Method for determining critical desorption pressure of coalbed methane reservoir based on mid- and late-stage production data

Abstract

The present invention discloses a method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data, comprising: assuming that the water saturation of the reservoir is stable and the desorption zone expands at a uniform rate in the mid- to late-stage coalbed methane development, linearizing the mid- to late-stage gas production equation, analyzing the linear relationship between #imgabs0# and the number of production days t using a graphical method, and obtaining a gas production data analysis equation; linearizing the mid- to late-stage water production equation, analyzing the linear relationship between #imgabs1# and the number of production days t using a graphical method, and obtaining a water production data analysis equation; and jointly solving the gas and water production data analysis equations, iteratively solving the critical desorption pressure of the coalbed methane reservoir using a bisection method. The present invention inverts the critical desorption pressure based on mid- to late-stage coalbed methane production data, providing a simple and highly adaptable production data analysis method that facilitates the formulation of coalbed methane development plans and capacity forecasting.

Description

Technical Field

[0001] The present invention belongs to the field of petroleum engineering - oil and gas field development engineering - unconventional oil and gas reservoir development technology, and specifically relates to a method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- and late-stage production data. Background Art

[0002] Coal reservoirs are typical dual-porosity media, consisting of a micron-scale microfracture (cleat) system and a nanoscale matrix system. The difference in pore size between the two influences fluid storage characteristics. Regarding the initial fluid storage characteristics of coalbed methane reservoirs, there is currently a consensus that the microfracture system is saturated with water or contains a small amount of free gas, with the gas phase primarily adsorbed within the matrix system, typically exceeding 80%. Matrix systems rich in nanopores have a larger specific surface area and can store more gas at atmospheric pressure than conventional sandstone gas reservoirs. During coalbed methane development, water from the microfractures is initially extracted from the surface, gradually decreasing its pressure. When the water pressure drops to a certain value, the gas phase desorbs from the coal matrix system and diffuses into the microfracture system. It is worth noting that this specific value is the critical desorption pressure of the coalbed methane reservoir. Since the entry of gas into the microfracture system changes the flow regime within the coalbed from "single-phase water flow" to "gas-water two-phase flow," the critical desorption pressure, to a certain extent, determines the timing of this flow regime change, thereby influencing the coalbed methane production pattern. For example, in coal reservoirs with high critical desorption pressures, the flow regime within the coal seam transforms into gas-water two-phase flow in the early stages of production, with the production pattern primarily controlled by the gas-water two-phase flow. In contrast, in coal reservoirs with low critical desorption pressures, the production pattern is primarily controlled by single-phase water flow in the early stages of production, gradually becoming dominated by gas-water two-phase flow in the middle and later stages. Therefore, determining the critical desorption pressure is crucial for ensuring efficient coalbed methane development.

[0003] Despite decades of research on coalbed methane (CBM) development, methods for determining its critical desorption pressure (CDP) remain immature. CBM field engineers typically consider the CDP to be equal to the bottomhole pressure at the moment casing pressure begins to appear in the well. Therefore, field statistics for CDP are derived from daily well production reports. However, the onset of casing pressure indicates the presence of a significant amount of free gas at the bottomhole. Coalbed gas desorption in the near-wellbore region should occur before the onset of casing pressure, indicating that this method of determination can lead to significant errors. Numerous theoretical studies have focused on the impact of CDP on CBM well productivity, but these theories generally consider CDP as a sensitivity factor and pay less attention to its determination. Furthermore, CBM research has been conducted through laboratory experiments, which, due to limitations in sample size, often focus on the adsorption-desorption capacity, diffusion dynamics, and fluid permeability of the coal, with little attention paid to the CDP.

[0004] In summary, critical desorption pressure is a key parameter affecting the gas production characteristics of coalbed methane wells. However, research on the determination method of critical desorption pressure is still weak and urgently needs in-depth research. Summary of the Invention

[0005] Technical problem to be solved: Based on the principles of porous media seepage mechanics and artificial fracture reservoir transformation, the present invention combines the expansion law of the desorption zone in the middle and late stages of coalbed methane and the characteristics of the change of water saturation field to establish a method for determining the critical desorption pressure of (un) fractured coal reservoirs. The critical desorption pressure is the basis for judging whether the adsorbed gas in a local area of the coal reservoir is desorbed or not, and directly affects the flow state of the fluid inside the coal reservoir (single-phase water flow, gas-water two-phase flow). Its accurate calibration is of great significance to ensuring the efficient development of coalbed methane.

[0006] Technical solution:.

[0007] A method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data comprises the following steps:

[0008] S1, assuming that the water saturation of the reservoir is stable in the middle and late stages of coalbed methane development and the desorption zone expands at a uniform rate, the gas production equation in the middle and late stages is linearized and analyzed by the graphic method. The linear relationship between the desorption zone and the production days t is obtained, and the gas production data analysis equation is obtained; the desorption zone is the coal seam where the reservoir pressure is lower than the critical desorption pressure. For the reservoir inside the desorption zone, the fluid is mainly gas-water two-phase flow or single-phase gas, and the pressure drop distribution changes from the bottom hole pressure P w Critical desorption pressure P at the edge of the desorption zone d ;q g Including the daily gas production of unfractured coalbed methane wells q g-1 and gas production of fractured coalbed methane wells q g-2 ;

[0009] S2, linearize the water production equation in the middle and late stages, analyze the water production data of gas wells by the plate method, and analyze The linear relationship between q and the production days t gives the water production data analysis equation; w Including the daily water production of unfractured coalbed methane wells q w-1 and water production of fractured coalbed methane wells q w-2 ;

[0010] S3, the gas and water production data analysis equations are combined to solve the critical desorption pressure of the coalbed methane reservoir through bisection iteration.

[0011] Furthermore, in step S1, for an unfractured coalbed methane well, the process of obtaining a gas production data analysis equation includes the following steps:

[0012] S101, for unfractured coalbed methane wells, the mid-to-late gas production equation is:

[0013]

[0014] Among them, q g-1 Represents the daily gas production of unfractured coalbed methane wells, in m 3 / d;K g represents gas permeability, in mD; h represents coal seam thickness, in m; P e Represents the initial pressure of the coal seam, in MPa; P w represents the bottom hole pressure, in MPa; T represents the coal reservoir temperature, in K; Represents pressure (P e +P w ) / 2 gas viscosity, unit is cp; Represents pressure (P e +P w ) / 2 gas compressibility factor, dimensionless; r e Represents the distance between the coalbed methane reservoir boundary and the bottom of the well, in meters; r w represents the wellbore radius, in meters; S represents the gas well skin factor, dimensionless;

[0015] S102, r in formula (1) e The term is replaced by the distance r between the edge of the desorption zone and the bottom of the well d , we get formula (2):

[0016]

[0017] Without considering the problems of imperfect gas well perforation technology and reservoir pollution around the well, the skin factor is considered to be zero, and the following is obtained:

[0018]

[0019] The water saturation of the coal cleat remains stable in the middle and late stages of production, which means that the gas permeability does not change in this stage. The following equation (3) can be transformed to:

[0020]

[0021] For the right side of formula (4), the gas permeability K g , reservoir thickness h, and reservoir temperature T are all constants;

[0022] Formula (4) can be further simplified as:

[0023]

[0024] Where C1 represents a constant;

[0025] S103, for the left side of equation (5), the wellbore radius is a constant; the desorption zone gradually expands outward with time, showing a linear relationship, which is:

[0026]

[0027] Among them, C2 and C3 represent constants, and t represents production time in days;

[0028] S104 is obtained from formula (5):

[0029]

[0030] make:

[0031]

[0032] Simplify formula (7) to:

[0033]

[0034] S105, combining equations (6) and (9), we obtain:

[0035]

[0036] According to the analysis of formula (10), There is a linear relationship with t; for any time in the middle and late stages of production of unfractured coalbed methane wells, record the production time t and daily gas production q g-1 and bottom hole pressure P w , by assuming that the critical desorption pressure of coalbed methane reservoir P d In the rectangular coordinate system, we get and t relationship curve; if the curve satisfies the linear relationship, the assumed value is the critical desorption pressure; if it does not satisfy the linear relationship, continue to assume.

[0037] Furthermore, in step S2, for an unfractured coalbed methane well, the process of obtaining a water production data analysis equation includes the following steps:

[0038] S201, without considering the capillary force of gas and water phases in coal rock cutting, the water production equation of unfractured coalbed methane wells in the middle and late stages is:

[0039]

[0040] Among them, q w-1 Represents daily water production, unit is m 3 / d;K w Represents water phase permeability, unit is mD; μ w Represents the viscosity of the water phase, the unit is cp;

[0041] S202, transform equation (11) to obtain:

[0042]

[0043] Combining equation (12) and equation (6), we get:

[0044]

[0045] S203, in the middle and late stages of coalbed methane production, the water permeability K w , reservoir thickness h and water phase viscosity μ w is a constant, and Equation (13) is further transformed into:

[0046]

[0047]

[0048] Among them, C5 is a constant;

[0049] S204, obtained from formula (15) The linear relationship between it and production time:

[0050]

[0051] S205, using linear relationship (10) plus linear relationship (16), we get:

[0052]

[0053] make:

[0054]

[0055]

[0056] Among them, C6 and C7 are constants.

[0057] get:

[0058]

[0059] In the middle and late stages of production, record the production time, gas production, water production and bottom hole pressure, and assume the critical desorption pressure to calculate the corresponding pressure for each production time. and Calculate the corresponding left side value of formula (20) and draw it in the rectangular coordinate system If the curve shows a linear relationship with the production time t, the critical desorption pressure of the coalbed methane reservoir is an assumed value. If it does not show a linear relationship, the calculation process is continued in a cycle.

[0060] Furthermore, for a fractured coalbed methane well, the process of obtaining a gas production data analysis equation includes the following steps:

[0061] In the middle and late stages of production, the gas and water production equations of fractured coalbed methane wells are:

[0062]

[0063]

[0064] Among them, q g-2 With q w-2 Respectively represent the gas production and water production of fractured coalbed methane wells, unit is m 3 / d;L f Represents the half-length of the crack, in m; r a With r b They represent the major and minor semi-axes of the desorption zone of the fractured coalbed methane well, respectively, in meters;

[0065] Assuming that the desorption zone has expanded much longer than the fracture half-length L in the middle and late stages of CBM production, f , transform equations (21) and (22) into:

[0066]

[0067]

[0068] S113, for fractured coalbed methane wells, there are two linear relationships:

[0069]

[0070]

[0071] The final linear relationship judgment equation for fractured coalbed methane wells is:

[0072]

[0073] C8, C9, C 10 、C 11 、C 12 and C 13 are all constants.

[0074] Furthermore, in step S3, for an unfractured coalbed methane well, the process of simultaneously analyzing the gas and water production data equations and solving the critical desorption pressure of the coalbed methane reservoir by bisection iteration includes the following steps:

[0075] S301, selecting mid- and late-stage production data of unfractured coalbed methane wells when bottomhole pressure, gas production, and water production are stable, and collecting the production time, gas production, water production, and bottomhole pressure of the coalbed methane wells for a preset period of time;

[0076] S302, set the maximum value Max of the critical desorption pressure assumption value to the original coal seam pressure P e , the minimum value Min is the minimum value of the bottom hole pressure P during the collection period w ; Assume that the critical desorption pressure of each cycle is half of the maximum and minimum values, that is, (Max+Min) / 2;

[0077] S303, calculate the value on the left side of formula (10), that is, Calculate the value on the left side of formula (16), that is Based on formula (20) and the current moment and the previous moment Value, calculate the slope at the current moment;

[0078]

[0079] Among them, C t represents the slope at time t; represents the calculated value on the left side of equation (20) at time t; represents the calculated value on the left side of formula (20) at time t-1;

[0080] S304: Calculate the slope at any time within the time period through step S303, and calculate the average slope C based on the arithmetic mean. ave ;

[0081]

[0082] Among them, t total Represents the total number of days of this production period; C ave represents the average slope of this production period;

[0083] S305: Compare the slope at any moment with the average slope and calculate the slope deviation ε at each moment t ;

[0084] ε t =abs(C t -C ave ) / C ave (30);

[0085] If the slope deviation at each moment is less than 1%, the cycle is stopped and the critical desorption pressure at the current moment is the accurate value; if the slope deviation at any moment is greater than 1%, it is considered that the condition is not met and the process returns to step S302; if the slope deviation increases with the production time, the critical desorption pressure assumed at the current moment is set to the maximum value Max in step S302; if the slope deviation decreases with the production time, the critical desorption pressure assumed at the current moment is set to the minimum value Min in step S302.

[0086] Furthermore, in step S3, for a fractured coalbed methane well, the process of simultaneously analyzing the gas and water production data equations and solving the critical desorption pressure of the coalbed methane reservoir by bisection iteration includes the following steps:

[0087] S311, selecting mid- and late-stage production data of fractured coalbed methane wells when bottomhole pressure, gas production, and water production are stable; collecting the production time, gas production, water production, bottomhole pressure, and fracture half-length of the coalbed methane wells for a preset time period;

[0088] S312, set the maximum value Max of the critical desorption pressure assumption value to the original coal seam pressure P e , the minimum value Min is the minimum value of the bottom hole pressure P during the collection period w ; Assume that the critical desorption pressure of each cycle is half of the maximum and minimum values, that is, (Max+Min) / 2;

[0089] S313, calculate the value on the left side of formula (25), that is, Calculate the value on the left side of formula (26), that is Based on formula (27) and the current moment and the previous moment Value, calculate the slope at the current moment;

[0090] S314: Calculate the slope at any time within the time period through step S313, and calculate the average slope C based on the arithmetic mean. ave ;

[0091] S315, compare the slope at any moment with the average slope and calculate the slope deviation ε at each moment t ; If the slope deviation at each moment is less than 1%, stop the cycle and the critical desorption pressure at the current moment is the accurate value; if the slope deviation at any moment is greater than 1%, it is considered that the condition is not met and return to step S312 for loop calculation; among them, if the slope deviation increases with the increase of production time, the critical desorption pressure assumed at the current moment is set to the maximum value Max in step S302; if the slope deviation decreases with the increase of production time, the critical desorption pressure assumed at the current moment is set to the minimum value Min in step S302.

[0092] Beneficial effects:

[0093] The method for determining the critical desorption pressure of coalbed methane reservoirs based on mid- and late-stage production data proposed in this paper first "linearizes" the mid- and late-stage gas production equation, assumes that the water saturation of the reservoir is stable in the mid- and late-stage of coalbed methane development and the desorption zone expands at a uniform rate, and then analyzes the critical desorption pressure of coalbed methane reservoirs using the plate method. The linear relationship between the production days t and the production days t. Similarly, the water production data of gas wells can be analyzed by the plate method. The critical desorption pressure of a coalbed methane reservoir is solved by iteratively using the "bisection method" based on a linear relationship between the pressure and the number of production days t. This method inverts the critical desorption pressure based on mid- to late-stage coalbed methane production data, providing a simple and adaptable production data analysis method that facilitates coalbed methane development plan formulation and capacity forecasting. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 This is a schematic diagram of the principle of dynamic expansion of the desorption zone during the production process of coalbed methane wells;

[0095] Figure 2 Determine a flow chart for the critical desorption pressure of an unfractured coalbed methane well;

[0096] Figure 3 Flowchart for determining the critical desorption pressure for fractured coalbed methane wells. DETAILED DESCRIPTION

[0097] The following examples may enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0098] The entry of desorbed gas from the matrix into the cleat system occurs instantaneously, disregarding the fluid mass transfer process within the coal matrix. The focus is on the impact of fluid saturation and flow within the cleat system on CBM well productivity. Initially, coal cleats are generally assumed to be saturated with water. As production progresses, the coal reservoir pressure decreases, allowing desorbed gas from the matrix system to enter the cleat system, causing the cleat system's water saturation to begin to decrease. Notably, during the mid-to-late production phase of a CBM well, water saturation within the cleat remains relatively stable, barely changing over time.

[0099] For unfractured coalbed methane wells, the mid-to-late gas production equation is:

[0100]

[0101] Among them, q g-1 Represents the daily gas production of unfractured coalbed methane wells, in m 3 / d;K g represents gas permeability, in mD; h represents coal seam thickness, in m; P e Represents the initial pressure of the coal seam, in MPa; P w represents the bottom hole pressure, in MPa; T represents the coal reservoir temperature, in K; Represents pressure (P e +P w ) / 2 gas viscosity, unit is cp; Represents pressure (P e +P w ) / 2, dimensionless gas compressibility factor; re Represents the distance between the coalbed methane reservoir boundary and the bottom of the well, in meters; r w represents the wellbore radius, in meters; S represents the gas well skin factor, which is dimensionless.

[0102] It should be noted that in the middle and late stages of coalbed methane well production, the pressure at the distal end of the coal reservoir will drop to the critical desorption pressure and remain near the critical desorption pressure for a considerable period of time. Studies have tracked the pressure drop characteristics of the gas reservoir boundary during the entire production life cycle of coalbed methane and found that the boundary pressure changes from the initial coalbed pressure (P e ) drops to the critical desorption pressure (P d ) takes dozens of days, and then it will maintain at the critical desorption pressure for thousands of days. This is because after the coal reservoir pressure is lower than the critical desorption pressure, the internal flow is gas-water two-phase flow, which greatly hinders the pressure transmission speed and causes the boundary pressure to drop slowly. Therefore, P in formula (1) e Items can be P in the later stages of production d In addition, the dynamic pressure field of coal reservoir in the middle and late stages can be considered as the expansion process of the desorption zone with the critical desorption pressure as the maximum value. The desorption zone is the coal seam where the reservoir pressure is lower than the critical desorption pressure (such as Figure 1 As shown in Figure 2). For the reservoir inside the desorption zone, the fluid is mainly gas-water two-phase flow or single-phase gas, and the pressure drop distribution changes from the bottom hole pressure (P w ) to the critical desorption pressure (P d ); For the external reservoir of the desorption zone, the fluid is composed of single-phase water. The external coal seam pressure is near the critical desorption pressure for a long time. The pressure difference is very small and can be ignored in engineering calculations. Therefore, in the middle and late stages of production, it is considered that the external reservoir of the desorption zone does not contribute to the production of the coalbed methane well. The r of formula (1) e The term can be replaced by the distance r between the edge of the desorption zone and the bottom of the well d , we get formula (2):

[0103]

[0104] Without considering the problems of imperfect gas well perforation technology and reservoir pollution around the well, the skin factor is considered to be zero, and the following is obtained:

[0105]

[0106] The water saturation of the coal cleat remains stable in the middle and late stages of production, which means that the gas permeability does not change in this stage. The following equation (3) can be transformed to:

[0107]

[0108] For the right side of Equation (4), the gas permeability (K g), reservoir thickness (h), and reservoir temperature (T) are all constants. Furthermore, the product of the average methane viscosity and the compressibility factor can be considered a constant at low pressures (less than 10 MPa). Coalbed methane reservoirs are typical low-pressure gas reservoirs, with the initial pressure of most reservoirs less than 10 MPa. Equation (4) can be further simplified as:

[0109]

[0110] Where C1 represents a constant.

[0111] For the left side of equation (5), the wellbore radius is a constant. The desorption zone gradually expands outward with time, showing a linear relationship, as follows:

[0112]

[0113] Among them, C2 and C3 represent constants, and t represents production time in days.

[0114] From formula (5), we can know that:

[0115]

[0116] make:

[0117]

[0118] Formula (7) can be simplified as:

[0119]

[0120] Combining equations (6) and (9), we can obtain:

[0121]

[0122] According to formula (10), There is a linear relationship with t. For any time in the middle and late stages of the production of unfractured coalbed methane wells, record the production time (t), daily gas production (q g-1 ) and bottom hole pressure (P w ), it is only necessary to assume that the critical desorption pressure of the coalbed methane reservoir (P d ) can be obtained in the rectangular coordinate system The relationship curve between t and t. If the curve satisfies the linear relationship, the critical desorption pressure is assumed. If it does not satisfy the linear relationship, the assumption is continued. It should be noted here that multiple solutions may occur, that is, assuming that multiple critical desorption pressures can all obtain a linear relationship. To eliminate the possible multiple solutions, the water production data analysis method in the middle and late stages of production is introduced here, ignoring the influence of the capillary force of the gas and water phases of the coal rock cut. The water production equation of the unfractured coalbed methane well in the middle and late stages is:

[0123]

[0124] Among them, q w-1 Represents daily water production, unit is m 3 / d;K w Represents water phase permeability, unit is mD; μ w Represents the viscosity of the water phase, the unit is cp.

[0125] By transforming formula (11), we can get:

[0126]

[0127] Combining equation (12) and equation (6), we get:

[0128]

[0129] In the middle and late stages of coalbed methane production, the water permeability (K w ), reservoir thickness (h) and water phase viscosity (μ w ) is a constant, formula (13) can be further transformed into:

[0130]

[0131]

[0132] Wherein, C5 is a constant.

[0133] From formula (15), we can get:

[0134]

[0135] Formula (16) is similar to formula (10), indicating that There is a linear relationship with the production time t.

[0136] Adding linear relationship (10) to linear relationship (16), we get:

[0137]

[0138] make:

[0139]

[0140]

[0141] Among them, C6 and C7 are constants.

[0142] get:

[0143]

[0144] In the middle and late stages of production, the production time, gas production, water production and bottom hole pressure were recorded to obtain data in Table 1. Assuming the critical desorption pressure, the corresponding values of each production time were calculated. and Calculate the corresponding left side value of formula (20) and draw it in the rectangular coordinate system If the curve shows a linear relationship with the production time t, the critical desorption pressure of the coalbed methane reservoir is an assumed value. If it does not show a linear relationship, the calculation process is continued in a cycle.

[0145] Table 1. Coalbed methane well mid- and late-stage production data processing table

[0146]

[0147]

[0148] In addition, observing equations (10) and (16), it can be seen that the calculated value on the left side is monotonically related to the assumed critical desorption pressure, and the increase is getting larger and larger. If the assumed critical desorption pressure is greater than the accurate value, as the assumed value increases, the deviation of the relationship between the rectangular coordinate system and the linear relationship becomes larger; if the assumed value is less than the accurate value, as the assumed value decreases, the deviation of the relationship between the linear relationship also increases. Moreover, if the assumed value is greater than the actual value, the slope of the relationship gradually increases with production time; if the assumed value is less than the actual value, the slope of the relationship gradually decreases with production time. Therefore, in the above iterative calculation, the "binary method" can be used to assign the assumed critical desorption pressure for each cycle. If the slope of the relationship in the previous cycle gradually increases with production time, it indicates that the assumed value is too large, and the assumed value should be reduced in the next cycle; if the slope of the relationship in the previous cycle gradually decreases with production time, it indicates that the assumed value is too small, and the assumed value should be increased in the next cycle. The maximum value of the critical desorption pressure in the "binary method" cycle is set to the initial coal seam pressure, and the minimum value is the bottom hole pressure. During the cyclic calculation, when the slope of the relationship (the slope calculated value at each moment, see the data in the rightmost column of Table 1) changes less than 1% with the production time, the cycle ends; if it is not satisfied, the cycle is repeated.

[0149] The above describes an analysis method for mid- to late-stage production data from unfractured CBM wells. However, to pursue economical and efficient CBM development, most coal seams currently undergo fracturing. Therefore, it is also necessary to provide an analysis method for mid- to late-stage production data from fractured CBM wells. It should be noted that the analysis methods for fractured CBM wells are similar to those for unfractured CBM wells and will be briefly described below.

[0150] Unlike the "circular" expansion of the desorption zone in unfractured coalbed methane wells, the desorption zone in fractured coalbed methane wells expands in an "elliptical" shape. The expansion speed of the desorption zone along the fracture tip is faster than that perpendicular to the fracture direction. In the middle and late stages of production, the gas and water production equations of fractured coalbed methane wells are:

[0151]

[0152]

[0153] Among them, q g-2 With q w-2 Respectively represent the gas production and water production of fractured coalbed methane wells, unit is m 3 / d;L f Represents the half-length of the crack, in m; r a With r b They represent the major and minor semi-axes of the desorption zone of the fractured coalbed methane well, respectively, and the unit is m.

[0154] As the coalbed methane well produces, the desorption zone continues to expand outward, and the gap between the major and minor semi-axes of the desorption zone will become smaller and smaller, gradually changing from an ellipse to a circle. The invention focuses on the middle and late stages of coalbed methane well production, and believes that the desorption zone in the middle and late production stages has evolved from an ellipse to a circle. The assumption here is that the expansion distance of the desorption zone is much greater than the fracture half-length (Lf). At this time, equations (21) and (22) can be transformed into:

[0155]

[0156]

[0157] Observe the gas production equation (3), water production equation (11) of unfractured coalbed methane well and the gas production equation (23), water production equation (24) of fractured coalbed methane well. The only difference between them is the r of unfractured coalbed methane well. w Item is replaced by L f / 2 items. Due to r w With L f / 2 can be treated as a constant and will not affect the subsequent cycle process and calculation method. Therefore, the method for determining the critical desorption pressure of fractured coalbed methane wells can be used for unfractured coalbed methane wells. The specific calculation equation has been given in this embodiment and will not be further deduced in detail.

[0158] From the above analysis, we can see that for fractured coalbed methane wells, the following two linear relationships still exist:

[0159]

[0160]

[0161] Observing Equations (25) and (26), since the calculated values on the left sides of Equations (25) and (26) still show a monotonic relationship with the assumed critical desorption pressure, the above-mentioned “dichotomy method” can still be used to solve the critical desorption pressure of coalbed methane reservoirs.

[0162] Similar to unfractured CBM wells, the final linear relationship judgment equation for fractured CBM wells is:

[0163]

[0164] It should also be noted that the data in columns 1 to 4 of Table 1 are collected and recorded on-site. The critical desorption pressure is assumed in any cycle. For unfractured coalbed methane wells, the data in columns 5 and 6 are calculated by formula (10) and formula (16), respectively. For fractured coalbed methane wells, the data in columns 5 and 6 are calculated by formula (25) and formula (26), respectively. For the slope calculation at any moment, based on formula (27), the sum of the calculated values on the left side of the current production moment is subtracted from the sum of the calculated values on the left side of the previous production moment, and then divided by the production interval. Since the production interval is only one day apart, the slope at any moment is the sum of the calculated values on the left side of the current production moment minus the sum of the calculated values on the left side of the previous production moment. The specific formula is shown at the nth moment in Table 1. The specific iterative calculation process is shown in Figure 2 (Unfractured CBM wells) and Figure 3 (Fracturing Coalbed Methane Wells).

[0165] See also Figure 2 For unfractured CBM wells, the steps for determining the critical desorption pressure based on the production data in the middle and late stages of production are as follows:

[0166] ① Select the mid-to-late production data of unfractured CBM wells, which generally require stable bottom hole pressure, gas production, and water production.

[0167] ② Collect the production time, gas production, water production and bottom hole pressure of the coalbed methane well within a period of time (required to be more than 100 days).

[0168] ③ The maximum value of the critical desorption pressure is assumed to be the original coal seam pressure (P e ), the minimum value is the minimum value of the bottom hole pressure during the collection period.

[0169] ④ Assume that the critical desorption pressure of each cycle is half of the maximum and minimum values in step ③, that is, (Max+Min) / 2.

[0170] ⑤The value on the left side of formula (10), that is Calculate the value on the left side of formula (16), that is

[0171] ⑥ In formula (20) and the current moment and the previous moment Value, calculate the slope at the current moment:

[0172]

[0173] Among them, C t represents the slope at time t; represents the calculated value on the left side of equation (20) at time t; Represents the calculated value on the left side of equation (20) at time t-1.

[0174] ⑦ Obtain the slope at any time during the time period through step ⑥, and calculate the average slope C based on the arithmetic mean. ave :

[0175]

[0176] Among them, t total Represents the total number of days of this production period; C ave Represents the average slope of this production period.

[0177] ⑧ Compare the slope at any moment with the average slope and calculate the slope deviation ε at each moment t ;

[0178] ε t =abs(C t -C ave ) / C ave (30);

[0179] If the slope deviation at any moment is greater than 1%, it is considered that the condition is not met and it is necessary to return to step ③ for loop calculation; here, if the slope deviation increases with the increase of production time, the maximum value of step ③ is set to the critical desorption pressure assumed at the current moment; if the slope deviation decreases with the increase of production time, the minimum value of step ③ is set to the critical desorption pressure assumed at the current moment; until the slope deviation at each moment is less than 1%, the cycle is stopped and the critical desorption pressure at the current moment is the accurate value.

[0180] See also Figure 3 For fractured coalbed methane wells, the steps for determining the critical desorption pressure based on production data in the middle and late stages of production are as follows:

[0181] ① Select the mid- and late-stage production data of fractured coalbed methane wells, which generally require stable bottom hole pressure, gas production, and water production.

[0182] ② Collect the production time, gas production, water production, bottom hole pressure and fracture half-length of the coalbed methane well within a period of time (required to be more than 100 days).

[0183] ③ Set the maximum value of the critical desorption pressure assumption to the original coal seam pressure (P e ), the minimum value is the minimum value of the bottom hole pressure during the collection period.

[0184] ④ Assume that the critical desorption pressure of each cycle is half of the maximum and minimum values in step ③, that is, (Max+Min) / 2.

[0185] ⑤Calculate the value on the left side of formula (25), that is Calculate the value on the left side of formula (26), that is

[0186] ⑥ Based on formula (27) and the current moment and the previous moment value, calculate the slope at the current moment.

[0187] ⑦ Obtain the slope at any time within the time period through step ⑥, and calculate the average slope C based on the arithmetic mean. ave .

[0188] ⑧ Compare the slope at any moment with the average slope and calculate the slope deviation ε at each moment t If the slope deviation at any moment is greater than 1%, it is considered that the condition is not met and it is necessary to return to step ③ for loop calculation. Here, if the slope deviation increases with the increase of production time, the maximum value of step ③ is set to the critical desorption pressure assumed at the current moment. If the slope deviation decreases with the increase of production time, the minimum value of step ③ is set to the critical desorption pressure assumed at the current moment. The cycle is stopped until the slope deviation at each moment is less than 1%, and the critical desorption pressure at the current moment is the accurate value.

Claims

1. A method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data, characterized in that: The determination method comprises the following steps: S1, assuming that the water saturation of the reservoir is stable in the middle and late stages of coalbed methane development and the desorption zone expands at a uniform rate, the gas production equation in the middle and late stages is linearized and analyzed by the graphic method. The linear relationship between the desorption zone and the production days t is obtained, and the gas production data analysis equation is obtained; the desorption zone is the coal seam where the reservoir pressure is lower than the critical desorption pressure. For the reservoir inside the desorption zone, the fluid is mainly gas-water two-phase flow or single-phase gas, and the pressure drop distribution changes from the bottom hole pressure P w Critical desorption pressure P at the edge of the desorption zone d ; When it is an unfractured coalbed methane well, q g is the daily gas production of unfractured coalbed methane wells q g-1 , when it is a fractured coalbed methane well, q g is the daily gas production of the fractured coalbed methane well q g-2 ; S2, linearize the water production equation in the middle and late stages, analyze the water production data of gas wells by the plate method, and analyze The linear relationship between q and production days t is obtained, and the water production data analysis equation is obtained; when it is an unfractured coalbed methane well, q w is the daily water production of the unfractured CBM well q w-1 , when it is a fractured coalbed methane well, q w is the daily water production of the fractured CBM well q w-2 ; S3, the gas and water production data analysis equations are combined to solve the critical desorption pressure of the coalbed methane reservoir through bisection iteration.

2. The method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data according to claim 1, characterized in that: In step S1, for an unfractured coalbed methane well, the process of obtaining a gas production data analysis equation includes the following steps: S101, for unfractured coalbed methane wells, the mid-to-late gas production equation is: Among them, q g-1 Represents the daily gas production of unfractured coalbed methane wells, in m 3 / d;K g represents gas permeability, in mD; h represents coal seam thickness, in m; P e Represents the initial pressure of the coal seam, in MPa; P w represents the bottom hole pressure, in MPa; T represents the coal reservoir temperature, in K; Represents pressure (P e +P w ) / 2 gas viscosity, unit is cp; Represents pressure (P e +P w ) / 2, dimensionless gas compressibility factor; r e Represents the distance between the coalbed methane reservoir boundary and the bottom of the well, in meters; r w represents the wellbore radius, in meters; S represents the gas well skin factor, dimensionless; S102, r in formula (1) e The term is replaced by the distance r between the edge of the desorption zone and the bottom of the well d , we get formula (2): Without considering the problems of imperfect gas well perforation technology and reservoir pollution around the well, the skin factor is considered to be zero, and the following is obtained: The water saturation of the coal cleat remains stable in the middle and late stages of production. By transforming formula (3), we can obtain: For the right side of formula (4), the gas permeability K g , reservoir thickness h, reservoir temperature T, are all constants; Formula (4) can be further simplified as: Where C1 represents a constant; S103, for the left side of equation (5), the wellbore radius is a constant; the desorption zone gradually expands outward with time, showing a linear relationship, which is: Among them, C2 and C3 represent constants, and t represents production time in days; S104 is obtained from formula (5): make: Simplify formula (7) to: S105, combining equations (6) and (9), we obtain: According to the analysis of formula (10), There is a linear relationship with t; for any time in the middle and late stages of production of unfractured coalbed methane wells, record the production time t and daily gas production q g-1 and bottom hole pressure P w , by assuming that the critical desorption pressure of coalbed methane reservoir P d In the rectangular coordinate system, we get and t relationship curve; if the curve satisfies the linear relationship, the assumed value is the critical desorption pressure; if it does not satisfy the linear relationship, continue to assume.

3. The method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data according to claim 2, characterized in that: In step S2, for an unfractured coalbed methane well, the process of obtaining a water production data analysis equation includes the following steps: S201, without considering the capillary force of gas and water phases in coal rock cutting, the water production equation of unfractured coalbed methane wells in the middle and late stages is: Among them, q w-1 Represents daily water production, unit is m 3 / d;K w Represents water phase permeability, unit is mD; μ w Represents the viscosity of the water phase, the unit is cp; S202, transform equation (11) to obtain: Combining equation (12) and equation (6), we get: S203, in the middle and late stages of coalbed methane production, the water permeability K w , reservoir thickness h and water phase viscosity μ w is a constant, and Equation (13) is further transformed into: Among them, C5 is a constant; S204, obtained from formula (15) The linear relationship between it and production time: S205, using linear relationship (10) plus linear relationship (16), we get: make: Among them, C6 and C7 are constants; get: In the middle and late stages of production, record the production time, daily gas production, daily water production and bottom hole pressure, and assume the critical desorption pressure to calculate the corresponding pressure for each production time. and Calculate the corresponding left side value of formula (20) and draw it in the rectangular coordinate system If the curve shows a linear relationship with the production time t, the critical desorption pressure of the coalbed methane reservoir is an assumed value. If it does not show a linear relationship, the calculation process is continued in a cycle.

4. The method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data according to claim 3, characterized in that: For fractured coalbed methane wells, the process of obtaining the gas production data analysis equation includes the following steps: In the middle and late stages of production, the gas and water production equations of fractured coalbed methane wells are: Among them, q g-2 With q w-2 Respectively represent the daily gas production and water production of fractured coalbed methane wells, in m 3 / d;L f Represents the half-length of the crack, in m; r a With r b They represent the long semi-axis and short semi-axis of the desorption zone of the fractured coalbed methane well, respectively, in meters; K w Represents water phase permeability, unit is mD; μ w Represents the viscosity of the water phase, the unit is cp; P d represents the critical desorption pressure at the edge of the desorption zone; K g represents gas permeability, in mD; h represents coal seam thickness, in m; P w represents the bottom hole pressure, in MPa; T represents the coal reservoir temperature, in K; Represents pressure (P e +P w ) / 2 gas viscosity, unit is cp; Represents pressure (P e +P w ) / 2, dimensionless; assuming that in the middle and late stages of coalbed methane well production, the desorption zone extension distance is much greater than the fracture half-length L f , transform equations (21) and (22) into: S113, for fractured coalbed methane wells, there are two linear relationships: The final linear relationship judgment equation for fractured coalbed methane wells is: C8, C9, C 10 、C 11 、C 12 and C 13 are all constants.

5. The method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data according to claim 3, characterized in that: In step S3, for an unfractured coalbed methane well, the process of analyzing the gas and water production data by combining the equations and iteratively solving the critical desorption pressure of the coalbed methane reservoir by the bisection method includes the following steps: S301, selecting mid- and late-stage production data of unfractured coalbed methane wells when bottomhole pressure, daily gas production, and daily water production are stable, and collecting the production time, daily gas production, daily water production, and bottomhole pressure of the coalbed methane wells for a preset period of time; S302, set the maximum value Max of the critical desorption pressure assumption value to the original coal seam pressure P e , the minimum value Min is the minimum value of the bottom hole pressure P during the collection period w ; Assume that the critical desorption pressure of each cycle is half of the maximum and minimum values, that is, (Max+Min) / 2; S303, calculate the value on the left side of formula (10), that is, Calculate the value on the left side of formula (16), that is Based on formula (20) and the current moment and the previous moment Value, calculate the slope at the current moment; Among them, C t represents the slope at time t; represents the calculated value on the left side of equation (20) at time t; represents the calculated value on the left side of formula (20) at time t-1; S304: Calculate the slope at any time within the time period through step S303, and calculate the average slope C based on the arithmetic mean. ave ; Among them, t total Represents the total number of days of this production period; C ave represents the average slope of this production period; S305: Compare the slope at any moment with the average slope and calculate the slope deviation ε at each moment t ; ε t =abs(C t -C ave ) / C ave (30)； If the slope deviation at each moment is less than 1%, the cycle is stopped and the critical desorption pressure at the current moment is the accurate value; if the slope deviation at any moment is greater than 1%, it is considered that the condition is not met and the process returns to step S302; if the slope deviation increases with the production time, the critical desorption pressure assumed at the current moment is set to the maximum value Max in step S302; if the slope deviation decreases with the production time, the critical desorption pressure assumed at the current moment is set to the minimum value Min in step S302.

6. The method for determining the critical desorption pressure of a coalbed methane reservoir based on mid- to late-stage production data according to claim 5, characterized in that: In step S3, for a fractured coalbed methane well, the gas and water production data analysis equations are combined to iteratively solve the critical desorption pressure of the coalbed methane reservoir by bisection method, including the following steps: S311, selecting mid- and late-stage production data of fractured coalbed methane wells when bottomhole pressure, daily gas production, and daily water production are stable; collecting the production time, daily gas production, daily water production, bottomhole pressure, and fracture half-length of the coalbed methane wells for a preset time period; S312, set the maximum value Max of the critical desorption pressure assumption value to the original coal seam pressure P e , the minimum value Min is the minimum value of the bottom hole pressure P during the collection period w ; Assume that the critical desorption pressure of each cycle is half of the maximum and minimum values, that is, (Max+Min) / 2; S313, calculate the value on the left side of formula (25), that is, Calculate the value on the left side of formula (26), that is Based on formula (27) and the current moment and the previous moment Value, calculate the slope at the current moment; S314: Calculate the slope at any time within the time period through step S313, and calculate the average slope C based on the arithmetic mean. ave ; S315, compare the slope at any moment with the average slope and calculate the slope deviation ε at each moment t ; If the slope deviation at each moment is less than 1%, stop the cycle and the critical desorption pressure at the current moment is the accurate value; if the slope deviation at any moment is greater than 1%, it is considered that the condition is not met and return to step S312 for loop calculation; among them, if the slope deviation increases with the increase of production time, the critical desorption pressure assumed at the current moment is set to the maximum value Max in step S312; if the slope deviation decreases with the increase of production time, the critical desorption pressure assumed at the current moment is set to the minimum value Min in step S312.

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