CN112878987A - Method for calculating shale gas well control reserves by using production data - Google Patents

Method for calculating shale gas well control reserves by using production data Download PDF

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CN112878987A
CN112878987A CN202110098565.8A CN202110098565A CN112878987A CN 112878987 A CN112878987 A CN 112878987A CN 202110098565 A CN202110098565 A CN 202110098565A CN 112878987 A CN112878987 A CN 112878987A
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张艺钟
杨龙
张茂林
鞠斌
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Abstract

The invention discloses a method for calculating shale gas well control reserves by using production data, which aims at the defects that the pressure drop equation of the conventional shale gas reservoir does not consider free gas in a crack, and simultaneously aims at the defects of low porosity and low permeability, slow pressure recovery influences production and difficult application of the pressure drop equation of the shale gas reservoir in the process of closing a well and back pressure. The idea of calculating the formation pressure by using the shale gas reservoir pressure drop equation considering the free gas in the fracture and by assuming single well control reserves and using single well production data is provided, and the formation pressure can be obtained under the condition of not closing the well. And then, regression is carried out by adopting a derived equation and utilizing the calculated formation pressure and single-well production data to obtain the control reserve of the single well. And finally, comparing the difference value of the assumed single-well control reserve and the calculated single-well control reserve until the precision requirement is met, and automatically calculating the single-well control reserve by adopting a test algorithm, so that the problem that the average formation pressure is difficult to measure is solved, and the accuracy of reserve calculation is improved.

Description

Method for calculating shale gas well control reserves by using production data
Technical Field
The invention relates to the field of evaluation of shale gas well control reserves, in particular to a method for calculating shale gas well control reserves by using production data.
Background
At present, shale gas well control reserves commonly used at home and abroad are calculated by a material balance method, a pressure drop method and a flowing material balance method, and the application of the methods needs to measure the average formation pressure. For a low-porosity and low-permeability gas reservoir of the shale gas reservoir, the average formation pressure measured by closing a well and measuring the back pressure can influence production; in addition, free gas in the cracks is not considered in the methods, the considered factors are incomplete, and the calculation result is inaccurate. Thus, the existing calculation methods are still to be improved and improved.
Disclosure of Invention
In view of the defects of the prior art, the invention provides the method for calculating the shale gas well control reserves by using the production data, the single-well control reserves can be calculated by using the production dynamic data without closing the well and measuring the pressure, and the practicability of the method is improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a method for calculating shale gas well control reserves by using production data, which comprises the following steps:
s1, acquiring basic data of the gas well, wherein the basic data comprises static data: the organic matter comprises a substrate bound water saturation, a langmuir volume, a langmuir pressure, a substrate porosity, a shale density, a gas reservoir original temperature, a gas reservoir original pressure, a kerogen density, an adsorption phase porosity in the organic matter, a free porosity in the organic matter and a TOC content; phase state data: pressure and compression factor, pressure and gas viscosity; production data: daily gas production, accumulated gas production and bottom hole flow pressure;
s2, assuming that the reserves are controlled by a single well, and calculating the average formation pressure by using a shale gas reservoir pressure drop equation considering free gas in the fracture;
s3, according to the average formation pressure calculated in the step S2, a derivation equation of a shale gas reservoir pressure drop equation considering free gas in the fracture is utilized, and the single well control reserve is calculated by utilizing gas well production data fitting regression;
s4, comparing the difference value of the single well control reserve assumed in the step S2 with the single well control reserve calculated in the step S3, if the difference value meets the precision requirement, stopping calculation, wherein the assumed single well control reserve is the required single well control reserve; if not, the single well control reserve assumed in step S2 is made equal to the single well control reserve calculated in step S3, and steps S2-S4 are repeated
Further, in step S2, the shale gas reservoir pressure drop equation considering the free gas in the fracture is as follows:
Figure BDA0002915224260000021
wherein:
Figure BDA0002915224260000022
Figure BDA0002915224260000023
Figure BDA0002915224260000024
Figure BDA0002915224260000025
Figure BDA0002915224260000026
Figure BDA0002915224260000027
Figure BDA0002915224260000028
Figure BDA0002915224260000029
Figure BDA00029152242600000210
Figure BDA00029152242600000211
Figure BDA0002915224260000031
Figure BDA0002915224260000032
Figure BDA0002915224260000033
in the formula: p is the formation pressure, MPa; z*To correct the compression factor; gpFor cumulative production, 108m3(ii) a G is the control reserve, 108m3(ii) a Z is a deviation factor; c. CmThe compression coefficient of the matrix rock is 1/MPa; c. CwThe coefficient of compression of the bound water is 1/MPa; c. CfThe compression coefficient of the fractured rock is 1/MPa; rhobIs rock density, g/cm3；ρscIs the density of shale gas in g/cm under the ground condition3；ρsDensity of the adsorbed phase in g/cm under formation conditions3；VE(p) is the isothermal adsorption capacity, m3/t；VD(p) is solubility, m3/m3；GmFree gas reserves in the matrix, 108m3；sfree、Ca、Cd、Cmf、CadIs an intermediate variable, and has no dimension; gaFor adsorbed gas reserves at virgin formation pressure, 108m3；GdDissolved gas reserves at virgin formation pressure, 108m3；BgIs the volume coefficient, m3/m3；GfFree gas reserves in cracks, 108m3；sfwcIrreducible water saturation in the fracture, f; phi is afFracture porosity, f; phi is amIs the matrix porosity, f; smwcIrreducible water saturation in the matrix, f; t is the formation temperature, K; TOC is organic carbon content,%; phi is aadsIs the porosity of an adsorption phase in organic matters, f; phi is aorgIs free porosity, f, in the organic matter; rhokoIs the density of kerogen in g/cm3；VLIs the Langmuir volume, m3/t；pLLane pressure, MPa; p is a radical ofscThe pressure under standard conditions is MPa; t isscTemperature under standard conditions, K; zscIs a deviation factor under standard conditions; i is an initial state; b1＝-0.018931；b2＝-0.85048；b3＝827.26；b4＝-635.26。
Further, in step S3, the equation for calculating the single-well controlled reserves by fitting regression using the gas well production data is:
Figure BDA0002915224260000034
wherein:
Figure BDA0002915224260000035
Figure BDA0002915224260000036
Figure BDA0002915224260000037
Figure BDA0002915224260000041
Figure BDA0002915224260000042
Figure BDA0002915224260000043
Figure BDA0002915224260000044
Figure BDA0002915224260000045
Figure BDA0002915224260000046
solving to obtain:
Figure BDA0002915224260000047
in the formula: μ is the gas viscosity, mPas; m (p)i) Simulating pressure, MPa, for the original formation2/mPa·s；m(pwf) Is the bottom hole pseudo pressure, MPa2/mPa·s；
Figure BDA0002915224260000048
Simulating time for material balance, d; q (t) is the daily gas production, m3D; k is permeability, μm2(ii) a h is the effective thickness of the reservoir, m; r iseIs the equivalent percolation radius, m; r iswIs the wellbore radius, m;
Figure BDA0002915224260000049
is a comprehensive compression coefficient, MPa-1；cgIs a free gas compression coefficient, MPa-1；
Figure BDA00029152242600000410
Simulating the compressibility, MPa, for rock and bound water expansion-1；
Figure BDA00029152242600000411
Simulating the compression factor for the volume change of the adsorption phase, MPa-1；
Figure BDA00029152242600000412
Simulating a compressibility factor, MPa, for the adsorbed gas-1；
Figure BDA00029152242600000413
Simulating the compression coefficient for the solution gas, MPa-1；kpssIs the slope of the regression analysis of equation (15).
Compared with the prior art, the method for calculating the shale gas well control reserves by using the production data does not need to carry out well shut-in pressure measurement, and can obtain the single-well control reserves and the average formation pressure only by analyzing the existing production data of the gas well under the condition of not influencing the production plan of the gas well; meanwhile, the method provided by the invention considers the free gas in the crack, the considered factors are more perfect, and the calculation result is more accurate.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a production dynamic diagram for an X3 well provided by the present invention;
FIG. 3 is a shale gas well reserves calculation fit of an X3 well provided by the present invention;
Detailed Description
The invention provides a method for calculating shale gas well control reserves by utilizing production data, and in order to make the purposes, technical schemes and effects of the invention clearer and clearer, the invention is further described in detail by referring to the attached drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, a method for calculating a shale gas well control reserve using production data according to an embodiment of the present invention includes the following steps:
s1, acquiring basic data of the gas well, wherein the basic data comprises static data: the organic matter comprises a substrate bound water saturation, a langmuir volume, a langmuir pressure, a substrate porosity, a shale density, a gas reservoir original temperature, a gas reservoir original pressure, a kerogen density, an adsorption phase porosity in the organic matter, a free porosity in the organic matter and a TOC content; phase state data: pressure and compression factor, pressure and gas viscosity; production data: daily gas production, accumulated gas production and bottom hole flow pressure;
specifically, the method comprises the following steps:
analyzing and obtaining a relational expression between pressure and a compression factor by adopting a regression analysis method and utilizing data between the pressure and the compression factor, wherein Z is f (p);
analyzing a relation between pressure and a compression factor by using data between the pressure and the gas viscosity by adopting a regression analysis method, wherein mu is g (p);
s2, assuming that the reserves are controlled by a single well, and calculating the average formation pressure by using a shale gas reservoir pressure drop equation considering free gas in the fracture;
the shale gas reservoir pressure drop equation considering the free gas in the fracture is:
Figure BDA0002915224260000051
wherein:
Figure BDA0002915224260000061
Figure BDA0002915224260000062
Figure BDA0002915224260000063
Figure BDA0002915224260000064
Figure BDA0002915224260000065
Figure BDA0002915224260000066
Figure BDA0002915224260000067
Figure BDA0002915224260000068
Figure BDA0002915224260000069
Figure BDA00029152242600000610
Figure BDA00029152242600000611
Figure BDA00029152242600000612
Figure BDA00029152242600000613
in the formula: p is the formation pressure, MPa; z*To correct the compression factor; gpFor cumulative production, 108m3(ii) a G is the control reserve, 108m3(ii) a Z is a deviation factor; c. CmThe compression coefficient of the matrix rock is 1/MPa; c. CwThe coefficient of compression of the bound water is 1/MPa; c. CfThe compression coefficient of the fractured rock is 1/MPa; rhobIs rock density, g/cm3；ρscIs the density of shale gas in g/cm under the ground condition3；ρsDensity of the adsorbed phase in g/cm under formation conditions3；VE(p) is the isothermal adsorption capacity, m3/t；VD(p) is solubility, m3/m3；GmFree gas reserves in the matrix, 108m3；sfree、Ca、Cd、Cmf、CadIs an intermediate variable, and has no dimension; gaFor adsorbed gas reserves at virgin formation pressure, 108m3；GdDissolved gas reserves at virgin formation pressure, 108m3；BgIs the volume coefficient, m3/m3；GfFree gas reserves in cracks, 108m3；sfwcIrreducible water saturation in the fracture, f; phi is afFracture porosity, f; phi is amIs the matrix porosity, f; smwcIrreducible water saturation in the matrix, f; t is the formation temperature, K; TOC is organic carbon content,%; phi is aadsIs the porosity of an adsorption phase in organic matters, f; phi is aorgIs free porosity, f, in the organic matter; rhokoIs the density of kerogen in g/cm3；VLIs the Langmuir volume, m3/t；pLLane pressure, MPa; p is a radical ofscThe pressure under standard conditions is MPa; t isscTemperature under standard conditions, K; zscIs a deviation factor under standard conditions; i is an initial state; b1＝-0.018931；b2＝-0.85048；b3＝827.26；b4＝-635.26。
S3, due to the fact that the shale gas reservoir is low in porosity and permeability and slow in pressure recovery, the material balance method is not suitable for calculating reserves of the shale gas reservoir, but abundant production data exist in actual production. Therefore, the derivation may use methods of production dynamics data to calculate control reserves for a single well.
Order:
C＝Cmf+Cad+Ca+Cd (15)
substituting (15) into (7) yields:
Figure BDA0002915224260000071
defining the pseudo pressure:
Figure BDA0002915224260000072
(1) the formula is derived over time to obtain:
Figure BDA0002915224260000073
then there are:
Figure BDA0002915224260000081
and because:
Figure BDA0002915224260000082
substituting (19) and (20) into (18) can obtain:
Figure BDA0002915224260000083
Figure BDA0002915224260000084
order:
Figure BDA0002915224260000085
and:
Figure BDA0002915224260000086
Figure BDA0002915224260000087
Figure BDA0002915224260000088
Figure BDA0002915224260000089
Figure BDA0002915224260000091
Figure BDA0002915224260000092
Figure BDA0002915224260000093
then the simultaneous (21) and (23) result in:
Figure BDA0002915224260000094
under the quasi-steady flow state, for the case of variable flow/variable pressure, the material balance quasi-time is introduced:
Figure BDA0002915224260000095
integrating (31) and substituting (32) into (31) yields:
Figure BDA0002915224260000096
substituting (10) into (33) can obtain:
Figure BDA0002915224260000097
the following steps are provided:
Figure BDA0002915224260000098
substituting equation (35) into (34) and deriving it yields:
Figure BDA0002915224260000099
at any radius r, equation (36) can be organized as:
Figure BDA00029152242600000910
suppose that
Figure BDA00029152242600000911
Then from equation (36) and equation (37) one can obtain:
Figure BDA0002915224260000101
from darcy's law:
Figure BDA0002915224260000102
Figure BDA0002915224260000103
by substituting formulae (40) and (17) for formula (39):
Figure BDA0002915224260000104
suppose that
Figure BDA0002915224260000105
Very small, then equation (41) can be deformed as:
Figure BDA0002915224260000106
Figure BDA0002915224260000107
formula (42) may be substituted for formula (43):
Figure BDA0002915224260000108
integrating to obtain:
Figure BDA0002915224260000109
order:
Figure BDA00029152242600001010
substituting (45) into (44) to obtain:
m(p)＝m(pwf)+qbpss (46)
substitution of formula (46) for formula (33) can be achieved:
Figure BDA00029152242600001011
Figure BDA0002915224260000111
according to equation (48), the single well control reserve can be calculated.
S4, comparing the difference value of the single well control reserve assumed in the step S2 with the single well control reserve calculated in the step S3, if the difference value meets the precision requirement, stopping calculation, wherein the assumed single well control reserve is the required single well control reserve; if not, the steps S2-S4 are repeated with the single well control reserve assumed in step S2 equal to the single well control reserve calculated in step S3.
In a specific application, basic data of a gas well is collected, including static data: the organic matter comprises a substrate bound water saturation, a langmuir volume, a langmuir pressure, a substrate porosity, a shale density, a gas reservoir original temperature, a gas reservoir original pressure, a kerogen density, an adsorption phase porosity in the organic matter, a free porosity in the organic matter and a TOC content; phase state data: pressure and compression factor, pressure and gas viscosity; production data: daily gas production, accumulated gas production and bottom hole flow pressure; production dynamics data are shown in figure 2.
By adopting the shale gas well reserves calculation method provided by the invention, a shale gas well reserves calculation fitting graph can be obtained, as shown in FIG. 3, the graph shows that the method provided by the invention has high fitting degree, and the correlation coefficient reaches 0.9944; the reserves calculation results are shown in the following table 1, and the calculation results are rich.
TABLE 1 reserves calculation results
Item Value of
Controlling the reserve (10)4m3) 12213.9394
Free gas reserve of substrate (10)4m3) 6982.5706
Fracture free gas reserve (10)4m3) 1914.4133
Adsorbed gas reserves (10)4m3) 1735.8552
Reserve of dissolved gas (10)4m3) 1581.1002
In summary, the method for calculating the shale gas well control reserves by using the production data can solve the problem that the gas well production is influenced by the well closing back pressure in the reserve calculation process; meanwhile, the considered factors are more comprehensive, the calculation result is more accurate, and the method has high application value.
It should be understood that equivalents and modifications of the technical solution and inventive concept thereof may occur to those skilled in the art, and all such modifications and alterations should fall within the scope of the appended claims.

Claims (3)

1. A method for calculating shale gas well control reserves by using production data is characterized by comprising the following steps:
s1, acquiring basic data of the gas well, wherein the basic data comprises static data: the organic matter comprises a substrate bound water saturation, a langmuir volume, a langmuir pressure, a substrate porosity, a shale density, a gas reservoir original temperature, a gas reservoir original pressure, a kerogen density, an adsorption phase porosity in the organic matter, a free porosity in the organic matter and a TOC content; phase state data: pressure and compression factor, pressure and gas viscosity; production data: daily gas production, accumulated gas production and bottom hole flow pressure;
s2, assuming that the reserves are controlled by a single well, and calculating the average formation pressure by using a shale gas reservoir pressure drop equation considering free gas in the fracture;
s3, according to the average formation pressure calculated in the step S2, a derivation equation of a shale gas reservoir pressure drop equation considering free gas in the fracture is utilized, and the single well control reserve is calculated by utilizing gas well production data fitting regression;
s4, comparing the difference value of the single well control reserve assumed in the step S2 with the single well control reserve calculated in the step S3, if the difference value meets the precision requirement, stopping calculation, wherein the assumed single well control reserve is the required single well control reserve; if not, the steps S2-S4 are repeated with the single well control reserve assumed in step S2 equal to the single well control reserve calculated in step S3.
2. The method of utilizing production data to calculate shale gas well control reserves of claim 1 wherein in step S2 the shale gas reservoir pressure drop equation for the free gas in the fracture is considered as:
Figure FDA0002915224250000011
wherein:
Figure FDA0002915224250000012
Figure FDA0002915224250000013
Figure FDA0002915224250000014
Figure FDA0002915224250000021
Figure FDA0002915224250000022
Figure FDA0002915224250000023
Figure FDA0002915224250000024
Figure FDA0002915224250000025
Figure FDA0002915224250000026
Figure FDA0002915224250000027
Figure FDA0002915224250000028
Figure FDA0002915224250000029
Figure FDA00029152242500000210
in the formula: p is the formation pressure, MPa; z*To correct the compression factor; gpFor cumulative production, 108m3(ii) a G is the control reserve, 108m3(ii) a Z is a deviation factor; c. CmThe compression coefficient of the matrix rock is 1/MPa; c. CwThe coefficient of compression of the bound water is 1/MPa; c. CfThe compression coefficient of the fractured rock is 1/MPa; rhobIs rock density, g/cm3；ρscIs the density of shale gas in g/cm under the ground condition3；ρsDensity of the adsorbed phase in g/cm under formation conditions3；VE(p) is the isothermal adsorption capacity, m3/t；VD(p) is solubility, m3/m3；GmFree gas reserves in the matrix, 108m3；sfree、Ca、Cd、Cmf、CadIs an intermediate variable, and has no dimension; gaFor adsorbed gas reserves at virgin formation pressure, 108m3；GdDissolved gas reserves at virgin formation pressure, 108m3；BgIs the volume coefficient, m3/m3；GfFree gas reserves in cracks, 108m3；sfwcIrreducible water saturation in the fracture, f; phi is afFracture porosity, f; phi is amIs the matrix porosity, f; smwcIrreducible water saturation in the matrix, f; t is the formation temperature, K; TOC is organic carbon content,%; phi is aadsIs the porosity of an adsorption phase in organic matters, f; phi is aorgIs free porosity, f, in the organic matter; rhokoIs the density of kerogen in g/cm3；VLIs the Langmuir volume, m3/t；pLLane pressure, MPa; p is a radical ofscThe pressure under standard conditions is MPa; t isscTemperature under standard conditions, K; zscIs a deviation factor under standard conditions; i is an initial state; b1＝-0.018931；b2＝-0.85048；b3＝827.26；b4＝-635.26。
3. The method of utilizing production data to calculate shale gas well control reserves of claim 1 wherein in step S3, utilizing gas well production data, fitting a regression to calculate the equation for single well control reserves is:
Figure FDA0002915224250000031
wherein:
Figure FDA0002915224250000032
Figure FDA0002915224250000033
Figure FDA0002915224250000034
Figure FDA0002915224250000035
Figure FDA0002915224250000036
Figure FDA0002915224250000037
Figure FDA0002915224250000038
Figure FDA0002915224250000039
Figure FDA00029152242500000310
solving to obtain:
Figure FDA00029152242500000311
in the formula: μ is the gas viscosity, mPas; m (p)i) Simulating pressure, MPa, for the original formation2/mPa·s；m(pwf) Is the bottom hole pseudo pressure, MPa2/mPa·s；
Figure FDA00029152242500000312
Simulating time for material balance, d; q (t) is the daily gas production, m3D; k is permeability, μm2(ii) a h is the effective thickness of the reservoir, m; r iseIs the equivalent percolation radius, m; r iswIs the wellbore radius, m;
Figure FDA0002915224250000041
is a comprehensive compression coefficient, MPa-1；cgIs a free gas compression coefficient, MPa-1；
Figure FDA0002915224250000042
Simulating the compressibility, MPa, for rock and bound water expansion-1；
Figure FDA0002915224250000043
Simulating the compression factor for the volume change of the adsorption phase, MPa-1；
Figure FDA0002915224250000044
Simulating a compressibility factor, MPa, for the adsorbed gas-1；
Figure FDA0002915224250000045
Simulating pressure for dissolved gasCoefficient of shrinkage, MPa-1；kpssIs the slope of the regression analysis of equation (15).
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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN113464129A (en) * 2021-08-03 2021-10-01 中国石油大学(北京) Method and device for calculating average formation pressure of coal bed gas reservoir
CN116050629A (en) * 2023-01-18 2023-05-02 重庆科技学院 Dynamic prediction method for storage capacity of gas storage in consideration of formation water evaporation salting-out
CN117634900A (en) * 2023-11-07 2024-03-01 中国科学院地质与地球物理研究所 Shale in-situ gas quantity evaluation method and device, computer equipment and storage medium

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