A method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance

Abstract

This invention belongs to the field of gas reservoir development technology, specifically relating to a method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance. It includes the following steps: S1, constructing a model of the rock compressibility coefficient varying with water saturation and effective stress; S2, based on a starting pressure gradient experiment, constructing a model of the starting pressure gradient of cores with different permeability varying with water saturation and formation pressure; S3, constructing a gas seepage and movement model; S4, constructing a material balance model for the water-bearing gas reservoir; S5, based on the models constructed in steps S1-S4, predicting the dynamic reserves of the water-bearing gas reservoir. This invention achieves a simple and accurate calculation of the dynamic reserves of gas reservoirs, which is of great significance for correctly evaluating the development effect of gas reservoirs, accurately predicting the dynamics of gas reservoir development, and making sound gas reservoir development plans.

Description

Technical Field

[0001] This invention belongs to the field of gas reservoir development technology, specifically relating to a method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance. Background Technology

[0002] my country possesses abundant tight sandstone gas reservoirs, which often contain water that occupies a portion of the reservoir's pore space. During the depletion and development of these reservoirs, macroscopic water-locking and microscopic water-sealing effects occur, leading to losses in reservoir / well productivity and dynamic reserves, thus impacting reservoir recovery and final development outcomes. Researching and accurately determining the dynamic reserves of gas reservoirs is crucial for reservoir production, and is essential for calculating, dynamically analyzing, and numerically simulating reservoir well production. Furthermore, studying the dynamic reserves of water-bearing gas reservoirs facilitates timely adjustments to production plans in the mid-to-late stages of reservoir development, thereby improving gas recovery.

[0003] Currently, there are many methods for calculating gas reservoir reserves, mainly including the mass balance method, pressure drop testing method, and pressure recovery testing method. Applying these conventional reserve calculation methods to low-permeability gas reservoirs requires adapting to relatively harsh conditions, undergoing complex corrections, and conducting long-term shut-in testing, which brings many inconveniences to field applications. Patent document CN110219624A discloses a method for determining parameters of water-drive gas reservoirs under conditions of rock pore shrinkage and bound water expansion. This method only considers rock pore shrinkage and bound water expansion to determine the dynamic reserves of the gas reservoir, without considering the impact of changes in start-up pressure with the degree of exploitation on the dynamic reserves. Patent document CN118469334A discloses an equivalent evaluation method for the dynamic reserves of the entire gas reservoir. This method is only applicable to homogeneous gas reservoirs and has poor adaptability to highly heterogeneous water-drive gas reservoirs or low-permeability gas reservoirs. Patent document CN117669397A discloses an evaluation method for the utilization of reserves in highly heterogeneous carbonate gas reservoirs. This method relies on pseudo-pressure equations and flow mass balance equations, requiring fitting and normalization parameters, a large amount of production data, and early well test results. The calculation process is complex, requiring multiple equation corrections and chart comparisons, making the operation cumbersome. Patent documents CN108612525A and CN119572215A disclose a method for calculating dynamic reserves of gas reservoirs, respectively. Neither of these methods mentions the reservoir's initiation pressure gradient and stress sensitivity, leading to a significant increase in calculation errors. Since the initiation pressure gradient and stress sensitivity change during development, causing inaccuracies in dynamic reserve results, a method is needed to consider the dynamic changes in the initiation pressure gradient and stress sensitivity for dynamic reserve calculation. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in current calculation methods by proposing a non-steady-state seepage response and dynamically evolving multi-physics coupled reserve calculation method. This method constructs a rock compressibility coefficient and initiation pressure gradient model jointly controlled by water saturation and effective stress, and combines the production capacity equation and the deformation material balance equation to form a dynamic reserve calculation method that evolves in real time with production dynamics. This ensures accurate and reasonable assessment 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 objectives, the present invention adopts the following technical solution:

[0006] Step S1: Establish the relationship between the rock compressibility coefficient and the stress sensitivity coefficient:

[0007] (7)

[0008] Reservoir core samples were obtained, and a stress-sensitive experimental device was constructed (referring to the method disclosed in the patent document CN115200977A, entitled "A Device and Method for Evaluating Core Stress Sensitivity under High Temperature and High Pressure Conditions"). The permeability variation law under different effective stresses and initial water saturation of the core was determined. Based on the experimental results, a model of rock stress sensitivity with water content and stress variation was constructed.

[0009] (1)

[0010] The transformed equation is the rock compressibility coefficient as a function of water saturation and effective stress:

[0011] (2)

[0012] In the formula: C p The compressibility coefficient of the rock is given in MPa. -1 ; K 0 represents the original permeability of the rock, in mD; K Let mD be the permeability of the rock under different effective stresses. S w The water saturation level is %; Δσ The pressure difference (the pressure difference between confining pressure and pore pressure, also called effective stress) is expressed in MPa. a、b It is a constant.

[0013] Step S2: Obtain reservoir core samples and construct a start-up pressure gradient experimental device (refer to the method disclosed by Ding Jingchen, Yang Shenglai, Shi Yunqing, et al. Experimental study on dynamic start-up pressure gradient of tight gas reservoir [J]. Oil & Gas Geology and Recovery, 2017, 24(05):64-69.DOI:10.13673 / j.cnki.cn37-1359 / te.2017.05.010). Determine the variation law of start-up pressure gradient under different formation pressures, core permeability, and water saturation. Based on the experimental results, construct a model of the change of start-up pressure gradient of cores with different permeabilities as a function of water saturation and formation pressure.

[0014] (3)

[0015] In the formula: P e λ is the formation pressure, MPa; λ is the starting pressure gradient, MPa / m; c, d, e, and f are constants.

[0016] Step S3: Establish the gas seepage motion equation considering the initiation pressure gradient as follows:

[0017] (8)

[0018] (9)

[0019] Substituting equation (9) into equation (8) and integrating both sides, we obtain the gas seepage motion model:

[0020] (4)

[0021] In the formula: μ The viscosity is expressed in mPa·s. v The seepage velocity is in m / s; P wf The bottom hole flowing pressure is in MPa. P e Formation pressure, MPa; r w Let be the radius of the wellbore, in meters (m). r e Let be the oil drain radius, in meters. Q For gas well production, m 3 / d; Z This is the natural gas deviation factor; h Let be the reservoir thickness, in meters (m). d It is a differential; In It is the natural logarithm function.

[0022] Step S4: The material balance equation for a water-bearing gas reservoir considering rock pore shrinkage and bound water expansion can be expressed as:

[0023] (10)

[0024] i=1,2,…,t (11)

[0025] After transformation, a material balance model of a water-bearing gas reservoir is obtained:

[0026] (5)

[0027] In the formula: (12)

[0028] (13)

[0029] (14)

[0030] In the formula, G p The cumulative gas production of the gas reservoir, m 3 ; B g0 This represents the original gas volume factor of the gas reservoir; B g This represents the gas volume coefficient of the gas reservoir. W The water content of the gas reservoir, m 3 ; W p The cumulative water production of the gas reservoir, m 3 ; B w0 This is the volume factor of the original water in the gas reservoir; B w This is the volume factor for produced water from the gas reservoir; G m represents the dynamic reserves of the gas reservoir to be measured. 3 ; C w The coefficient of expansion of bound water is MPa. -1 ; The pressure drop of the gas reservoir is expressed in MPa. P e0 The original formation pressure of the gas reservoir is MPa; P ei The formation pressure at a certain moment during gas reservoir production, in MPa; ω The water volume coefficient; P sc Ground standard pressure, MPa; T The gas reservoir temperature is expressed in °C. T sc The ground standard temperature; Z 0 represents the natural gas deviation factor under the original conditions;

[0031] Formula for changes in water saturation of gas reservoir during development:

[0032] (6)

[0033] In the formula V p This represents the pore volume of the gas reservoir.

[0034] Step S5: Predicting the dynamic reserves of water-bearing gas reservoirs: The above equations combine to form a dynamic prediction model for low-permeability gas reservoirs. Solving this model simultaneously yields time-varying parameters such as production and pressure. The dynamic prediction model solution mainly includes five steps:

[0035] S51. 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, calculate the cumulative gas production of the gas reservoir. G p and cumulative water production W p The current water saturation of the gas reservoir is calculated according to formula (6). S W .

[0036] S52, Assume the formation pressure at this time is... P ei The reservoir permeability at this time is calculated according to formulas (1) and (2). K and rock compressibility coefficient C p The starting pressure gradient λ is calculated according to formula (3).

[0037] S53, K from step S52, C p , λ and P ei Substitute the input into equation (4) to obtain the bottom hole flowing pressure, and compare it with the measured bottom hole flowing pressure. If | P wf计算 - P wf实际 If | < 0.001, proceed to step S54. If | P wf计算 - P wf实际 If |≥0.001, return to step S52 and readjust. P ei Value, until | P wf计算 - P wf实际 |<0.001;

[0038] S54, Formation pressure P ei Current water saturation of the gas reservoir SW 、 Cumulative gas production of gas reservoir G p 、 Cumulative water production of gas reservoir W p Substitute into equation (5) to calculate the dynamic reserves of the gas reservoir to be tested. G ;

[0039] S55. Repeat steps S51~S54 to calculate the dynamic reserves of the gas reservoir at different times. The direct 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.

[0040] Compared with the prior art, the beneficial effects of the present invention are:

[0041] This method does not require shutting in the entire gas well to obtain formation parameters. Without affecting the gas well production plan, it only requires processing and analyzing existing gas reservoir production data, establishing a dynamic model of stress sensitivity and start-up pressure gradient through experiments, determining rock compressibility and start-up pressure gradient at different development stages, and then calculating the dynamic reserves of a single well. This invention achieves a simple and accurate calculation of dynamic gas reservoir reserves, which is of great significance for correctly evaluating gas reservoir development effects, accurately predicting gas reservoir development dynamics, and making sound gas reservoir development plans. Attached Figure Description

[0042] Figure 1 A schematic diagram illustrating the material balance principle and material balance equation of a water-driven gas reservoir;

[0043] Figure 2 A schematic diagram of the starting pressure gradient under different formation pressures and water saturation levels;

[0044] Figure 3 A schematic diagram of stress sensitivity curves under different formation pressures and water saturation levels;

[0045] Figure 4 Flowchart for calculating dynamic reserves of water-bearing gas reservoirs;

[0046] Figure 5 Comparison of different methods for calculating dynamic geological reserves. Detailed Implementation

[0047] The technical solutions in the embodiments of the present invention will now be clearly and completely described in conjunction with the accompanying drawings.

[0048] Example 1

[0049] This embodiment discloses a method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance, such as... Figure 4 As shown, it includes the following steps:

[0050] Step S1:

[0051] Establish the relationship between the rock compressibility coefficient and the stress sensitivity coefficient (7), obtain core samples from the target gas reservoir, build a stress sensitivity experimental device, and simulate different effective stress conditions (such as 5 MPa, 10 MPa, 15 MPa, 20 MPa, etc.). Measure the permeability changes of the core samples under different effective stresses and initial water saturation levels (such as 35%, 45%, 55%, 65%). Based on the experimental data fitting formula (1), determine the values ​​of constants a and b:

[0052] (7)

[0053] (1)

[0054] The transformed equation is the rock compressibility coefficient as a function of water saturation and effective stress:

[0055] (2)

[0056] In the formula: C p The compressibility coefficient of the rock is given in MPa. -1 ; K 0 represents the original permeability of the rock, in mD; K Let mD be the permeability of the rock under different effective stresses. S w The water saturation level is %; Δσ Pressure difference, MPa; a、b It is a constant.

[0057] Step S2:

[0058] A starting pressure gradient experimental setup was constructed using the same core sample to simulate different formation pressures (e.g., 10 MPa, 15 MPa, 20 MPa, 25 MPa) and water saturation conditions. The starting pressure gradient values ​​under different conditions were recorded. Based on the experimental data fitting formula (3), a dynamic variation model of the starting pressure gradient with formation pressure and water saturation was established.

[0059] (3)

[0060] In the formula: P e λ is the formation pressure, MPa; λ is the starting pressure gradient, MPa / m; c, d, e, and f are constants, determined by fitting formula (3) based on experimental data.

[0061] Step S3: Establish the gas seepage motion equation considering the initiation pressure gradient as follows:

[0062] (8)

[0063] (9)

[0064] Substituting equation (9) into equation (8) and integrating both sides, we obtain:

[0065] (4)

[0066] In the formula: μ The viscosity is expressed in mPa·s. v The seepage velocity is in m / s; P wf The bottom hole flowing pressure is in MPa. P e Formation pressure, MPa; r w Let be the radius of the wellbore, in meters (m). r e Let be the oil drain radius, in meters. Q For gas well production, m 3 / d; Z This is the natural gas deviation factor; h Let be the reservoir thickness, in meters (m). d It is a differential; In It is the natural logarithm function.

[0067] Step S4:

[0068] Based on the gas reservoir type, nodal state analysis is conducted to establish a material balance equation for the water-bearing gas reservoir that considers rock pore shrinkage and bound water expansion conditions (e.g., ...). Figure 1 As shown):

[0069] (10)

[0070] i=1,2,…,t(11)

[0071] Transformed into the modified mass balance equation: (5)

[0072] In the formula: (12)

[0073] in, G p The cumulative gas production of the gas reservoir, m 3 ; B g0 This represents the original gas volume factor of the gas reservoir; B g This represents the gas volume coefficient of the gas reservoir. W The water content of the gas reservoir, m 3 ; Wp The cumulative water production of the gas reservoir, m 3 ; B w0 This is the volume factor of the original water in the gas reservoir; B w This is the volume factor for produced water from the gas reservoir; G m represents the dynamic reserves of the gas reservoir to be measured. 3 ; C w The coefficient of expansion of bound water is MPa. -1 ; ∆P The pressure drop of the gas reservoir is expressed in MPa. P e0 The original formation pressure of the gas reservoir is MPa; P ei ω represents the formation pressure at a certain moment during gas reservoir production, in MPa; ω is the water volume coefficient; P sc T represents the standard surface pressure, in MPa; T represents the reservoir temperature, in °C. sc This refers to the standard ground temperature.

[0074] Formula for changes in water saturation of gas reservoir during development:

[0075] (6)

[0076] In the formula Vp This represents the pore volume of the gas reservoir.

[0077] Step S5: Combining the above equations constructs a dynamic prediction model for low-permeability gas reservoirs. Solving this model simultaneously yields time-varying parameters such as production and pressure. The dynamic prediction model solution mainly involves five steps:

[0078] S51. Calculate the cumulative gas production and cumulative water production based on the gas production and water production of the previous time period, and calculate the current water saturation according to formula (6).

[0079] S52. Assume the formation pressure at this time is P. ei The reservoir permeability K and rock compressibility C are calculated according to formulas (1) and (2). p The starting pressure gradient λ is calculated according to formula (3).

[0080] S53. Substitute K, λ, and formation pressure into formula (4) to calculate the bottom hole flowing pressure, and compare it with the measured bottom hole flowing pressure. If |P wf计算 - P wf实际 If | < 0.001, then the formation pressure P can be obtained. ei Otherwise, continue iterative calculation.

[0081] S54. Substitute the formation pressure into formula (5) to calculate the dynamic reserves.

[0082] S55. Repeat steps S51-S54 to calculate the dynamic reserves at different times until t reaches the given prediction time, or the bottomhole flowing pressure is lower than the given bottomhole abandoned flowing pressure, or the daily gas production... Q Below the given gas well limit production.

[0083] Example 1 illustrates the calculation of dynamic reserves of tight water-bearing gas wells using the method of the present invention, taking the Dongsheng gas field on the eastern edge of the Ordos Basin as an example.

[0084] Step 1: Test and collect basic geological parameters, including original formation pressure, reservoir temperature, water saturation, reservoir permeability, reservoir thickness, wellbore radius, and drainage radius, as shown in Table 1.

[0085] Table 1 Basic Geological Parameters of Gas Wells

[0086]

[0087] Step 2: Obtain reservoir core samples, construct a stress-sensitive experimental setup, set a confining pressure of 29 MPa, and pore pressures of 24 MPa, 19 MPa, 14 MPa, and 9 MPa, with core water saturation of 35%, 45%, 55%, and 65%. Determine the permeability variation under different effective stresses and initial water saturation levels. Based on the experimental results, construct a model of rock stress sensitivity as a function of water content and stress, as follows: Figure 3 As shown:

[0088]

[0089] Step 3: Obtain reservoir core samples, construct a start-up pressure gradient experimental setup, and set pore pressures of 10 MPa, 15 MPa, 20 MPa, and 25 MPa, with confining pressure 3 MPa higher than pore pressure. Set core water saturation levels of 35%, 45%, 55%, and 65%. Determine the variation of the start-up pressure gradient under different formation pressures and water saturation levels for cores with different permeabilities. Based on the experimental results, a model of the reservoir core start-up pressure gradient as a function of water saturation and formation pressure is constructed. Figure 2 As shown:

[0090]

[0091] Step 4: Collect test production data and pressure measurement data from the gas well. Specifically, the collected test production data includes daily water production, daily gas production, and bottom hole 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.

[0092] Table 2 Gas Well Production Data

[0093]

[0094] Step 5: Assume a value smaller than the formation pressure from the previous time step, then calculate the formation pressure value for the next time step. Calculate the reservoir permeability K and rock compressibility C using formulas (1), (2), and (3). p And the starting pressure gradient λ. Substitute K, λ and formation pressure into formula (4) to calculate the bottom hole flowing pressure, and compare it with the measured bottom hole flowing pressure. If |P wf计算 -P wf实际 If | < 0.001, the formation pressure is obtained; otherwise, the iterative calculation continues. The formation pressure is substituted into formula (5) to calculate the dynamic reserves. The calculation data points are shown in Table 3.

[0095] Table 3 Intermediate Calculation Data for Dynamic Reserves of Gas Wells

[0096]

[0097] To further verify the accuracy and reliability of the calculation results obtained by the method presented in this paper, and to compare them with the apparent geological reserves method, which has shown good practical application results (…),… Figure 5 The comparison was conducted using traditional methods, and the results are as follows: Figure 5 As shown, the method of the present invention ( Figure 5 The dynamic geological reserves calculated using the Sino-Singapore method for the mid-to-late stable phase are 0.392 × 10⁻⁶. 8 m 3 The difference between the two is 0.022 × 10 8 m 3 The error is 5%. This demonstrates that the calculation results of the method of the present invention are accurate and reliable.

Claims

1. A method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance, characterized in that, Includes the following steps: S1. Construct a model of how the rock compressibility varies with water saturation and effective stress, specifically including the following sub-steps: S11. Construct a model of rock stress sensitivity as a function of water saturation and effective stress based on stress sensitivity experiments: (1) In equation (1), K is the permeability of the rock under different effective stresses, mD; K0 is the original permeability of the rock, mD; e It is an exponential function; S w The water saturation level is %; a and b are constants; Δσ is the pressure difference between the confining pressure and the pore pressure, in MPa; S12. Based on the relationship between rock compressibility coefficient and rock stress sensitivity coefficient, and the model of rock stress sensitivity variation with water saturation and effective stress constructed in step S11, construct a model of rock compressibility coefficient variation with water saturation and effective stress: (2) In equation (2), C p The compressibility coefficient of the rock is given in MPa. -1 ; S2. Based on the starting pressure gradient experiment, a model was constructed to show the variation of the starting pressure gradient of cores with different permeabilities as a function of water saturation and formation pressure: (3) In equation (3), λ is the starting pressure gradient, MPa / m; P e Formation pressure, MPa; c, d, e, f It is a constant; S3. Construct a gas seepage motion model: (4) In equation (4), P wf The bottom hole flowing pressure is in MPa; r e Let be the oil drain radius, in meters. r w Let be the radius of the wellbore, in meters (m). Q For gas well production, m 3 / d; Z is the natural gas deviation factor; h is the reservoir thickness in meters; In is the natural logarithm function; S4. Construct a material balance model for water-bearing gas reservoirs: (5) In equation (5), P ei Let be the formation pressure at a certain moment during gas reservoir production, in MPa; i takes values ​​of 1, 2, ..., t; C w The coefficient of expansion of bound water is MPa. -1 ; ∆P ω represents the pressure drop of the gas reservoir, in MPa; ω is the water storage volume coefficient. P e0 The original formation pressure of the gas reservoir is MPa; Z 0 represents the natural gas deviation factor under original conditions; Gp represents the cumulative gas production of the reservoir, m 3 ; G m represents the dynamic reserves of the gas reservoir to be measured. 3 ; Constructing a model of water saturation changes in gas reservoirs during development: (6) In equation (6), W The water content of the gas reservoir, m 3 ; W p The cumulative water production of the gas reservoir, m 3 ; B w V is the volume factor of the produced water from the gas reservoir. p This refers to the pore volume of the gas reservoir. S5. Based on the model constructed in steps S1 to S4, predict the dynamic reserves of water-bearing gas reservoirs, 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 The current water saturation of the gas reservoir is calculated according to equation (6). S W ; S52, Assume the formation pressure at this time is... P ei The reservoir permeability K and rock compressibility coefficient are calculated according to formulas (1) and (2). C p The starting pressure gradient λ is calculated according to equation (3); S53, Combine K, λ, and... from step S52 P ei Substitute the input into equation (4) to obtain the bottom hole flowing pressure, and compare it with the measured bottom hole flowing pressure. If | P wf计算 - P wf实际 If | < 0.001, proceed to step S54. If | P wf计算 - P wf实际 If |≥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 equation (5) to calculate the dynamic reserves of the gas reservoir to be tested. G ; S55. Repeat steps S51-S54 to calculate the dynamic reserves of the gas reservoir at different times until t reaches the given prediction time, or the bottomhole flowing pressure is lower than the given bottomhole abandoned flowing pressure, or the gas well production... Q Below the given gas well production limit.

2. The method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 1, characterized in that, In step S1, The relationship between the rock compressibility coefficient and the rock stress sensitivity coefficient is as follows: (7)。 3. The method for calculating the dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 1, characterized in that, Step S3 is as follows: S31. Establish the gas seepage motion equation considering the initiation pressure gradient: (8) In equation (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 the dynamic reserves of water-bearing gas reservoirs based on material balance according to claim 1, characterized in that, Step S4 is as follows: S41. Establish the material balance equation for water-bearing gas reservoirs that considers rock pore shrinkage and bound water expansion: (10) i =1，2，…，t(11) In equation (10), B g0 This represents the original gas volume factor of the gas reservoir; B w0 The volume factor of the original water in the gas reservoir; B g This represents the gas volume coefficient of the gas reservoir. S42. The material balance model of the water-bearing gas reservoir is obtained from equations (10) and (11) in equation (5).

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

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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