Method for determining recovery factor of deep coal bed methane wells

Description

CROSS REFERENCE OF RELATED APPLICATION

The present invention claims priority under 35 U.S.C. 119 (a-d) to CN 202311456103.4, filed Nov. 3, 2023.

BACKGROUND OF THE PRESENT INVENTION

Field of Invention

The present invention relates to the oil and gas field development research, and more particularly to a method for determining a recovery factor of a deep coal bed methane well.

Description of Related Arts

In recent years, the development technology of deep coal bed methane (CBM) has made a breakthrough, and deep CBM has become an important energy resource like conventional natural gas. Practice shows that there are both free gas and adsorbed gas in deep CBM. At present, the prediction methods of the recovery factor of CBM mainly include analogy method, desorption method, isothermal adsorption curve method and gas reservoir numerical simulation method. Among them, the analogy method is more arbitrary and less reliable, which is mainly used in the early development stage of lack of basic data. The desorption method and the isothermal adsorption curve method are widely used in the development of shallow CBM, but these two methods are only able to be used to determine the recovery factor of adsorbed gas, but are unable to consider the influence of free gas on the recovery factor of CBM, so they are not suitable for determining the recovery factor of the deep CBM in which free gas and adsorbed gas coexist. The gas reservoir numerical simulation method is able to comprehensively consider the influence of heterogeneous geological characteristics and seepage characteristics of coal bed. However, this method needs to collect a large number of data. The research process is complex and the application is difficult. Moreover, the reliability of the simulation results is greatly affected by the understanding of the researchers on geological conditions of the target area, and the experience and technical level of the researchers. Therefore, it is urgent to provide a new method for determining a recovery factor of a deep coal bed methane well.

SUMMARY OF THE PRESENT INVENTION

An object of the present invention is to provide a method for determining a recovery factor of a deep coal bed methane (CBM) well. The method is able to solve the problem that the existing technology does not consider the influence of free gas on the recovery factor of CBM, and is not suitable for the determination of the recovery factor of the deep CBM well in which free gas and adsorbed gas coexist.

Accordingly, a method for determining a recovery factor of a deep coal bed methane (CBM) well comprises steps of:

• • (step 1) collecting an original formation pressure P_i and pressure-volume-temperature (PVT) experimental data of the CBM well, obtaining deviation factors corresponding to different pressures at a formation temperature of CBM, and establishing a relationship table between the pressures and the deviation factors;
  • (step 2) obtaining isothermal adsorption experimental data, an adsorbed gas content G_0ad and a free gas content G_0f at the original formation pressure and an original temperature for the deep coal rock;
  • (step 3) according to the isothermal adsorption experimental data, determining Langmuir's pressure P_L and Langmuir's volume V_L;
  • (step 4) according to a depth of burial of the CBM well, determining an abandoned formation pressure P_ab in CBM well exploitation;
  • (step 5) according to the relationship table between the pressures and the deviation factors in the (step 1), obtaining a deviation factor Z_i at the original formation pressure P_i and a deviation factor Z_ab at the abandoned formation pressure P_ab; and (step 6) according to the original formation pressure P_i in the (step 1), the adsorbed gas content G_0ad and the free gas content G_0f at the original formation pressure and the original temperature in the (step 2), the Langmuir's pressure P_L in the (step 3), the abandoned formation pressure P_ab in the (step 4), the deviation factor Z_i at the original formation pressure P_i and the deviation factor Z_ab at the abandoned formation pressure P_ab in the (step 5), by a model of

R = G of × ( 1 - P ab ⁢ Z i P i ⁢ Z ab ) + G oad × ( 1 - P ab P i × P i × P L P ab + P L ) G oad + G of ,

• • calculating the recovery factor of the CBM well.

Preferably, the (step 3) specifically comprises:

taking ⁢ y ( i ) = 1 V g ⁡ ( i ) ⁢ and ⁢ x ( i ) = 1 P ( i ) , wherein ⁢ i = 1 , 2 , … , n ;

• • according to adsorbed gas volumes V_g(1), V_g(2), . . . , V_g(n) corresponding to different pressures P₍₁₎, P₍₂₎, . . . , P_(n) at the formation temperature of the CBM, obtaining a series of observation points (y_(i), x_(i)); and
  • obtaining a line equation by performing linear fitting on the observation points, wherein the Langmuir's volume V_L is equal to a reciprocal of an intercept of the line equation, and the Langmuir's pressure P_L is equal to a slope of the line equation divided by the intercept of the line equation.

Preferably, in the (step 4), the abandoned formation pressure P_ab in CBM well exploitation is determined by analog method or empirical formula method.

Preferably, in the (step 5), according to the relationship table between the pressures and the deviation factors in the (step 1), the deviation factor Z_i at the original formation pressure P_i and the deviation factor Z_ab at the abandoned formation pressure P_ab are obtained by interpolation method;

or according to the relationship table between the pressures and the deviation factors in the (step 1), a fitted function relationship Z=f(P) between the deviation factors and the pressures is established by taking the deviation factors as a dependent variable and the pressures as an independent variable, and then by the fitted function relationship, obtaining the deviation factor Z_i=f(P_i) at the original formation pressure P_i, and the deviation factor Z_ab=f(P_ab) at the abandoned formation pressure P_ab.

Beneficial effects as follows.

(1) Based on the PVT experimental data and the isothermal adsorption experimental data of the CBM, the present invention provides a new method for determining a recovery factor of a deep coal bed methane (CBM) well, which is able to effectively solving the problems of the analog method, desorption method, isothermal adsorption curve method and gas reservoir numerical simulation method. The method provided by the present invention not only considers the influence of free gas and adsorbed gas exploitation on the recovery factor of CBM, but also avoids the application difficulty of gas reservoir numerical simulation method. It is simple and convenient in application, easy to understand and realize, has strong operability, is effective and practical, and has good popularization and application value.

(2) The recovery factor is an essential index for development plan preparation, development benefit evaluation and development feasibility demonstration of CBM, so the determination of recovery factor has very important practical value in the mine field.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of a method for determining the recovery factor of deep coal bed methane wells according to a preferred embodiment of the present invention.

FIG. 2 is a linear fitting diagram of observation point data in the process of determining Langmuir's pressure and Langmuir's volume.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, a flow chart of a method for determining a recovery factor of a deep coal bed methane (CBM) well according to a preferred embodiment of the present invention is illustrated. The method comprises steps of:

(step 1) collecting an original formation pressure P_i and pressure-volume-temperature (PVT) experimental data of the CBM well, obtaining deviation factors corresponding to different pressures at a formation temperature of CBM, and establishing a relationship table between the different pressures and the deviation factors;

(step 2) obtaining isothermal adsorption experimental data, an adsorbed gas content G_0ad and a free gas content G_0f at the original formation pressure and an original temperature for the deep coal rock;

(step 3) according to the isothermal adsorption experimental data, determining Langmuir's pressure P_L and Langmuir's volume V_L, wherein:

• • an isothermal adsorption equation of CBM is

V g = V L × P P + P L , ( 1 )

• • by taking the reciprocal at both sides of the equation (1), an equation (2) is obtained as follows

1 V g = P + P L V L × P , ( 2 )

• • and then based on the equation (2), an equation (3) is obtained as follows

1 V g = 1 V L + P L V L × 1 P ; ( 3 ) taking ⁢ y ( i ) = 1 V g ⁡ ( i ) , and ( 4 ) x ( i ) = 1 P ( i ) , ( 5 )

• • here, i is isothermal adsorption experimental data point number, i=1, 2, . . . , n, V_g(i) (m³/t) is adsorbed gas volume at the i^th experimental data point, P_(i) (MPa) is pressure at the i^th experimental data point, V_L (m³/t) is Langmuir's volume, P_L (MPa) is Langmuir's pressure,
  • according to adsorbed gas volumes V_g(1), V_g(2), . . . , V_g(n) corresponding to different pressures P₍₁₎, P₍₂₎, . . . , P_(n) at the formation temperature of CBM in the isothermal adsorption experimental data, a series of observation points (y_(i), x_(i)) are obtained by the equations (4) and (5), linear fitting is performed on the observation points, wherein according to the equation (3), it is able to be known that the Langmuir's volume V_L is reciprocal of an intercept of a line equation obtained by linear fitting, and the Langmuir's pressure P_L is equal to a slope of the fitted line equation divided by the intercept of the fitted line equation;
  • (step 4) according to a buried depth of the CBM well, determining an abandoned formation pressure P_ab of CBM well exploitation, which comprises determining the abandoned formation pressure by analogy method or empirical formula method, wherein preferably, the abandoned formation pressure is calculated by a Meck empirical formula of P_ab=2.149×10⁻³ D, here, P_ab (MPa) is the abandoned formation pressure, D (m) is the buried depth of the CBM well;
  • (step 5) according to the relationship table between the different pressures and the deviation factors in the (step 1), obtaining deviation factors Z_i and Z_ab by interpolation method, or according to the relationship table between the different pressures and the deviation factors in the (step 1), by taking the deviation factors as a dependent variable and the pressures as an independent variable, establishing fitted function relationship Z=f(P) between the different pressures and the deviation factors, and then by the fitted function relationship, obtaining the deviation factor Z_i=f(P_i) at the original formation pressure P_i, and the deviation factor Z_ab=f(P_ab) at the abandoned formation pressure P_ab; and
  • (step 6) according to the original formation pressure P_i in the (step 1), the adsorbed gas content G_0ad and free gas content G_0f at the original formation pressure and original temperature in the (step 2), the Langmuir's pressure P_L in the (step 3), the abandoned formation pressure P_ab in the (step 4), and the deviation factor Z at the original formation pressure P_i and the deviation factor Z_ab at the abandoned formation pressure P_ab in the (step 5), using a model of

R = G of × ( 1 - P ab ⁢ Z i P i ⁢ Z ab ) + G oad × ( 1 - P ab P i × P i × P L P ab + P L ) G oad + G of

• •  to obtain the recovery factor of the CBM well, wherein:

according to the isothermal adsorption equation (1) of CBM, an adsorbed gas volume V_gi at the original formation pressure P_i is obtained and expressed by an equation of

V gi = V L × P i P i + P L , ( 6 )

• • an adsorbed gas volume V_gab at the abandoned formation pressure P_ab is expressed by an equation of

V gab = V L × P ab P ab + P L ,

• •  so an absorbed gas cumulative production G_pa at the abandoned formation pressure P_ab is expressed by an equation of

G pa = V gi - V gab = V L × P i P i + P L - V L × P ab P ab + P L , ( 7 )

• • an adsorbed gas recovery factor R_a at the abandoned formation pressure P_ab is expressed by an equation of

R a = G pa / V gi , ( 8 )

• • it is able to be obtained from the equations (6), (7) and (8) that

R a = V L × P i P i + P L × V L × P ab P ab + P L V L × P i P i + P L = 1 - P ab P i ⁢ P i + P L P ab + P L , ( 9 )

• • here, the equation (9) is a model for calculating the adsorbed gas recovery factor at the abandoned formation pressure P_ab,
  • a material balance equation of free gas is expressed as

P Z = ( 1 - G P G 0 ) ⁢ P i Z i , ( 10 )

• • a free gas recovery factor R_f at the abandoned formation pressure P_ab is expressed as an equation of

R f = G P G 0 = 1 - P ab ⁢ Z i P i ⁢ Z ab , ( 11 )

• • when the free gas content at the original formation pressure and original temperature is G_0f, and the free gas recovery factor at the abandoned formation pressure P_ab is R_f, then a free gas cumulative production G_pf at the abandoned formation pressure is expressed as an equation of

G pf = G 0 ⁢ f × R f , ( 12 )

• • it is able to be obtained from the equations (11) and (12) that

G pf = G 0 ⁢ f × ( 1 - P ab ⁢ Z i P i ⁢ Z ab ) , ( 13 )

• • when the adsorbed gas content at the original formation pressure and original temperature is G_0ad, and the adsorbed gas recovery factor at the abandoned formation pressure P_ab is R_a, then the adsorbed gas cumulative production G_pa at the abandoned formation pressure is expressed as an equation of

G pa = G 0 ⁢ ad × R a , ( 14 )

• • it is able to be obtained from the equations (9) and (14) that

G pa = G 0 ⁢ ad × ( 1 - P ab P i ⁢ P i + P L P ab + P L ) , ( 15 )

• • it is able to be obtained from the equations (13) and (15) that a total cumulative production G_p of the free gas and the adsorbed gas at the abandoned formation pressure P_ab is expressed as

G p = G pf + G pa = G 0 ⁢ f × ( 1 - P ab ⁢ Z i P i ⁢ Z ab ) + G 0 ⁢ ad × ( 1 - P ab P i ⁢ P i + P L P ab + P L ) , ( 16 )

• • then, the recovery factor R of CBM at the abandoned formation pressure P_ab is expressed as an equation of

R = G p / ( G 0 ⁢ a + G 0 ⁢ f ) = G 0 ⁢ f × ( 1 ⁢ P ab ⁢ Z i P i ⁢ Z ab ) + G 0 ⁢ ad × ( 1 - P ab ⁢ P i + P L P i ⁢ P ab + P L ) G 0 ⁢ ad + G 0 ⁢ f , ( 17 )

• • wherein the equation (17) is a computation expression of the recovery factor of CBM at the abandoned formation pressure P_ab,
  • here, P_i (MPa) is the original formation pressure, V_g(t) (m³/t) is the adsorbed gas volume at the original formation pressure P_i, P_ab (MPa) is the abandoned formation pressure, P (MPa) is the formation pressure, V_g (m³/t) is the adsorbed gas volume at the formation pressure P, G_pa (m³/t) is the adsorbed gas cumulative production at the abandoned formation pressure, R_a is the adsorbed gas recovery factor at the abandoned formation pressure and is a decimal fraction, G_pf (m³/t) is the free gas cumulative production at the abandoned formation pressure, R_f is the free gas recovery factor at the abandoned formation pressure and is a decimal fraction, z is the gas deviation factor at the formation pressure P and is a decimal fraction, Z_i is the gas deviation factor at the original formation pressure and is a decimal fraction, Z_ab is the gas deviation factor at the abandoned formation pressure P_ab and is a decimal fraction, G_P (m³) is the natural gas cumulative production, G₀ (m³) is the natural gas original reserve, G_0f (m³/t) is the free gas content at the original formation pressure and original temperature, G_0a (m³/t) is the adsorbed gas content at the original formation pressure and original temperature, R is the recovery factor of CBM at the abandoned formation pressure P_ab and is a decimal fraction, P_L (MPa) is Langmuir's pressure, and V_L (m³/t) is Langmuir's volume.

According to the preferred embodiment of the present invention, the original formation pressure and PVT experimental data are collected to establish the relationship table between the pressures and the deviation factors; the isothermal adsorption experimental data, the original adsorbed gas content and the original free gas content at the original formation pressure and original temperature for the deep coal rock are collected; the Langmuir's pressure and the Langmuir's volume are determined by the isothermal adsorption experimental data for the CBM well; the abandoned formation pressure of the CBM well is determined; the derivation factor at the original formation pressure and the derivation factor at the abandoned formation pressure are determined; based on the above original formation pressure, the original adsorbed gas content and the original free gas content at the original formation pressure and original temperature, the Langmuir's pressure, the abandoned formation pressure, the derivation factor at the original formation pressure and the derivation factor at the abandoned formation pressure, the recovery factor of the CBM well is determined. The method provided by the present invention is simple, easy to understand, operable, effective and practical, and has good popularization and application value.

In addition, the present invention is explained with the embodiment as follows, but the protective scope of the present invention is not limited to this embodiment.

First Embodiment

(1) The collected basic data of the CBM well are as follows. The original formation pressure P_i=28 MPa. The relationship between the pressures and the deviation factors of the PVT parameters is shown in Table 1.

(2) The collected isothermal adsorption experimental data for deep CBM are shown in Table 2. At the original formation pressure and original temperature, the adsorbed gas content G_0ad is 18.34 m³/t, and the free gas content G_0f is 7.66 m³/t.

(3) According to adsorbed gas volumes V_g(1), V_g(2), . . . , V_g(n) corresponding to different pressures P₍₁₎, P₍₂₎, . . . , P_(n) at the formation temperature of CBM, when

y ( i ) = 1 V g ⁡ ( i ) ,

x_(i)=1/P_(i), i=1, 2, . . . , n, a series of observation points (y_(i), x_(i)) (as shown in Table 2) are obtained. Referring to FIG. 2, the linear fitting is performed on the observation points, the Langmuir's volume V_L is reciprocal of the intercept of the line equation obtained by the linear fitting, that is,

V L = 1 0.049 = 2 ⁢ 0 . 4 ⁢ 0 ⁢ 8 ⁢ 2

m³/t, and the Langmuir's pressure P_L is equal to the slope of the fitted line equation divided by the intercept of the fitted line equation, that is,

P L = 0.1536 0.049 = 3 . 1 ⁢ 347 ⁢ MPa .

(4) The abandoned formation pressure in the CBM well exploitation is determined by analogy method or empirical formula method. In this embodiment, the abandoned formation pressure is calculated by a Meck empirical formula of P_ab=2.149×10⁻³ D, here, P_ab (MPa) is the abandoned formation pressure, D (m) is the buried depth of the CBM well and is about 2850 m, so the abandoned formation pressure is

P ab = 2.149 × 1 ⁢ 0 - 3 ⁢ D = 2 . 1 ⁢ 49 × 10 - 3 × 2850 = 6 . 1 ⁢ 2 ⁢ 4 ⁢ 6 ⁢ MPa .

(5) According to the relationship table between the pressures and the deviation factors in the step (1), by linear interpolation method, it is obtained that the gas derivation factor Z_i=0.8805 at the original formation pressure P_i=28 MPa, and the gas derivation factor Z_ab=0.9035 at the abandoned formation pressure P_ab=6.1246 MPa.

(6) According to the original formation pressure P_i=28 MPa in the step (1), the adsorbed gas content G_0ad=18.34 m³/t and the free gas content G_0f=7.66 m³/t at the original formation pressure and original temperature in the step (2), the Langmuir's pressure P_L=3.1347 MPa in the step (3), the abandoned formation pressure P_ab=6.1246 MPa in the step (4), and the deviation factor Z_i=0.8805 at the original formation pressure P_i and the deviation factor Z_ab=0.9035 at the abandoned formation pressure P_ab in the step (5), by a model of

R = G 0 ⁢ f × ( 1 - P ab ⁢ Z i P i ⁢ Z ab ) + G 0 ⁢ ad × ( 1 - P ab P i × P i + P L P ab + P L ) G 0 ⁢ ad + G 0 ⁢ f ,

the recovery factor of the CBM well is obtained, namely,

R = G 0 ⁢ f × ( 1 - P ab ⁢ Z i P i ⁢ Z ab ) + G 0 ⁢ ad × ( 1 - P ab P i × P i + P L P ab + P L ) G 0 ⁢ ad + G 0 ⁢ f = 7.66 × ( 1 - 6 . 1 ⁢ 2 ⁢ 4 ⁢ 6 × 0 . 8 ⁢ 8 ⁢ 0 ⁢ 5 2 ⁢ 8 × 0 . 9 ⁢ 0 ⁢ 3 ⁢ 5 ) + 18.34 × ( 1 - 6 . 1 ⁢ 2 ⁢ 4 ⁢ 6 2 ⁢ 8 × 2 ⁢ 8 + 3 . 1 ⁢ 3 ⁢ 4 ⁢ 7 6 . 1 ⁢ 2 ⁢ 4 ⁢ 6 + 3 . 1 ⁢ 3 ⁢ 4 ⁢ 7 ) 18.3 4 + 7 . 6 ⁢ 6 = 0.4183 .

Therefore, according to the first embodiment of the present invention, the recovery factor of the CBM well is 41.83%.

The above embodiment is the preferred embodiment of the present invention, but not the limitation to other embodiments of the present invention. Any other changes that do not deviate from the present invention shall be equivalent replacement modes and shall be included in the protective scope of the present invention.