Quasi-static prediction method based on plugging performance of foams in pore network

Abstract

The invention relates to the technical field of oil and gas field development, in particular to a quasi-static prediction method based on foam plugging performance in a pore network, which comprises the following steps: generating a pore network model; according to the foam injection condition, the foam migration front position and candidate to-be-displaced pore throats are recognized; calculating a displacement threshold value of the foam migration path; under the constraint of an inlet constant-pressure boundary condition, judging the opening state of a foam migration path, and adjusting the boundary pressure condition; active foam migration paths are analyzed, the displacement speeds of all foam migration paths before displacement are calculated, the maximum displacement speed is selected, and displacement is completed; and continuously circulating until the foam breaks through the pore network. According to the method, the problems that experimental verification is difficult to carry out on traditional pore-scale foam modeling based on a memory intrusion percolation method, and potential algorithm conflicts are generated when displacement in a weak foam state or displacement combined with a foam coalescence mechanism is simulated are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas field development, and particularly to a quasi-static prediction method based on the foam plugging performance in a pore network. Background Art

[0002] Foam plays a crucial role in the production process of the petroleum industry, and its application scope is extensive, covering multiple key links such as drilling assistance, well stimulation, enhanced oil recovery, refining, and emerging medium- and long-term carbon dioxide sequestration projects in abandoned reservoirs; in order to deeply understand and optimize these foam-assisted processes, various models have been proposed in the prior art, aiming to explore the flow behavior of foam in porous media at different scales.

[0003] Among these models, although the total balance model and others have certain practicality, there are still some limitations; for example, the processing of important parameters such as foam generation / coalescence rate and flowing foam fraction often relies on empirical data, which to a certain extent limits the accuracy and reliability of the model; this is because these key parameters are difficult to directly obtain through traditional experimental means.

[0004] In order to improve the accuracy and reliability of foam description in these foam-assisted processes, the pore network model intertwined with the memory invasion percolation method has become a powerful tool for studying the flow characteristics of foam in porous media, which can predict relative permeability and mobile gas fraction, fully considering the pore-scale mechanisms of foam generation, destruction, and migration; however, the assumption of a fully sufficient incremental pressure difference used in traditional pore-scale foam modeling based on the memory invasion percolation method is strict, which is not only difficult to conduct relevant experimental verification, but also may cause potential algorithm conflicts when simulating displacement in a weak foam state or displacement combined with the foam coalescence mechanism. Summary of the Invention

[0005] Aiming at the deficiencies of the existing methods, the present invention incorporates a mixed sorting rule into the foam migration model based on the memory invasion percolation method, and conducts displacement by quantitatively describing the transition between fixed foam clusters and flowing foam flows, thereby obtaining the key characteristics that define the pore-scale foam behavior under excessive pressure constraints.

[0006] The technical solution adopted by the present invention is: a quasi-static prediction method based on the foam plugging performance in a pore network includes the following steps:

[0007] Step 1: Set the geometric characteristics, foam thermodynamic characteristics, and boundary conditions of the pore network to generate a pore network model;

[0008] As a preferred embodiment of the present invention, a truncated lognormal distribution is used in the pore network model to model the pore throat radius and the factor of pore throat distribution heterogeneity.

[0009] As a preferred embodiment of the present invention, the formula for the truncated lognormal distribution is:

[0010]

[0011] wherein, R tmax , R tmin respectively represent the average value, the maximum and minimum radii of the pore throats; σ is a factor characterizing the heterogeneity of the pore throat distribution.

[0012] Step Two: According to the injection situation of the foam, identify the position of the foam migration front and the candidate pore throats to be displaced; calculate the displacement threshold of the foam migration path; under the constraint of the inlet constant pressure boundary condition, judge the opening state of the foam migration path, and adjust the boundary pressure condition; analyze the active foam migration paths, calculate the displacement velocities of the displacement fronts of all foam migration paths, and select the maximum displacement velocity to complete the displacement;

[0013] As a preferred embodiment of the present invention, Step Two includes: Step 21: Construct a foam displacement process model, specifically including:

[0014] Step 211: Calculate the pressure difference Δp of the foam liquid film L at the throat unit ij L,ij ;

[0015] Step 212: Calculate the total pressure threshold V required for the flow of all foam liquid films distributed along the flow path connecting the pore volume × to the pore network inlet x ;

[0016] Step 213: Quantify the relationship between the displacement time t F of the displacement step and the remaining liquid film thickness h F therebetween.

[0017] As a preferred embodiment of the present invention, Step Two further includes: Step 22: Introduce an improved pressure constraint algorithm and a Bingham fluid model, adjust the pressure threshold and introduce time dependence to correct the displacement pressure, specifically including:

[0018] Step 221: Calculate the relationship between the flow rate and the pressure drop of the Bingham fluid flowing in a cylindrical capillary;

[0019] Step 222: Perform a dimensionless conversion on the capillary volume flow rate;

[0020] Step 223: Convert the relationship between the flow rate and the pressure drop of the Newtonian fluid according to Poiseuille's law;

[0021] Step 224: Calculate the dimensionless flow rate q ab ;

[0022]

[0023] Among them, P a is the pressure of pore a, P b is the pressure of pore b

[0024] As a preferred embodiment of the present invention, the dimensionless flow rate q in step 224 ab includes a throat filled with the displaced phase and containing a foam liquid film, and a throat filled with the displaced phase

[0025] Step 225: Calculate the displacement velocity of the displacement front interface using the dimensionless flow rate

[0026] As a preferred embodiment of the present invention, the formula for the displacement velocity is

[0027]

[0028] Among them, x ju is the path distance between pores j and u, q ju is the flow rate between pores j and u

[0029] As a preferred embodiment of the present invention, step two further includes: step 23, introducing the dynamic update of the minimum threshold path and the gradual accumulation of the pressure difference. The formula for the minimum threshold is

[0030] S(i,j) = p cap (i,j) + V(i)(21)

[0031] Among them, p cap is the frontal capillary force at the entrance of the candidate pore throat; V is the resistance required for the foam flow path to displace all liquid films

[0032] Step three: After the displacement is completed, synchronously update the thickness and quantity of the foam liquid film in the pore network, and identify the newly formed bound foam area; continuously identify the position of the new foam displacement front and the candidate pore throats to be displaced, and continuously cycle until the foam breaks through the pore network

[0033] As a preferred embodiment of the present invention, a quasi-static prediction system for the foam plugging performance in a pore network includes: a memory for storing instructions executable by a processor; a processor for executing the instructions to implement a quasi-static prediction method for the foam plugging performance in a pore network

[0034] As a preferred embodiment of the present invention, a computer-readable medium storing computer program code, which, when executed by a processor, implements a quasi-static prediction method based on the foam plugging performance within a pore network.

[0035] Advantages of the present invention:

[0036] 1. Displacement is carried out by quantitatively describing the transition between fixed foam clusters and flowing foam streams, thereby obtaining the key characteristics defining pore-scale foam behavior under excessive pressure constraints;

[0037] 2. By quantitatively describing the evolution and transformation between bound foam and flowing foam, the quasi-static displacement process and plugging performance of foam within the pore network can be predicted under constant pressure constraints;

[0038] 3. The identification of the minimum threshold path (MTP) is adjusted. This path is determined by combining a gradually updated velocity field when multiple foam flow paths become movable under a large pressure difference, thereby avoiding potential conflicts caused by weak foam regions or foam coalescence mechanisms. Description of the Drawings

[0039] Figure 1 is an improved algorithm flow chart for simulating foam displacement in a pore network by the present invention under controllable pressure constraints;

[0040] Figure 2 is a frequency histogram of pore throat radii generated by truncating the log-normal distribution of the present invention;

[0041] Figure 3 is the present invention's in-situ generated liquid film pinch-off point distribution diagram under different effective liquid film generation rates P SO , marked in green;

[0042] Figure 4 is a schematic diagram of the fluctuations during the transportation of the liquid film within the pore network of the present invention;

[0043] Figure 5 a in is a schematic diagram of the traditional IPM method restricted by an asymmetric incremental pressure difference; b is a typical foam displacement scenario diagram using the traditional IPM method; c is a schematic diagram of the improved IPM method proposed by the present invention restricted by a fixed incremental pressure difference; d is a representative foam displacement scenario diagram using the improved IPM method proposed by the present invention; e is a schematic diagram of the improved IPM method proposed by the present invention restricted by a constant pressure difference;

[0044] Figure 6 is a schematic diagram of the displacement patterns of three activated displacement candidate paths of the foam flow paths u, v, w of the present invention under an excessive pressure p X ; Detailed Embodiments

[0045] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner. Therefore, it only shows the components related to the present invention.

[0046] As Figure 1 shown, a quasi-static prediction method based on the foam plugging performance in a pore network includes the following steps:

[0047] Step 1: Construct a pore network model to describe the geometric characteristics of the pore network, explain the role of capillary force in the pore network and its control mechanism for fluid flow; use a log-normal distribution to model the pore throat size, and detail the control and description of the structural characteristics of the pore network;

[0048] The present invention focuses on the scenario of foam seepage, but the constitutive model can be described more broadly and is suitable for more immiscible displacement processes in pore networks, as long as two assumptions are met:

[0049] 1. The compressibility of the displaced phase can be ignored;

[0050] 2. The rheology of the displacing phase has certain Bingham fluid characteristics;

[0051] The pore throat size in the pore network model is specified by a truncated log-normal distribution shown in formula (1):

[0052]

[0053] Where R tmax 、R tmin respectively represent the average value, the maximum and minimum radii of the pore throat radius; σ is a factor characterizing the heterogeneity of the pore throat distribution. The closer σ is to 0, the more uniform the pore throat. In this embodiment, the average pore throat radius, the maximum radius and the minimum radius are 10 μm, 22 μm and 1 μm respectively; the heterogeneity factor σ is set to 0.25, indicating that the pore network structure is relatively uniform, and the corresponding pore throat radius distribution is as Figure 2 shown.

[0054] The sharp distribution generally adopted in the prior art cannot accurately describe the characteristics of reservoir pores and throats; it also includes the normal logarithmic distribution, but the defects of the normal logarithmic distribution cannot limit the upper and lower limits of the pore throat structure, so it is possible to calculate singularities that deviate from the actual situation; therefore, the present invention adopts a truncated log-normal distribution, and its advantage is that it can simultaneously describe the median, the maximum and minimum sizes, and the degree of heterogeneity in the statistics of pores in one formula. This distribution can guide both throats and pores and can describe the pore network more precisely.

[0055] Step 2: Identify the foam migration front position and candidate pores and throats to be displaced according to the foam injection situation; calculate the displacement threshold S of all foam migration paths; under the constraint of the inlet constant-pressure boundary condition, judge the opening state of the foam migration paths, and adjust the boundary pressure condition; analyze the active foam migration paths, calculate the displacement velocity dx / dt of the displacement front of all foam migration paths, and select the maximum displacement velocity dx / dt to complete the displacement.

[0056] Step 21: Simulate the foam migration mechanism at the pore scale, study the foam generation, the dynamic change of the liquid film, and the resistance mechanism during the foam flow process, and construct a relatively complete foam displacement process model.

[0057] After establishing the pore network, the fracture points are determined by assigning a random number P between 0 and 1 to all pores and throats, and the pores and throats with the assigned P < P SO are regarded as fracture points; as Figure 3 shown, if the continuous gas phase passes through a pore and throat identified as a fracture point for liquid film generation, a new foam liquid film will be formed at this pore and throat and will stand in the pore and throat accordingly; according to the hypothesis, when the discontinuous gas phase displaces the fracture point together with the flowing foam liquid film, no new foam liquid film will be formed again. Figure 3 In, the foam generation in the pore network is controlled by the assigned P so P so is equivalent to a specific point, which is the probability of the bubble formation point. The larger P so is ( Figure 3 a, b, c, d in increase gradually), the more bubble formation points (the green part in the figure), and the greater the probability of forming more foam liquid films.

[0058] The resistance of the effective liquid film is quantified by accumulating the pressure threshold applied on the liquid film. The pressure threshold is accumulated along each foam liquid film flow path on the foam flow path. Once the foam liquid film is formed in the direction perpendicular to the foam liquid film flow path, it will make the flowing gas phase discontinuous and introduce additional resistance in the pore and throat ij, as shown in formula (2):

[0059]

[0060] where, R t,ij is the radius of the pore and throat ij; γ is the interfacial tension between the displacing phase and the displaced phase; Δp L,ij is the pressure difference to overcome the foam liquid film L at the throat unit ij, that is, after the gas phase in the pore and throat unit ij becomes discontinuous gas phase after the formation of the foam liquid film L, the additional resistance that needs to be overcome if this part of the gas phase wants to flow.

[0061] The sum of the corresponding resistances exerted by all active liquid films in the foam flow path is the pressure threshold required for flowing foam, as shown in Equation (3):

[0062]

[0063] where V x is the total pressure threshold required for flowing all the foam liquid films distributed along the flow path connecting the pore volume × to the pore network inlet; n′ is the number of remaining active foam liquid films within the flow path guided by pore x in the foam flow path.

[0064] By introducing an assumed time dependence into the memory invasion percolation model, the foam coalescence mechanism is introduced into the pore-scale immiscible displacement process; for static foam liquid films, Equation (4) is proposed to quantify the displacement time t F of a specific displacement step and the remaining liquid film thickness h F The relationship between them is as follows:

[0065]

[0066] where μ L is the liquid phase viscosity enclosed in the liquid film, R F is the equivalent radius of the liquid film, P cap is the local capillary pressure, h FO is the initial liquid film thickness, and Π is the repulsive pressure.

[0067] Step 22, Modify the displacement pressure constraint: Introduce an improved pressure constraint algorithm and Bingham fluid model to address the limitations of the traditional memory invasion percolation method in dealing with the foam coalescence mechanism and multiple displacements occurring simultaneously. By adjusting the pressure threshold and introducing time dependence, more accurately simulate the dynamic changes of the foam liquid film;

[0068] For the traditional IPM-based foam displacement modeling method, displacement events are determined by minimizing the pressure threshold on each candidate foam flow path until the latest displacement step; then, p X is the pressure difference added in the pore network from the inlet to the outlet, and then an incremental pressure difference Δp i is added, which is just sufficient to trigger another displacement event; as shown in Figure 5 a of, subsequently, more displacement candidate points adjacent to pore j are added. Such a recursively determined quasi-static displacement process proceeds without additional requirements for time-sensitive characteristics until recently, considering the foam coalescence mechanism, which introduces time dependence for dealing with unstable thinning foam liquid films; therefore, a fixed time step Δt is introduced into the traditional IPM-based foam migration process, as shown in Figure 4As shown in b, where the pressure difference accumulates at a steady pressure increment rate; when the increased pressure drop is sufficient to activate the corresponding displacement event, it is assumed that the displacement is completed immediately, and the next pressure accumulation process also begins.

[0069] However, under the action of the foam coalescence mechanism, the previously applied pressure difference at the inlet may exceed the updated pressure threshold, resulting in an algorithm conflict and unable to continue using the single displacement assumption for displacement, because multiple displacement events may be activated simultaneously at this time, as Figure 4 shown in c, the pressure thresholds of two additional displacement events, labeled S ik and S nm , are satisfied together with S ij , and the traditional method cannot appropriately simulate this displacement process.

[0070] To solve these problems, the present invention processes the gradually increasing pressure during the foam migration process by modifying the displacement sequence algorithm, and achieves this by combining the frontal displacement velocity dX / dt and the time-sensitive variable pressure threshold; as a result, the proposed method allows the application of controllable and uniform pressure constraints, as Figure 4 shown in d of and e of 4, the pressure difference increases in a fixed incremental pressure difference and a regular constant pressure difference manner, respectively.

[0071] The relationship formula between the flow rate and the pressure drop of a Bingham fluid flowing in a cylindrical capillary is:

[0072]

[0073] Q ij =0, τ ij ≤τ e (6)

[0074] where τ ij represents the deviatoric stress in the capillary, τ e represents the yield stress, μ is the fluid viscosity, Q ij , ΔP ij , L ij and R ij represent the volume flow rate, pressure drop, length, and radius of the capillary ij, respectively.

[0075] Equation (5) is converted into a dimensionless form as shown in Equation (7). Based on the dimensionless expressions in Equations (9) to (12), these expressions have been applied to multiple pore-scale foam migration studies:

[0076]

[0077]

[0078] where, R′ij is the reference radius and μ is the fluid viscosity.

[0079] Equation (7) can be simplified to Equation (13):

[0080]

[0081] According to Poiseuille's law, the relationship between the flow rate and pressure drop of Newtonian fluid can be converted to Equation (15):

[0082]

[0083] where M is the viscosity ratio between the displacing phase and the displaced phase, defined as the ratio of the viscosity of the displaced phase to the viscosity of the displacing phase.

[0084] As Figure 6 ij, ik, and mn shown in, all the pores of the displaced phase connected to the outlet, and for any pore a within these regions, the following relationship holds:

[0085]

[0086] where Z is the number of pore throats connected to pore a.

[0087] To solve Equation (16), by specifying the fluid configuration between pore a and its movable neighboring pore b, the p-q relationship is given. If a pore throat is filled with the displaced phase and there is no liquid film structure, the dimensionless flow rate q ab is given by:

[0088]

[0089] where P a is the pressure of pore a, and P b is the pressure of pore b,

[0090] If a pore throat is filled with the displaced phase and contains a foam liquid film, the dimensionless flow rate q ab is given by:

[0091]

[0092] If a pore throat is filled with the displaced phase, the dimensionless flow rate q ab is given by:

[0093]

[0094] The pressures of each pore and the throat flow rates within the pore network are obtained by solving the matrix generated according to formulas (16)-(19). By formulating a system of non-linear homogeneous equations, the pressure at each pore and the flow rate at each throat (between two adjacent pores) can be calculated by solving the matrix; these results can be applied to formula (20) to obtain the displacement velocity of the displacement front interface:

[0095]

[0096] where x ju is the path distance between pores j and u, and q ju is the flow rate between pores j and u.

[0097] Step 23: Simulate foam percolation in the pore network, improve the traditional memory invasion percolation method, and more accurately simulate the foam displacement process in the context of multiple displacement and foam coalescence mechanisms; introduce the dynamic update of the minimum threshold path (MTP) and the gradual accumulation of pressure differences to better handle weak foam regions and multi-path displacement problems;

[0098] The displacement threshold S required to displace each candidate throat is determined by the sum of the frontal capillary force p cap at the entrance of the candidate pore throat and the resistance V required to displace all liquid films along the corresponding foam flow path, as shown in formula (21):

[0099] S(i,j) = p cap (i,j) + V(i ) (21)

[0100] Step three: After the displacement is completed, synchronously update the thickness and quantity of the foam liquid films within the pore network and identify the newly formed bound foam regions; subsequently, continuously identify the positions of the new foam displacement fronts and the candidate pore throats to be displaced, and keep cycling until the foam breaks through the pore network;

[0101] Compared with the research based on traditional methods, the most significant adjustment of the present invention lies in the identification of the minimum threshold path (MTP), which is determined by combining the gradually updated velocity field when the path becomes movable under the action of an excessive pressure difference through multiple foam flow paths, thus avoiding potential conflicts caused by weak foam regions or foam coalescence mechanisms.

[0102] Inspired by the ideal embodiments of the present invention described above, through the above description, relevant staff can make various changes and modifications within the scope not deviating from the technical idea of the present invention. The technical scope of the present invention is not limited to the content in the specification, and must be determined according to the scope of the claims.

Claims

1. A quasi-static prediction method based on the foam plugging performance in the pore network, characterized in that: The following steps are involved: Step 1: Set the geometric characteristics of the pore network, the foam thermodynamic characteristics and boundary conditions to generate a pore network model; Step 2: According to the foam injection situation, identify the foam migration front position and candidate pore throats to be displaced; Calculate the displacement threshold of the foam migration path; under the constraint of the inlet constant pressure boundary condition, determine the open state of the foam migration path and adjust the boundary pressure condition; analyze the active foam migration path, calculate the displacement front displacement speed of all foam migration paths, and select the maximum displacement speed to complete the displacement; Step 3: After the displacement is completed, the thickness and quantity of the foam liquid film in the pore network are updated synchronously, and the newly formed bound foam area is identified; the new foam displacement front position and candidate pore throats to be displaced are continuously identified, and the cycle continues until the foam breaks through the pore network.

2. The quasi-static prediction method based on the foam plugging performance in the pore network according to claim 1 is characterized in that: Step 2 includes: Step 21, constructing a foam displacement process model, specifically including: Step 211, calculate the pressure difference Δp of the foam liquid film L at the throat unit ij L,ij ; Step 212: Calculate the total pressure threshold V required for all foam liquid films distributed along the flow path connecting the pore volume × to the pore network inlet. x ; Step 213: quantify the displacement time t of the displacement step F and the remaining liquid film thickness h F The relationship between.

3. The quasi-static prediction method based on the foam plugging performance in the pore network according to claim 2, characterized in that: Step 2 also includes: Step 22, introducing an improved pressure constraint algorithm and a Bingham fluid model, adjusting the pressure threshold and introducing time dependence, and correcting the displacement pressure, specifically including: Step 221, calculating the relationship between the flow rate and the pressure drop of the Bingham fluid flowing in the cylindrical capillary; Step 222, performing dimensionless conversion on the capillary volume flow rate; Step 223, converting the relationship between the flow rate and the pressure drop of the Newtonian fluid according to Poiseuille's law; Step 224: Calculate the dimensionless flow rate q between pore a and its mobile neighbor pore b ab ; Among them, P a is the pressure of pore a, P b is the pressure at pore b, Step 225: Calculate the displacement velocity of the displacement front interface using the dimensionless flow rate.

4. The quasi-static prediction method based on the foam plugging performance in the pore network according to claim 3, characterized in that: The dimensionless flow rate q in step 224 ab It includes a throat filled with a displacing phase and containing a foam liquid film, and a throat filled with a displaced phase.

5. The quasi-static prediction method based on the foam plugging performance in the pore network according to claim 3, characterized in that: The formula for displacement speed is: Among them, x ju is the path distance between pores j and u, q ju is the flow rate between pores j and u, 6. The quasi-static prediction method based on the foam plugging performance in the pore network according to claim 3, characterized in that: Step 2 also includes: Step 23, introducing dynamic update of the minimum threshold path and gradual accumulation of pressure difference, the formula of the minimum threshold is: S(i,j)=p cap (i,j)+V(i) (21) Among them, p cap is the front capillary force at the candidate pore throat entrance; V is the resistance required for the foam flow path to displace all liquid films.

7. The quasi-static prediction method based on the foam plugging performance in the pore network according to claim 1, characterized in that: The truncated log-normal distribution is used in the pore network model to model the factors of pore throat radius and pore throat distribution heterogeneity.

8. The quasi-static prediction method based on the foam plugging performance in the pore network according to claim 7, characterized in that: The formula for the truncated lognormal distribution is: in, R tmax , R tmin They represent the average, maximum and minimum radius of the pore throat respectively; σ is a factor that characterizes the heterogeneity of pore throat distribution.

9. A quasi-static prediction system based on the foam plugging performance in the pore network, characterized in that: include: a memory for storing instructions executable by a processor; A processor, configured to execute instructions to implement the quasi-static prediction method based on the foam plugging performance within the pore network as described in any one of claims 1-8.

10. A computer readable medium storing computer program code, characterized in that: The computer program code, when executed by a processor, implements the quasi-static prediction method based on the foam plugging performance in the pore network as described in any one of claims 1 to 8.

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