CN115853503B - Method for calculating formation pressure of gas well based on consideration of reservoir stress sensitivity - Google Patents
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Abstract
The invention relates to a method for calculating formation pressure of a gas well based on consideration of reservoir stress sensitivity, which comprises the following steps: calculating average deviation coefficient in initial state of gas wellAnd gas viscosityFormation pressure iteration initial value at control radius at any given momentCalculating the average deviation coefficient at the momentAnd gas viscosityCalculating a binomial capacity equation coefficient A 2 and B 2 at the moment; substituting the gas yield q g2 and the bottom hole flow pressure P wf2 at the moment into a binomial capacity equation to recalculate the formation pressureWith an iterative initial value of formation pressure in step 2Or the final iteration initial value is used as the final formation pressure at the moment. According to the method, the stratum pressure at any moment can be rapidly calculated without shutting in the well by utilizing the test data before the production of the gas well, the productivity test data and the bottom hole flow pressure and the yield data at any moment, and the productivity of the gas well is evaluated, so that the method has important significance for dynamic analysis of the production of the gas well.
Description
Technical Field
The invention relates to the technical field of oil and gas field development, in particular to a quick calculation method for formation pressure of a gas well based on consideration of reservoir stress sensitivity.
Background
Formation pressure is a key parameter in assessing gas well productivity and analyzing gas well potential. The conventional methods for calculating the formation pressure mainly comprise a testing method and a calculating method. Stratum pressure is directly obtained through pressure recovery test and shut-in pressure measurement, but a tight sandstone gas reservoir is low in pressure, a reservoir is tight, pressure recovery time is long, each well cannot be tested in order to ensure production tasks and economic benefits of the gas field, and part of gas wells do not have the condition that a pressure gauge is arranged in the middle of a production layer to measure pressure. The material balance equation can be established by calculating the formation pressure by a material balance method which is commonly used at present and requiring more than 2 pressure measuring points, and the accurate measurement of the formation pressure after the production of a gas well requires closing the well to restore the pressure, so that the method is not suitable for large-scale application for low-permeability tight gas reservoirs. And the reservoir permeability changes along with the change of the formation pressure due to the reservoir stress sensitivity phenomenon, so that the calculation result of the formation pressure has larger error compared with the actual calculation result.
Therefore, how to effectively utilize production data of a gas well to realize rapid and accurate calculation of formation pressure is a problem to be solved.
Disclosure of Invention
The invention aims to solve the problems and provides a simple, quick and accurate formation pressure calculation method.
The technical scheme of the invention is as follows:
For hypotonic tight reservoirs, the non-darcy flow effect is small, so the darcy law is used to derive a planar radial flow binomial capacity equation that accounts for stress-sensitive effects. The capacity equation under quasi-steady state is known to be expressed by:
wherein: p re is the formation pressure at the radius of control at a certain moment, MPa;
P wf is the bottom hole pressure corresponding to P re, MPa; q g is ground gas production, m 3/d;
k is the gas layer permeability, 10 -3μm2; h is the effective thickness of the air layer, m;
r e is the gas well control radius, m; r w is the wellbore radius, m; r is any radius from the well axis, m;
T is the formation temperature, K;
Is the average gas viscosity, mpa.s;
is an average deviation coefficient, and is dimensionless;
P is the pressure at r and MPa.
Because of the stress sensitivity phenomenon, the gas bed permeability k changes along with the change of the formation pressure, so that the form of the productivity equation changes, and the method adopts the most commonly used exponential stress sensitivity expression:
Wherein: k i is the initial permeability of the gas layer, 10 -3μm2;
Omega is stress sensitivity index, dimensionless;
P i is the initial formation pressure, MPa;
Bringing formula (2) into formula (1) yields:
Integrating and simplifying the formula (3) to obtain the following components:
wherein: s is a skin coefficient, and is dimensionless; gamma g is the relative density of the gas, dimensionless;
A. B is the productivity equation coefficient corresponding to P re, and is dimensionless;
The initial formation pressure P i and bottom hole flow pressure P wf1 of the gas well are obtained through test data, the productivity equation coefficient A 1、B1 is obtained through productivity well test data, and the stress sensitivity index omega is obtained through experiments. The surface gas yield q g2 and the bottom hole pressure P wf2 are known at any moment, the formation pressure P re and the coefficients of the binomial productivity equations a 2 and B 2 are unknown, and the productivity equations at the moment need to be solved to obtain P re、A2 and B 2.
The solving process is as follows:
First, the capacity equation coefficient A 2、B2 and the initial capacity equation coefficient A 1、B1 at any moment are divided respectively and correspondingly:
Wherein: the method is an average deviation coefficient of a gas well in an initial state, and is dimensionless;
the average deviation coefficient corresponding to P re is dimensionless;
The average viscosity of the gas well in the initial state is mpa.s;
the average viscosity corresponding to P re, mpa.s;
A 1、B1 is a binomial capacity equation coefficient of the gas well in the initial state of the gas well, and is dimensionless;
A 2、B2 is a gas well binomial productivity equation coefficient corresponding to P re, and is dimensionless;
Wherein P re is an iteration variable; initial initiation When iteration occurs, P re = formation pressure obtained in step 4; calculating A 2 and B 2 firstly obtains the average deviation coefficient of the momentAnd gas viscosity
A method for calculating formation pressure of a gas well based on consideration of reservoir stress sensitivity comprises the following steps:
step 1: initial average formation pressure from pre-production testing of gas wells And stratum temperature T, calculating average deviation coefficient in initial state of gas wellAnd gas viscosity at initial state of gas well
Deviation coefficient Z equation:
wherein:
M＝1.39(Tpr-0.92)0.5-0.36Tpr-0.101 (10)
C＝0.132-0.32 logTpr (12)
Tpr＝T/Tpc (15)
Wherein: C. d, M, N is a fitting coefficient, dimensionless;
Is the average formation pressure, MPa;
P pr is the quasi-contrast pressure, dimensionless;
T pr represents the temperature to be compared, and has no dimension;
p pc is critical pressure, MPa; t pc is critical temperature, K;
Equation of gas viscosity:
wherein:
Y＝0.2(12-X) (19)
wherein: F. x, Y is a fitting coefficient, dimensionless;
M g is the relative molecular mass of the gas, and is dimensionless;
R is a gas constant, taking
Step 2: formation pressure iteration initial value at control radius at any given momentCalculating the average deviation coefficient at the momentAnd gas viscosity
1) Formation pressure iteration initial value at control radius at any given momentOrder theObtaining the average formation pressure at the moment
2) By average formation pressureCalculating the moment in time for the quasi-contrast pressure with the formation temperature TThe subsequent steps are the same as the step 1; further, the average deviation coefficient at the time is obtainedAnd gas viscosity
Step 3: and (3) calculating the binomial capacity equation coefficients A 2 and B 2 of the moment through the formula (7) and the formula (8).
Step 4: substituting the ground gas production q g2 and the bottom hole flow pressure P wf2 at the moment into a binomial capacity equation (4) to obtain the formation pressure
Step 5: judgingIf it meets the requirement, thenThe final formation pressure at the moment;
Otherwise, by And repeating calculation until the accuracy requirement is met as a new iteration initial value, and taking the iteration initial value which finally meets the accuracy condition as the final formation pressure at the moment.
The invention has the technical effects that:
The method provided by the invention has relatively less test data, is based on a gas well binomial productivity equation considering stress sensitivity, can realize rapid calculation of formation pressure at any moment without well shut-in by using test data before gas well production, productivity well test data and bottom hole flow pressure and yield data at any moment, evaluates gas well productivity, and has important significance for gas well production dynamic analysis.
Drawings
FIG. 1 is a flow chart of a method of calculating formation pressure for a gas well based on consideration of reservoir stress sensitivity in accordance with the present invention.
Detailed Description
A method for calculating formation pressure of a gas well based on consideration of reservoir stress sensitivity comprises the following steps:
step 1: initial average formation pressure from pre-production testing of gas wells And stratum temperature T, calculating average deviation coefficient in initial state of gas wellAnd gas viscosityThe method comprises the following specific steps:
1) By initial average formation pressure Substituting the formation temperature T into a formula (14) and a formula (15) to calculate the quasi-contrast pressure P pr1 and the quasi-contrast temperature T pr at the moment;
2) Substituting the pressure P pr1 to be compared and the temperature T pr to be compared into a formula (10) -a formula (13) to respectively calculate coefficients M 1、N1、C1 and D 1 of a deviation coefficient Z equation;
3) Substituting the coefficient M 1、N1、C1 and the coefficient D 1 into a deviation coefficient Z equation (formula (9)) to calculate and obtain the average deviation coefficient in the initial state of the gas well
4) Average deviation coefficient of gas well in initial stateCarrying out (20) calculation of the gas density rho g1;
5) Bringing the relative molecular weight M g of the gas and the formation temperature T into a formula (17) -a formula (19) to obtain parameters F 1、X1 and Y 1 required by calculating a gas viscosity equation;
6) Substituting rho g1, parameters F 1、X1 and Y 1 into (16) to calculate gas viscosity in initial state of gas well
Step 2: formation pressure iteration initial value at control radius at any given momentCalculating the average deviation coefficient at the momentAnd gas viscosity
1) Formation pressure iteration initial value at control radius at any given momentOrder theObtaining the average formation pressure at the moment
2) By which time the formation pressure is averagedPseudo-critical pressure corresponding to formation temperature Tcalculation
3) The subsequent steps are the same as the step 1; further, the average deviation coefficient at the time is obtainedAnd gas viscosity
Step 3: the binomial capacity equation coefficients a 2 and B 2 at this time are calculated by the equation (7) and the equation (8).
Step 4: substituting the ground gas production q g2 and the bottom hole flow pressure P wf2 at the moment into a binomial productivity equation (4) to obtain the stratum pressure at the moment
Step 5: judgingIf it meets the requirement, thenThe final formation pressure at the moment;
Otherwise, by And repeating calculation until the accuracy requirement is met as a new iteration initial value, and taking the iteration initial value which finally meets the accuracy condition as the final formation pressure at the moment.
Specific experimental example-southeast gas field J32 well of Erdos basin
The well was put into production in 2019, 7 months, the initial formation pressure P i was measured to be 32.2MPa, the gas relative molecular weight M g was 17.76, the relative density gamma g was 0.614, the formation temperature T was 389K, the average ground gas yield q g2 in 2022, 5 months was 15000M 3/d, the bottom hole flow pressure P wf2 was 12.96MPa, and the stress sensitivity index omega was 0.032.
And obtaining a binomial productivity equation coefficient A 1＝0.004484,B1＝3.03×10-9 according to the productivity test before production.
A method for calculating formation pressure of a gas well based on consideration of reservoir stress sensitivity comprises the following steps:
step 1: initial average formation pressure obtained from well testing of production energy before production of gas well The average deviation coefficient of the gas well in the initial state is calculated at 22.58MPa, the stratum temperature T is 389K0.9267, Gas viscosity0.0242 Mpa.s;
step 2: given an initial iteration value of formation pressure at a control radius of 5 months 2022 The average deviation coefficient at this time was calculated to be 13.46MPa0.939, Gas viscosity0.0169 Mpa.s;
step 3: the binomial capacity equation coefficients a 2 =0.0031 and B 2＝2.11×10-9 at the moment are obtained through calculation of the formula (7) and the formula (8);
step 4: substituting the ground gas yield q g2 and the bottom hole flow pressure P wf2 at the moment into a binomial productivity equation (4) to calculate and obtain a first iteration value of the formation pressure
Step 5: judgingDoes not meet the precision requirement, and makes a first iteration toAs the initial value of the first iteration, calculatePerforming a second iteration toAs the initial value of the second iteration, calculateAnd if the precision requirement is met, the formation pressure of the j32 well is considered to be 15.8923MPa at the moment.
Claims (5)
1. A method for calculating formation pressure of a gas well based on consideration of reservoir stress sensitivity, characterized by: the method comprises the following steps:
step 1: initial average formation pressure from pre-production testing of gas wells And stratum temperature T, calculating average deviation coefficient in initial state of gas wellAnd gas viscosityThe specific process is as follows:
(1) Obtaining initial average formation pressure from pre-production test data of gas well Formation temperature T and binomial capacity equation coefficients a 1 and B 1;
(2) Average deviation coefficient under the initial state of the gas well is obtained through calculation of deviation coefficient Z equation of fitting Standing-Katz plate
(3) Calculating to obtain the gas viscosity of the gas well in the initial state through a gas viscosity equation
Step 2: formation pressure iteration initial value at control radius at any given momentUsing the average formation pressure at that momentAnd the stratum temperature T, calculating the average deviation coefficient at the momentAnd gas viscosityThe specific process is as follows:
1) Formation pressure iteration initial value at control radius at any given moment Order theObtaining the average formation pressure at the moment
Wherein: the initial value of formation pressure iteration at the radius is controlled at any moment, and the pressure is MPa;
p wf2 is Corresponding to the bottom hole flow pressure, MPa;
Is that Corresponding average formation pressure, MPa;
2) Average formation pressure through this instant Calculating the quasi-contrast pressure at the moment with the formation temperature TAnd a quasi-contrast temperature T pr;
3) The subsequent steps are the same as the step 1; further, the average deviation coefficient at the time is obtained And gas viscosity
Step 3: establishing a binomial capacity equation considering reservoir stress sensitivity, and calculating binomial capacity equation coefficients A 2 and B 2 at the moment;
Step 4: substituting the gas yield q g2 and the bottom hole flow pressure P wf2 at the moment into a binomial capacity equation to recalculate the formation pressure
Step 5: judging the stratum pressure obtained in the step 4Iterative initial value with formation pressureWhether the absolute value of the relative error between the two values meets the accuracy requirement of less than or equal to the upper error limit, if so, the iteration initial value of the formation pressure in the step 2The final formation pressure at the moment; if not, using the formation pressure obtained in step 4And (3) repeating the steps 2-4 until the accuracy requirement is met as a new iteration initial value, and taking the last iteration initial value as the final formation pressure at the moment.
2. The method of calculating gas well formation pressure based on consideration of reservoir stress sensitivity as recited in claim 1, wherein: the specific calculation process of the step 1 is as follows:
1) By initial average formation pressure Calculating a quasi-contrast pressure P pr1 and a quasi-contrast temperature T pr at corresponding moments with the formation temperature T;
2) Calculating coefficients M 1、N1、C1 and D 1 of a deviation coefficient Z equation respectively through the quasi-contrast pressure P pr1 and the quasi-contrast temperature T pr;
3) Substituting the coefficient M 1、N1、C1、D1 of the deviation coefficient Z equation into the deviation coefficient Z equation to calculate and obtain the average deviation coefficient of the gas well in the initial state
4) By mean deviation coefficient in initial state of gas wellCalculating a gas density ρ g1;
5) Obtaining parameters F 1、X1 and Y 1 required by a gas viscosity equation through the relative molecular weight M g and the formation temperature T;
6) Substituting the gas density ρ g1 and the parameter F 1、X1 and Y 1 into a gas viscosity equation to calculate the gas viscosity in the initial state of the gas well
3. The method of calculating gas well formation pressure based on consideration of reservoir stress sensitivity as claimed in claim 2, wherein: the specific calculation process of the step 3 is as follows:
Calculating according to the following formula (7) and formula (8) to obtain A 2 and B 2;
Wherein: p i is the initial formation pressure, MPa;
P re is the formation pressure at the radius at any time, MPa;
Wherein P re is an iteration variable; initial initiation When iteration occurs, P re = formation pressure obtained in step 4;
the method is an average deviation coefficient of a gas well in an initial state, and is dimensionless;
the average deviation coefficient corresponding to P re is dimensionless;
The average viscosity of the gas well in the initial state is mpa.s;
the average viscosity corresponding to P re, mpa.s;
A 1、B1 is a binomial productivity equation coefficient of the gas well in the initial state of the gas well, and is dimensionless;
A 2、B2 is a gas well binomial productivity equation coefficient corresponding to P re, and is dimensionless;
omega is stress sensitivity index, dimensionless.
4. A method of calculating gas well formation pressure based on consideration of reservoir stress sensitivity as claimed in claim 3, wherein: the specific calculation process in the step 4 is as follows:
the capacity equation for a gas well at any one time is assumed to be as follows:
Wherein: p wf is the bottom hole pressure corresponding to P re, MPa; q g is the ground gas production corresponding to P re, m 3/d;
A. B is the productivity equation coefficient corresponding to P re, and is dimensionless;
Substituting the ground gas production q g2 and the bottom hole flow pressure P wf2 at the moment into the formula (4) to obtain the stratum pressure at the moment
5. The method of calculating gas well formation pressure based on consideration of reservoir stress sensitivity as recited in claim 4, wherein: the specific calculation process in the step 5 is as follows:
Judging If it meets the requirement, thenThe final formation pressure at the moment;
Otherwise, by And repeating calculation until the accuracy requirement is met as a new iteration initial value, and taking the iteration initial value which finally meets the accuracy condition as the final formation pressure at the moment.
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| CN106677764A (en) * | 2015-11-04 | 2017-05-17 | 中石化石油工程技术服务有限公司 | Stress sensitive gas reservoir test production differential pressure calculation method |
| CN114611307A (en) * | 2022-03-17 | 2022-06-10 | 陕西延长石油（集团）有限责任公司 | Fixed yield gas well yield splitting coefficient calculation method based on recursion and iteration |
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| RU2125151C1 (en) * | 1998-06-11 | 1999-01-20 | Вяхирев Рем Иванович | Method for determining parameters of gas-bearing bed and output of wells drilled in bed |
| RU2657917C1 (en) * | 2017-03-21 | 2018-06-18 | Общество с ограниченной ответственностью "Газпром добыча Ямбург" | Method of update of the geological-gas flue model of the gas deposit according to the data of operation |
| CN111810119B (en) * | 2020-07-21 | 2022-06-28 | 重庆科技学院 | A method for calculating the productivity of gas wells in high-pressure carbonate gas reservoirs with water |
| CN114611306B (en) * | 2022-03-17 | 2024-11-22 | 陕西延长石油（集团）有限责任公司 | A method for calculating single well controlled reserves based on pressure difference conversion coefficient |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106677764A (en) * | 2015-11-04 | 2017-05-17 | 中石化石油工程技术服务有限公司 | Stress sensitive gas reservoir test production differential pressure calculation method |
| CN114611307A (en) * | 2022-03-17 | 2022-06-10 | 陕西延长石油（集团）有限责任公司 | Fixed yield gas well yield splitting coefficient calculation method based on recursion and iteration |
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