Method and system for calculating start-up pressure gradient of tight oil reservoir under effective stress

Abstract

The present invention provides a method and system for calculating the start-up pressure gradient of a tight oil reservoir under effective stress, including: performing a force analysis on the oil-water two-phase flow in a capillary to construct a mechanical equilibrium equation; calculating and obtaining a first parameter set of the capillary; calculating and obtaining a second parameter set of the capillary under effective stress through the first parameter; substituting the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate and obtain a flow equation of the capillary; integrating the flow equation of the capillary to calculate and obtain a flow equation through a core; setting the flow in the flow equation through the core to 0, and calculating and obtaining the start-up pressure gradient of the tight oil reservoir. The mechanical equilibrium equation constructed by the present invention comprehensively considers the influence of factors such as capillary pressure, effective stress, boundary layer adsorption, viscosity, and interface molecular force potential on the start-up pressure gradient of the oil-water two-phase seepage in a tight oil reservoir, thereby realizing efficient prediction of the start-up pressure gradient of the oil-water two-phase seepage in a tight oil reservoir.

Description

Technical Field

[0001] The present invention relates to the technical field of unconventional oil reservoir resource exploitation, and in particular to a method and system for calculating a start-up pressure gradient of a tight oil reservoir under effective stress. Background Art

[0002] Unconventional oil and gas have the characteristics of abundant resources. More and more unconventional oil and gas resources (such as tight oil) occupy an increasing proportion of the world oil market. Tight oil reservoir development has become a hot spot for global unconventional oil exploration and development. However, compared with traditional oil energy, due to the small and complex pore throats, extremely low permeability, and high water saturation of tight reservoirs, the fluid flow has nonlinear characteristics, and the production is difficult and costly. In tight oil reservoirs, the fluid cannot flow when the driving pressure gradient is small. Only when the driving pressure gradient reaches a certain value, the fluid will flow. The driving pressure gradient at this time is the starting pressure gradient. Due to the existence of the starting pressure gradient, the fluid flow in dense porous media is more complicated than that in conventional reservoirs. Related experimental studies and field experiments are very time-consuming and laborious, and it is difficult to fully characterize the characteristics of the entire reservoir; numerical simulation technology has high requirements on computer performance and will be affected by numerical dispersion. In contrast, theoretical technology can avoid the above problems and well predict the starting pressure gradient value by establishing a model, which is convenient for further formulating a reasonable and efficient production plan. Therefore, theoretical technology is a very economical and efficient method to study this complex seepage process.

[0003] In order to solve the problem of predicting the start-up pressure gradient of tight oil reservoirs, existing studies have mainly used experimental methods to qualitatively analyze the relationship between core permeability and the start-up pressure gradient of tight oil reservoirs. However, the existing methods cannot mechanistically analyze the cause of the start-up pressure gradient of tight oil reservoirs and the evolution law of the start-up pressure gradient under effective stress conditions. In addition, the current theoretical model is limited by the complex pore structure of the core, with low calculation efficiency and difficulty in quantitatively characterizing the influence of factors such as effective stress, pore structure parameters, boundary layer adsorption, viscosity and interface molecular force potential on the start-up pressure gradient. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a method for calculating the start-up pressure gradient of a tight oil reservoir under effective stress, comprising the steps of:

[0005] S1: Conduct force analysis on oil-water two-phase flow in capillaries and construct mechanical equilibrium equations;

[0006] S2: Based on fractal theory, the first parameter set of the capillary is calculated;

[0007] S3: calculating and obtaining a second parameter set of the capillary under the effective stress through the first parameter;

[0008] S4: Substituting the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate and obtain the flow equation of the capillary;

[0009] S5: Integrate the flow equation of the capillary to calculate the flow equation through the core;

[0010] S6: Assume the flow rate in the flow equation through the core to be 0, and calculate the start-up pressure gradient of the tight oil reservoir.

[0011] Preferably, the expression of the mechanical equilibrium equation is:

[0012]

[0013] Where ΔP is the pressure drop; S o is the oil saturation; φ is the oil phase porosity; τ0 is the limiting shear stress; μ is the fluid viscosity; v is the fluid seepage velocity; r is the capillary radius; F is the shape factor determined by the geometric shape of the medium and the direction of fluid flow; σ is the surface tension of oil and water; is the contact angle; L t is the actual length of the capillary; δ is the thickness of the boundary layer water film; η is the interfacial molecular force potential.

[0014] Preferred:

[0015] The first parameter set includes: actual length L of the capillary t , tortuosity fractal dimension D T and the initial pore fractal dimension D f0 .

[0016] Preferably, step S3 specifically comprises:

[0017] S31: The parameter ξ is introduced to characterize the ratio of the capillary number under effective stress to the initial capillary number. The expression of ξ is:

[0018]

[0019] Among them, p cr is the critical stress, n is the deformation index, p eff is the effective stress;

[0020] S32: Calculate the maximum pore radius r under effective stress max and minimum pore radius r min , the calculation formula is:

[0021]

[0022] Among them, r max,0 is the initial maximum pore radius; r min,0 is the initial minimum pore radius; Df0 is the initial pore fractal dimension;

[0023] S33: Calculate the pore fractal dimension D under effective stress f , the calculation formula is:

[0024]

[0025] S34: Calculate the oil phase porosity φ, the calculation formula is:

[0026]

[0027] Among them, S o is the oil saturation;

[0028] S35: The second parameter set includes: oil phase porosity φ and pore fractal dimension D under effective stress f .

[0029] Preferably, step S4 is specifically:

[0030] S41: Substitute the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate the capillary flow velocity equation v, which is calculated as follows:

[0031]

[0032] Among them, D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary;

[0033] S42: The flow equation q of the capillary is obtained by calculating the flow rate equation, and the calculation formula is:

[0034]

[0035] Wherein, a is the first calculation parameter; b is the second calculation parameter; c is the third calculation parameter; d is the fourth calculation parameter; S wc is the bound water saturation.

[0036] Preferably, the calculation formulas of the first calculation parameter a, the second calculation parameter b, the third calculation parameter c and the fourth calculation parameter d are:

[0037]

[0038] d=π(1-S wc ) 3 / 2 .

[0039] Preferably, the calculation formula of the flow equation Q through the core is:

[0040]

[0041] Among them, S wc is the bound water saturation; r max is the maximum pore radius under effective stress; r min is the minimum pore radius under effective stress; D f is the pore fractal dimension under effective stress; D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary.

[0042] Preferably, step S6 specifically comprises:

[0043] Let the flow equation Q through the core be 0, and calculate the start-up pressure gradient λ of the tight oil reservoir. The calculation formula is:

[0044]

[0045] Wherein, e is the fifth calculation parameter; f is the sixth calculation parameter; S wc is the bound water saturation; r max is the maximum pore radius under effective stress; D f is the pore fractal dimension under effective stress; D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary.

[0046] Preferably, the calculation formulas of the fifth calculation parameter e and the sixth calculation parameter f are:

[0047]

[0048] A system for calculating the start-up pressure gradient of a tight oil reservoir under effective stress, comprising:

[0049] Mechanical equilibrium equation construction module, used to analyze the force of oil-water two-phase flow in capillaries and construct mechanical equilibrium equations;

[0050] A first parameter calculation module, used for calculating and obtaining a first parameter set of the capillary based on fractal theory;

[0051] A second parameter calculation module, used for calculating and obtaining a second parameter set of the capillary under the effective stress through the first parameter;

[0052] A capillary flow equation building module is used to substitute the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate and obtain the capillary flow equation;

[0053] The core flow equation building module is used to integrate the flow equation of the capillary tube and calculate the flow equation through the core;

[0054] The pressure gradient calculation module is used to set the flow rate in the flow equation through the core to 0 and calculate the start-up pressure gradient of the tight oil reservoir.

[0055] The present invention has the following beneficial effects:

[0056] The mechanical equilibrium equation constructed in the present invention comprehensively considers the influence of factors such as capillary pressure, effective stress, boundary layer adsorption, viscosity and interface molecular force potential on the starting pressure gradient of oil-water two-phase seepage in tight oil reservoirs, realizes efficient prediction of the starting pressure gradient of oil-water two-phase seepage in tight oil reservoirs, and reveals the mechanism of evolution of the starting pressure gradient of oil-water two-phase seepage in tight oil reservoirs under effective stress conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a flow chart of a method according to an embodiment of the present invention;

[0058] Figure 2 This is a conceptual physical model diagram of oil-water two-phase flow in dense porous media under effective stress;

[0059] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0060] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0061] Reference Figure 1 The present invention provides a method for calculating the start-up pressure gradient of a tight oil reservoir under effective stress, which can efficiently predict the start-up pressure gradient of a tight oil reservoir and reveal the evolution mechanism of the start-up pressure gradient of a tight oil reservoir during the fluid-solid coupling process;

[0062] Includes steps:

[0063] S1: Conduct force analysis on oil-water two-phase flow in capillaries and construct mechanical equilibrium equations;

[0064] S2: Based on fractal theory, the first parameter set of the capillary is calculated;

[0065] S3: calculating and obtaining a second parameter set of the capillary under the effective stress through the first parameter;

[0066] S4: Substituting the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate and obtain the flow equation of the capillary;

[0067] S5: Integrate the flow equation of the capillary to calculate the flow equation through the core;

[0068] S6: Assume the flow rate in the flow equation through the core to be 0, and calculate the start-up pressure gradient of the tight oil reservoir.

[0069] Furthermore, for the oil-water two-phase flow in any capillary, according to the mechanical equilibrium relationship, Figure 2 , we get the seepage balance equation:

[0070] The expression of the mechanical equilibrium equation is:

[0071]

[0072] Where ΔP is the pressure drop; S o is the oil saturation; φ is the oil phase porosity; τ0 is the limiting shear stress; μ is the fluid viscosity; v is the fluid seepage velocity; r is the capillary radius; F is the shape factor determined by the geometric shape of the medium and the direction of fluid flow; σ is the surface tension of oil and water; is the contact angle; L t is the actual length of the capillary; δ is the thickness of the boundary layer water film; η is the interfacial molecular force potential.

[0073] Specifically, the expression of the boundary layer water film thickness δ is:

[0074]

[0075] Where: S wc is the bound water saturation.

[0076] Further:

[0077] The first parameter set includes: actual length L of the capillary t , tortuosity fractal dimension D T and the initial pore fractal dimension D f0 .

[0078] Specifically, the actual length of the capillary L t The expression is:

[0079]

[0080] Where: L0 is the characteristic length of the capillary; D T is the tortuosity fractal dimension;

[0081] Tortuosity fractal dimension D T The expression is:

[0082]

[0083] Where: D f is the pore fractal dimension;

[0084] Initial pore fractal dimension D f0:

[0085] D f0 =2-ln(φ0) / ln(r min,0 / r max,0 )

[0086] Where: φ0 is the initial porosity; r max,0 is the initial maximum pore radius; r min,0 is the initial minimum pore radius.

[0087] Furthermore, based on the assumption that the pore structure of dense porous media under stress has similar characteristics, the total capillary number characterizing the unit volume is Under the action of stress, the porous medium will deform, resulting in a change in the total capillary number;

[0088] Step S3 is specifically as follows:

[0089] S31: The parameter ξ is introduced to characterize the ratio of the capillary number under effective stress to the initial capillary number. The expression of ξ is:

[0090]

[0091] Among them, p cr is the critical stress, n is the deformation index, p eff is the effective stress;

[0092] Specifically, ξ varies with effective stress p eff In general, when the effective stress is small, ξ is approximately equal to 1. When the effective stress is large, ξ changes with p. eff As the effective stress increases, the rate of decrease of ξ also increases;

[0093] S32: Calculate the maximum pore radius r under effective stress max and minimum pore radius r min , the calculation formula is:

[0094]

[0095] Among them, r max,0 is the initial maximum pore radius; r min,0 is the initial minimum pore radius; D f0 is the initial pore fractal dimension;

[0096] S33: Calculate the pore fractal dimension D under effective stress f , the calculation formula is:

[0097]

[0098] S34: Calculate the oil phase porosity φ, the calculation formula is:

[0099]

[0100] Among them, S o is the oil saturation;

[0101] S35: The second parameter set includes: oil phase porosity φ and pore fractal dimension D under effective stress f .

[0102] Furthermore, the scale is upgraded through fractal theory to obtain the flow equation of the capillary;

[0103] Step S4 is specifically as follows:

[0104] S41: Substitute the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate the capillary flow velocity equation v, which is calculated as follows:

[0105]

[0106] Among them, D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary;

[0107] S42: The flow equation q of the capillary is obtained by calculating the flow rate equation, and the calculation formula is:

[0108]

[0109] Wherein, a is the first calculation parameter; b is the second calculation parameter; c is the third calculation parameter; d is the fourth calculation parameter; S wc is the bound water saturation.

[0110] Furthermore, the calculation formulas of the first calculation parameter a, the second calculation parameter b, the third calculation parameter c and the fourth calculation parameter d are:

[0111]

[0112] d=π(1-S wc ) 3 / 2 .

[0113] Furthermore, the expression for the total flow through the core is:

[0114]

[0115] Where:

[0116] Based on the Hertz contact theory, the maximum and minimum pore sizes under effective stress are

[0117]

[0118] Where: E is the elastic modulus; υ is the Poisson's ratio; β is the power law exponent;

[0119] Practice shows that for porous media, there is min / r max <10 -2 , and 1<D f <2,1<D T <2, so 3+D T -D f >2,2+D T -D f >1,3-D f >1,0<2-D f <1;

[0120] but It can be ignored in the calculation process. In addition, due to therefore, It cannot be ignored;

[0121] make

[0122] The simplified calculation formula of the flow equation Q through the core is:

[0123]

[0124] Among them, S wc is the bound water saturation; r max is the maximum pore radius under effective stress; r min is the minimum pore radius under effective stress; D f is the pore fractal dimension under effective stress; D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary.

[0125] Furthermore, step S6 is specifically as follows:

[0126] Let the flow equation Q through the core be 0, and calculate the start-up pressure gradient λ of the tight oil reservoir. The calculation formula is:

[0127]

[0128] Wherein, e is the fifth calculation parameter; f is the sixth calculation parameter; S wc is the bound water saturation; r max is the maximum pore radius under effective stress; D f is the pore fractal dimension under effective stress; D Tis the fractal dimension of tortuosity; L0 is the characteristic length of the capillary.

[0129] Furthermore, the calculation formulas of the fifth calculation parameter e and the sixth calculation parameter f are:

[0130]

[0131] The present invention provides a system for calculating the start-up pressure gradient of a tight oil reservoir under effective stress, comprising:

[0132] Mechanical equilibrium equation construction module, used to analyze the force of oil-water two-phase flow in capillaries and construct mechanical equilibrium equations;

[0133] A first parameter calculation module, used for calculating and obtaining a first parameter set of the capillary based on fractal theory;

[0134] A second parameter calculation module, used for calculating and obtaining a second parameter set of the capillary under the effective stress through the first parameter;

[0135] A capillary flow equation building module is used to substitute the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate and obtain the capillary flow equation;

[0136] The core flow equation building module is used to integrate the flow equation of the capillary tube and calculate the flow equation through the core;

[0137] The pressure gradient calculation module is used to set the flow rate in the flow equation through the core to 0 and calculate the start-up pressure gradient of the tight oil reservoir.

[0138] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0139] The serial numbers of the embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In a unit claim that lists several means, several of these means may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order and these words may be interpreted as identifiers.

[0140] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for calculating the start-up pressure gradient of a tight oil reservoir under effective stress, characterized in that: Includes steps: S1: Conduct force analysis on oil-water two-phase flow in capillaries and construct mechanical equilibrium equations; S2: Based on fractal theory, the first parameter set of the capillary is calculated; S3: calculating and obtaining a second parameter set of the capillary under the effective stress through the first parameter; S4: Substituting the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate and obtain the flow equation of the capillary; S5: Integrate the flow equation of the capillary to calculate the flow equation through the core; S6: Set the flow rate in the flow equation through the core to 0 and calculate the start-up pressure gradient of the tight oil reservoir; The expression of the mechanical equilibrium equation is: Where ΔP is the pressure drop; S o is the oil saturation; φ is the oil phase porosity; τ0 is the limiting shear stress; μ is the fluid viscosity; v is the fluid seepage velocity; r is the capillary radius; F is the shape factor determined by the geometric shape of the medium and the direction of fluid flow; σ is the surface tension of oil and water; θ is the contact angle; L t is the actual length of the capillary; δ is the thickness of the boundary layer water film; η is the interfacial molecular force potential; The first parameter set includes: actual length L of the capillary t , tortuosity fractal dimension D T and the initial pore fractal dimension D f0 ; The second parameter set includes: oil phase porosity φ and pore fractal dimension D under effective stress f ; Step S4 is specifically as follows: S41: Substitute the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate the capillary flow velocity equation v, which is calculated as follows: Among them, D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary; S42: The flow equation q of the capillary is obtained by calculating the flow rate equation, and the calculation formula is: Wherein, a is the first calculation parameter; b is the second calculation parameter; c is the third calculation parameter; d is the fourth calculation parameter; S wc is the bound water saturation; The calculation formula of the flow equation Q through the core is: Among them, S wc is the bound water saturation; r max is the maximum pore radius under effective stress; r min is the minimum pore radius under effective stress; D f is the pore fractal dimension under effective stress; D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary.

2. The method for calculating the start-up pressure gradient of a tight oil reservoir under effective stress according to claim 1, characterized in that: Step S3 is specifically as follows: S31: The parameter ξ is introduced to characterize the ratio of the capillary number under effective stress to the initial capillary number. The expression of ξ is: Among them, p cr is the critical stress, n is the deformation index, p eff is the effective stress; S32: Calculate the maximum pore radius r under effective stress max and minimum pore radius r min , the calculation formula is: Among them, r max,0 is the initial maximum pore radius; r min,0 is the initial minimum pore radius; D f0 is the initial pore fractal dimension; S33: Calculate the pore fractal dimension D under effective stress f , the calculation formula is: S34: Calculate the oil phase porosity φ, the calculation formula is: Among them, S o is the oil saturation.

3. The method for calculating the start-up pressure gradient of a tight oil reservoir under effective stress according to claim 1, characterized in that: The calculation formulas for the first calculation parameter a, the second calculation parameter b, the third calculation parameter c and the fourth calculation parameter d are:

4. The method for calculating the start-up pressure gradient of a tight oil reservoir under effective stress according to claim 1, characterized in that: Step S6 is specifically as follows: Let the flow equation Q through the core be 0, and calculate the start-up pressure gradient λ of the tight oil reservoir. The calculation formula is: Wherein, e is the fifth calculation parameter; f is the sixth calculation parameter; S wc is the bound water saturation; r max is the maximum pore radius under effective stress; D f is the pore fractal dimension under effective stress; D T is the fractal dimension of tortuosity; L0 is the characteristic length of the capillary.

5. The method for calculating the start-up pressure gradient of a tight oil reservoir under effective stress according to claim 4, characterized in that: The calculation formulas of the fifth calculation parameter e and the sixth calculation parameter f are:

6. A system for calculating the starting pressure gradient of a tight oil reservoir under effective stress, used to implement the method for calculating the starting pressure gradient of a tight oil reservoir under effective stress as claimed in any one of claims 1 to 5, characterized in that: include: Mechanical equilibrium equation construction module, used to analyze the force of oil-water two-phase flow in capillaries and construct mechanical equilibrium equations; A first parameter calculation module, used for calculating and obtaining a first parameter set of the capillary based on fractal theory; A second parameter calculation module, used for calculating and obtaining a second parameter set of the capillary under the effective stress through the first parameter; A capillary flow equation building module is used to substitute the first parameter set and the second parameter set into the mechanical equilibrium equation to calculate and obtain the capillary flow equation; The core flow equation building module is used to integrate the flow equation of the capillary tube and calculate the flow equation through the core; The pressure gradient calculation module is used to set the flow rate in the flow equation through the core to 0 and calculate the start-up pressure gradient of the tight oil reservoir.

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