Rock core permeability determination method based on pressure drop method

Abstract

The invention provides a rock core permeability determination method based on a pressure drop method, and relates to the technical field of oil-gas field development, the method comprises the following steps: S1, obtaining the pore volume Vp of a rock core; s2, placing the rock core in a pressure drop method gas permeability testing device; s3, recording gas balance pressure P1 in the testing device; s4, recording process data when the pressure drops to a target value Pn; and S5, calculating the core permeability according to the obtained pressure drop data. The invention provides an efficient and universal rock core permeability determination method by improving a pressure drop method and combining a transient flow equation and an iterative algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas field development, and in particular to a method for determining core permeability based on the pressure drop method. Background Art

[0002] Core permeability is a key parameter for evaluating the seepage capacity of oil and gas reservoirs, and its accurate determination is crucial for the design of oil and gas field development plans. Traditional permeability testing methods are mainly divided into steady-state methods and unsteady-state methods, but both of these methods have significant limitations, especially in low-permeability, high-permeability cores and samples with special mineral compositions.

[0003] Traditional steady-state methods for determining permeability require a long time to stabilize the flow rate and rely on flow meters, resulting in a long test cycle and large errors for low-permeability samples. In addition, brine as the test fluid will react with clay minerals, affecting the accuracy of the results. Although existing unsteady-state methods shorten the test time, most of them do not calibrate the gas slippage effect and the Forchheimer inertial effect simultaneously, resulting in insufficient test accuracy for medium-high permeability cores.

[0004] Therefore, there is an urgent need for a method for determining core permeability based on the pressure drop method to solve the above technical problems. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for determining core permeability based on the pressure drop method, which is applicable to the rapid evaluation of the permeability of cores in oil and gas reservoirs, especially for optimizing the test efficiency and calculation accuracy of low-permeability, extra-low-permeability, high-permeability, and extra-high-permeability cores. The many technical effects that can be produced by the preferred technical solutions provided by the present invention are described in detail below.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for determining core permeability based on the pressure drop method provided by the present invention includes the following steps:

[0008] Step S1: Obtain the pore volume Vp of the core;

[0009] Step S2: Place the core in a pressure drop method gas permeability test device;

[0010] Step S3: Record the gas equilibrium pressure P1 in the test device;

[0011] Step S4: Record the process data during the pressure drop to the target value Pn;

[0012] Step S5: Calculate the core permeability according to the obtained pressure drop data.

[0013] Preferably, the obtaining of the pore volume Vp of the core includes the following steps:

[0014] Step S11: Obtain the diameter D and length L of the core.

[0015] Step S12: Connect the core to a pressure vessel with volume V1.

[0016] Step S13: Fill the container with test gas and obtain the initial pressure P1.

[0017] Step S14: Record the equilibrium pressure P2 after the gas flows into the pores of the core.

[0018] Step S15: Based on Boyle's law, calculate the pore volume Vp of the core according to the formula: P1V1 = P2(V1 + Vp).

[0019] Preferably, in step S4, it includes inducing a pressure transient and recording the process data of the pressure drop to the target value Pn, specifically including the following steps:

[0020] Step S41: Open the outlet valve of the test device to trigger the pressure drop process.

[0021] Step S42: When the upstream pressure drops to 0.85P1, continuously record the pressure-time data until the pressure drops to the target value Pn.

[0022] Preferably, in step S42, continuously recording the pressure-time data includes:

[0023] In the high-pressure stage, record once every 0.1 second;

[0024] In the low-pressure stage, record once every 0.5 second.

[0025] Preferably, the high-pressure stage includes: P > 0.5P1;

[0026] The low-pressure stage includes: P ≤ 0.5P1.

[0027] Preferably, in step S5, based on the integral form of the Forchheimer equation calibrated by transient flow slip, calculate the Klinkenberg permeability K∞, slip factor b, and Forchheimer inertial coefficient β of the core.

[0028] Preferably, in step S5, calculate the permeability parameters by iteratively solving the following equation:

[0029]

[0030] where A1 and A2 are linear regression coefficients, Pm is the average pressure, y c is the calibrated flow rate function, f FO is the Forchheimer correction factor.

[0031] Preferably, the volume V1 of the pressure vessel is V 标定 × [1 + α(T - T 标定 ))], where α is the material expansion coefficient.

[0032] Preferably, the test gas includes helium.

[0033] Preferably, the test device includes a test main body and an upstream gas manifold, a core holder, a calibration gas tank, a high-precision pressure sensor, and an outlet valve provided on the test main body.

[0034] The core permeability determination method based on the pressure drop method provided by the present invention includes step S1: obtaining the pore volume Vp of the core; step S2: placing the core in a pressure drop method gas permeability test device; step S3: recording the gas equilibrium pressure P1 in the test device; step S4: recording the process data during the pressure drop to the target value Pn; step S5: calculating the core permeability according to the obtained pressure drop data. By performing an inlet-end pressure drop test on the core to obtain pressure drop data, and using the method of solving the integral equation of the slip-calibrated Forchheimer equation for transient flow, the core permeability is obtained, and both the gas slip effect and the Forchheimer effect are considered simultaneously during the calculation of the core permeability. It is an efficient and universal core permeability determination method, and the test method is simple and the calculation result is accurate. It is applicable to the rapid evaluation of the permeability of cores in oil and gas reservoirs, especially for optimizing the test efficiency and calculation accuracy of low-permeability, extra-low-permeability, high-permeability, and extra-high-permeability cores. Description of the Drawings

[0035] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0036] Figure 1 is a flowchart of an embodiment of the core permeability determination method based on the pressure drop method of the present invention;

[0037] Figure 2 is a structural schematic diagram of the test device in the present invention. Detailed Embodiments

[0038] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be described in detail below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other implementation manners obtained by those of ordinary skill in the art without creative efforts belong to the scope protected by the present invention.

[0039] In the description of the present invention, it should also be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection", and "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0040] First, the deficiencies of the prior art will be illustrated with specific cases:

[0041] 1. Efficiency and accuracy issues of the steady-state method

[0042] The steady-state method calculates the permeability by establishing a steady flow state and using Darcy's formula. However, it relies on a long-time flow balance and requires a high-precision flowmeter.

[0043] Case 1: In the test of a shale gas reservoir core (permeability K≈0.05mD), when using the steady-state method, a pressure difference of 10MPa needs to be applied, and it takes 72 hours to obtain a stable flow rate (0.001cm 3 / s). Finally, due to the insufficient resolution of the flowmeter at low flow rates (±0.0005cm 3 / s), the deviation of the calculated permeability result reaches ±25%.

[0044] Case 2: In the test of extra-high permeability sandstone (K>500mD), in the steady-state method, since a very low pressure difference (<0.01MPa) needs to be controlled to avoid turbulence, it is difficult to maintain a steady flow state in actual operation, and the repeatability error of the test results exceeds ±15%.

[0045] 2. Defects in the theoretical models of the unsteady-state method [[ID=२६]]

[0046] Although the unsteady-state method (such as the pressure pulse decay method) shortens the test time, most models do not calibrate the gas slippage effect (Klinkenberg effect) and the Forchheimer inertial effect (Forchheimer effect) simultaneously, resulting in limited application ranges.

[0047] Case 3: For a certain tight sandstone (K≈0.1 mD), when tested by the traditional pressure pulse decay method, the calculated permeability is 40% lower than the true value due to the neglect of the slippage effect. After injecting brine into the same sample, the test value is further distorted due to the swelling of clay minerals in water.

[0048] Case 4: In the test of high-permeability carbonate rock (K = 1200 mD), the traditional unsteady-state method does not consider the inertial effect, resulting in a deviation in the fitting of the pressure decay curve, and finally the estimated permeability is 30% higher.

[0049] 3. Selection limitations of test fluids

[0050] As a commonly used test fluid, brine will undergo physical and chemical reactions with the core, especially having a significant impact on samples with a high clay mineral content.

[0051] Case 5: After testing a muddy sandstone reservoir (clay content 15%) in a certain gulf area with brine, the core swelling rate is as high as 8%, the permeability test value drops from the initial 2 mD to 0.3 mD, and the core cannot be reused.

[0052] Therefore, the existing technology has the following defects:

[0053] Low-permeability core: The steady-state method takes too long, and the unsteady-state method ignores the slippage effect, resulting in significant errors.

[0054] High-permeability core: The steady-state method is difficult to control the flow state, and the unsteady-state method ignores the inertial effect, resulting in insufficient accuracy.

[0055] Special lithology: Brine testing triggers mineral reactions, damaging the sample and distorting the results.

[0056] In response to this, this embodiment provides a method for determining core permeability based on the pressure drop method, which can meet the following requirements:

[0057] Applicable to the full permeability range: covering low-permeability (<5 mD), medium-permeability (5 - 500 mD), high-permeability (>500 mD), and extra-high-permeability (>2000 mD) cores.

[0058] Coexisting high efficiency and high precision: shortening the test time (<30 minutes), and at the same time calibrating the slippage and inertial effects through a theoretical model.

[0059] Non-destructive testing: Using an inert gas (such as helium) as the test medium to avoid fluid-core interaction.

[0060] Specifically, as Figure 1As shown, a method for measuring core permeability based on the pressure drop method. This method for measuring core permeability based on the pressure drop method is an efficient and universal method for measuring core permeability, applicable to the rapid evaluation of the permeability of cores in oil and gas reservoirs, especially for optimizing the test efficiency and calculation accuracy of low-permeability, extra-low-permeability, high-permeability, and extra-high-permeability cores. The specific steps are as follows:

[0061] Step S1: Obtain the pore volume Vp of the core;

[0062] In this embodiment, the pore volume measurement is based on Boyle's law, and rapid and accurate measurement is achieved through the compressibility of gas in a closed system, providing a reference parameter for subsequent pressure drop data.

[0063] The specific steps are as follows:

[0064] Step S11: Obtain the diameter D and length L of the core; Specifically, in this embodiment, the core (diameter D, length L) is dried to a constant weight to avoid the influence of residual liquid in the pores on the test.

[0065] Step S12: Connect the core to a pressure vessel with volume V1; Specifically, in this embodiment, the core is connected to a pressure vessel with a known volume (V1) to ensure the system tightness.

[0066] Step S13: Fill the container with the test gas and obtain the initial pressure P1; Specifically, in this embodiment, the test gas includes helium, and the initial pressure is denoted as P1.

[0067] Step S14: Record the equilibrium pressure P2 after the gas flows into the pores of the core; Specifically, during the measurement, first open the connection valve to allow the gas to freely flow into the pores of the core, and the system pressure gradually drops to the equilibrium state, and record the pressure P2 at this time.

[0068] Step S15: Based on Boyle's law, according to the formula: P1V1 = P2(V1 + Vp), calculate the pore volume Vp of the core.

[0069]

[0070] Among them, P1 is the initial pressure (MPa), P2 is the pressure after connection (MPa), V1 is the volume of the pressure vessel (cm 3 ), V P is the pore volume of the core (cm 3 ).

[0071] It should be noted that during the measurement process, the errors are controlled, including:

[0072] A. Use a high-precision pressure sensor (resolution ±0.01MPa) to ensure the accuracy of P1 and P2 measurements.

[0073] B. Repeat the experiment multiple times and take the average value to reduce random errors.

[0074] C. When calibrating the container volume V1, consider temperature compensation (V1 = Vcalibration × [1 + α(T - Tcalibration)], where α is the material expansion coefficient).

[0075] Step S2: Place the core in the pressure drop method gas permeability test device;

[0076] As Figure 2 shown, the test device in this embodiment includes a test main body and a core holder 1, an upstream gas manifold 2, a calibration gas tank 3, a high-precision pressure sensor, and an outlet valve 4 provided on the test main body. [[ID=!3]]

[0077] Step S3: Record the gas equilibrium pressure P1 in the test device;

[0078] Step S4: Record the process data during the pressure drop to the target value Pn; including triggering a pressure transient and recording the process data during the pressure drop to the target value Pn, which specifically includes the following steps:

[0079] Step S41: Open the outlet valve of the test device to trigger the pressure drop process;

[0080] Specifically, during measurement, quickly open the outlet valve to release the gas from the outlet end of the core to the atmosphere and trigger the pressure drop process.

[0081] Step S42: When the upstream pressure drops to 0.85P1 (for example, when P1 = 3 MPa, the trigger point is 2.55 MPa), start continuously recording the pressure-time data until the pressure drops to the target value Pn (usually the ambient pressure or a preset cut-off pressure).

[0082] To ensure that the data density adapts to different pressure gradients, the acquisition interval is set as follows: record once every 0.1 second during the initial high-pressure stage (P > 0.5P1); record once every 0.5 second during the low-pressure stage (P ≤ 0.5P1).

[0083] Step S5: Calculate the core permeability based on the obtained pressure drop data.

[0084] In this embodiment, the permeability parameter is calculated by iteratively solving the following equation:

[0085]

[0086] where A1 and A2 are linear regression coefficients, Pm is the average pressure, y c is the calibration flow rate function, and f FO is the Forchheimer correction factor.

[0087] Specifically, in this embodiment, based on the transient flow slip calibration of the integral form of the Forchheimer equation, the core Klinkenberg permeability K∞, the slip factor b, and the Forchheimer inertial coefficient β are calculated.

[0088] By solving the integral form of the slip-calibrated Forchheimer equation, the Klinkenberg permeability K∞, the slip factor b, and the inertial coefficient β are calculated simultaneously, improving the test accuracy across the entire permeability range.

[0089] Before calculation, the experimental basic parameters need to be input: core size (D, L), gas viscosity μ, temperature T, upstream volume VT, and pressure data: the selected Pn-tn sequence.

[0090] The definitions and calculation steps of the key parameters include:

[0091] 1) Initial parameter setting:

[0092] Initial value of the slip factor:

[0093]

[0094] Among them,

[0095] VT is the upstream volume, calibrated by the experimental device.

[0096] 2) Forchheimer correction factor: Set fFO = 0.95 for the first iteration

[0097] 3) Variable calculation:

[0098] Average pressure:

[0099]

[0100] Among them, Gas compressibility factor:

[0101]

[0102] (For helium at 25°C, Bz = 4×10 -5 , Cz = -7×10 -10 )

[0103] Calibrated flow rate function:

[0104]

[0105] Among them, Gm is the nonlinear correction function.

[0106]

[0107] 3) Linear regression and iterative optimization:

[0108] Rewrite the equation into the linear form Yn = A1 + A2Xn, and fit A1 and A2 by the least squares method. 4) Calculate NFO and fFO:

[0109]

[0110]

[0111] 5) Repeat step 3) and step 4). Stop when the difference between two consecutive fFO values ≤ 0.001 (usually converges within 3 iterations).

[0112] 6) Calculate the standard error SE

[0113]

[0114] 7) Select a new b value, which is 10% larger than the first estimated value;

[0115] 8) Use the latest calculated set of fFO and the new b value to repeat steps 3) to 6);

[0116] 9) If the new SE value is lower than the previous value, then increase the b value by 10%, otherwise, decrease the original b value by 10%, and repeat step 8);

[0117] 10) Obtain the minimum SE value. This step is equivalent to obtaining the optimal b, A1, and A2 values by the least squares method. Calculate k∞ and β according to A1 and A2 respectively

[0118]

[0119] Among them,

[0120] C1 = 6.8046 * 10 -2

[0121] C2 = 1000

[0122] C3 = 3.2379 * 10 -8

[0123] R = 1205.8

[0124]

[0125] This core permeability measurement method based on the pressure drop method can obtain K∞, b, and β in a single experiment, avoiding the multi-step testing of traditional methods. It can achieve the synchronous solution of multiple parameters and uses a high-precision iterative algorithm. Through the nonlinear correction factor fFO and least squares optimization, the coupling error between the slippage effect and the inertial effect is significantly reduced. At the same time, it has wide applicability. The gas compressibility factor Zn and the temperature compensation term introduced in the formula ensure the test accuracy under high temperature and high pressure conditions. And modular gas cylinders and high-sensitivity pressure sensors are used to achieve rapid adaptation for a wide range of permeabilities (0.001 mD to 10 D).

[0126] The following takes a low-permeability sandstone core (L = 4.654 cm, D = 3.797 cm) as an example:

[0127] Pore volume measurement:

[0128] Initial pressure P1 = 5240.9106 psi, pressure after connection P2 = 163.7124 psi, container volume V1 = 337.0874 cm 3 , substituting into the formula gives V p = 10.4173 cm 3 .

[0129] Pressure drop test:

[0130] Equilibrium pressure P1 = 203.2104 MPa. After opening the outlet valve, record the time series data of the pressure drop to 0.85P1 (174.299 psi).

[0131]

[0132]

[0133] Parameter calculation:

[0134] Initial setting b = 0.803×(D2 / μHe·L·y_cm)^0.467 = 3.24,

[0135] After 6 iterations of convergence, finally

[0136] K∞ = 31.307 mD,

[0137] b = 5.605 psi,

[0138] β = 9.70E+07 ft -1 ,

[0139] Standard error SE = 0.018.

[0140] This core permeability determination method based on the pressure drop method is a non-steady state testing technique. It conducts a pressure drop test on the inlet end of the core to obtain pressure drop data, and calculates the core permeability by solving the integral equation of the slip-calibrated Forchheimer equation for transient flow. During the calculation of core permeability, both the gas slip effect and the Forchheimer effect are considered. Therefore, for low-permeability, extra-low-permeability, medium-permeability, high-permeability, and extra-high-permeability samples, their permeabilities can be quickly and accurately measured. The testing method is simple and the calculation results are accurate.

[0141] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for determining the core permeability based on the pressure drop method, characterized in that It includes the following steps: Step S1: Obtain the pore volume Vp of the core; Step S2: Place the core in a pressure-drop method gas permeability testing device; Step S3: Record the gas equilibrium pressure P1 in the testing device; Step S4: Record the process data during the pressure drop to the target value Pn; Step S5: Calculate the core permeability based on the obtained pressure drop data.

2. The core permeability measurement method based on the pressure drop method according to claim 1, characterized in that: The obtaining of the pore volume Vp of the core includes the following steps: Step S11: Obtain the diameter D and length L of the core; Step S12: Connect the core to a pressure vessel with a volume of V1; Step S13: Fill the container with a test gas and obtain the initial pressure P1; Step S14: Record the equilibrium pressure P2 after the gas flows into the pores of the core; Step S15: Based on Boyle's law, calculate the pore volume Vp of the core according to the formula: P1V1 = P2(V1 + Vp).

3. The method for determining core permeability based on the pressure drop method according to claim 2, characterized in that: In Step S4, it includes inducing a pressure transient and recording the process data during the pressure drop to the target value Pn, specifically including the following steps: Step S41: Open the outlet valve of the testing device to trigger the pressure drop process; Step S42: When the upstream pressure drops to 0.85P1, continuously record the pressure-time data until the pressure drops to the target value Pn.

4. The method for measuring core permeability based on the pressure drop method according to claim 3, characterized in that: In Step S42, the continuous recording of the pressure-time data includes: In the high-pressure stage, record once every 0.1 second; In the low-pressure stage, record once every 0.5 second.

5. The core permeability determination method based on the pressure-drop method according to claim 4, wherein: The high-pressure stage includes: P > 0.5P1; The low-pressure stage includes: P ≤ 0.5P1.

6. The method for determining core permeability based on the pressure drop method according to any one of claims 1-5, characterized in that: In Step S5, based on the integral form of the Forchheimer equation calibrated by transient flow slip, calculate the Klinkenberg permeability K∞, slip factor b, and Forchheimer inertia coefficient β of the core.

7. The core permeability measurement method based on the pressure drop method according to claim 6, characterized in that: In Step S5, calculate the permeability parameters by iteratively solving the following equation: where A1 and A2 are linear regression coefficients, Pm is the average pressure, y c is the calibration flow rate function, and f FO is the Forchheimer correction factor.

8. The method for determining the core permeability based on the pressure drop method according to any one of claims 2-5, characterized in that: The volume V1 of the pressure vessel is V1 = V 标定 × [1 + α(T - T 标定 ), where α is the material expansion coefficient.

9. The method for measuring the core permeability based on the pressure drop method according to any one of claims 2-5, characterized in that: The test gas includes helium.

10. The method for determining the core permeability based on the pressure drop method according to any one of claims 1-5, characterized in that: The testing device includes a test main body and an upstream gas manifold, a core holder, a calibration gas tank, a high-precision pressure sensor, and an outlet valve provided on the test main body.

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