A numerical simulation method for acidizing by following fractures and finding holes

Abstract

The numerical simulation method for acidizing by following fractures and finding caves described in the present invention establishes a reservoir geological model capable of performing numerical simulation of acidizing by following fractures and finding caves by assigning a dual-scale mathematical model capable of describing centimeter- to micrometer-scale porous media to a carbonate reservoir geological model containing random natural fractures and multiple caves, simulating the process of acid communicating with natural fractures in different directions and connecting caves through the communicating natural fractures, clarifying the extension path of the acid-etched fractures and the orientation and number of caves communicating along the natural fractures, facilitating the judgment of the ability of the acid-etched fractures to communicate with potential fracture-cavity oil and gas reservoirs around the wellbore, and guiding the formulation of acidizing engineering plans for fracture-cavity carbonate reservoirs.

Description

Technical Field

[0001] The invention relates to the technical field of development of fracture-cavity oil reservoirs, and in particular to a numerical simulation method for acidification by following fractures to find cavities. Background Art

[0002] The key to acidizing carbonate oil and gas wells is to dredge and improve the oil and gas flow channels to achieve the purpose of increasing production. Compared with sandstone acidizing, the reaction between hydrochloric acid and carbonate rock is more intense, which often leads to the appearance of advantageous channels with higher conductivity during the acidizing of carbonate reservoirs, called wormholes. The formation process of carbonate rock acid wormholes is that when the acid enters the pores and fractures in the carbonate reservoir rock, it dissolves the rock. Due to the heterogeneity of the pore distribution, the acid injected into the reservoir preferentially flows into the larger pore network. The acid reacts with the minerals on the pore rock wall, dissolves the minerals, and expands the pores. Due to the flow-dissolution-flow cycle, the expanded pore network after acid etching forms wormholes along the acid flow path. In addition to wormhole dissolution, acid dissolution also includes surface dissolution and uniform dissolution. The scope of surface dissolution is mainly limited to the area near the wellbore, resulting in a waste of acid. In the case of uniform dissolution, although the pores and fractures in the formation in a larger range are dredged, the average increase in porosity is far less effective in improving the formation permeability than wormhole dissolution. In order to improve the utilization rate of acid and the acidizing effect, it is necessary to study the law of acid etching.

[0003] The invention patent with application number 201710860364.0 discloses a full simulation method for an acidizing flow experiment, comprising the following steps: (1) measuring the chemical reaction rate between the acid system and rock minerals within a certain acid concentration range to obtain a concentration-reaction rate curve; (2) measuring the chemical reaction rate between the acid system and rock minerals within a certain temperature range to obtain a temperature-reaction rate curve; (3) using the difference method to discretize the fluid seepage continuity equation and the acid mass transfer diffusion reaction equation, and at the same time establishing the hydrogen ion local equilibrium equation, the porosity change equation, the permeability change equation, and the pore throat radius change equation; (4) substituting the initial conditions and boundary conditions of the simulation equation; (5) using the equations, initial conditions, and boundary conditions described in steps (3) and (4) to compile a calculation program; (6) scanning the experimental core to obtain the porosity spatial distribution parameters; and (7) establishing a porosity spatial distribution model. Based on the established porosity spatial distribution model, the program compiled in step (5) is used to perform a computational simulation of the acidizing flow experiment. This computational simulation method is a numerical simulation of conventional homogeneous carbonate reservoirs, which does not take into account the conditions of natural fractures and caves in the reservoir and is not suitable for computational simulation of fracture-cavity carbonate reservoirs. Summary of the invention

[0004] The present invention provides a numerical simulation method for acidizing by following fractures and finding caves, establishes a dual-scale mathematical model capable of describing micron- to centimeter-scale porous media, constructs a geological model including different natural fracture densities, directions, lengths, and caves in different orientations, simulates and calculates the process in which acid communicates with natural fractures in different directions during acidizing under the conditions of natural fracture and cave development in fracture-cavity carbonate reservoirs, and connects caves through the communicated natural fractures, clarifies the extension path of acid-etched fractures and the orientation and number of caves communicated along natural fractures, facilitates the judgment of the ability of acid-etched fractures to communicate with potential fracture-cavity oil and gas reservoirs around the wellbore, and guides the formulation of acidizing engineering plans for fracture-cavity carbonate reservoirs.

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

[0006] A numerical simulation method for acidification by crack tracking and hole finding, characterized by comprising the following steps:

[0007] S1, establishing a dual-scale mathematical model, wherein the dual-scale mathematical model includes a Darcy scale model and a pore scale model, and the pore scale model provides parameter support for the Darcy scale model; specifically, the dual-scale mathematical model is used in a reservoir geological model containing natural fractures to calculate the flow of acid in the natural fractures and the reaction with carbonate rocks, and simulate the flow path of acid in fracture-finding and hole-finding acidification, and the simulated flow path of acid in fracture-finding and hole-finding acidification is used for the design of carbonate reservoir acidification engineering;

[0008] S 1.1 Establishing Darcy scale model: Darcy scale model is used to describe the model of centimeter-scale to micrometer-scale porous media. The acid solution flows in centimeter-scale to micrometer-scale porous media as Darcy seepage;

[0009] (1) Acid flow in the matrix

[0010] The acid is injected into the formation at a certain speed. Under the macroscopic movement (convection) and concentration gradient (diffusion) in the fluid, the hydrogen ions in the acid are transferred from the porous medium fluid to the carbonate rock surface to react, thereby changing the formation porosity and permeability. The flow of the acid in the matrix formation is controlled by Darcy's law:

[0011]

[0012] The fluid pressure distribution is governed by the continuity equation for incompressible fluids:

[0013]

[0014] The concentration distribution of hydrogen ions in the fluid is controlled by the convection-diffusion equation, which is divided into two cases: case 1 is that the acid does not completely dissolve the rock (ε<1), and case 2 is that the acid completely dissolves the rock (ε=1);

[0015] The convection-diffusion equation when the acid does not completely dissolve the rock (ε<1) needs to consider the consumption of hydrogen ions on the rock surface and the change of porosity:

[0016]

[0017] The convection-diffusion equation when the acid completely dissolves the rock (ε=1) does not need to consider the consumption of hydrogen ions on the rock surface and the change of porosity:

[0018]

[0019] In the formula, is the Darcy velocity vector, m / s; k is the formation permeability, m2; μ is the acid viscosity, Pa s; P is the acid pressure, Pa; ε is the formation porosity; t is the reaction time, s; C f is the acid concentration in the rock pores, mol / m 3 ;D e is the acid diffusion tensor, m 2 / s;k c is the local mass transfer coefficient of the acid solution, m / s; a v is the pore area per unit volume of rock, m 2 / m 3 ; C s is the acid concentration on the rock surface, mol / m 3 ; α is the mass of rock that can be dissolved by unit mole of acid, kg / mol; ρ s is the rock density, kg / m 3 ;

[0020] (2) Acid flow in cracks

[0021] The flow of acid in natural fractures corresponds to different mechanisms from the flow in the matrix. The flow in natural fractures is free flow, while the flow in the matrix is ​​porous medium seepage controlled by Darcy's law. The flow of acid in natural fractures regards natural fractures as areas with higher permeability based on the concept of equivalent permeability. The above mathematical model is used to study the dissolution phenomenon of acid in fractured formations, and the mesh of natural fractures that have a greater impact on the pressure field is encrypted to speed up the calculation and ensure the convergence of the calculation.

[0022] S1.2 establishing a pore scale model to provide parameter support including permeability, pore radius, specific surface area, porosity, diffusion tensor, and mass transfer coefficient for the Darcy scale model;

[0023] S2, obtaining natural fracture characteristic distribution data and karst cave characteristic distribution data based on well logging data, core data, natural fracture occurrence data, drilling and draining data and seismic interpretation data of actual carbonate reservoirs, and establishing a geological model containing natural fractures and karst caves based on the natural fracture characteristic distribution data and karst cave characteristic distribution data;

[0024] S3, gridding the constructed geological model containing natural fractures and karst caves, assigning the parameters calculated by the dual-scale mathematical model in step 1 to the grid units and nodes of the geological model containing natural fractures and karst caves in step 2, and obtaining a three-dimensional reservoir geological model capable of acidification numerical simulation after gridding and attribute parameter assignment;

[0025] S4, performing simulation calculation on the three-dimensional geological model of the reservoir capable of acidification numerical simulation; and displaying the calculation result of step 4 by drawing a graph;

[0026] Among them, the order of S1 and S2 is adjustable.

[0027] Preferably, in S1.2, the pore scale model provides parameter support including permeability, pore radius, specific surface area, porosity, diffusion tensor, and mass transfer coefficient for the Darcy scale model, and the relationship between permeability, pore radius, specific surface area, and porosity includes:

[0028] The formation permeability, pore radius, specific surface area and porosity are directly related. The empirical formula used to describe the relationship between formation permeability, pore radius, specific surface area and porosity is:

[0029]

[0030] In the formula, ε(0<ε<1), k, r p 、a v are porosity, permeability, pore radius, and specific surface area; ε0, k0, r0, and a0 are initial porosity, permeability, pore radius, and specific surface area, respectively; β is a constant related to the pore structure, and β=1;

[0031] Generally speaking, the flow velocity of the acid in the formation is very small, which can be regarded as laminar flow. The fracture can be regarded as a thin circular tube, and the circular tube laminar flow formula can be used to examine the flow rate.

[0032]

[0033] Where Q is the flow rate, cm 3 / s; AP is the driving pressure difference, 0.1MPa; D is the crack diameter, cm; A is the cross-sectional area, cm2; μ is the fluid viscosity, Pa s; L is the crack length, cm;

[0034] The flow rate calculated using Darcy's formula is as follows:

[0035]

[0036] When the fracture width is 0.2 cm, the equivalent permeability corresponding to the natural fracture is calculated based on formula (6) and formula (7) as k = D 2 / 32=125x10 3 μm 2 Let the porosity of natural fractures ε max =0.999(ε0=0.05, k0=0.32), substituting into formula (5) to obtain the permeability K:

[0037]

[0038] k and K are of the same order of magnitude, that is, from the perspective of flow resistance, it is reasonable to treat a natural fracture with a width of 0.2 cm as equivalent to a matrix with a porosity of 0.999. For natural fractures with a width exceeding 0.2 cm, since the permeability of natural fractures is already quite high relative to the matrix, the fracture width is not a factor limiting the fracture conductivity (the product of permeability and fracture width), so the natural fracture can be treated as a fracture with a width of 0.2 cm.

[0039] Preferably, in S1.2, the pore scale model provides parameter support for the Darcy scale model including permeability, pore radius, specific surface area, porosity, diffusion tensor and mass transfer coefficient. Due to the sedimentation and compaction of the stratum, the pore structure is different in the horizontal and vertical directions. The diffusion tensor includes a horizontal diffusion tensor DeX and a vertical diffusion tensor DeT.

[0040] Preferably, the diffusion tensor and the molecular diffusion coefficient D m , pore structure, flow velocity, etc., where the Péclet number is a dimensionless number representing the ratio of convection to diffusion;

[0041]

[0042] The diffusion tensor is divided into the horizontal diffusion tensor D eX and the vertical diffusion tensor D eT The formula is:

[0043] D eX =(α os +λx·P eP )D m (10)

[0044] D eT =(α os +λ T P eP )D m(11)

[0045] In the formula, α os is a constant related to the pore structure, taking α os =0.5; from the core diffusion experiment, we get λx=0.5, λ T =0.1; D m is the molecular diffusion coefficient; PeP is the Péclet number;

[0046] Preferably, in S1.2, the pore scale model provides parameter support including permeability, pore radius, specific surface area, porosity, diffusion tensor, and mass transfer coefficient for the Darcy scale model.

[0047] Mass transfer coefficient k c The calculation method is:

[0048]

[0049] In the formula, Sh ∞ is the asymptotic Sherwood number; Re p is the pore-scale Reynolds number, Sc is the Schmidt number,

[0050] Preferably, the permeability, pore radius, specific surface area, porosity, diffusion tensor and mass transfer coefficient are calculated by the pore scale model and substituted into the Darcy scale model to obtain the changes in porosity and permeability of the rock dissolved by the acid over the penetration time.

[0051] Preferably, the calculation results in S5 include the acid flow path, the location and number of caves connected by fractures, and the pressure distribution.

[0052] Preferably, the natural fracture characteristic distribution data include the direction of the natural fracture, the angle between the natural fracture and the horizontal maximum ground stress, and the length and density of the natural fracture.

[0053] Preferably, the cave characteristic distribution data includes the diameter, number and distribution orientation data of the caves.

[0054] The advantages of the present invention over the prior art are as follows: the numerical simulation method for acidizing by following fractures and finding caves described in the present invention, by giving a dual-scale mathematical model of porous media that can describe centimeter- to micron-scales to a geological model containing random natural fractures and caves, constructs a fracture-cavity carbonate rock geological model that can perform numerical simulation of acidizing, simulates the process of acid activating natural fractures and connecting caves, calculates the extension direction and number of acid-etched fractures, and the orientation and number of caves connected by acid following fractures, thereby facilitating the judgment of the ability of acid-etched fractures to communicate with potential reservoirs around the well, and providing a basis for on-site construction design. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of a numerical simulation method for acidizing by following seams and finding holes in the present invention;

[0056] Figure 2 This is an embodiment of a numerical simulation method for acidizing by following fractures to find caves in the present invention. A reservoir geological model containing random natural fractures and caves is established based on relevant information of the target reservoir. The horizontal axis is the length of the reservoir geological model, and the vertical axis is the width of the reservoir geological model. The linear black is the natural fracture, and the circular black is the cave.

[0057] Figure 3 According to a numerical simulation method for acidizing by following fractures and finding caves of the present invention, a reservoir geological model containing random natural fractures and caves is gridded;

[0058] Figure 4 According to the present invention, a numerical simulation method for acidizing along fractures to find caves is used to perform numerical simulation calculations of acidizing. The direction of the acid extending along the fractures and the number of acid-etched fractures at 500s are shown. The horizontal coordinate is the length of the reservoir geological model, and the vertical coordinate is the width of the reservoir geological model. The linear black is a natural fracture, and the circular black is a cave.

[0059] Figure 5 According to the present invention, a numerical simulation method for acidizing along fractures to find caves is used to perform numerical simulation calculations of acidizing. The direction of the acid extending along the fractures and the number of acid-etched fractures at 1000s are shown. The horizontal coordinate is the length of the reservoir geological model, and the vertical coordinate is the width of the reservoir geological model. The linear black is a natural fracture, and the circular black is a cave.

[0060] Figure 6 According to the numerical simulation method of acidizing for finding caves along fractures of the present invention, numerical simulation calculation of acidizing is performed, the direction of extension of acid along fractures, the number of acid-etched fractures, the orientation and number of connected caves at 1500s, the horizontal axis is the length of reservoir geological model, the vertical axis is the width of reservoir geological model, the linear black is natural fracture, and the circular black is cave;

[0061] Figure 7 A numerical simulation method for acidizing by following fractures to find caves according to the present invention is used. When performing numerical simulation calculations for acidizing, the result diagram of following fractures to find caves is shown. The horizontal axis is the length of the reservoir geological model, and the vertical axis is the width of the reservoir geological model. The linear black area is a natural fracture, the circular black area is a cave, and the white area is a high-pressure area, which is also the area affected by the acid. DETAILED DESCRIPTION

[0062] In order to facilitate the understanding of the present invention, the present invention is described in more detail below in conjunction with specific embodiments.

[0063] A numerical simulation method for acidizing by following cracks and finding holes, the process is as follows: Figure 1As shown, the following steps are included:

[0064] S1, establishing a dual-scale mathematical model, wherein the dual-scale mathematical model includes a Darcy scale model and a pore scale model, and the pore scale model provides parameter support for the Darcy scale model;

[0065] S1.1 Establishing Darcy scale model: Darcy scale model is used to describe the model of centimeter-scale to micrometer-scale porous media. The acid solution flows in centimeter-scale to micrometer-scale porous media as Darcy seepage;

[0066] (1) Acid flow in the matrix

[0067] The acid is injected into the formation at a certain speed. Under the macroscopic movement (convection) and concentration gradient (diffusion) in the fluid, the hydrogen ions in the acid are transferred from the porous medium fluid to the carbonate rock surface to react, thereby changing the formation porosity and permeability. The flow of acid in the matrix formation is controlled by Darcy's law:

[0068]

[0069] The fluid pressure distribution is governed by the continuity equation for incompressible fluids:

[0070]

[0071] The concentration distribution of hydrogen ions in the fluid is controlled by the convection-diffusion equation, which is divided into two cases: case 1 is that the acid does not completely dissolve the rock (ε < 1), and case 2 is that the acid completely dissolves the rock (ε = 1);

[0072] The convection-diffusion equation when the acid does not completely dissolve the rock (ε<1) needs to consider the consumption of hydrogen ions on the rock surface and the change of porosity:

[0073]

[0074] The convection-diffusion equation when the acid completely dissolves the rock (ε=1) does not need to consider the consumption of hydrogen ions on the rock surface and the change of porosity:

[0075]

[0076] In the formula, is the Darcy velocity vector, m / s; k is the formation permeability, m2; μ is the acid viscosity, Pa·s; P is the acid pressure, Pa; ε is the formation porosity; t is the reaction time, s; Cf is the acid concentration in the rock pores, mol / m 3 ; De is the acid diffusion tensor, m2 / s; kc is the local mass transfer coefficient of the acid, m / s; av is the pore area per unit volume of rock, m 2 / m 3 ; Cs is the acid concentration on the rock surface, mol / m 3 ; α is the mass of rock that can be dissolved by unit mole of acid, kg / mol; ρs is the rock density, kg / m 3 ;

[0077] (2) Acid flow in cracks

[0078] The flow of acid in natural fractures corresponds to different mechanisms from the flow in the matrix. The flow in natural fractures is free flow, while the flow in the matrix is ​​porous medium seepage controlled by Darcy's law. The flow of acid in natural fractures regards natural fractures as areas with higher permeability based on the concept of equivalent permeability. The above mathematical model is used to study the dissolution phenomenon of acid in fractured formations, and the mesh of natural fractures that have a greater impact on the pressure field is encrypted to speed up the calculation and ensure the convergence of the calculation.

[0079] S1.2 Establish a pore scale model to provide parameter support for the Darcy scale model, including permeability, pore radius, specific surface area, porosity, diffusion tensor, and mass transfer coefficient; (1) Relationship between permeability, pore radius, specific surface area, and porosity

[0080] The formation permeability, pore radius, specific surface area and porosity are directly related. The empirical formula used to describe the relationship between formation permeability, pore radius, specific surface area and porosity is:

[0081]

[0082] In the formula, ε(0<ε<1), k, r p 、a v They are porosity, permeability, pore radius and specific surface area respectively; ε0, k0, r0 and a0 are initial porosity, permeability, pore radius and specific surface area respectively; β is a constant related to the pore structure, and β=1.

[0083] Generally speaking, the flow velocity of acid in the formation is very small and can be regarded as laminar flow. The fracture can be regarded as a thinner circular tube, and the circular tube laminar flow formula can be used to examine the flow rate.

[0084]

[0085] Where Q is the flow rate, cm 3 / s; ΔP is the driving pressure difference, 0.1MPa; D is the crack diameter, cm; A is the cross-sectional area, cm2; L is the crack length, cm.

[0086] The flow rate calculated using Darcy's formula is as follows.

[0087]

[0088] When the crack width is 0.2 cm, the equivalent permeability corresponding to the crack is calculated based on formula (6) and formula (7) as k = D 2 / 32=125×10 3 μm 2 Let the fracture porosity ε max =0.999(ε0=0.05, k0=0.32), substituting into formula (5) to obtain the permeability K:

[0089]

[0090] k and K are of the same order of magnitude, that is, from the perspective of flow resistance, it is reasonable to treat a crack with a width of 0.2 cm as equivalent to a matrix with a porosity of 0.999. For cracks with a width of more than 0.2 cm, since the permeability of the crack is quite high relative to the matrix, the crack width is not a factor that limits the fracture conductivity (the product of permeability and crack width), so the crack can be treated as a crack with a width of 0.2 cm.

[0091] (2) Diffusion tensor and mass transfer coefficient

[0092] Calculation of the diffusion tensor: and the molecular diffusion coefficient D m , pore structure, flow velocity, etc. Among them, the Péclet number is a dimensionless number that represents the relative proportion of convection and diffusion.

[0093]

[0094] Due to the sedimentation and compaction of the strata, the pore structure is different in the horizontal and vertical directions. The diffusion tensor is divided into the horizontal diffusion tensor D eX and the vertical diffusion tensor D eT .

[0095] DeX=(αos+λx·PeP)Dm (10)

[0096] DeT=(αos+λT·PeP)Dm (11)

[0097] In the formula, α os is a constant related to the pore structure, taking α os =0.5; from the core diffusion experiment, we get λx=0.5, λT=0.1; Dm is the molecular diffusion coefficient; D m is the molecular diffusion coefficient; P eP is the Péclet number.

[0098] Mass transfer coefficient k c Calculation method:

[0099]

[0100] In the formula, Re p is the pore-scale Reynolds number, Sc is the Schmidt number,

[0101] S2, according to the logging data, core data, natural fracture occurrence data, drilling and emptying data and seismic interpretation data of the actual carbonate reservoir, obtain the natural fracture characteristic distribution data and the karst cave characteristic distribution data, and establish the geological model containing natural fractures and karst caves according to the natural fracture characteristic distribution data and the karst cave characteristic distribution data; Figure 2 The figure shows a geological model containing random natural fractures and caves established based on the relevant information of the target reservoir. The horizontal axis is the length of the reservoir geological model, and the vertical axis is the width of the reservoir geological model. The linear black color is the natural fracture, and the circular black color is the cave. The model size is 100m×100m×1m, with 300 natural fractures. The length of the natural fractures is 1 to 5m and is randomly distributed. The angle between the natural fractures and the X-axis direction is 0-60° and is randomly distributed. The width of the natural fractures is 2mm, and the radial distance between the cave center and the wellbore (geometric center of the model) is 30m. There are 8 caves with a cave diameter of 5m, a matrix porosity of 0.01, and a matrix permeability of 1mD.

[0102] S3, the constructed geological model containing natural fractures and caves is Figure 3 The gridding process shown in the figure assigns the parameters calculated by the dual-scale mathematical model of S1 to the grid units and nodes of the geological model of S2 containing natural fractures and caves, and obtains a three-dimensional reservoir geological model capable of acidification numerical simulation after gridding and attribute parameter assignment;

[0103] S4, based on the geologic model after gridding and attribute parameter assignment described in S3, simulation calculation is performed; the calculation result of step 4 is plotted and displayed; the result is as follows Figure 4 , 5 , 6, and 7, Figure 4 Acidizing numerical simulation calculations were performed. At 500 s, the direction of the acid extending along the fractures and the number of acid-etched fractures were calculated. The horizontal axis was the length of the reservoir geological model, and the vertical axis was the width of the reservoir geological model. The linear black ones were natural fractures, and the circular black ones were caves. Figure 5 It is to carry out numerical simulation calculation of acidizing. At 1000s, the direction of acid extension along the fracture and the number of acid-etched fractures are shown. The horizontal axis is the length of the reservoir geological model, and the vertical axis is the width of the reservoir geological model. The linear black is the natural fracture, and the circular black is the cave. Figure 6It is to carry out numerical simulation calculation of acidification. At 1500s, the direction of the acid extending along the fracture, the number of acid-etched fractures, the orientation and number of connected caves, the horizontal axis is the length of the reservoir geological model, the vertical axis is the width of the reservoir geological model, the linear black is the natural fracture, and the circular black is the cave; Figure 7 This is the result diagram of finding holes by following the fractures when performing acidizing numerical simulation calculations. The horizontal axis is the length of the reservoir geological model, and the vertical axis is the width of the reservoir geological model. The black linear area is a natural fracture, the black circular area is a cave, and the white area is a high-pressure area, which is also the area affected by the acid. Figure 4-7 It can be seen that at the beginning of acidizing, the acid fluid preferentially communicates with the natural fractures around the well. Under the action of convection diffusion, hydrogen ions are rapidly transferred along the natural fractures. With the dissolution of the rock near the well wall, the acid fluid gradually enters the natural fractures that are slightly farther away. Finally, the acid fluid diffuses in three directions and dissolves the formation, communicating with the three caves in the extension direction of the acid dissolution fractures.

[0104] It should be noted that the above-described specific embodiments can enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail with reference to the drawings and embodiments, those skilled in the art should understand that the present invention can still be modified or replaced by equivalents. In short, all technical solutions and changes that do not deviate from the spirit and scope of the present invention should be included in the protection scope of the patent of the present invention.

Claims

1. A numerical simulation method for acidizing by following cracks and finding holes, characterized in that: The following steps are involved: S1, establishing a dual-scale mathematical model, wherein the dual-scale mathematical model includes a Darcy scale model and a pore scale model, and the pore scale model provides parameter support for the Darcy scale model; S1.1 Establishing Darcy scale model: Darcy scale model is used to describe the model of centimeter-scale to micrometer-scale porous media. The acid solution flows in centimeter-scale to micrometer-scale porous media as Darcy seepage; (1) Acid flow in the matrix The acid is injected into the formation at a certain speed. Under the convection and diffusion effects in the fluid, the hydrogen ions in the acid are transferred from the porous medium fluid to the carbonate rock surface to react, thereby changing the formation porosity and permeability. The flow of the acid in the matrix formation is controlled by Darcy's law: The fluid pressure distribution is governed by the continuity equation for incompressible fluids: The concentration distribution of hydrogen ions in the fluid is controlled by the convection diffusion equation, in which the convection diffusion equation is divided into two cases. Case 1 is that the acid does not completely dissolve the rock, that is, ε<1; Case 2 is that the acid completely dissolves the rock, that is, ε=1; The convection-diffusion equation when the acid does not completely dissolve the rock, that is, when ε<1, needs to consider the consumption of hydrogen ions on the rock surface and the change in porosity: The convection-diffusion equation for the case where the acid completely dissolves the rock, i.e., ε = 1, does not need to consider the consumption of hydrogen ions on the rock surface and the change in porosity: In the formula, is the Darcy velocity vector, m / s; k is the formation permeability, m 2 ; μ is acid viscosity, Pa·s; P is acid pressure, Pa; ε is formation porosity; t is reaction time, s; Cf is acid concentration in rock pores, mol / m 3 ; De is the acid diffusion tensor, m 2 / s; kc is the local mass transfer coefficient of acid, m / s; av is the pore area per unit volume of rock, m 2 / m 3 ; Cs is the acid concentration on the rock surface, mol / m 3 ; α is the mass of rock that can be dissolved by unit mole of acid, kg / mol; ρs is the rock density, kg / m 3 ; (2) Acid flow in cracks The flow of acid in natural fractures corresponds to different mechanisms from the flow in the matrix. The flow in natural fractures is free flow, while the flow in the matrix is ​​porous medium seepage controlled by Darcy's law. The flow of acid in natural fractures regards natural fractures as areas with high permeability based on the concept of equivalent permeability. The above mathematical model is used to study the dissolution phenomenon of acid in fractured formations, and the mesh of natural fractures that have a great influence on the pressure field is encrypted to speed up the calculation and ensure the convergence of the calculation. S1.2 establishing a pore scale model to provide parameter support including permeability, pore radius, specific surface area, porosity, diffusion tensor, and mass transfer coefficient for the Darcy scale model; S2, obtaining natural fracture characteristic distribution data and karst cave characteristic distribution data based on well logging data, core data, natural fracture occurrence data, drilling and draining data and seismic interpretation data of actual carbonate reservoirs, and establishing a geological model containing natural fractures and karst caves based on the natural fracture characteristic distribution data and karst cave characteristic distribution data; S3, gridding the constructed geological model containing natural fractures and karst caves, and assigning the parameters calculated by the dual-scale mathematical model in step 1 to the grid units and nodes of the geological model containing natural fractures and karst caves in step 2; Obtaining a reservoir geological model that can be used for acidizing numerical simulation after gridding and attribute parameter assignment; S4, performing simulation calculation on the reservoir geological model capable of acidification numerical simulation; and displaying the calculation results in a drawing; The order of S1 and S2 is adjustable.

2. The numerical simulation method for acidizing by following fractures and finding holes according to claim 1 is characterized in that: In S1.2, the pore scale model provides parameter support for the Darcy scale model, including permeability, pore radius, specific surface area, porosity, diffusion tensor, and mass transfer coefficient. The relationship between permeability, pore radius, specific surface area, and porosity includes: The formation permeability, pore radius, specific surface area and porosity are directly related. The empirical formula used to describe the relationship between formation permeability, pore radius, specific surface area and porosity is: Where, ε, k, rp, av are porosity, permeability, pore radius, and specific surface area, respectively; ε0, k0, r0, a0 are initial porosity, permeability, pore radius, and specific surface area, respectively; β is a constant related to the pore structure, and β=1; The flow velocity of the acid in the formation is very small, which can be regarded as laminar flow. The fracture can be regarded as a thin circular tube, and the circular tube laminar flow formula can be used to examine the flow rate. Where Q is the flow rate, cm 3 / s; ΔP is the driving pressure difference, 0.1MPa; D is the crack diameter, cm; A is the cross-sectional area, cm 2 ; μ is fluid viscosity, Pa·s; L is crack length, cm; The flow rate calculated using Darcy's formula is as follows: When the fracture width is 0.2 cm, the equivalent permeability corresponding to the natural fracture is calculated based on formula (6) and formula (7) as k = D2 / 32 = 125 × 10 3 μm 2 ; Let the natural fracture porosity εmax = 0.999, where ε0 = 0.05, k0 = 0.32, and substitute into formula (5) to obtain the permeability K: k and K are of the same order of magnitude, that is, from the perspective of flow resistance, it is reasonable to treat a natural fracture with a width of 0.2 cm as equivalent to a matrix with a porosity of 0.

999. For natural fractures with a width exceeding 0.2 cm, since the permeability of natural fractures is already quite high relative to the matrix, the fracture width is not a factor that limits the fracture conductivity, i.e., the product of permeability and fracture width. Therefore, the natural fracture can be treated as a fracture with a width of 0.2 cm.

3. The numerical simulation method for acidizing by following fractures and finding holes according to claim 1 or 2, characterized in that: In S1.2, the pore scale model provides parameter support for the Darcy scale model, including permeability, pore radius, specific surface area, porosity, diffusion tensor, and mass transfer coefficient. Due to the sedimentation and compaction of the stratum, the pore structure is different in the horizontal and vertical directions. The diffusion tensor includes the horizontal diffusion tensor DeX and the vertical diffusion tensor DeT.

4. The numerical simulation method for acidizing by following fractures and finding holes according to claim 3 is characterized in that: The diffusion tensor is related to the molecular diffusion coefficient Dm, the pore structure, and the flow velocity, wherein the Péclet number is a dimensionless number representing the ratio of convection to diffusion; The diffusion tensor is divided into the horizontal diffusion tensor DeX and the vertical diffusion tensor DeT. The formula is: DeX=(αos+λx·PeP)Dm (10) DeT=(αos+λT·PeP)Dm (11) Where αos is a constant related to the pore structure, αos = 0.5; λx = 0.5, λT = 0.1 obtained from core diffusion experiments; Dm is the molecular diffusion coefficient; PeP is the Peclet number, and rp is the pore radius.

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