Method for determining productivity of coalbed methane well without shutting down the well

Abstract

A method for determining a productivity of a coalbed methane well without shutting down the well includes steps of: obtaining coalbed methane basic data; based on PVT experimental data, determining a relationship table between a pressure and a coalbed methane deviation factor, and a relationship table between the pressure and a pseudo-pressure; recording daily gas production rates, bottomhole flow pressures, and cumulative gas productions at each stabilized flow pressure test moment in at least three different production stages; determining formation pressures corresponding to each stabilized flow pressure test moment based on a material balance equation; according to the formation pressures, the bottomhole flow pressures and the production rates, determining coefficients in a deliverability equation of the coalbed methane well for determining the deliverability equation; substituting the formation pressures and the bottomhole flow pressures into the deliverability equation for obtaining corresponding productivity.

Description

CROSS REFERENCE OF RELATED APPLICATION

The present invention claims priority under 35 U.S.C. 119(a-d) to CN 202311456011.6, filed Nov. 3, 2023.

BACKGROUND OF THE PRESENT INVENTION

Field of Invention

The present invention relates to coalbed methane development and research, and more particularly to a method for determining a productivity of a coalbed methane well without shutting down the well.

Description of Related Arts

Determining the deliverability equation and productivity of coalbed methane wells is a very important daily work in dynamic analysis, which is also an important basis for the prediction of gas well production law, analysis of production potential and optimization of working system. To determine the productivity of gas wells, it is necessary to determine the deliverability equation thereof, and the determination of the deliverability equation of gas wells mainly adopts a well test method, which requires shutting down the wells to carry out the pressure build-up test, thus affecting the production of the well. On the other hand, due to the large fracturing scale of conventional coalbed methane wells, the amount of fluid used is often over 1 ten-thousand cubic meters, even up to 5 ten-thousand cubic meters or more. As a result, it is easy to water flooded and difficult to resume production after shutting down the wells. There are few reports in the literature on determining the deliverability equations of gas wells without shutting down the wells, and less than five articles are available. The method of determining the deliverability equation of a gas well without shutting down the well reported in the literature needs to satisfy two conditions: one is that the formation pressure remains basically unchanged during different stabilized bottomhole flow pressure tests of the gas well; and the other is that the gas well must maintain a stabilized seepage state during the bottomhole flow pressure tests of the gas well under various production conditions. Stabilized bottomhole flow pressure tests under three different production conditions are often required to determine the gas well deliverability equation. The permeability of coal seams is generally less than 0.1 mD, and the permeability is relatively poor, which leads to the fact that it usually takes a long time to re-achieve a stabilized seepage state after the production rate of a coalbed methane well is changed, resulting in significant changes in the formation pressure corresponding to the moment of the stabilized bottomhole flow pressure tests, and it is difficult to keep it basically unchanged. Consequently, for coalbed methane wells, the reported method for determining the gas well deliverability equation without shutting down the wells has application conditions that are difficult to satisfy, so it cannot be applied to coalbed methane wells. The following is a brief introduction to the related knowledge.

Validation of the application conditions of conventional method for determining the gas well deliverability equations without shutting down the wells:

It is known from the literature that a period required for a gas well to re-attain a stabilized seepage state after the operating regime is changed (i.e., after the production rate is changed) can be calculated by equation (1).

$\begin{array}{cc}t=74.241\frac{\varnothing S_g{\overline{u}}_g{r}^2}{K{P}_r}& \left(1\right)\end{array}$

wherein t is a time period required for the gas well to stabilize seepage, hours; ∅ is a porosity of a gas layer, decimal; S_g is a gas saturation, decimal; ū_g is a gas viscosity, mPa·s; r is a gas drainage radius, m; K is a gas formation permeability, mD; P_r is a formation pressure, MPa.

The following is an example of the relevant parameters of a typical deep coalbed methane horizontal well in a block to verify that for coalbed methane wells, the application conditions of the conventional method for determining the gas well deliverability equation without shutting down the well are difficult to satisfy. The corresponding average reservoir porosity of a coalbed methane well is ∅=0.05; gas saturation is S_g=0.7; gas viscosity under formation conditions is ū_g=0.02 mPa·s; drainage radius of gas wells is r=160 m; effective formation permeability is K=0.1 mD; and formation pressure is P_r=28 MPa. Based on the above parameters, the calculation using equation (1) shows that it takes 475.14 hours, about 19.8 days, for the gas well to re-achieve a stabilized seepage state after changing the working regime. If the continuous stabilized flow pressure test is carried out under three different production rates (4.5 ten-thousand cubic meters per day, 3 ten-thousand cubic meters per day, and 1.5 ten-thousand cubic meters per day), it will take about 59.4 days, and the cumulative gas production from the gas well during this period will be 4.5*19.8+3*19.8+1.5*19.8=178.2 ten-thousand cubic meters. The average dynamic reserve of the deep coalbed methane horizontal well in this area is about 5500 ten-thousand cubic meters, then according to the material balance equation, after extracting 178.2 ten-thousand cubic meters of gas, the formation pressure will significantly change about 178.2/5500*28=0.9072 MPa. Therefore, for coalbed methane wells, the prerequisite of “the formation pressure remains basically unchanged during the gas well flow pressure test” required by the conventional method for determining the gas well deliverability equations is difficult to be satisfied.

SUMMARY OF THE PRESENT INVENTION

An object of the present invention is to provide a method for determining a productivity of a coalbed methane well without shutting down the well, thereby solving a technical problem that applicable conditions of conventional method for determining a deliverability equation of a gas well without shutting down the well are difficult to be satisfied.

Accordingly, in order to accomplish the above objects, the present invention provides a method for determining a productivity of a coalbed methane well without shutting down the well, comprising steps of:

• • step 1: obtaining basic data of a target coalbed methane well, comprising coalbed methane PVT experimental data, an original formation pressure P_Ri, a bottomhole flow pressure P_wf of the coalbed methane well during production, and a daily production rate q_sc;
  • step 2: based on the coalbed methane PVT experimental data obtained in the step 1, determining a relationship table between a pressure P and a coalbed methane deviation factor Z, and further determining a relationship table between the pressure P and a pseudo-pressure P_s, wherein P_s=P/Z;
  • step 3: performing stabilized bottomhole flow pressure test under constant production conditions in no less than three production stages of the coalbed methane well, and recording daily gas production rates q_sc(1), q_sc(2), . . . , q_sc(n), bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n), and cumulative gas productions GP₍₁₎, GP₍₂₎, . . . , GP_(n) of the coalbed methane well at each stabilized flow pressure test moment;
  • step 4: setting an initial iterative assumption value G0 of a gas well dynamic reserve, combining the cumulative gas productions GP₍₁₎, GP₍₂₎, . . . , GP_(n) at each stabilized flow pressure test moment in different production stages, and determining formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) corresponding to each stabilized flow pressure test moment based on a material balance equation;
  • step 5: according to the formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) corresponding to each stabilized flow pressure test moment determined based on the material balance equation, the bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n) and the production rates q_sc(1), q_sc(2), . . . , q_sc(n), determining coefficients A and B in a binomial deliverability equation for the coalbed methane well: P_R²−Pwf²=Aq_sc+Bq_sc², wherein P_R is the formation pressure, P_wf is the bottomhole flow pressure of the coalbed methane well, and q_sc is the daily production rate of the coalbed methane well;
  • step 6: based on the binomial deliverability equation for the coalbed methane well P_R²−Pwf²=Aq_sc+Bq_sc² determined in the step 5, combining the bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n) and the production rates q_sc(1), q_sc(2), . . . , q_sc(n) corresponding to each stabilized flow pressure test moment obtained in the step 3, and adopting P_R=√{square root over (Pwf²=Aq_sc+Bq_sc²)} to determine formation pressures P_Rp(1), P_Rp(2), . . . , P_Rp(n) corresponding to each stabilized flow pressure test moment, which means obtaining the formation pressures P_Rp(1), P_Rp(2), . . . , P_Rp(n) based on the binomial deliverability equation; and
  • step 7: performing an error test between the formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) based on the material balance equation and the formation pressures P_Rp(1), P_Rp(2), . . . , P_Rp(n) based on the binomial deliverability equation corresponding to each stabilized flow pressure test moment; if an error between the formation pressures obtained by different methods fails to meet a preset accuracy requirement, then repeating the steps 4-6 to iterate until the preset accuracy requirement is satisfied, wherein the binomial deliverability equation obtained when the preset accuracy requirement is met is a deliverability equation for the coalbed methane well; substituting the formation pressures and the bottomhole flow pressures into the deliverability equation of the coalbed methane well for solving, thereby obtaining the productivity of the coalbed methane well under corresponding formation pressure and bottomhole flow pressure conditions.

Preferably, in the step 4, the formation pressures corresponding to each stabilized flow pressure test moment are determined as follows:

• • determining formation pseudo-pressures P_Rs(1), P_Rs(2), . . . , P_Rs(n) corresponding to each stabilized flow pressure test moment based on a pseudo-pressure material balance equation, and then adopting interpolation or function fitting to calculate the corresponding formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) based on the relationship table between the pressure P and the pseudo-pressure P_s.

Preferably, in the step 5, the coefficients A and B in the binomial deliverability equation for the coalbed methane well are determined by:

• • making

$y_{\left(i\right)}=\frac{P_{R\left(i\right)}^2-P_{\mathrm{wf}\left(i\right)}^2}{q_{\mathrm{sc}\left(i\right)}},$

• •  x_(i)=q_sc(i), i=1, 2, . . . , n; according to the gas production rates q_sc(1), q_sc(2), . . . , q_sc(n) of the coalbed methane well at each stabilized flow pressure test moment in different production stages and corresponding bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n), obtaining a series of observation points (y_(i), x_(i)); processing observation point data with linear fit, so that A is equal to an intercept of a linear equation obtained from the linear fit, and B is equal to a slope of the linear equation obtained from the linear fit.

Beneficial Effects

• • (1) The method of the present invention effectively overcomes the shortcomings of conventional well test method in determining the deliverability equation of gas wells, which requires shutting down the wells and affects the production. The method also avoids the problem that applicable conditions of conventional method for determining the deliverability equation of a gas well without shutting down the well are difficult to be satisfied, and fills in the blank of “determining the productivity of coalbed methane wells without shutting down the wells”.
  • (2) Determining the deliverability equation and productivity of coalbed methane wells is a very important daily work in dynamic analysis, which is also an important basis for the prediction of gas well production law, analysis of production potential and optimization of working system, thus having a very important practical value for mining
  • (3) The method of the present invention is simple, easy to understand and realize, highly operable, effective and practical, which deserves popularization and utilization.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of a method for determining a productivity of a coalbed methane well without shutting down the well according to an embodiment of the present invention;

FIG. 2 is functional relationship fitting between a pseudo-pressure and a pressure; and

FIG. 3 is linear fitting for observation points.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1 of the drawings, the present invention provides a method for determining a productivity of a coalbed methane well without shutting down the well, comprising steps of:

• • step 1: obtaining basic data of a target coalbed methane well, comprising coalbed methane PVT experimental data, an original formation pressure P_Ri, a bottomhole flow pressure P_wf of the coalbed methane well during production, and a daily production rate q_sc;
  • step 2: based on the coalbed methane PVT experimental data obtained in the step 1, determining a relationship table between a pressure P and a coalbed methane deviation factor Z, and further determining a relationship table between the pressure P and a pseudo-pressure P_s, wherein P_s=P/Z;
  • step 3: performing stabilized bottomhole flow pressure test under constant production conditions in no less than three production stages of the coalbed methane well, and recording daily gas production rates q_sc(1), q_sc(2), . . . , q_sc(n), bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n), and cumulative gas productions GP₍₁₎, GP₍₂₎, . . . , GP_(n) of the coalbed methane well at each stabilized flow pressure test moment;
  • step 4: setting an initial iterative assumption value G0 of a gas well dynamic reserve, combining the cumulative gas productions GP₍₁₎, GP₍₂₎, . . . , GP_(n) at each stabilized flow pressure test moment in different production stages, and determining formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) corresponding to each stabilized flow pressure test moment based on a material balance equation; and then adopting interpolation or function fitting to calculate the corresponding formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) based on the relationship table between the pressure P and the pseudo-pressure P_s·(P_s=P/Z);
  • step 5: according to the formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) corresponding to each stabilized flow pressure test moment determined based on the material balance equation, the bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n) and the production rates q_sc(1), q_sc(2), . . . , q_sc(n), making

$y_{\left(i\right)}=\frac{P_{R\left(i\right)}^2-P_{\mathrm{wf}\left(i\right)}^2}{q_{\mathrm{sc}\left(i\right)}},$

• •  x_(i)=q_sc(i), i=1, 2, . . . , n, and obtaining a series of observation points (y_(i), x_(i)); processing observation point data with linear fit for determining coefficients A and B in a binomial deliverability equation for the coalbed methane well: P_R²−Pwf²=Aq_sc+Bq_sc², wherein A is equal to an intercept of a linear equation obtained from the linear fit, and B is equal to a slope of the linear equation obtained from the linear fit;
  • step 6: based on the binomial deliverability equation for the coalbed methane well P_R²−Pwf²=Aq_sc+Bq_sc² determined in the step 5, combining the bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n) and the production rates q_sc(1), q_sc(2), . . . , q_sc(n) corresponding to each stabilized flow pressure test moment obtained in the step 3, and adopting P_R=√{square root over (Pwf²=Aq_sc+Bq_sc²)} to determine formation pressures P_Rp(1), P_Rp(2), . . . , P_Rp(n) corresponding to each stabilized flow pressure test moment, which means obtaining the formation pressures P_Rp(1), P_Rp(2), . . . , P_Rp(n) based on the binomial deliverability equation; and
  • step 7: performing an error test between the formation pressures P_Rm(1), P_Rm(2), . . . , P_Rm(n) based on the material balance equation and the formation pressures P_Rp(1), P_Rp(2), . . . , P_Rp(n) based on the binomial deliverability equation corresponding to each stabilized flow pressure test moment; if an error between the formation pressures obtained by different methods fails to meet a preset accuracy requirement, then repeating the steps 4-6 to iterate until the preset accuracy requirement is satisfied, wherein the binomial deliverability equation obtained when the preset accuracy requirement is met is a deliverability equation for the coalbed methane well; substituting the formation pressures and the bottomhole flow pressures into the deliverability equation of the coalbed methane well for solving, thereby obtaining the productivity of the coalbed methane well under corresponding formation pressure and bottomhole flow pressure conditions.

EXPLANATION OF SYMBOLS

P_Ri: original formation pressure, MPa; P_wf: bottomhole flow pressure, MPa; q_sc: gas well production rate, ten-thousand cubic meters per day; P: pressure, MPa; Z: gas deviation factor, dimensionless, decimal; P_s (P_s=P/Z): pseudo-pressure, MPa; g_sc(i): daily production rate corresponding to stabilized flow pressure test point i, ten-thousand cubic meters per day; P_wf(i): stabilized bottomhole flow pressure corresponding to the production rate q_sc(i); GP_(i): cumulative gas production corresponding to stabilized flow pressure test point i, ten-thousand cubic meters; P_Rm(i): formation pressure corresponding to stabilized flow pressure test point i based on material balance equation; P_Rp(i): formation pressure corresponding to stabilized flow pressure test point i based on deliverability equation; i: stabilized flow pressure test point number, i=1, 2, . . . , n; P_R: formation pressure, MPa; G₀: dynamic reserve, ten-thousand cubic meters.

Preferably, in the step 4, the pseudo-pressure material balance equation is

$P_{Rs}=\left(1-\frac{G_P}{G_0}\right)P_{Rsi},$

which is specifically derived as follows:

An expression for generalized material balance equation is:

$\begin{array}{cc}\frac{P_R}{z}=\left(1-\frac{G_P}{G_0}\right)\frac{P_{Ri}}{z_i}& \left(2\right)\end{array}$

• • wherein P_R is the formation pressure, and Z is the gas deviation factor corresponding to the formation pressure P_R; G_P is the cumulative gas production, and G₀ is the dynamic reserve; P_Ri is the original formation pressure, and Z_i is the deviation factor corresponding to the original formation pressure P_Ri.

A ratio of the formation pressure P_R to its corresponding deviation factor Z is defined as the pseudo-pressure P_Rs, and a ratio of the original formation pressure P_Ri to its corresponding deviation factor Z_i is defined as the pseudo-pressure P_Rsi, i.e.:

$\begin{array}{cc}{P}_{Rs}=\frac{P_R}{z}& \left(3\right)\end{array}$ $\begin{array}{cc}{P}_{Rsi}=\frac{P_{Ri}}{z_i}& \left(4\right)\end{array}$

• • then from Eqs. (2), (3), and (4), the material balance equation based on the pseudo-pressure can be obtained:

$\begin{array}{cc}{P}_{Rs}=\left(1-\frac{G_P}{G_0}\right)P_{Rsi}& \left(5\right)\end{array}$

Eq. (5) is the pseudo-pressure material balance equation to be used in the present invention. If the pseudo-pressure P_Rsi of the original formation pressure P_Ri, the cumulative production G_P of the gas well and the dynamic reserve G₀ have been determine, the pseudo-pressure P_Rs of the corresponding formation pressure P_R can be determined by Eq. (5). Then, according to the relationship table between pressure and the pseudo-pressure of the formation pressure, the corresponding formation pressure can be determined by an interpolation method or function fitting method.

Preferably, in the step 5, the coefficients in the binomial deliverability equation for the coalbed methane well are determined by:

• • the binomial deliverability equation for the gas well is:

$\begin{array}{cc}{P}_R^2-P_{wf}^2=A{q}_{\mathrm{sc}}+B{q}_{sc}^2& \left(6\right)\end{array}$

• • dividing both ends of Eq. (6) by q_sc:

$\begin{array}{cc}\frac{P_R^2-P_{wf}^2}{q_{sc}}=A+B{q}_{sc}& \left(7\right)\end{array}$

Since the coefficients A and B in the binomial deliverability equation are constants related to formation characteristics, they can be obtained by linear fitting based on the bottomhole flow pressure and the corresponding formation pressure under different production rate conditions.

$\begin{array}{cc}\mathrm{making}{y}_{\left(i\right)}=\frac{P_{R\left(i\right)}^2-P_{\mathrm{wf}\left(i\right)}^2}{q_{\mathrm{sc}\left(i\right)}}& \left(8\right)\end{array}$
x_(i)=q_sc(i)  (9)

• • wherein i is a stabilized flow pressure test point number, i=1, 2, . . . , n; P_R(i) is a formation pressure corresponding to the stabilized flow pressure test point i; P_wf(i) is a stabilized bottomhole flow pressure corresponding to the production rate q_sc(i); and q_sc(i) is a daily production rate corresponding to the stabilized flow pressure test point i. According to the gas production rates q_sc(i), q_sc(2), . . . , q_sc(n) of the coalbed methane well at each stabilized flow pressure test moment in different production stages and corresponding bottomhole flow pressures P_wf(1), P_wf(2), . . . , P_wf(n), a series of observation points (y_(i), x_(i)) can be obtained with Eqs. (8) and (9). After processing observation point data with linear fit, it can be seen from Eq. (7) that A is equal to an intercept of a linear equation obtained from the linear fit, and B is equal to a slope of the linear equation obtained from the linear fit.

This embodiment is achieved by obtaining the basic data of a coalbed methane well; based on the coalbed methane PVT experimental data, determining a relationship table between a pressure and a coalbed methane deviation factor, and further determining a relationship table between the pressure and a pseudo-pressure (the pseudo-pressure is equal to the pressure divided by the deviation factor); performing stabilized bottomhole flow pressure test under constant production conditions in no less than three production stages of the coalbed methane well, and recording daily gas production rates, bottomhole flow pressures and cumulative gas productions; setting an initial iterative assumption value of a gas well dynamic reserve, combining the cumulative gas productions at each stabilized flow pressure test moment in different production stages, and determining formation pressures corresponding to each stabilized flow pressure test moment based on a material balance equation; according to the formation pressures corresponding to each stabilized flow pressure test moment, the bottomhole flow pressures and the production rates, determining coefficients in a binomial deliverability equation for the coalbed methane well; based on the binomial deliverability equation, combining the bottomhole flow pressures and the production rates corresponding to each stabilized flow pressure test moment, and determining formation pressures corresponding to each stabilized flow pressure test moment; and performing an error test between the formation pressures based on the material balance equation and the formation pressures based on the binomial deliverability equation corresponding to each stabilized flow pressure test moment; if an error between the formation pressures obtained by different methods fails to meet a preset accuracy requirement, then iterating until the preset accuracy requirement is satisfied, wherein the binomial deliverability equation obtained when the preset accuracy requirement is met is a deliverability equation for the coalbed methane well; substituting the formation pressures and the bottomhole flow pressures into the deliverability equation of the coalbed methane well for solving, thereby obtaining the productivity of the coalbed methane well under corresponding formation pressure and bottomhole flow pressure conditions. The method effectively overcomes the shortcomings of conventional well test method in determining the deliverability equation of gas wells, which requires shutting down the wells and affects the production. The method also avoids the problem that applicable conditions of conventional method for determining the deliverability equation of a gas well without shutting down the well are difficult to be satisfied, and fills in the blank of “determining the productivity of coalbed methane wells without shutting down the wells”. The method is simple, highly operable, effective and practical, which deserves popularization and utilization.

In addition, the technical solutions of the present invention will be further illustrated below with specific examples, but the protection scope of the present invention is not limited thereto.

Validation Example 1

A coalbed methane well has a vertical depth of 2880 m in the central part of the formation, an original formation pressure of 28 MPa, and a formation temperature of 81.3° C.

According to the method for determining the productivity of the coalbed methane well without shutting down the well of the embodiment:

• • (1) Collecting basic data of the coalbed methane well, wherein the original formation pressure P_Ri=28 MPa, and a relationship between the deviation factor and the pressure in the PVT parameters is shown in Table 1.

TABLE 1
relationship between pressure, deviation factor and pseudo-pressure
	deviation	pseudo-
pressure	factor	pressure
P	Z	Ps = P/Z
(MPa)	(decimal)	(Mpa)
31	0.9133	33.943
28	0.8805	31.800
25	0.8716	28.683
22	0.8609	25.555
19	0.8631	22.014
16	0.8619	18.564
13	0.8715	14.917
10	0.8770	11.403
8.5	0.8843	9.612
6	0.9047	6.632
3	0.9405	3.190

• • (2) According to the relationship experimental data between the coalbed methane pressure and the deviation factor obtained in the step (1), dividing the pressure P in the table by the corresponding deviation factor Z, so as to obtain a relationship table between the pressure P and the pseudo-pressure P_s (P_s=PAZ) (see Table 1); based on the relationship data between the pressure P and the pseudo-pressure P_s (P_s=P/Z), adopting function fitting (see FIG. 2) to obtain a functional relationship between the two as Ps=1.127P+0.1596.
  • (3) During production of the well, employing three production rates in three production stages, which were q_sc(1)=8.3 ten-thousand cubic meters per day, q_sc(2)=7.5 ten-thousand cubic meters per day, and q_sc(3)=7.2 ten-thousand cubic meters per day; wherein the stabilized bottomhole flow pressures under the three production rates were P_wf(1)=8.8 MPa, P_wf(2)=8.7 MPa and P_wf(3)=7.1 MPa, respectively; the cumulative gas productions at each stabilized flow pressure test moment were GP₍₁₎=173.57 ten-thousand cubic meters, GP₍₂₎=852.07 ten-thousand cubic meters and GP₍₃₎=1199.21 ten-thousand cubic meters, respectively.
  • (4) Using the functional relationship Ps=1.127P+0.1596 between the pressure P and the pseudo-pressure P_s obtained in the step (2), determining the pseudo-pressure P_Rsi=31.7156 MPa corresponding to the original formation pressure P_Ri=28 MPa; adopting a dynamic reserve iteration model where G0_(iter+1)=G0_(iter)*(1+0.021), i.e., an assumed value of dynamic reserve at the iter+1st iteration is 1.021 times to that of the iter th iteration; setting an initial iteration assumption value G0 of the gas well dynamic reserve to 3000 ten-thousand cubic meters, wherein the iteration assumption value of the dynamic reserve is G₀=7803.7867 ten-thousand cubic meters for the 46th iteration; combining the cumulative gas productions GP₍₁₎=173.57 ten-thousand cubic meters, GP₍₂₎=852.07 ten-thousand cubic meters and GP₍₃₎=1199.21 ten-thousand cubic meters at each stabilized flow pressure test moment in different production stages, and using a material balance equation based on pseudo-pressure

$P_{Rs}=\left(1-\frac{G_P}{G_0}\right)P_{Rsi}$

to determine the formation pseudo-pressures corresponding to each stabilized flow pressure test moment to be P_Rs(1)=31.0102 MPa, P_Rs(2)=28.2527 MPa and P_Rs(3)=26.8419 MPa; and then using the functional relationship Ps=1.127P+0.1596 between the pressure P and the pseudo-pressure P_s obtained in the step (2) to determine the corresponding formation pressure based on the material balance equation to be P_Rm(1)=27.3741 MPa, P_Rm(2)=24.9273 MPa and P_Rm(3)=23.6755 MPa.

• • (5) According to the formation pressures P_Rm(1)=27.3741 MPa, P_Rm(2)=24.9273 MPa and P_Rm(3)=23.6755 MPa corresponding to each stabilized flow pressure test moment determined based on the material balance equation, the bottomhole flow pressures P_wf(1)=8.8 MPa, P_wf(2)=8.7 MPa and P_wf(3)=7.1 MPa, and the production rates q_sc(1)=8.3 ten-thousand cubic meters per day, q_sc(2)=7.5 ten-thousand cubic meters per day, and q_sc(3)=7.2 ten-thousand cubic meters per day, making

$y_{\left(i\right)}=\frac{P_{R\left(i\right)}^2-P_{\mathrm{wf}\left(i\right)}^2}{q_{\mathrm{sc}\left(i\right)}},$

• •  x_(i)=q_sc(i), i=1, 2, . . . , n, and obtaining a series of observation points (y_(i), x_(i)) (see table 2); processing observation point data with linear fit (see FIG. 3) for determining coefficients in a binomial deliverability equation for the coalbed methane well:

$P_R^2-{\mathrm{Pwf}}^2={\mathrm{Aq}}_{\mathrm{sc}}+B{q}_{sc}^2,$

• •  wherein A=2.7698 and B=9.4022.

TABLE 2
Data table for observation point construction
			qsc(i)		y(i) =
observation			(ten-thousand		[Pr2(i) −
point No.	Pr(i)	Pwf(i)	cubic meters	x(i) =	pwf2(i)]/
(i)	(Mpa)	(MPa)	per day)	qsc(i)	qsc(i)
1	27.3741	8.8	8.3	8.3	80.9520
2	24.9273	8.7	7.5	7.5	72.7574
3	23.6755	7.1	7.2	7.2	70.8499

• • (6) based on the binomial deliverability equation for the coalbed methane well P_R²−Pwf²=2.7698q_sc9.4022q_sc² determined in the step 5, combining the bottomhole flow pressures P_wf(1)=8.8 MPa, P_wf(2)=8.7 MPa and P_wf(3)=7.1 MPa, and the production rates q_sc(1)=8.3 ten-thousand cubic meters per day, q_sc(2)=7.5 ten-thousand cubic meters per day, and q_sc(3)=7.2 ten-thousand cubic meters per day corresponding to each stabilized flow pressure test moment obtained in the step 3, and adopting P_R=√{square root over (Pwf²=Aq_sc+Bq_sc²)} to determine formation pressures corresponding to each stabilized flow pressure test moment to be P_Rp(1)=27.3523 MPa, P_Rp(2)=25.0067 MPa and P_Rp(3)=23.6170 MPa.
  • (7) Performing an error test between the formation pressures P_Rm(1)=27.3741 MPa, P_Rm(2)=24.9273 MPa and P_Rm(3)=23.6755 MPa based on the material balance equation obtained in the step (4) and the formation pressures P_Rp(1)=27.3523 MPa, P_Rp(2)=25.0067 MPa and P_Rp(3)=23.6170 MPa based on the binomial deliverability equation obtained in the step (6) corresponding to each stabilized flow pressure test moment; calculating relative errors with Err(i)=abs(P_Rm(i)−P_Rp(i))/P_Rm(i), wherein the relative errors between the formation pressures obtained by different methods were Err(1)=0.000797, Err(2)=0.003187 and Err(3)=0.002471, which were apparently less than 5‰, satisfying the accuracy requirements for mine application; in the iteration meeting the accuracy requirements, the coefficients of gas well deliverability equation obtained were A=2.7698 and B=9.4022, and thus the binomial deliverability equation for the gas well in the embodiment was P_R²−Pwf²=2.7698q_sc+9.4022q_sc²; when the formation pressure P_R=21 MPa and P_wf=7 MPa, the deliverability equation of the gas well was 9.4024q_sc², 2.7698q_sc−21²+7²=0; by solving the deliverability equation we can get q_sc=6.3113 ten-thousand cubic meters per day; thus, when the formation pressure was 21 MPa and the bottomhole flow pressure was 7 MPa, the productivity of the gas well was 6.3113 ten-thousand cubic meters per day.

The above is preferred embodiment of the present invention, but the embodiments of the present invention are not limited by the above description. Any modifications without deviating from the present invention shall be equivalent replacement methods, and are included in the protection scope of the present invention.

Claims

1. A method for determining a productivity of a coalbed methane well without shutting down the well, comprising steps of:

step 1: obtaining basic data of a target coalbed methane well, comprising coalbed methane PVT experimental data, an original formation pressure PRi, a bottomhole flow pressure Pwf of the coalbed methane well during production, and a daily production rate qsc;

step 2: based on the coalbed methane PVT experimental data obtained in the step 1, determining a relationship table between a pressure P and a coalbed methane deviation factor Z, and further determining a relationship table between the pressure P and a pseudo-pressure Ps, wherein Ps=P/Z;

step 3: performing stabilized bottomhole flow pressure test under constant production conditions in no less than three production stages of the coalbed methane well, and recording daily gas production rates qsc(1), qsc(2),..., qsc(n), bottomhole flow pressures Pwf(1), Pwf(2),..., Pwf(n), and cumulative gas productions GP(1), GP(2),..., GP(n) of the coalbed methane well at each stabilized flow pressure test moment;

step 4: setting an initial iterative assumption value G0 of a gas well dynamic reserve, combining the cumulative gas productions GP(1), GP(2),..., GP(n) at each stabilized flow pressure test moment in different production stages, and determining formation pressures PRm(1), PRm(2),..., PRm(n) corresponding to each stabilized flow pressure test moment based on a material balance equation;

step 5: according to the formation pressures PRm(1), PRm(2),..., PRm(n) corresponding to each stabilized flow pressure test moment determined based on the material balance equation, the bottomhole flow pressures Pwf(1), Pwf(2),..., Pwf(n) and the production rates qsc(1), qsc(2),..., qsc(n), determining coefficients A and B in a binomial deliverability equation for the coalbed methane well: PR2−Pwf2=Aqsc+Bqsc2, wherein PR is the formation pressure, Pwf is the bottomhole flow pressure of the coalbed methane well, and qsc is the daily production rate of the coalbed methane well;

step 6: based on the binomial deliverability equation for the coalbed methane well PR2−Pwf2=Aqsc+Bqsc2 determined in the step 5, combining the bottomhole flow pressures Pwf(1), Pwf(2),..., Pwf(n) and the production rates qsc(1), qsc(2),..., qsc(n) corresponding to each stabilized flow pressure test moment obtained in the step 3, and adopting PR=√{square root over (Pwf2=Aqsc+Bqsc2)} to determine formation pressures PRp(1), PRp(2),..., PRp(n) corresponding to each stabilized flow pressure test moment, which means obtaining the formation pressures PRp(1), PRp(2),..., PRp(n) based on the binomial deliverability equation; and

step 7: performing an error test between the formation pressures PRm(1), PRm(2),..., PRm(n) based on the material balance equation and the formation pressures PRp(1), PRp(2),..., PRp(n) based on the binomial deliverability equation corresponding to each stabilized flow pressure test moment; if an error between the formation pressures obtained by different methods fails to meet a preset accuracy requirement, then repeating the steps 4-6 to iterate until the preset accuracy requirement is satisfied, wherein the binomial deliverability equation obtained when the preset accuracy requirement is met is a deliverability equation for the coalbed methane well; substituting the formation pressures and the bottomhole flow pressures into the deliverability equation of the coalbed methane well for solving, thereby obtaining the productivity of the coalbed methane well under corresponding formation pressure and bottomhole flow pressure conditions.

2. The method, as recited in claim 1, wherein in the step 4, the formation pressures corresponding to each stabilized flow pressure test moment are determined as follows:

determining formation pseudo-pressures PRs(1), PRs(2),..., PRs(n) corresponding to each stabilized flow pressure test moment based on a pseudo-pressure material balance equation, and then adopting interpolation or function fitting to calculate the corresponding formation pressures PRm(1), PRm(2),..., PRm(n) based on the relationship table between the pressure P and the pseudo-pressure Ps.

3. The method, as recited in claim 1, wherein in the step 5, the coefficients A and B in the binomial deliverability equation for the coalbed methane well are determined by: y ( i ) = P R ⁡ ( i ) 2 - P wf ⁡ ( i ) 2 q sc ⁡ ( i ),

making

 x(i)=qsc(i), i=1, 2,..., n; according to the gas production rates qsc(1), qsc(2),..., qsc(n) of the coalbed methane well at each stabilized flow pressure test moment in different production stages and corresponding bottomhole flow pressures Pwf(1), Pwf(2),..., Pwf(n), obtaining a series of observation points (y(i), x(i));

processing observation point data with linear fit, so that A is equal to an intercept of a linear equation obtained from the linear fit, and B is equal to a slope of the linear equation obtained from the linear fit.