Permeability prediction methods, apparatus and computer-readable storage media

Abstract

This invention discloses a permeability prediction method, apparatus, and computer-readable storage medium. The method includes: measuring a target rock using a target measuring device to obtain multiple sets of target data; fitting the multiple sets of target data using multiple preset three-dimensional fitting functions to obtain a target three-dimensional fitting function and target coefficients within the target three-dimensional fitting function; determining a target permeability two-dimensional prediction curve based on the target coefficients and the multiple sets of target data to characterize the relationship between the permeability of the target rock and the effective stress it experiences; obtaining the target effective stress of the target rock for prediction; and determining the permeability prediction result corresponding to the target effective stress using the target permeability two-dimensional prediction curve. This invention solves the technical problems of being unable to accurately determine the effective stress of a rock based on confining pressure and pore pressure, and the insufficient accuracy of rock permeability prediction.

Description

Technical Field

[0001] This invention relates to the field of petroleum exploration and development, and more specifically, to a method, apparatus, and computer-readable storage medium for permeability prediction. Background Technology

[0002] In related technologies, there are technical problems such as the inability to accurately determine the effective stress on the rock based on confining pressure and pore pressure, and the insufficient accuracy of rock permeability prediction.

[0003] There is currently no effective solution to the above problems. Summary of the Invention

[0004] This invention provides a permeability prediction method, apparatus, and computer-readable storage medium to at least solve the technical problems of being unable to accurately determine the effective stress on a rock based on confining pressure and pore pressure, and the inaccuracy of rock permeability prediction.

[0005] According to one aspect of the present invention, a permeability prediction method is provided, comprising: measuring a target rock using a target measuring device to obtain multiple sets of target data, wherein the multiple sets of target data include: multiple sets of first-type measurement data corresponding to the target rock experiencing a fixed pore pressure and multiple changes in confining pressure within the target device; multiple sets of second-type measurement data corresponding to the target rock experiencing a fixed confining pressure and multiple changes in pore pressure within the target device; and multiple sets of permeability, wherein the multiple sets of permeability include multiple sets of first-type permeability corresponding to the multiple sets of first-type measurement data, and multiple sets of second-type measurement data corresponding to... The system obtains multiple sets of second-type permeability data; it uses multiple preset three-dimensional fitting functions to fit multiple sets of target data, obtaining the target three-dimensional fitting function and the target coefficients in the target three-dimensional fitting function. The target coefficients are used to determine the functional relationship between the confining pressure and pore pressure on the target rock and the effective stress on the target rock; based on the target coefficients and multiple sets of target data, it determines the target permeability two-dimensional prediction curve to characterize the relationship between the permeability of the target rock and the effective stress; it obtains the target effective stress for prediction of the target rock; and it uses the target permeability two-dimensional prediction curve to determine the permeability prediction result corresponding to the target effective stress.

[0006] Optionally, the target measurement device includes: a confining pressure loading and control module, a pore pressure loading and control module, a back pressure control module, a core holder, a gas flow meter, and a pressure meter.

[0007] Optionally, the multiple sets of permeability are calculated by the following method: based on multiple sets of first-type measurement data and multiple sets of second-type measurement data, using the permeability calculation formula for compressible fluids, multiple sets of first-type permeability corresponding to multiple sets of first-type measurement data and multiple sets of second-type permeability corresponding to second-type measurement data are calculated; the multiple sets of first-type permeability and multiple sets of second-type permeability are determined as the multiple sets of permeability.

[0008] Optionally, multiple preset 3D fitting functions are used to fit multiple sets of target data to obtain the target 3D fitting function and the target coefficients in the target 3D fitting function. This includes: using multiple preset 3D fitting functions to fit multiple sets of target data to obtain multiple candidate 3D fitting functions and multiple candidate coefficients corresponding to the multiple candidate 3D fitting functions; determining multiple fitting accuracy values ​​corresponding to the multiple candidate 3D fitting functions; determining the candidate 3D fitting function corresponding to the highest fitting accuracy value among the multiple fitting accuracy values ​​as the target 3D fitting function; and determining the candidate coefficients corresponding to the target 3D fitting function as the target coefficients.

[0009] Optionally, based on the target coefficient and multiple sets of target data, a two-dimensional prediction curve for target permeability is determined to characterize the relationship between the permeability of the target rock and the effective stress. This includes: determining the functional relationship between confining pressure and pore pressure and effective stress based on the target coefficient; processing the confining pressure and pore pressure in multiple sets of target data based on the functional relationship to obtain multiple sets of effective stress data; and determining the two-dimensional prediction curve for target permeability based on multiple sets of effective stress data and multiple sets of permeability.

[0010] Optionally, the target rock has a porosity higher than a first threshold and a permeability lower than a second threshold.

[0011] According to another aspect of the present invention, a permeability prediction device is also provided, comprising: a measurement module, configured to measure a target rock using a target measurement device to obtain multiple sets of target data, wherein the multiple sets of target data include: multiple sets of first-type measurement data corresponding to a target rock subjected to a fixed pore pressure and multiple changes in confining pressure in the target device; multiple sets of second-type measurement data corresponding to a target rock subjected to a fixed confining pressure and multiple changes in pore pressure in the target device; and multiple sets of permeability, wherein the multiple sets of permeability include multiple sets of first-type permeability corresponding to multiple sets of first-type measurement data and multiple sets of second-type permeability corresponding to multiple sets of second-type measurement data; The fitting module is used to fit multiple sets of target data using multiple preset three-dimensional fitting functions to obtain the target three-dimensional fitting function and the target coefficients in the target three-dimensional fitting function. The target coefficients are used to determine the functional relationship between the confining pressure and pore pressure on the target rock and the effective stress on the target rock. The determination module is used to determine the target permeability two-dimensional prediction curve based on the target coefficients and multiple sets of target data, which characterizes the relationship between the permeability of the target rock and the effective stress. The acquisition module is used to acquire the target effective stress of the target rock for prediction. The prediction module is used to determine the permeability prediction result corresponding to the target effective stress using the target permeability two-dimensional prediction curve.

[0012] Optionally, the target measurement device includes: a confining pressure loading and control module, a pore pressure loading and control module, a back pressure control module, a core holder, a gas flow meter, and a pressure meter.

[0013] According to another aspect of an optional embodiment of the present invention, a computer-readable storage medium is also provided, the computer-readable storage medium including a stored program, wherein, when the program is executed, it controls the device where the computer-readable storage medium is located to perform the penetration prediction method of any of the above.

[0014] According to another aspect of the present invention, a computer device is also provided, comprising: a memory and a processor, the memory storing a computer program; and a processor for executing the computer program stored in the memory, wherein the computer program, when executed, causes the processor to perform the penetration prediction method of any of the above-described embodiments.

[0015] In this embodiment of the invention, by using two measurement methods on the target rock (1) with constant pore pressure and multiple changes in confining pressure, and (2) with constant confining pressure and multiple changes in pore pressure, multiple sets of data and the permeability corresponding to each set of measurement data are measured. Multiple preset three-dimensional fitting functions are used to fit multiple sets of target data, and the function with the best fitting effect is selected as the target three-dimensional fitting function. Since the target three-dimensional fitting function characterizes the relationship between the permeability, confining pressure and pore pressure of the target rock, and the effective stress on the target rock can be determined by the confining pressure and pore pressure, the target coefficient in the target three-dimensional fitting function can be used to determine the relationship between the two pressures of confining pressure and pore pressure and the effective stress, and a two-dimensional prediction curve of the target permeability characterizing the relationship between the permeability of the target rock and the effective stress is obtained. Based on the two-dimensional prediction curve of the target permeability, the corresponding permeability can be predicted according to the target effective stress of the target rock, thereby solving the technical problems of not being able to accurately determine the effective stress on the rock based on the confining pressure and pore pressure, and the inaccurate prediction of the rock permeability. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0017] Figure 1 This is a flowchart of a penetration rate prediction method according to an embodiment of the present invention;

[0018] Figure 2 This is a schematic diagram of a permeability stress-sensitive experimental apparatus provided according to an optional embodiment of the present invention;

[0019] Figure 3 This is a schematic diagram illustrating the relationship between the permeability ratio and the outlet pressure according to an optional embodiment of the present invention;

[0020] Figure 4 This is a schematic diagram illustrating detailed operating steps provided by an optional embodiment of the present invention;

[0021] Figure 5a This is a schematic diagram of the fitting effect of a rock sample 1 provided by an optional embodiment of the present invention using a quadratic polynomial fitting.

[0022] Figure 5b This is a schematic diagram of the fitting effect of rock sample 1 using an exponential model according to an optional embodiment of the present invention;

[0023] Figure 5c This is a schematic diagram of the fitting effect of a second rock sample 2 using a quadratic polynomial fitting according to an optional embodiment of the present invention.

[0024] Figure 5d This is a schematic diagram of the fitting effect of rock sample 2 using an exponential model according to an optional embodiment of the present invention;

[0025] Figure 6a The curve showing the relationship between permeability and corrected effective stress after fitting a quadratic polynomial to rock sample 1 provided by an optional embodiment of the present invention is shown.

[0026] Figure 6b The curve showing the relationship between permeability and corrected effective stress after the rock sample 1 is fitted using an exponential model according to an optional embodiment of the present invention.

[0027] Figure 6c The curve showing the relationship between permeability and corrected effective stress after the rock sample 2 provided by the optional embodiment of the present invention is fitted with a quadratic polynomial.

[0028] Figure 6d The curve showing the relationship between permeability and corrected effective stress after the rock sample 2 is fitted using an exponential model according to an optional embodiment of the present invention.

[0029] Figure 7 This is a structural block diagram of a permeability prediction device provided according to an embodiment of the present invention. Detailed Implementation

[0030] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0031] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0032] Terminology Explanation

[0033] Oil reservoirs refer to rocks containing hydrocarbons in their pores or fractures. Oil reservoirs are broadly classified into conventional and unconventional reservoirs. In unconventional reservoirs, the rocks have high porosity and low permeability, which can retain hydrocarbons in situ.

[0034] Permeability refers to the ability of a rock to allow fluid to pass through it under a certain pressure difference. It is a parameter that characterizes the ability of soil or rock to conduct liquids.

[0035] Effective stress refers to the average normal stress transmitted through the interparticle contact surface of soil under load, also known as interparticle stress. It causes soil deformation and determines the shear strength. The greater the effective stress of the soil, the greater its shear strength. Shear strength refers to the ultimate strength produced when the material is sheared, reflecting the material's ability to resist shear slip.

[0036] Confining pressure refers to the pressure exerted on a rock by the surrounding rock mass.

[0037] Pore ​​pressure is equal to the liquid column pressure if the fluid in the rock pores can flow directly to the surface. If the fluid cannot flow to the surface, the pressure affecting the fluid will be greater, and the pore pressure will be equal to the pore wall pressure, which is opposite to the direction of static rock stress and tectonic stress.

[0038] According to an embodiment of the present invention, a method embodiment for penetration rate prediction is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0039] Figure 1 This is a flowchart of a penetration rate prediction method according to an embodiment of the present invention, such as... Figure 1 As shown, the method includes the following steps:

[0040] Step S102: Measure the target rock using a target measuring device to obtain multiple sets of target data. The multiple sets of target data include: multiple sets of first-type measurement data corresponding to the target rock experiencing constant pore pressure and multiple changes in confining pressure within the target device; multiple sets of second-type measurement data corresponding to the target rock experiencing constant confining pressure and multiple changes in pore pressure within the target device; and multiple sets of permeability, including multiple sets of first-type permeability corresponding to the multiple sets of first-type measurement data and multiple sets of second-type permeability corresponding to the multiple sets of second-type measurement data.

[0041] Step S104: Multiple preset three-dimensional fitting functions are used to fit multiple sets of target data to obtain the target three-dimensional fitting function and the target coefficients in the target three-dimensional fitting function. The target coefficients are used to determine the functional relationship between the confining pressure and pore pressure on the target rock and the effective stress on the target rock.

[0042] Step S106: Based on the target coefficient and multiple sets of target data, determine the two-dimensional prediction curve of target permeability to characterize the relationship between target rock permeability and effective stress.

[0043] Step S108: Obtain the target rock for prediction of the target effective stress;

[0044] Step S110: Using the two-dimensional prediction curve of the target permeability, determine the permeability prediction result corresponding to the target effective stress.

[0045] Through the above steps, the target rock is measured using two methods: (1) constant pore pressure and multiple changes in confining pressure, and (2) constant confining pressure and multiple changes in pore pressure. Multiple sets of data and the permeability corresponding to each set of data are measured. Multiple preset three-dimensional fitting functions are used to fit the multiple sets of target data, and the function with the best fitting effect is selected as the target three-dimensional fitting function. Since the target three-dimensional fitting function represents the relationship between the permeability, confining pressure and pore pressure of the target rock, and the effective stress on the target rock can be determined by the confining pressure and pore pressure, the target coefficient in the target three-dimensional fitting function can be used to determine the relationship between the two pressures of confining pressure and pore pressure and the effective stress, and a two-dimensional prediction curve of the target permeability representing the relationship between the permeability of the target rock and the effective stress is obtained. Based on the two-dimensional prediction curve of the target permeability, the corresponding permeability can be predicted according to the target effective stress of the target rock, thereby solving the technical problems of not being able to accurately determine the effective stress on the rock based on the confining pressure and pore pressure, and the inaccurate prediction of the rock permeability.

[0046] As an optional embodiment, the target measurement device includes: a confining pressure loading and control module, a pore pressure loading and control module, a back pressure control module, a core holder, a gas flow meter, and a pressure meter.

[0047] The confining pressure loading and control module can consist of a booster and a confining pressure pump, providing a maximum confining pressure of 90 MPa. The pore pressure loading and control module can consist of a gas cylinder, an intermediate container, and a pore pressure pump, providing a maximum pore pressure of 60 MPa. The back pressure control module can consist of a back pressure valve, an intermediate container, and a back pressure pump, with a back pressure control range of 0.1–60 MPa. The gas flow meter can be a soap film flow meter. The pressure meter can use either a pressure gauge or a pressure sensor. Since the experimental fluid is a gas, its pressure fluctuates significantly. Intermediate containers can be included in both the pore pressure loading system and the back pressure system to buffer and reduce pressure fluctuations.

[0048] It should be noted that by applying back pressure at the outlet of the core holder, the pore pressure state in the core holder can be made closer to that of the actual reservoir, making the measurement data more accurate.

[0049] As an optional embodiment, the multiple sets of permeability are calculated by the following method: based on multiple sets of first-type measurement data and multiple sets of second-type measurement data, using the permeability calculation formula for compressible fluids, multiple sets of first-type permeability corresponding to the multiple sets of first-type measurement data and multiple sets of second-type permeability corresponding to the second-type measurement data are calculated; the multiple sets of first-type permeability and multiple sets of second-type permeability are determined as the multiple sets of permeability. In related technologies, liquids are typically used to measure various data of rocks. In this embodiment, gas is used as the measuring fluid, and the permeability is calculated using the permeability calculation formula for compressible fluids. The permeability calculation formula for compressible fluids is as follows:

[0050]

[0051] Where, k a q represents apparent permeability or gas permeability. down The volumetric flow rate at the outlet of the seepage section of the core holder is given in m³. 3 / s; A is the seepage cross-sectional area, m 2 μ is the fluid viscosity, Pa·s; dP / dx is the pressure gradient; L is the core length, m; P up and P down These represent the fluid pressures upstream and downstream of the target rock, respectively.

[0052] As an optional embodiment, multiple preset three-dimensional fitting functions are used to fit multiple sets of target data to obtain a target three-dimensional fitting function and target coefficients in the target three-dimensional fitting function. This includes: fitting multiple preset three-dimensional fitting functions to multiple sets of target data to obtain multiple candidate three-dimensional fitting functions and multiple candidate coefficients corresponding to the multiple candidate three-dimensional fitting functions; determining multiple fitting accuracy values ​​corresponding to the multiple candidate three-dimensional fitting functions; determining the candidate three-dimensional fitting function corresponding to the highest fitting accuracy value among the multiple fitting accuracy values ​​as the target three-dimensional fitting function; and determining the candidate coefficients corresponding to the target three-dimensional fitting function as the target coefficients.

[0053] To determine a more accurate fitting function that better fits the multiple sets of target data, this embodiment uses multiple preset functions to fit the multiple sets of target data. All preset functions are three-dimensional functions, and the target function is determined using a three-dimensional surface fitting method. After obtaining multiple candidate three-dimensional fitting functions corresponding to the multiple preset three-dimensional fitting functions, the one with the best fitting effect can be selected as the target three-dimensional fitting function based on the fitting accuracy. The preset three-dimensional fitting functions can include: power-law type, exponential type, quadratic polynomial type, etc.

[0054] During the fitting process, there are unknown coefficients in the preset three-dimensional fitting function. After multiple preset three-dimensional fitting functions are fitted respectively, and multiple candidate three-dimensional fitting functions are obtained, the values ​​of the coefficients in the function are determined. Among them, the coefficients include the effective stress coefficient of permeability. After the target three-dimensional fitting function is determined, the effective stress coefficient of permeability corresponding to the target three-dimensional fitting function can be determined as the target coefficient, that is, it represents the relative magnitude of the influence of pore pressure and confining pressure on permeability. In other words, the effective stress on the rock can be determined based on the confining pressure, pore pressure and the target coefficient. Since multiple fitting functions are used for fitting in this embodiment, and the fitting is performed by a three-dimensional surface, the accuracy of the target coefficient can be well guaranteed.

[0055] As an optional embodiment, based on target coefficients and multiple sets of target data, a two-dimensional prediction curve for target permeability is determined to characterize the relationship between the permeability of the target rock and the applied effective stress. This includes: determining the functional relationship between confining pressure and pore pressure and effective stress based on the target coefficients; processing the confining pressure and pore pressure in the multiple sets of target data based on the functional relationship to obtain multiple sets of effective stress data; and determining the two-dimensional prediction curve for target permeability based on the multiple sets of effective stress data and multiple sets of permeability. After obtaining the target coefficients, the functional relationship between confining pressure and pore pressure and effective stress can be determined based on these target coefficients. That is, the corresponding effective stress can be determined based on the confining pressure and pore pressure using this functional relationship. This allows for the correction of the aforementioned multiple sets of target data, transforming the original "confining pressure-pore pressure-permeability" relationship into an "effective stress-permeability" relationship, thus obtaining the two-dimensional prediction curve for target permeability.

[0056] As an optional embodiment, the target rock has a porosity higher than a first threshold and a permeability lower than a second threshold. Porosity refers to the ratio of the sum of the volumes of all pore spaces in a rock sample to the volume of the rock sample, called the total porosity of the rock, expressed as a percentage. The first threshold can be adjusted according to practical applications; for example, a porosity higher than 15% or 20%, etc. Permeability refers to the ability of a material to allow fluid to pass through without damaging the structure of the medium. The second threshold can also be adjusted according to practical applications; for example, a permeability lower than 0.001 meters per day, etc.

[0057] Based on the above embodiments and optional embodiments, the present invention proposes an optional implementation method, which will be described below.

[0058] For the development of ultra-low permeability, high-pressure gas reservoirs, studying the evolution of reservoir stress, strain, and permeability is crucial for revealing the production patterns of unconventional tight gas reservoirs. It is generally believed that as production time increases, formation fluid pressure decreases, leading to increased effective stress on the reservoir rock, pore compression deformation, and a decrease in permeability, thus affecting oil and gas well productivity. This phenomenon of permeability changing with effective stress is called the stress-sensitivity effect. The effective stress coefficient of permeability is an important indicator characterizing the change in permeability with effective stress, and its accuracy is vital for studying the stress sensitivity of oil and gas reservoir permeability. Calculating the effective stress coefficient helps in studying the deformation patterns and seepage characteristics of reservoir rocks and is the basis for stress sensitivity evaluation, which is of great significance for oil and gas productivity evaluation and efficient development.

[0059] However, in the relevant technologies, the calculation results of the two methods for calculating the effective stress coefficient of permeability are both biased, and the obtained effective stress coefficient of permeability cannot accurately describe the law of permeability change with confining pressure and pore pressure.

[0060] To address the aforementioned issues, this invention proposes an optional implementation method for calculating the effective stress coefficient of tight sandstone permeability based on the linear effective stress law, the definition of the effective stress coefficient of permeability, and the continuity assumption. This method utilizes a three-dimensional surface to fit permeability data under different confining pressures and pore pressures, comprehensively, intuitively, and accurately describing the evolution of permeability under effective stress. It can be used to predict permeability under different confining pressures and pore pressures, providing a reference for numerical simulation and production prediction of oil and gas reservoirs.

[0061] (1) First, the experimental method for stress sensitivity testing of low-permeability tight sandstone in an optional embodiment of the present invention will be introduced:

[0062] Because the permeability of unconventional low-permeability reservoir rocks such as tight sandstone and shale is extremely low, it is very difficult to measure permeability using liquid as the flow medium, and it is easily affected by water sensitivity effect and capillary pressure. Therefore, nitrogen with a purity of 99.9% is selected as the flow medium for permeability measurement.

[0063] 1) Experimental setup

[0064] Figure 2 This is a schematic diagram of a permeability stress-sensitive experimental apparatus provided according to an optional embodiment of the present invention, as shown below. Figure 2 As shown, the device mainly includes: a confining pressure loading and control system, a pore pressure loading and control system, a back pressure control system, a core holder, a gas flow meter, and a pressure measurement system. The confining pressure loading and control system consists of a booster and a confining pressure pump, capable of providing a maximum confining pressure of 90 MPa; the pore pressure loading and control system consists of a gas cylinder, an intermediate container, and a pore pressure pump, capable of providing a maximum pore pressure of 60 MPa; the back pressure control system consists of a back pressure valve, an intermediate container, and a back pressure pump, with a back pressure control range of 0.1–60 MPa; the gas flow meter is a soap film flow meter; the pressure measurement system uses both pressure gauges and pressure sensors. Because the experimental fluid is gas, the pressure fluctuations are significant; therefore, intermediate containers are provided in both the pore pressure loading system and the back pressure system to buffer and reduce pressure fluctuations.

[0065] 2) Experimental Design

[0066] Depending on the loading method of confining pressure and pore pressure, rock permeability stress-sensitive tests can be divided into two categories: variable confining pressure tests and constant confining pressure / variable pore pressure tests. Variable confining pressure tests are generally conducted by increasing or decreasing the confining pressure while maintaining a constant pressure difference between the core inlet and outlet. Since the pressure transmission medium in the confining pressure control system is liquid, variable confining pressure operation is safe and simple, and therefore widely used. Constant confining pressure / variable pore pressure tests are conducted by increasing or decreasing the pore pressure while maintaining a constant confining pressure; the maximum pore pressure should be less than the confining pressure. Compared to variable confining pressure operation, variable pore pressure operation is more difficult and harder to stabilize, especially when the test fluid is gas. In actual reservoirs, the overlying pressure changes very little, while the formation pressure changes continuously with the oil and gas extraction process. Therefore, the constant confining pressure / variable pore pressure loading method more closely approximates the actual stress conditions of reservoir rocks. To fully understand the influence of confining pressure and pore pressure on rock permeability, both variable confining pressure and constant confining pressure / variable pore pressure loading methods are used in the tests.

[0067] 3) Experimental Procedure

[0068] Before conducting stress sensitivity tests, all samples were dried. The rock samples were then tightly wrapped in heat-shrink tubing and placed in a core holder. After the testing equipment was calibrated, the rock samples underwent aging treatment to ensure the stability of their properties. The specific steps are as follows:

[0069] 1. Apply confining pressure to 5 MPa, then increase pore pressure to 3 MPa and continue for more than 24 hours;

[0070] 2. Keep the pore pressure constant, and slowly apply the confining pressure in sequence at 5MPa, 10MPa, 15MPa, 20MPa, 30MPa, 40MPa, 50MPa, 60MPa, and 65MPa. After the pressure and flow rate stabilize, record the inlet and outlet pressure and flow rate data.

[0071] 3. Keep the pore pressure constant and slowly unload the confining pressure in sequence at 65MPa, 60MPa, 50MPa, 40MPa, 30MPa, 20MPa, 15MPa, 10MPa and 5MPa. After the pressure and flow rate stabilize, record the inlet and outlet pressure and flow rate data.

[0072] 4. Repeat steps 2 and 3 until there is no significant difference in flow rate and permeability at each measuring point.

[0073] After the aging treatment is completed, variable confining pressure tests and constant confining pressure and variable pore pressure tests are conducted according to the test plan. To improve the reliability of the experimental data and minimize experimental errors, the confining pressure and inlet / outlet pressure must be kept stable after each pressure adjustment, and the stabilization time must be no less than 1 hour before collecting experimental data.

[0074] 4) Core permeability calculation

[0075] 1. The formula for calculating the permeability of an incompressible fluid is:

[0076]

[0077] Where, k l For liquid permeability measurement m 2 ;q down The volumetric flow rate at the outlet of the seepage section of the core holder is given in m³. 3 / s; A is the seepage cross-sectional area, m 2 μ is the fluid viscosity, Pa·s; dP / dx is the pressure gradient; L is the core length, m; P up and P down These represent the fluid pressures upstream and downstream of the rock sample, respectively.

[0078] 2. The formula for calculating the permeability of compressible fluids is:

[0079]

[0080] Where, k a This refers to apparent permeability or gas permeability.

[0081] It is important to note that the volumetric flow rate measured in core permeability testing is at atmospheric pressure. When the outlet pressure is not equal to atmospheric pressure, the volumetric flow rate at atmospheric pressure must be converted to P based on the real gas law. down Volumetric flow rate under pressure.

[0082] 3. Volumetric flow rate conversion

[0083] The gas volumetric flow rate measured in the experiment is the volumetric flow rate under atmospheric pressure. In conventional permeability experiments, the core outlet pressure is atmospheric pressure, so the volumetric flow rate at the core outlet is consistent with the measured volumetric flow rate, requiring no flow conversion. However, for permeability experiments with applied back pressure, the core outlet pressure is much higher than atmospheric pressure, resulting in a significant difference between the volumetric flow rate at the core outlet and the measured volumetric flow rate. Therefore, it is necessary to convert the gas volumetric flow rate under atmospheric pressure to the volumetric flow rate under the outlet pressure. Based on the isothermal assumption and the gas state equation, we can obtain:

[0084]

[0085] Where P0 is atmospheric pressure; Z0 is the gas deviation factor at atmospheric pressure; q0 is the gas flow rate at atmospheric pressure; Z down This is the gas deviation factor under the core outlet pressure.

[0086] 4. Comparison of Permeability Calculation Methods

[0087] For the same experimental data, the permeability obtained by different calculation methods will definitely differ. The ratio of the two permeability rates is used to quantitatively analyze the difference between them:

[0088]

[0089] In the formula, n is the ratio of the two permeability rates, and its value ranges from 1 < n < 1 + (P / N)^n. up -P down The result obtained using the incompressible fluid permeability calculation formula will inevitably be greater than the result obtained using the compressible fluid permeability calculation formula, and the greater the pressure difference, the greater the difference between the two permeability values. Taking a core inlet-outlet pressure differential of 3 MPa and an outlet pressure variation range of 0.1–100 MPa, Figure 3 This is a schematic diagram illustrating the relationship between the permeability ratio and the outlet pressure according to an optional embodiment of the present invention, such as... Figure 3 As shown, when the pressure difference is constant, the two permeability values ​​tend to be consistent as the outlet pressure increases.

[0090] When the pressure difference between the inlet and outlet is small and the back pressure is large, it is feasible to use the incompressible fluid permeability calculation formula; however, considering the large range of pore pressure changes during the experiment, the gas permeability calculation in the optional embodiments of the present invention uses the compressible fluid permeability formula.

[0091] 5) Advantages of stress-sensitive experimental methods compared to related technologies

[0092] 1. In traditional stress-sensitive experiments, the pore pressure at the core outlet is atmospheric pressure. However, in the optional embodiment of this invention, back pressure is applied at the core outlet, with a maximum pressure of 60 MPa, which is more consistent with the pore pressure state of the actual reservoir.

[0093] 2. Traditional stress-sensitive experiments use variable confining pressure loading, while the optional embodiments of this invention add constant confining pressure and variable pore pressure loading, which is more in line with the stress changes in the actual mining process.

[0094] 3. Traditional permeability calculation methods do not convert volumetric flow rate. In the optional embodiment of this invention, the volumetric flow rate is first converted according to the gas state equation, and then the permeability is calculated, resulting in a more accurate calculation result.

[0095] (2) Calculation method of effective stress coefficient of permeability

[0096] 1) Problems existing in related technologies

[0097] Existing techniques for determining the effective stress coefficient of permeability use a specific relationship between permeability and effective stress function, which cannot satisfy the fitting of experimental data for all rock types. Preprocessing the raw experimental data, such as taking the mean or difference, may lead to fitting errors or even distorted analytical results.

[0098] 2) Optimization algorithm for effective stress coefficient of permeability – three-dimensional surface fitting method

[0099] 1. Mathematical Model

[0100] In an optional embodiment of the present invention, the general expression for the fitting function of rock permeability and effective stress during the three-dimensional surface fitting process is as follows:

[0101] k = f k (σ eff )=f k (σ-aP)

[0102] Among them, f k is the fitting function for permeability and effective stress; a is the fitting parameter.

[0103] The functional relationship between permeability and effective stress mainly falls into three categories:

[0104] ① Power law type

[0105] k = b(σ - aP) -c

[0106] ② Exponential type

[0107] k = ce -b(σ-aP)

[0108] ③ Quadratic polynomial type

[0109] k = b(σ - aP) 2 +c(σ-aP)+d

[0110] Where a, b, c, and d are all fitting parameters.

[0111] Assuming that the effective stress is linearly related to the confining pressure and pore fluid pressure, and that the general expression for the fitting function of rock permeability to effective stress is continuously differentiable over the stress variation range, then:

[0112]

[0113] Permeability effective stress coefficient (α) k The ratio () represents the relative magnitude of the influence of pore fluid pressure and confining pressure on permeability, that is, evaluating the contribution of two independent variables (σ, P) to a dependent variable (k). It can be expressed as the ratio of the partial derivative coefficients of the two independent variables:

[0114]

[0115] The above equation shows that by fitting the experimental data of confining pressure, pore pressure and permeability to a three-dimensional surface using a fitting function, the obtained fitting parameter 'a' is the effective stress coefficient of permeability.

[0116] 2. Applicability verification of the method

[0117] Based on the above analysis, the problem of calculating the effective stress coefficient is transformed into a problem of fitting experimental data (confining pressure, pore fluid pressure, and permeability). The following section derives the three main types of fitting functions to verify the applicability of the method.

[0118] ① Power law type

[0119]

[0120] ② Exponential type

[0121]

[0122] ③ Quadratic polynomial type

[0123]

[0124] The above analysis demonstrates that, regardless of the type of fitting function, the fitting parameter 'a' obtained by the three-dimensional surface fitting method represents the effective stress coefficient of permeability. Therefore, the three-dimensional surface fitting method has universal applicability in calculating the effective stress coefficient of permeability.

[0125] 3. Usage steps

[0126] The effective stress coefficient of permeability can be calculated using the data fitting function in numerical calculation software. Any mathematical calculation software with data fitting function can refer to these steps for calculation.

[0127] Figure 4 This is a schematic diagram of detailed operation steps provided by an optional embodiment of the present invention, such as... Figure 4 As shown, the original experimental data (permeability, confining pressure, pore pressure, etc.) are first imported into the calculation software. Different fitting functions are compiled and the fitting command is executed on the original data to obtain the fitting parameters corresponding to different functions. Finally, the fitting parameter 'a' in the optimal fitting function is selected as the effective stress coefficient of permeability. After the data fitting is completed, the statistical parameters of various fitting functions (e.g., fitting accuracy, root mean square error of permeability, residual of permeability, etc.) and the three-dimensional surface fitting image can be obtained and output.

[0128] As an example, in an optional embodiment of the present invention, stress-sensitive data from two dense sandstones are selected, and the effective stress coefficient of permeability is calculated using a three-dimensional surface fitting method. Figure 5aThis is a schematic diagram of the fitting effect of a rock sample 1 provided by an optional embodiment of the present invention using a quadratic polynomial fitting. Figure 5b This is a schematic diagram of the fitting effect of rock sample 1 using an exponential model according to an optional embodiment of the present invention; Figure 5c This is a schematic diagram of the fitting effect of a second rock sample 2 using a quadratic polynomial fitting according to an optional embodiment of the present invention. Figure 5d This is a schematic diagram of the fitting effect of rock sample 2 using an exponential model according to an optional embodiment of the present invention.

[0129] By correcting the experimental data using the effective stress coefficient obtained through the three-dimensional surface fitting method, a fitting curve of the relationship between permeability and effective stress can be obtained. Figure 6a The curve showing the relationship between permeability and corrected effective stress after fitting a quadratic polynomial to rock sample 1 provided by an optional embodiment of the present invention is shown. Figure 6b The curve showing the relationship between permeability and corrected effective stress after the rock sample 1 is fitted using an exponential model according to an optional embodiment of the present invention. Figure 6c The curve showing the relationship between permeability and corrected effective stress after the rock sample 2 provided by the optional embodiment of the present invention is fitted with a quadratic polynomial. Figure 6d The curve showing the relationship between permeability and corrected effective stress after the rock sample 2 provided by the optional embodiment of the present invention is fitted using an exponential model.

[0130] and Figures 5a-5d The comparison shows that the originally scattered data points are more convergent after correction with the effective stress coefficient, and the fitting effect is better, with correlation coefficients ranging from 0.8396 to 0.9409, and an average correlation coefficient of 0.9106. Therefore, the effective stress coefficient of permeability calculated by the three-dimensional surface fitting method can accurately evaluate the influence of confining pressure and pore pressure on permeability, and helps to more accurately describe the relationship between permeability and effective stress.

[0131] According to embodiments of the present invention, a permeability prediction device is also provided. Figure 7 This is a structural block diagram of the permeability prediction device provided according to an embodiment of the present invention, such as... Figure 7 As shown, the device includes: a measurement module 71, a fitting module 72, a determination module 73, an acquisition module 74, and a prediction module 75. The device will be described below.

[0132] Measurement module 71 is used to measure the target rock using a target measuring device to obtain multiple sets of target data. These multiple sets of target data include: multiple sets of first-type measurement data corresponding to a fixed pore pressure and multiple changes in confining pressure within the target device; multiple sets of second-type measurement data corresponding to a fixed confining pressure and multiple changes in pore pressure within the target device; and multiple sets of permeability, including multiple sets of first-type permeability corresponding to the multiple sets of first-type measurement data and multiple sets of second-type permeability corresponding to the multiple sets of second-type measurement data. Fitting module 72, connected to the measurement module 71, is used to apply multiple preset three-dimensional fitting functions to the multiple sets of target data. The fitting process yields a target three-dimensional fitting function and target coefficients within that function. These target coefficients determine the functional relationship between the confining pressure and pore pressure on the target rock and the effective stress acting on it. A determination module 73, connected to the fitting module 72, determines a two-dimensional permeability prediction curve based on the target coefficients and multiple sets of target data, characterizing the relationship between the permeability of the target rock and the effective stress. An acquisition module 74, connected to the determination module 73, acquires the target effective stress for prediction. A prediction module 75, connected to the acquisition module 74, uses the two-dimensional permeability prediction curve to determine the permeability prediction result corresponding to the target effective stress.

[0133] As an optional embodiment, the target measurement device includes: a confining pressure loading and control module, a pore pressure loading and control module, a back pressure control module, a core holder, a gas flow meter, and a pressure meter.

[0134] According to an embodiment of the present invention, a computer-readable storage medium is also provided, the computer-readable storage medium including a stored program, wherein, when the program is executed, it controls the device where the computer-readable storage medium is located to execute the penetration prediction method described above.

[0135] According to an embodiment of the present invention, a computer device is also provided, comprising: a memory and a processor, wherein the memory stores a computer program; and the processor is configured to execute the computer program stored in the memory, wherein the computer program, when running, causes the processor to execute any of the above-described penetration prediction methods.

[0136] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0137] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0138] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0139] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0140] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0141] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0142] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for predicting penetration rate, characterized in that, include: The target rock is measured using a target measuring device to obtain multiple sets of target data. These multiple sets of target data include: multiple sets of first-type measurement data corresponding to a fixed pore pressure and multiple changes in confining pressure experienced by the target rock in the target measuring device; multiple sets of second-type measurement data corresponding to a fixed confining pressure and multiple changes in pore pressure experienced by the target rock in the target measuring device; and multiple sets of permeability, wherein the multiple sets of permeability include multiple sets of first-type permeability corresponding to the multiple sets of first-type measurement data, and multiple sets of second-type permeability corresponding to the multiple sets of second-type measurement data. Multiple preset three-dimensional fitting functions are used to fit the multiple sets of target data to obtain the target three-dimensional fitting function and the target coefficients in the target three-dimensional fitting function. The target coefficients are used to determine the functional relationship between the confining pressure and pore pressure on the target rock and the effective stress on the target rock. Based on the target coefficient and the multiple sets of target data, a two-dimensional prediction curve for target permeability is determined to characterize the relationship between the permeability of the target rock and the effective stress it is subjected to. The target rock is used to predict the effective stress of the target; Using the two-dimensional permeability prediction curve of the target, the permeability prediction result corresponding to the effective stress of the target is determined.

2. The method according to claim 1, characterized in that, The target measuring device includes: The system includes a confining pressure loading and control module, a pore pressure loading and control module, a back pressure control module, a core holder, a gas flow meter, and a pressure meter.

3. The method according to claim 1, characterized in that, The multiple sets of permeability rates were calculated using the following method: Based on the multiple sets of first-type measurement data and the multiple sets of second-type measurement data, the permeability calculation formula for compressible fluids is used to calculate multiple sets of first-type permeability corresponding to the multiple sets of first-type measurement data, and multiple sets of second-type permeability corresponding to the second-type measurement data. The plurality of first-type permeability and the plurality of second-type permeability are defined as the plurality of permeability groups.

4. The method according to claim 1, characterized in that, The step of fitting the multiple sets of target data with multiple preset three-dimensional fitting functions to obtain the target three-dimensional fitting function and the target coefficients in the target three-dimensional fitting function includes: Multiple preset three-dimensional fitting functions are used to fit the multiple sets of target data to obtain multiple candidate three-dimensional fitting functions and multiple candidate coefficients corresponding to the multiple candidate three-dimensional fitting functions respectively; Determine multiple fitting accuracy values ​​corresponding to the multiple candidate 3D fitting functions; The candidate 3D fitting function corresponding to the highest fitting accuracy value among the plurality of fitting accuracy values ​​is determined as the target 3D fitting function; The candidate coefficients corresponding to the target three-dimensional fitting function are determined as the target coefficients.

5. The method according to claim 1, characterized in that, The step of determining a two-dimensional prediction curve for target permeability, based on the target coefficient and the multiple sets of target data, to characterize the relationship between the target rock permeability and the applied effective stress, includes: Based on the target coefficients, the functional relationship between confining pressure and pore pressure and effective stress is determined; Based on the aforementioned functional relationship, the confining pressure and pore pressure in the multiple sets of target data are processed to obtain multiple sets of effective stress data; Based on the multiple sets of effective stress data and the multiple sets of permeability, a two-dimensional prediction curve for the target permeability is determined.

6. The method according to any one of claims 1 to 5, characterized in that, The target rock has a porosity higher than a first threshold and a permeability lower than a second threshold.

7. A permeability prediction device, characterized in that, include: The measurement module is used to measure a target rock using a target measurement device to obtain multiple sets of target data. These multiple sets of target data include: multiple sets of first-type measurement data corresponding to a fixed pore pressure and multiple changes in confining pressure experienced by the target rock in the target measurement device; multiple sets of second-type measurement data corresponding to a fixed confining pressure and multiple changes in pore pressure experienced by the target rock in the target measurement device; and multiple sets of permeability, wherein the multiple sets of permeability include multiple sets of first-type permeability corresponding to the multiple sets of first-type measurement data and multiple sets of second-type permeability corresponding to the multiple sets of second-type measurement data. The fitting module is used to fit the multiple sets of target data using multiple preset three-dimensional fitting functions to obtain the target three-dimensional fitting function and the target coefficients in the target three-dimensional fitting function. The target coefficients are used to determine the functional relationship between the confining pressure and pore pressure on the target rock and the effective stress on the target rock. The determination module is used to determine a two-dimensional prediction curve of target permeability based on the target coefficient and the multiple sets of target data, which characterizes the relationship between the permeability of the target rock and the effective stress it is subjected to. The acquisition module is used to acquire the target rock for predicting the target effective stress; The prediction module is used to determine the permeability prediction result corresponding to the target effective stress using the two-dimensional prediction curve of the target permeability.

8. The apparatus according to claim 7, characterized in that, The target measuring device includes: The system includes a confining pressure loading and control module, a pore pressure loading and control module, a back pressure control module, a core holder, a gas flow meter, and a pressure meter.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device containing the computer-readable storage medium to perform the penetration prediction method according to any one of claims 1 to 6.

10. A computer device, characterized in that, include: Memory and processor The memory stores computer programs; The processor is configured to execute a computer program stored in the memory, wherein when the computer program is executed, the processor performs the penetration prediction method according to any one of claims 1 to 6.

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