throat) to see if the pressure gradient reverses. After simulation inspection, there are three possible situations for the meniscus in the "transition state":

[0062] Case 1: If the meniscus is at P c1 If there is a tendency to shrink under the capillary pressure, the meniscus should shrink naturally under the action of the updated reverse pressure gradient. At the same time, other pore throats are selected as operating pore throats in this simulation step. After completing this simulation step, the pore throats that are usually checked are no longer in a "transition state".

[0063] Case 2: If the meniscus is at P c1 tends to move forward under the capillary pressure of Pc2 The meniscus cannot move to the next pore throat, and the capillary pressure should be kept at P c1 ; If the meniscus is at P c1 If the meniscus still tends to move to the next pore throat under the capillary pressure, the "transition state" pore throat is temporarily closed, and other pore throats are selected as operating pore throats in this simulation step. The closed "transition state" pore throat will be re-examined in the next step, and the meniscus will eventually move to the next pore throat when the pressure gradient is large enough to overcome the sudden change in capillary pressure.

[0064] Case 3: If the meniscus is at P c1 and P c2 If the meniscus tends to move forward under the capillary pressure (i.e., the pressure gradient is large enough to overcome the sudden change in capillary pressure), the position of the meniscus is updated to the next pore throat, and this update does not cause the meniscus to oscillate.

[0065] S2.6: Check for “closed” pore throats;

[0066] Specifically, a clustering algorithm is used to identify active gas masses connected to the outlet and deactivate the trapped meniscus, and steps S2.2-S2.6 are repeated as long as a dynamic meniscus exists in the pore network;

[0067] S2.7: When there is no dynamic meniscus in the pore network, the simulation stops and the pressure field in the pore network approaches a stable equilibrium state.

[0068] S3: Analyze the effect of pore size distribution on water vapor convection process;

[0069] Specifically, a series of convection simulations were performed based on the two-dimensional dynamic pore network model constructed by S2. During the simulation, the water inlet and air outlet were set at the top boundary of the network model, and the pressure at the inlet and outlet was set to a constant 1 atmosphere. The water-air convection patterns in the two-dimensional network model with different pore size distributions are shown in Figure 2. Figure 3 As shown in the figure, the water phase permeates downwards and the air phase flows upwards. Figure 3 As shown in a1, b1, and c1 in Figure 1, water directly penetrates into the network from the entrance at the top boundary, so a finger-like penetration pattern can be observed. However, as the infiltration proceeds, due to the heterogeneity of the capillaries, the initial finger-like penetration tends to expand and merge. Finally, in the late stage of infiltration (such as Figure 3A clear displacement front is formed in the network, and a piston-like infiltration pattern can be observed. During the entire convection process, at least one continuous air outflow path exists in the network and extends from the bottom to the top to ensure the free discharge of the air phase. If the air outflow path is completely merged by the infiltrating water, the infiltration process will stop and the air phase at the bottom will be trapped below the wetting front.

[0070] In addition, the number of simulation steps before infiltration stops is different under different pore size distribution conditions. When the pore size distribution is very non-uniform (e.g., k = 0.5), the air outflow path is quickly merged by the infiltrated water, and the simulation stops after only 359 steps, which means that water only invades a small number of pores and a large amount of air is trapped below the wetting front. And as the pore size distribution becomes more and more uniform (e.g., k increases from 0.5 to 3.0), the time step for the simulation to stop also increases from about 350 to 2300, indicating that the air outflow path exists for a longer time and ultimately less air is trapped in the medium. At the same time, as the pore size distribution becomes more uniform, the lateral merging of finger-like infiltration is suppressed, so after 500 simulation steps, there are more air outflow paths (3 paths when k = 3.0 and 1 path when k = 1.0).

[0071] In addition, an embodiment of the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium may store a program, which, when executed, includes part or all of the steps of the two-dimensional model construction method for simulating the water vapor convection process in any porous medium recorded in the above method embodiment.

[0072] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0073] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a memory and includes several instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned memory includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes.

[0074] A person skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable memory, which can include: a flash drive, a read-only memory, a random access memory, a magnetic disk or an optical disk, etc.

[0075] The specific implementation methods described above further illustrate the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only the specific implementation methods of the present application and is not intended to limit the scope of protection of the present application. Any modifications, equivalent substitutions, improvements, etc. made on the basis of the technical solutions of the present application should be included in the scope of protection of the present application.

Claims

1. A two-dimensional model construction method for simulating water vapor convection process in porous media, characterized in that: The method comprises the following steps: Constructing a two-dimensional pore network; A dynamic convection process simulation model is constructed, wherein a Two motion event is introduced in the meniscus renewal simulation. The Twomotion event introduces a transition state between the displacement process and the meniscus renewal. The transition state divides the displacement process and the meniscus renewal into two simulation steps. The displacement process specifically includes: Determine the pore throat to be operated; Determine whether the pore throat to be operated is in a transition state; If it is in the transition state, a simulation inspection operation is performed to control whether the meniscus of the pore throat to be operated is updated; if it is in the non-transition state, a moisture absorption / drainage operation is performed until the pore throat to be operated changes from the non-transition state to the transition state; The simulation inspection operation is specifically as follows: Modify the original capillary pressure of the meniscus in the pore throat to be operated to the minimum inlet pressure at the connected pore throat, and check whether the meniscus pressure gradient is reversed. When the pressure gradient can overcome the sudden change of capillary pressure, the meniscus in the pore throat to be operated is allowed to update, otherwise, close the pore throat to be operated and wait for the next simulation check; Based on the dynamic convection process simulation model analysis, the influence of the pore size distribution of the porous medium on the convection process is obtained. Specifically, the more uniform the pore size distribution, the longer the air outflow path exists, and the less air is trapped in the porous medium.

2. A two-dimensional model construction method for simulating water vapor convection process in porous media according to claim 1, characterized in that: The pore network was constructed based on the open source code OpenPNM, and the pore diameters were randomly assigned using the Weibull function.

3. The method for constructing a two-dimensional model for simulating water vapor convection process in porous media according to claim 1, characterized in that: The construction of the dynamic convection process simulation model comprises the following steps: Set initial and boundary conditions; Set the threshold of the dynamic meniscus; Check the pore throat; Solve for the pressure field in the pore network; Calculate local flow rates based on pore / pore throat pressure gradients to determine displacement processes; The pore throats are checked until there is no dynamic meniscus in the pore network, the simulation stops, the pressure field in the pore network approaches a stable equilibrium state, and the simulation model of the dynamic convection process is completed.

4. The method for constructing a two-dimensional model for simulating water vapor convection process in porous media according to claim 3, characterized in that: The initial conditions and boundary conditions are specifically: The pore network is initially filled with air, and the initial pressure field is solved; A water inlet and an air outlet are set at the top boundary of the pore network, and the remaining boundaries are set to a sealed state.

5. The method for constructing a two-dimensional model for simulating water vapor convection process in porous media according to claim 3, characterized in that: The threshold of the dynamic meniscus is set to 0.

6. The method for constructing a two-dimensional model for simulating water vapor convection process in porous media according to claim 3, characterized in that: The pore throats are examined using a clustering algorithm.

7. The method for constructing a two-dimensional model for simulating water vapor convection process in porous media according to claim 3, characterized in that: The inspection of the pore throat specifically includes: Identify trapped pore throats; Deactivate the trapped meniscus; Identify the oscillating meniscus; A pore throat that temporarily blocks oscillations.

8. A computer-readable storage medium, characterized in that: The storage medium contains a two-dimensional model construction method for simulating a water vapor convection process in a porous medium as described in any one of claims 1 to 7.

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