Water-containing gas reservoir dynamic reserve calculation method based on material balance

Abstract

The invention belongs to the technical field of gas reservoir development, and particularly relates to a water-containing gas reservoir dynamic reserve calculation method based on material balance. Comprising the following steps: S1, constructing a model of rock compressibility coefficient changing along with water saturation and effective stress; s2, on the basis of a starting pressure gradient experiment, constructing a model that starting pressure gradients of the cores with different permeability change along with water saturation and formation pressure; s3, constructing a gas seepage motion model; s4, constructing a water-containing gas reservoir material balance model; s5, predicting the dynamic reserves of the water-containing gas reservoir based on the models constructed in the steps S1 to S4; the method realizes simple and accurate calculation of the dynamic reserves of the gas reservoir, and is of great significance to correct evaluation of the development effect of the gas reservoir, accurate prediction of the development dynamics of the gas reservoir and well-made development planning of the gas reservoir.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of gas reservoir development, and particularly relates to a water-containing gas reservoir dynamic reserve calculation method based on material balance. BACKGROUND

[0002] China is rich in tight sandstone gas reservoirs, and gas reservoirs are often accompanied by a certain amount of water, which occupies a part of the pore space of the gas reservoir. During the depletion development of such gas reservoirs, macroscopic water lock phenomenon and microscopic water sealing gas effect may occur, resulting in loss of productivity and dynamic reserve of the gas reservoir / gas well, thereby affecting the recovery ratio and the final development effect of the gas reservoir. It is of great significance to study and accurately determine the dynamic reserve of the gas reservoir for the production of the gas reservoir, and is very important for the calculation of the reservoir gas well production, dynamic analysis and numerical simulation. The study of the dynamic reserve of the water-containing gas reservoir is also conducive to timely adjustment of the production plan in the middle and late stages of the gas reservoir and improvement of the recovery ratio of the gas reservoir.

[0003] At present, there are many gas reservoir reserve calculation methods, mainly including the material balance method, the pressure drop well test method, the pressure recovery well test method and the like. In low-permeability gas reservoirs, the application of these conventional reserve calculation methods needs to adapt to relatively harsh conditions or needs to be modified in a complex manner, and needs to be tested for a long time, which brings many inconveniences to the field application. The patent document with the publication number CN110219624A discloses a method for determining the parameters of a water-driven gas reservoir under the conditions of rock pore shrinkage and bound water expansion. This method only considers rock pore shrinkage and bound water expansion to determine the dynamic reserve of the gas reservoir, and does not consider the influence of the change of the starting pressure with the degree of exploitation on the dynamic reserve. The patent document with the publication number CN118469334A discloses a full gas reservoir dynamic reserve equivalent evaluation method. This method is only applicable to homogeneous gas reservoirs, and has poor adaptability to water-driven gas reservoirs with strong heterogeneity or low-permeability gas reservoirs. The patent document with the publication number CN117669397A discloses an evaluation method for the reserve and production of a strong heterogeneity carbonate rock gas reservoir. This method relies on a pseudo-pressure equation and a flowing material balance equation, needs to fit and normalize parameters, needs a large amount of production data and early well test results, and has a complex calculation process, needs to modify the equation multiple times and draw a chart for comparison, and is cumbersome to operate. The patent document with the publication number CN108612525A discloses a gas reservoir dynamic reserve calculation method, and the patent document with the publication number CN119572215A discloses a deepwater gas reservoir dynamic reserve calculation method. These two methods do not mention the starting pressure gradient and stress sensitivity of the gas reservoir, which may significantly increase the error of the calculation result. The starting pressure gradient and stress sensitivity may change during the development process, causing the inaccuracy of the dynamic reserve result, and therefore a dynamic reserve calculation method considering the dynamic change of the starting pressure gradient and stress sensitivity is needed. SUMMARY

[0004] The purpose of the present application is to solve the problems existing in the prior art calculation method, and to provide a multi-physical coupling reserve calculation method with unsteady seepage response and dynamic evolution. The method builds a rock compression coefficient and a starting pressure gradient model controlled by water saturation and effective stress, combines the productivity equation and the deformation material balance equation, forms a dynamic reserve calculation method that evolves dynamically in real time with production, and ensures accurate and reasonable evaluation of the dynamic reserves of water-driven gas reservoirs, providing data support and theoretical basis for gas reservoir development.

[0005] To achieve the above technical purposes, the present application adopts the following technical solutions: Step S1: establish the relationship between the rock compression coefficient and the stress sensitivity coefficient: (7) Obtain reservoir core samples, build a stress sensitivity experiment device (which can be built according to the method disclosed in the patent document with the publication number CN115200977A and the invention name of Core Stress Sensitivity Evaluation Device and Method under High Temperature and High Pressure Conditions), determine the permeability variation law of the core under different effective stresses and initial water saturation, and build a model of rock stress sensitivity varying with water saturation and stress based on the experimental results: (1) The transformed deformation is the equation of the rock compression coefficient with water saturation and effective stress: (2) In the formula: C p The compression coefficient of the rock is MPa -1 ; K 0 is the original permeability of the rock, mD; K is the permeability of the rock under different effective stresses, mD; S w is the water saturation, %; Δσ is the differential pressure (the differential pressure between the confining pressure and the pore pressure, also known as the effective stress), MPa; a, b is a constant.

[0006] Step S2: obtain reservoir core samples, build a starting pressure gradient experiment device (which can be built by referring to the method disclosed in Ding Jingchen, Yang Shenglai, Shi Yunqing, et al. Experimental study on dynamic starting pressure gradient of tight gas reservoirs [J]. Oil and gas geology and recovery efficiency, 2017, 24(05): 64-69. DOI: 10.13673 / j.cnki.cn37-1359 / te.2017.05.010.), determine the starting pressure gradient variation law of the core permeability and water saturation under different formation pressures, and build a model of the starting pressure gradient of different permeability cores varying with water saturation and formation pressure based on the experimental results: (3) In the formula: P e Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants.

[0007] Step S3: Establish the gas seepage motion equation considering the threshold pressure gradient as: (8) (9) Put formula (9) into formula (8), integrate both sides, and obtain the gas seepage motion model: (4) In the formula: μ Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. v Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. P wf Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. P e Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. r w Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. r e Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. Q Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. 3 Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. Z Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. h Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. d Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. In Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. Step S4: Establish the water-bearing gas reservoir material balance equation considering the conditions of rock pore shrinkage and bound water expansion, which can be expressed as: (10) i=1,2,…,t (11) Convert to the deformed to obtain the water-bearing gas reservoir material balance model: (5) In the formula: (12) (13) (14) In the formula, G p Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. 3 ; B g0 Pf is the formation pressure, MPa; λ is the threshold pressure gradient, MPa / m; c, d, e, and f are constants. Bg is the gas volume coefficient of the gas reservoir; W is the water content of the gas reservoir, m 3 ; W p is the cumulative water production of the gas reservoir, m 3 ; B w0 is the volume coefficient of the original water in the gas reservoir; B w is the volume coefficient of produced water in the gas reservoir; G is the dynamic reserves of the gas reservoir to be tested, m 3 ; C w is the bound water expansion coefficient, MPa -1 ; is the reservoir pressure drop, MPa; P e0 is the original formation pressure of the gas reservoir, MPa; P ei is the formation pressure at a certain moment of gas reservoir production, MPa; ω is the water storage volume coefficient; P sc is the ground standard pressure, MPa; T is the gas reservoir temperature, °C; T sc is the standard ground temperature; Z 0 is the natural gas deviation factor under original conditions; During the development process, the formula for the change of water saturation of gas reservoir is: (6) In the formula V p is the pore volume of the gas reservoir.

[0008] Step S5: Predicting the dynamic reserves of water-bearing gas reservoirs: The above equations are combined to form a dynamic prediction model for low-permeability gas reservoirs. By combining them, parameters such as production and pressure that change over time can be solved. Solving the dynamic prediction model mainly includes five steps: S51. Calculate the cumulative gas production of the gas reservoir based on the actual production data of the gas reservoir to be predicted, i.e., the gas production and water production in the previous time period. G p and cumulative water production W p , calculate the current water saturation of the gas reservoir according to formula (6) S W .

[0009] S52, assuming that the formation pressure is P ei Calculate the reservoir permeability at this time according to formula (1) (2) Kand rock compressibility C p The starting pressure gradient λ is calculated according to formula (3).

[0010] S53, K, C p , λ and P ei The bottom hole flowing pressure is obtained by substituting formula (4), and is compared with the measured bottom hole flowing pressure. If | ΔP | < 0.001, step S54 is performed. P wf计算 - P wf实际 If | ΔP | ≥ 0.001, step S52 is returned to, and the value of K, P wf计算 - P wf实际 is re-adjusted until | ΔP | < 0.001. P ei - P wf计算 - P wf实际 ; S54, the formation pressure P ei , the current water saturation of the gas reservoir S W 、 The cumulative gas production of the gas reservoir G p 、 The cumulative water production of the gas reservoir W p The dynamic reserve of the gas reservoir to be measured is calculated by substituting formula (5). G ; S55, steps S51-S54 are repeated to calculate the dynamic reserve of the gas reservoir at different time, until the value t reaches the given prediction time, or the bottom hole flowing pressure is lower than the given bottom hole abandoned flowing pressure, or the gas well production Q is lower than the given gas well limit production.

[0011] Compared with the prior art, the present application has the following beneficial effects: The present method does not need to shut down the gas well for the whole gas reservoir to obtain the formation parameters. Without affecting the production plan of the gas well, only the existing production data of the gas reservoir is processed and analyzed, and the stress sensitive and starting pressure gradient dynamic change model is established through experiments to obtain the rock compressibility and starting pressure gradient at different development stages, and then the single well dynamic reserve is obtained. The present application realizes the simple and accurate calculation of the dynamic reserve of the gas reservoir, which is of great significance for correctly evaluating the development effect of the gas reservoir, accurately predicting the development dynamics of the gas reservoir and making the development plan of the gas reservoir. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1This is a schematic diagram of the material balance principle and material balance equation for water drive gas reservoirs; Figure 2 Schematic diagram of starting pressure gradient under different formation pressures and water saturations; Figure 3 Schematic diagram of stress sensitivity curve under different formation pressure and water saturation; Figure 4 Flow chart for calculating dynamic reserves of water-bearing gas reservoirs; Figure 5 Comparison of dynamic geological reserves calculated using different methods. DETAILED DESCRIPTION

[0013] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings.

[0014] Example 1 This embodiment discloses a method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance. Figure 4 As shown, the following steps are included: Step S1: The relationship between rock compressibility and stress sensitivity was established (7). Core samples were obtained from the target gas reservoir, and a stress sensitivity experimental device was constructed to simulate different effective stress conditions (e.g., 5 MPa, 10 MPa, 15 MPa, 20 MPa, etc.). The permeability of the core was measured under different effective stresses and initial water saturations (e.g., 35%, 45%, 55%, 65%). The values ​​of constants a and b were determined by fitting equation (1) based on the experimental data: (7) (1) The transformed deformation is the equation of rock compressibility as a function of water saturation and effective stress: (2) Where: C p is the compression coefficient of rock, MPa -1 ; K 0 is the original permeability of rock, mD; K is the permeability of rock under different effective stresses, mD; S w is water saturation, %; Δσ is the pressure difference, MPa; a, b is a constant.

[0015] Step S2: The same core sample is used to build a starting pressure gradient experimental device to simulate different formation pressures (such as 10 MPa, 15 MPa, 20 MPa, and 25 MPa) and water saturation conditions. The starting pressure gradient values under different conditions are recorded. According to the experimental data fitting formula (3), a dynamic change model of the starting pressure gradient with the formation pressure and water saturation is established.

[0016] (3) In the formula: P e P is the formation pressure, MPa; λ is the starting pressure gradient, MPa / m; c, d, e, and f are constants, which are determined according to the experimental data fitting formula (3).

[0017] Step S3: The gas seepage motion equation considering the starting pressure gradient is established as: (8) (9) The formula (9) is brought into the formula (8), and the integral of both sides is obtained: (4) In the formula: μ μ is the fluid viscosity, mPa·s; v v is the seepage velocity, m / s; P wf Pwf is the bottom hole flowing pressure, MPa; P e P is the formation pressure, MPa; r w r is the wellbore radius, m; r e ro is the drainage radius, m; Q Q is the gas well production, m 3 / d; Z Z is the natural gas deviation factor; h h is the reservoir thickness, m; d is the differential; In ln is the natural logarithm function. Step S4: According to the type of gas reservoir, the node state analysis is performed, and the water-bearing gas reservoir material balance equation considering the conditions of rock pore shrinkage and bound water expansion (such as shown in Figure 1 ) is established: (10) i=1, 2, …, t (11) Transformed into the deformed material balance equation: (5) In the formula: (12) wherein, G p is the cumulative gas production of the gas reservoir, m 3 ; B g0 is the gas original volume factor of the gas reservoir; B g is the gas volume factor of the gas reservoir; W is the water content of the gas reservoir, m 3 ; W p is the cumulative water production of the gas reservoir, m 3 ; B w0 is the original water volume factor of the gas reservoir; B w is the produced water volume factor of the gas reservoir; G is the dynamic reserve of the gas reservoir to be measured, m 3 ; C w is the irreducible water swelling coefficient, MPa -1 ; ∆P is the pressure drop of the gas reservoir, MPa; P e0 is the original formation pressure of the gas reservoir, MPa; P ei is the formation pressure at a certain time of the gas reservoir, MPa; ω is the water storage volume factor; P sc is the standard ground pressure, MPa; T is the temperature of the gas reservoir, ℃; T sc is the standard ground temperature.

[0018] During the development process, the change formula of the water saturation of the gas reservoir is: (6) wherein Vp is the pore volume of the gas reservoir.

[0019] Step S5: According to the above equation combination, a dynamic prediction model of the low-permeability gas reservoir is formed, and the yield and pressure parameters changing with time can be solved by simultaneous equations. The solution of the dynamic prediction model mainly includes 5 steps: S51, according to the gas production and water production of the last time period, the cumulative gas production and cumulative water production are calculated, and the current water saturation is calculated according to formula (6).

[0020] S52, assuming that the formation pressure at this time is P ei , the reservoir permeability K and rock compressibility C p at this time are calculated according to formula (1) (2), and the starting pressure gradient λ is calculated according to formula (3).

[0021] S53, bring K and λ and formation pressure into formula (4) to calculate the bottom hole flowing pressure, compare with the measured bottom hole flowing pressure, if |P wf计算 - P wf实际 < 0.001, then the formation pressure P ei is obtained, otherwise continue to iterate calculation.

[0022] S54, bring the formation pressure into formula (5) to calculate the dynamic reserves.

[0023] S55, repeat steps S51-S54 to calculate the dynamic reserves at different times until t reaches the given prediction time, or the bottom hole flowing pressure is lower than the given bottom hole abandoned flowing pressure, or the daily gas production Q is lower than the given gas well limit production.

[0024] Example 1, taking the gas well in Dongsheng gas field on the eastern margin of Ordos Basin as an example to illustrate the use of the method of the application to calculate the dynamic reserves of tight water-bearing gas well.

[0025] Step one: test and collect basic geological parameters, including original formation pressure, gas reservoir temperature, water saturation, reservoir permeability, reservoir thickness, wellbore radius, drainage radius, etc., as shown in Table 1.

[0026] Table 1. Gas well basic geological parameter table

[0027] Step two: obtain reservoir core samples, build stress sensitive experimental device, set confining pressure 29MPa, pore pressure 24MPa, 19MPa, 14MPa, 9MPa, core water saturation 35%, 45%, 55%, 65%, measure the change rule of permeability under different effective stress and initial water saturation, and build a model of rock stress sensitivity changing with water and stress based on the experimental results as shown in Figure 3 .

[0028] Step three: obtain reservoir core samples, build starting pressure gradient experimental device, set pore pressure 10MPa, 15MPa, 20MPa, 25MPa, confining pressure 3MPa higher than pore pressure, core water saturation 35%, 45%, 55%, 65%, measure the change rule of starting pressure gradient under different formation pressure and water saturation of different permeability cores, and build a model of reservoir core starting pressure gradient changing with water saturation and formation pressure based on the experimental results as shown in Figure 2 .

[0029] Step 4: Collect gas well production test data and pressure measurement data. Specifically, the collected gas well production test data includes daily water production, daily gas production, and bottomhole flowing pressure. The cumulative gas production and cumulative water production are calculated based on the daily gas production and daily water production, as shown in Table 2.

[0030] Table 2 Gas well production data

[0031] Step 5: Based on the formation pressure of the previous time step, assume a value smaller than the formation pressure of the previous time step, and then calculate the formation pressure value as the formation pressure value of the next time step. Calculate the reservoir permeability K and rock compressibility C according to formulas (1)(2)(3): p and the starting pressure gradient λ. Substitute K, λ and the formation pressure into formula (4) to calculate the bottom hole flow pressure and compare it with the measured bottom hole flow pressure. If |P wf计算 −P wf实际 If |<0.001, the formation pressure is calculated; otherwise, the iterative calculation continues. Substitute the formation pressure into formula (5) to calculate the dynamic reserves. The calculated data points are shown in Table 3.

[0032] Table 3 Intermediate calculation data table for gas well dynamic reserves calculation

[0033] In order to further verify the accuracy and reliability of the calculation results of this method, the results were compared with the apparent geological reserves method ( Figure 5 The comparison results are as follows: Figure 5 As shown, the method of the present invention ( Figure 5 The dynamic geological reserves in the middle and late stable stage calculated by the new method are 0.392×10 8 m 3 , the difference between the two is 0.022×10 8 m 3 , with an error of 5%. This shows that the calculation results of the method of the present invention are accurate and reliable.

Claims

1. A method for calculating dynamic reserves of water-bearing gas reservoirs based on material balance, characterized in that: The steps include: S1. Construct a model for how rock compressibility changes with water saturation and effective stress, which specifically includes the following sub-steps: S11. Based on stress sensitivity experiments, a model was constructed to show how rock stress sensitivity changes with water saturation and effective stress. (1) In formula (1), K is the permeability of rock under different effective stresses, mD; K0 is the original permeability of rock, mD; e is an exponential function; S w is water saturation, %; a and b are constants; Δσ is the pressure difference between the confining pressure and the pore pressure, MPa; S12. Based on the relationship between the rock compressibility coefficient and the rock stress sensitivity coefficient, and the model of rock stress sensitivity changing with water saturation and effective stress constructed in step S11, a model of rock compressibility changing with water saturation and effective stress is constructed: (2) In formula (2), C p is the compression coefficient of rock, MPa -1 ; S2. Based on the start-up pressure gradient experiment, a model is constructed to show how the start-up pressure gradient of cores with different permeabilities changes with water saturation and formation pressure: (3) In formula (3), λ is the starting pressure gradient, MPa / m; P e is the formation pressure, MPa; c, d, e, f is a constant; S3. Constructing a gas seepage motion model: (4) In formula (4), P wf is the bottom hole pressure, MPa; r e is the oil leakage radius, m; r w is the wellbore radius, m; Q is the gas well production, m 3 / d; Z is the natural gas deviation factor; h is the reservoir thickness, m; In is the natural logarithm function; S4. Constructing a material balance model for water-bearing gas reservoirs: (5) In formula (5), P ei is the formation pressure at a certain moment of gas reservoir production, MPa; i takes values ​​of 1, 2, …, t; C w is the bound water expansion coefficient, MPa -1 ; ∆P is the gas reservoir pressure drop, MPa; ω is the water storage volume coefficient; P e0 is the original formation pressure of the gas reservoir, MPa; Z 0 is the natural gas deviation factor under the original condition; Gp is ​​the cumulative gas production of the gas reservoir, m 3 ; G is the dynamic reserves of the gas reservoir to be tested, m 3 ; Construct a model of water saturation changes in gas reservoirs during development: (6) In formula (6), W is the water content of the gas reservoir, m 3 ; W p is the cumulative water production of the gas reservoir, m 3 ; B w V is the volume coefficient of produced water in the gas reservoir; p is the pore volume of the gas reservoir; S5. Predicting the dynamic reserves of water-bearing gas reservoirs based on the model constructed in steps S1 to S4, including the following sub-steps: S51. Calculate the cumulative gas production of the gas reservoir based on the actual production data of the gas reservoir to be predicted. G p and cumulative water production W p , calculate the current water saturation of the gas reservoir according to formula (6) S W ; S52, assuming that the formation pressure is P ei Calculate the reservoir permeability K and rock compressibility coefficient at this time according to formulas (1) and (2): C p , calculate the starting pressure gradient λ according to formula (3); S53, K, λ and P ei Substitute into formula (4) to obtain the bottom hole pressure, and compare it with the measured bottom hole pressure. If P wf计算 − P wf实际 |<0.001, proceed to step S54, if | P wf计算 − P wf实际 |≥0.001, return to step S52 and readjust P ei Value, until | P wf计算 − P wf实际 ∣<0.001; S54, will P ei 、 S W 、G p 、W p Substitute into formula (5) to calculate the dynamic reserves of the gas reservoir to be tested G ; S55, repeat steps S51 to S54 to calculate the dynamic reserves of the gas reservoir at different times until t reaches the given prediction time, or the bottom hole flow pressure is lower than the given bottom hole abandonment flow pressure, or the gas well production is Q Lower than the given gas well limit production.

2. The method for calculating dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 1, characterized in that: In step S1, The relationship between rock compressibility and rock stress sensitivity is: (7)。 3. The method for calculating dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 1, characterized in that: Step S3 is specifically as follows: S31. Establish the gas seepage motion equation considering the starting pressure gradient: (8) In formula (8), d is the differential; μ is the fluid viscosity, mPa·s; v is the seepage velocity, m / s; (9) S32. Substitute equation (9) into equation (8) and integrate both sides to obtain the gas seepage motion model of equation (4).

4. The method for calculating dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 1, characterized in that: Step S4 is specifically as follows: S41. Establish the material balance equation for water-bearing gas reservoirs taking into account the rock pore shrinkage and irreducible water expansion conditions: (10) i =1，2，…，t(11) In formula (10), B g0 is the original volume coefficient of gas in the gas reservoir; B w0 is the volume coefficient of the original water in the gas reservoir; B g is the gas volume coefficient of the gas reservoir; S42. The material balance model of water-bearing gas reservoirs of formula (5) is obtained from formula (10) and formula (11).

5. The method for calculating dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 4, characterized in that: In step S4: In formula (5): (12)。 6. The method for calculating dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 5, characterized in that: In step S4: In formula (10) or formula (12): (13)， In formula (13), P sc is the surface standard pressure, MPa; T is the gas reservoir temperature, °C; T sc is the standard ground temperature, ℃.

7. The method for calculating dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 4, characterized in that: In step S4: In formula (10): (14)。

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