A method for predicting effective permeability of unconventional reservoirs based on self-suction experiment

Abstract

The application discloses a kind of unconventional reservoir effective permeability prediction methods based on self-suction experiment, comprising: (1) obtaining unconventional reservoir physical property parameters, pore size distribution parameters, clay mineral basic characteristic parameters and fracturing fluid performance parameters;(2) establish unconventional reservoir self-suction micro force calculation model, including capillary force calculation model, clay mineral penetration pressure calculation model;(3) establish unconventional reservoir effective permeability model based on self-suction capacity, calculate the effective permeability of unconventional reservoir using self-suction capacity coefficient C.The application comprehensively considers the influence of tortuosity characteristics and self-suction force in unconventional reservoir, and based on Darcy's law, a theoretical model for predicting the matrix permeability of unconventional reservoir based on self-suction capacity is derived, which has the advantages of easy to obtain basic parameters, novel calculation method, small error and fast and convenient.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and natural gas development, and in particular to a method for predicting the effective permeability of unconventional reservoirs based on self-imbibition experiments. Background Art

[0002] At present, my country's ultra-deep tight sandstone gas, shale gas and other unconventional gas reservoirs have entered the stage of large-scale development. Reasonable gas field development plans are an important guarantee for increasing natural gas reserves and production. Accurately obtaining the basic physical parameters of gas reservoir rocks, especially the permeability of reservoir rocks, is the primary issue in determining whether gas reservoirs can be effectively developed. It also plays a vital basic guiding role in the evaluation of gas reservoir exploitation. The permeability of unconventional reservoirs is extremely low, and it is difficult to obtain the permeability intuitively through experiments. In addition, there are many factors affecting the experimental test process, resulting in inaccurate test values, making it difficult to accurately obtain the permeability of unconventional reservoirs. Therefore, there is an urgent need for an effective method that can accurately measure the effective permeability of unconventional reservoirs.

[0003] Research has shown that for unconventional reservoirs, the imbibition coefficient (C) is related to wettability, fluid viscosity, relative permeability, and absolute permeability. Existing techniques can determine the imbibition coefficient (C) from a simple mass water imbibition test. In this case, the measured value of the coefficient remains constant regardless of core length. This provides a way to indirectly determine the effective permeability of unconventional reservoirs through water imbibition tests. Summary of the Invention

[0004] In response to the problems existing in the prior art, the present invention provides a method for predicting the effective permeability of unconventional reservoirs based on self-imbibition experiments. Through the test results of the water absorption experiment, the present invention comprehensively considers the influence of factors such as capillary force, osmotic pressure, tortuosity, etc. in unconventional reservoirs, and based on the basic principle of capillary seepage, derives the specific relationship between permeability and self-imbibition capacity coefficient C, so that the permeability can be calculated accurately and simply.

[0005] The present invention is achieved by providing a method for predicting the effective permeability of unconventional reservoirs based on self-imbibition experiments, the method comprising the following steps:

[0006] (1) Obtain unconventional reservoir physical properties, pore size distribution parameters, basic characteristic parameters of clay minerals, and fracturing fluid performance parameters;

[0007] (2) Establishment of a calculation model for the microscopic forces of self-imbibition in unconventional reservoirs, including a capillary force calculation model and a clay mineral osmotic pressure calculation model;

[0008] (3) Establish a model for predicting the effective permeability of unconventional reservoirs based on self-imbibition capacity, and use the self-imbibition capacity coefficient C to calculate the effective permeability of unconventional reservoirs.

[0009] Preferably, in step (1), the unconventional reservoir physical property parameters include mineral composition, wetting angle, porosity, and formation temperature; the pore size distribution parameters include average pore size, tortuosity, and fractal dimension; the basic characteristic parameters of clay minerals include density and cation exchange capacity; and the fracturing fluid performance parameters include salinity, viscosity, and interfacial tension.

[0010] Preferably, the capillary force calculation model in step (2) is:

[0011]

[0012] Where:

[0013] P c —capillary force, MPa;

[0014] P e —Threshold pressure, related to the maximum aperture, MPa;

[0015] P max —Maximum capillary pressure of self-priming, related to the minimum pore diameter, MPa;

[0016] λ—constant, λ=3-D f , D f is the fractal dimension;

[0017] S or —Residual oil-water saturation;

[0018] S wi —Imbound water saturation.

[0019] Preferably, the calculation model of the clay mineral osmotic pressure in step (2) is:

[0020] P π =εE π RTΔC=εE π RT(C sh -C f ) (12)

[0021] Where:

[0022] P π —Osmotic pressure, KPa;

[0023] ε—the number of ions after solute ionization, dimensionless;

[0024] E π —Semipermeable membrane efficiency;

[0025] R—gas constant, 0.08314 (L·KPa) / (mol·K);

[0026] T—formation temperature, K;

[0027] C sh —the molar concentration of solutes in the original formation water, mol / L;

[0028] C f —The molar concentration of the solute in the external working fluid in the fracture, mol / L;

[0029]

[0030] Where:

[0031] C s —The arithmetic mean of the solute in the solution on both sides of the semipermeable membrane, mol / L;

[0032] C a —Anion concentration in the semipermeable membrane pores, mol / L;

[0033] C c —cation concentration in the semipermeable membrane, mol / L;

[0034] R is the friction coefficient ratio, which is defined as:

[0035]

[0036] Where:

[0037] f—represents the friction coefficient, and the subscripts c, a, w, and m represent cations, anions, water, and semipermeable membranes; φ C —Porosity of semipermeable membranes in clay minerals.

[0038] Preferably, the unconventional reservoir effective permeability model in step (3) is

[0039]

[0040] Where:

[0041] K—permeability, mD;

[0042] ΔP—self-priming force, MPa;

[0043] τ—pore throat tortuosity, dimensionless;

[0044] μ w —Viscosity of water phase, mPa·s;

[0045] —porosity, dimensionless;

[0046] C—Self-priming capacity coefficient,

[0047] In combination with all the above-mentioned technical solutions, the advantages and positive effects possessed by the present invention are as follows: the method for predicting the effective permeability of unconventional reservoirs based on self-imbibition experiments provided by the present invention comprehensively considers the tortuosity characteristics of unconventional reservoirs, the influence of self-imbibition forces (especially the osmotic pressure effect in clay infiltration self-imbibition flow), and based on Darcy's law, derives a theoretical model for predicting the permeability of unconventional reservoir matrices based on self-imbibition capacity. The basic calculation parameters required for the permeability prediction method provided in the present invention are easy to obtain, the self-imbibition capacity coefficient C can be fitted using the results of the water absorption experiment, and the self-imbibition coefficient itself is a parameter that characterizes the physical properties of rocks and fluids, so it is reliable to calculate the permeability using this parameter. The permeability prediction method proposed by the present invention is novel, and has been verified to have the advantages of small errors, fast and convenient use. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0049] Figure 1 3 is a curve showing the change of the self-absorption water absorption of the embodiment of the present invention over time.

[0050] Figure 2 3 is a curve showing the change of the self-priming length versus the square root of time in an embodiment of the present invention.

[0051] Figure 3 3 is a curve showing the variation of capillary force with water saturation in an embodiment of the present invention.

[0052] Figure 4 3 is a curve showing the change of effective permeability versus the square root of self-imbibition time, calculated considering different self-imbibition forces according to an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The details of the present invention can be more clearly understood by referring to the accompanying drawings and the description of the specific embodiments of the present invention. However, the specific embodiments of the present invention described herein are only for the purpose of explaining the present invention and are not to be construed as limiting the present invention in any way. Based on the teachings of the present invention, a skilled person can conceive of any possible variations based on the present invention, and such variations should be considered to fall within the scope of the present invention.

[0054] In response to the problems of the prior art, the present invention aims to provide a method for predicting the effective permeability of unconventional reservoirs based on self-imbibition capacity. This method can fully consider the tortuosity characteristics and osmotic pressure effects of unconventional reservoirs, accurately characterize the self-imbibition capacity of multi-scale pores in unconventional reservoirs, and further predict reservoir permeability. The present invention provides a method for predicting the effective permeability of unconventional reservoirs based on self-imbibition capacity, comprising the following steps:

[0055] (1) Obtain unconventional reservoir physical properties, pore size distribution parameters, basic characteristic parameters of clay minerals, and fracturing fluid performance parameters;

[0056] The unconventional reservoir physical property parameters include mineral composition, wetting angle, porosity, and formation temperature; the pore size distribution parameters include average pore size, tortuosity, and fractal dimension; the basic characteristic parameters of clay minerals include density and cation exchange capacity; and the fracturing fluid performance parameters include mineralization, viscosity, and interfacial tension.

[0057] (2) Establish a calculation model for the microscopic forces of self-imbibition in unconventional reservoirs, including a capillary force calculation model and a clay mineral permeability pressure calculation model.

[0058] Capillary force calculation model

[0059] According to the direction of capillary self-priming, there is no gravity in the horizontal direction, and self-priming is only affected by capillary force, while in the vertical direction it is affected by both capillary force and gravity. ) can predict the contribution of capillary or gravity-dominated shale self-imbibition. The calculation formula is shown in formula (1), where the numerator is the capillary force and the denominator is the gravity.

[0060]

[0061] Where:

[0062] σ—interfacial tension between two phases, mN / m;

[0063] φ—porosity, %;

[0064] K—permeability, mD;

[0065] Δρ—density difference between two phases, g / cm 3 ;

[0066] H—height of porous medium, cm;

[0067] C—Geometric dimension coefficient (round tube ≈ 0.4).

[0068] Table 1 Reciprocal classification interval of Bond number

[0069]

[0070] The value is affected by the pore size: the main pore size distribution range of conventional sandstone is >2μm; the pore size distribution range of tight sandstone is 30nm~2μm; and the pore size distribution range of shale is 0.7nm~0.1μm. The values ​​are all greater than 1, and the It is obviously greater than 5, that is, the dominant force of shale self-imbibition is capillary force, and gravity can be ignored.

[0071] The capillary force can be calculated using the LY equation, as shown in formula (2).

[0072]

[0073] Where:

[0074] P c —capillary force, MPa;

[0075] P e —Threshold pressure, related to the maximum aperture, MPa;

[0076] P max —Maximum capillary pressure of self-priming, related to the minimum pore diameter, MPa;

[0077] λ—constant, λ=3-D f , D f is the fractal dimension;

[0078] S or —Residual oil-water saturation;

[0079] S wi —Imbound water saturation.

[0080] (2) Calculation model of clay mineral osmotic pressure

[0081] In a preferred embodiment, based on the mathematical relationship of thermodynamics, the osmotic pressure calculation formula is shown in formula (3).

[0082]

[0083] Where:

[0084] P π —Osmotic pressure, KPa;

[0085] a f 、a i —are the activities of external fracturing fluid and original formation water, respectively, dimensionless, and the activity of clean water is 1;

[0086] R—gas constant, 0.08314 (L·KPa) / (mol·K);

[0087] T—formation temperature, K;

[0088] V w —The molar volume of water is 0.018 L / mol.

[0089] E π —Semipermeable membrane efficiency, the calculation formula is shown in formula (4).

[0090]

[0091] Among them, K s is the distribution coefficient of solute in the semipermeable membrane:

[0092] K s =C a / C s (5)

[0093] Where:

[0094] C s —The arithmetic mean of the solute in the solution on both sides of the semipermeable membrane, mol / L;

[0095] C a —Anion concentration in the pores of the semipermeable membrane, mol / L.

[0096]

[0097] Where:

[0098] C sh —Molar concentration of solutes in the original formation water of shale formation, mol / L;

[0099] C f —The molar concentration of solutes in the external working fluid (such as fracturing fluid) in the fracture, mol / L.

[0100] Among them, C a It can be calculated by the following formula:

[0101]

[0102] Where:

[0103] E CEC —Cation exchange capacity of clay mineral, mmol / 100g;

[0104] ρ clay —Density of clay minerals, g / cm 3 , the clay mineral composition can be obtained by whole-rock analysis and calculated by weighted average;

[0105] φ C—Porosity of the semipermeable membrane in clay minerals, that is, the porosity of clay minerals, %.

[0106] φ c =V c ×ρ clay (8)

[0107] Where:

[0108] V c —Pore volume of clay minerals in shale, cm 3 / g.

[0109] In formula (4), C c is the cation concentration in the semipermeable membrane, calculated by the following formula:

[0110] C c =C a +E CEC ρ clay (1-φ c ) (9)

[0111] In formula (4), R is the friction coefficient ratio, which is specifically defined as:

[0112]

[0113] Where:

[0114] f—represents the friction coefficient, and the subscripts c, a, w, and m represent cations, anions, water, and semipermeable membranes. ij Represents the frictional resistance between 1 mole of component i and an infinite number of components j.

[0115] The cation-water friction coefficient f can be obtained by consulting the literature cw , the friction coefficient f of the anion-water system aw ; R ca-m It can be obtained by the ratio of the hydrodynamic radius of the cation and the anion (for NaCl, R ca-m =1.8); f am It can be obtained by diffusion coefficient test. For abnormally loose semipermeable membrane, f am < <f aw For an extremely dense semipermeable membrane, the friction coefficient between the anion and the semipermeable membrane is very large, f am ≥f aw .

[0116]

[0117] From formula (11), we can see that when a f <a i When the osmotic pressure is the driving force, the external working fluid flows into the shale pores; when a f =ai When a, the osmotic pressure is 0, and the fluid neither flows in nor out; f <a i When the seepage pressure becomes resistance, the original water in the shale flows out.

[0118] In a preferred embodiment, in practical applications, the difference in salinity can be used to directly calculate the osmotic pressure of clay minerals, as shown in formula (12). It has been verified that when ΔC is less than 1 mol / L, the error of the calculated result is less than 5%:

[0119] P π =εE π RTΔC=εE π RT(C sh -C f ) (12)

[0120] Where:

[0121] ε—The number of ions after the solute is ionized, dimensionless, such as 2 for NaCl.

[0122] (3) Establish a model to predict the effective permeability of unconventional reservoirs based on self-imbibition capacity.

[0123] Calculation model of self-imbibition matrix permeability

[0124] Assuming quasi-steady-state capillary flow of the aqueous phase, fully developed laminar flow of an immiscible, incompressible Newtonian liquid in a uniform porous medium with concurrent absorption. Therefore, the average linear velocity is obtained by taking into account the effect of the tortuosity of the current path and dividing the total flow velocity (Darcy's law) by the pore area.

[0125]

[0126] Integrating the above formula yields:

[0127]

[0128] Where:

[0129] L—water phase self-priming length, mm;

[0130] K—permeability, mD;

[0131] ΔP—self-priming force, MPa;

[0132] τ—pore throat tortuosity, dimensionless;

[0133] From formula (14), it can be seen that the average self-priming length L is related to t 1 / 2 For a given porous medium and water phase, the ratio of the imbibition length to the square root of the time is a constant, and its value represents the imbibition capacity, as shown in Equation (16).

[0134]

[0135] Therefore, based on the linear relationship between the self-priming length and the square root of the self-priming time, it can be obtained:

[0136]

[0137] In the formula: C—self-priming capacity coefficient,

[0138] By rearranging Equation (17), we can obtain the permeability expression as shown in (18).

[0139]

[0140] For the flow path of fracturing fluid in unconventional reservoirs, the average tortuosity expression can be obtained:

[0141]

[0142] Let λ min / λ max =β, fractal dimension D f can be written as:

[0143] D f =d-lnφ / lnβ (20)

[0144] Where:

[0145] d—Euclidean dimension, d=2.

[0146] Formula (18) is an expression for predicting the effective permeability of unconventional reservoirs based on the relationship between the imbibition length and time.

[0147] Prediction of matrix permeability based on self-imbibition experiments

[0148] In order to obtain the value of the parameter that quantifies the rock self-imbibition capacity C, the water absorption mass is divided by the contact area with the brine to obtain the self-imbibition length. Based on the change of the water absorption mass with the self-imbibition time, the self-imbibition length change curve is obtained, which is then plotted as function, where C = 0.5k, k is the slope of the straight line segment of the self-priming curve.

[0149] Table 2 Experimental data

[0150]

[0151]

[0152]

[0153]

[0154] The fluid and core properties are shown in the table:

[0155] Table 3 Basic parameters of fracturing fluid and core

[0156]

[0157] The experiment uses shale cores. The curve of shale core water absorption versus self-imbibition time is shown in the figure below. Figure 1 As shown, the imbibition curve is processed on a double logarithmic curve to reveal two straight lines, representing the imbibition section and the diffusion section. The rock sample enters the diffusion section of the fracturing fluid at 3000 min. The Jamin effect and water lock effect in this diffusion section are enhanced, and the fracturing fluid flow relies on molecular diffusion. Therefore, experimental data from the imbibition section (<3000 min) were selected for model validation.

[0158] like Figure 2 As shown, the self-imbibition coefficient obtained by fitting the rock sample is 3×10 -5 m / s 1 / 2 Combining formula (15) with Tables 2 and 3, the capillary force of the experimental rock sample is obtained as follows: Figure 3 As shown, the osmotic pressure is 0.38 MPa. Substituting the known fracturing fluid viscosity, porosity, tortuosity, self-imbibition capacity coefficient, and self-imbibition microscopic force into formula (18), the change of shale effective permeability over time is calculated as follows: Figure 4 As shown in the figure; if the influence of osmotic pressure is ignored, the permeability value will be larger than the permeability when both osmotic pressure and capillary force are considered at the same time, indicating that the influence of osmotic pressure cannot be ignored when testing permeability through self-imbibition experiment.

[0159] The present invention has been specifically described above through examples. It is necessary to point out that these examples are merely preferred embodiments of the present invention and do not limit the present invention in any way, nor are they limited to the forms disclosed herein, and should not be construed as excluding other embodiments. Modifications and simple variations made by those skilled in the art that do not depart from the technical concept and scope of the present invention are within the scope of protection of the technical solution of the present invention.

Claims

1. A method for predicting effective permeability of unconventional reservoirs based on self-imbibition experiments, comprising the following steps: (1) Obtain unconventional reservoir physical properties, pore size distribution parameters, basic characteristic parameters of clay minerals, and fracturing fluid performance parameters; (2) Establishment of a calculation model for the microscopic forces of self-imbibition in unconventional reservoirs, including a capillary force calculation model and a clay mineral osmotic pressure calculation model; (3) Establish a model for predicting the effective permeability of unconventional reservoirs based on self-imbibition capacity, and use the self-imbibition capacity coefficient C to calculate the effective permeability of unconventional reservoirs; The capillary force calculation model in step (2) is: Where: P c —capillary force, MPa; P e —Threshold pressure, related to the maximum aperture, MPa; P max —Maximum capillary pressure of self-priming, related to the minimum pore diameter, MPa; λ—constant, λ=3-D f , D f is the fractal dimension; S or —Residual oil-water saturation; S wi —Immobilized water saturation; The calculation model of clay mineral osmotic pressure in step (2) is: P π E π RTΔC=εE π RT(C sh -C f ) (12) Where: P π —Osmotic pressure, KPa; ε—the number of ions after solute ionization, dimensionless; E π —Semipermeable membrane efficiency; R—gas constant, 0.08314 (L·KPa) / (mol·K); T—formation temperature, K; C sh —the molar concentration of solutes in the original formation water, mol / L; C f —The molar concentration of the solute in the external working fluid in the fracture, mol / L; The effective permeability model of the unconventional reservoir in step (3) is: Where: K—permeability, mD; ΔP—self-priming force, numerically equal to P c With P π The sum, MPa; τ—pore throat tortuosity, dimensionless; μ w —Viscosity of water phase, mPa·s; φ—porosity, dimensionless; C—Self-priming capacity coefficient, 2. The method for predicting the effective permeability of unconventional reservoirs based on self-imbibition experiments according to claim 1, wherein the unconventional reservoir physical property parameters in step (1) include mineral composition, wetting angle, porosity, and formation temperature; the pore size distribution parameters include average pore size and tortuosity fractal dimension; the basic characteristic parameters of clay minerals include density and cation exchange capacity; and the fracturing fluid performance parameters include salinity, viscosity, and interfacial tension.

3. The method for predicting effective permeability of unconventional reservoirs based on self-imbibition experiments according to claim 1, wherein the semipermeable membrane efficiency in formula (12) is: Where: C s —The arithmetic mean of the solute in the solution on both sides of the semipermeable membrane, mol / L; C a —Anion concentration in the semipermeable membrane pores, mol / L; C c —cation concentration in the semipermeable membrane, mol / L; R ca-w —Ratio of the coefficient of friction between cations and water to the coefficient of friction between anions and water; R ca-m - the ratio of the friction coefficient of the cation-semipermeable membrane to the friction coefficient of the anion-semipermeable membrane; R a-mw —Ratio of the friction coefficient of anion-semipermeable membrane to the friction coefficient of anion-water; φ C —Porosity of semipermeable membranes in clay minerals.

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