CN108133086A - Water Fractured Gas Wells fracture half-length's inversion method is produced in a kind of stress sensitive reservoir - Google Patents
Water Fractured Gas Wells fracture half-length's inversion method is produced in a kind of stress sensitive reservoir Download PDFInfo
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Abstract
The present invention relates to water Fractured Gas Wells fracture half-length's inversion method is produced in a kind of stress sensitive reservoir, include the following steps：(1) gas well daily creation data, reservoir properties, physical properties of fluids, stress sensitive data are compiled；(2) the equivalent relative permeability of air water under the conditions of different pressures is calculated；(3) it calculates and considers that parameter is intended in the improvement of stress sensitive reservoir air water two-phase complicated percolation feature；(4) it draws and utilizes time graph identification stratum linear flow under improved radical sign；(5) data point in layer linear flow stage carries out linear regression over the ground, based on obtained straight slope, is calculated using inverse model, realizes half long inverting of fracture.The complicated percolations feature such as phase percolation curve stress sensitive, absolute permeability stress sensitive, slippage effect when present invention can consider air water two phase fluid flow in stress sensitive reservoir, the error caused by Traditional calculating methods is eliminated, is evaluated after can be widely used for the pressure of stress sensitive reservoir production water Fractured Gas Wells.
Description
Technical Field
The invention relates to the technical field of post-hydraulic fracturing evaluation, in particular to a half-length inversion method for a fracture of a water-producing fractured gas well in a stress-sensitive reservoir.
Background
In the production process of the stress sensitive reservoir, the pore throat structure of the reservoir can be changed along with the continuous change of the formation stress condition. For a water producing gas well in a stress sensitive reservoir, the pore throat structure changes along with stress, so that complex seepage characteristics such as absolute permeability stress sensitivity, phase seepage curve stress sensitivity, dynamic slippage effect and the like are presented in a gas-water two-phase seepage process. On the other hand, stress sensitive reservoirs are generally low in permeability and require fracturing modification to obtain industrial gas flow. The half-length of the fracture formed by fracturing is an important index for evaluating the fracturing effect, and has very important significance for subsequent capacity prediction and development scheme formulation. Due to the existence of gas-water two-phase complex seepage characteristics in the stress sensitive reservoir, the inversion of the half-length of the fracture of the water producing fracturing well is greatly different from that of a conventional gas well.
However, some existing fracture half-length inversion methods do not comprehensively consider the gas-water two-phase complex seepage characteristics of the stress-sensitive reservoir, particularly ignore the stress sensitivity of a gas-water phase seepage curve, and the obtained fracture half-length value and the true value are usually different from each other, so that the method is not suitable for the fracture half-length inversion of the water-producing fractured gas well in the stress-sensitive reservoir.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in order to overcome the defects in the prior art, the invention provides a half-length inversion method for a fracture of a water-producing fractured gas well in a stress-sensitive reservoir, which comprehensively considers gas-water two-phase seepage characteristics of stress sensitivity of a phase seepage curve and the like, so that the accuracy of a fracture inversion result is improved.
The technical scheme adopted by the invention for solving the technical problems is as follows: a half-length inversion method for a fracture of a water-producing fractured gas well in a stress-sensitive reservoir comprises the following steps:
(1) collecting and sorting daily production data, reservoir physical properties, fluid physical properties, gas-water phase permeability data and stress sensitive data of a gas well;
(2) comprehensively considering stress sensitivity of a phase permeation curve, stress sensitivity of absolute permeability and dynamic slippage effect, and calculating equivalent gas-water relative permeability of gas-water two-phase complex seepage characteristics under different pressure conditions;
(3) calculating improved pseudo-pressure and pseudo-time considering the gas-water two-phase complex seepage characteristics of the stress sensitive reservoir according to the following formula by using the equivalent gas-water phase seepage curve and combining with the gas well production data;
wherein psitwoThe improved pseudo pressure MPa/cp for considering the gas-water two-phase complex seepage characteristic of the stress sensitive reservoir; t is ttwoThe simulation time d for considering the improvement of the gas-water two-phase complex seepage characteristic of the stress sensitive reservoir; p is pressure MPa; p is a radical ofaIs a reference pressure MPa; t is the real time d; t is taIs a reference time d; rhogIs gas phase underground density kg/m3；ρwUnderground density of water kg/m3；ρwscGround standard density of water kg/m3；Gas phase underground density kg/m corresponding to average pressure3；The standard density of the water phase ground corresponding to the average pressure is kg/m3；krgEIs the gas phase equivalent relative permeability; k is a radical ofrwEIs the water phase equivalent relative permeability;the gas phase equivalent relative permeability corresponding to the average pressure;the equivalent relative permeability of the water phase corresponding to the average pressure; mu.sgIs the gas viscosity cp; mu.swIs the viscosity of water cp; mu.sgiIs the gas viscosity at virgin formation pressure cp;gas viscosity, cp, corresponding to the average pressure;the viscosity cp of water corresponding to the average pressure; ct-twoiIs the gas-water two-phase comprehensive compression coefficient MPa under the original formation pressure-1；Gas-water two-phase comprehensive compression coefficient MPa corresponding to average pressure-1；
(4) Based on the improved pseudo-pressure and pseudo-time obtained by calculation, drawing and utilizing an improved time curve under the root to identify formation linear flow;
(5) and performing linear regression on scattered points on the curve, and calculating by using an inversion model according to the slope of a straight line obtained by regression so as to realize the inversion of the half length of the crack.
In the step (1), the necessary data to be collected and collated includes: comprising the water yield qwGas production qgMoisture, water vaporRatio fwSleeve pressure pcOr bottom hole flow pressure pwfProduction data in situ for the gas well; reservoir thickness h and porosity phi under original formation pressure conditionsiAbsolute permeability kiGas slip factor biAnd the like reservoir physical property parameters; fluid viscosity μ under different pressure conditionsg、μwAnd compression factor Cg、CwAnd other fluid physical parameters; end point value (S) of permeability curve corresponding to original formation pressurewci、Sgri、krgendi、krwendi) Reservoir absolute permeability, porosity, stress sensitivity coefficient of end point value of the facies permeability curve (α, gamma, C, D, E, F), and the like;
in the step (2), the calculation model of the equivalent gas-water relative permeability is as follows:
wherein,andthe calculation formulas of (A) and (B) are respectively as follows:
wherein k isrgE-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Gas phase equivalent relative permeability; k is a radical ofrwE-p1<Sw>At a certain pressure (p)1) And saturation (S)w) The equivalent relative permeability of the water phase; k is a radical ofrg-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Relative permeability of the gas phase; k is a radical ofrw-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Relative permeability of the aqueous phase; biSlip factor corresponding to original formation pressure, slip factor regression coefficient, permeability stress sensitivity coefficient MPa α-1；krgendiIs the gas phase permeability endpoint value at the original formation pressure; swThe water saturation; swciIrreducible water saturation at the original formation pressure; sgriThe residual gas saturation under the original formation pressure, lambda is the capillary distribution index, η is the capillary bending coefficient, krwendiIs the water phase permeability endpoint value under the original formation pressure; c is the stress sensitivity coefficient of the gas phase infiltration endpoint value with the unit of MPa-1(ii) a D is the stress sensitivity coefficient of the water phase seepage endpoint value with the unit of MPa-1(ii) a E is the stress sensitivity coefficient of the saturation of the irreducible water in MPa-1(ii) a F is the residual gas saturation stress sensitivity coefficient with the unit of MPa-1(ii) a p is the specified formation pressure in MPa; p is a radical ofiIs the original formation pressure in MPa;
in the step (3), the calculation method of the pseudo pressure comprises the following steps:
(a) utilizing the gas production q corresponding to each time point tgAnd water yield qwCalculating the ratio q of water yield to gas yield corresponding to each time pointw/qg；
(b) At time t1For example, a first pressure point p is selected within the integration range1Based on the relation between the physical parameters of gas phase and water phase and pressure, the related physical parameter value (mu) corresponding to the pressure value is calculatedg、Bg、μw、Bw)；
(c) Calculating the pressure p by using the following formula1Ratio k of equivalent relative permeability of water phase and gas phase under the conditionrwE/krgE；
(d) And (3) further determining the ratio (k) of the equivalent relative permeability of the water phase to the equivalent relative permeability of the gas phase under each pressure condition by using the equivalent relative permeability curves under different pressure conditions established in the step (2)rwE/krgE) A characteristic of change with water saturation;
(e) combining the results of the step (c) and the step (d), determining the water saturation value corresponding to the pressure point, and calculating the pressure point p by using the saturation1Corresponding gas phase equivalent relative permeability krgEAnd water phase equivalent relative permeability krwE；
(f) Selecting the next pressure point p in the integral range2And analyzing by similar method to obtain pressure point p2Corresponding gas phase equivalent relative permeability and water phase equivalent relative permeability … … are analogized in turn, if the number of the pressure points selected in the integral range is enough, the pressure value and the gas phase and water phase equivalent relative permeability k can be establishedrgEOr krwESubstituting the relation into the following formula to realize the numerical integration of the relevant parameters and obtain the improved simulated pressure suitable for the gas-water two-phase seepage of the stress sensitive reservoir;
wherein q isgFor ground gas production, m3/d；qwWater yield on the ground, m3/d；BgIs the gas volume coefficient; b iswIs the volume factor of water.
In the step (3), the calculation method of the pseudo-time comprises the following steps:
(a) selecting a time point t within the integration range1Determining the pressure influence range or the average formation pressure in the reservoir by a pressure propagation distance formula or a flowing material balance methodFurther determining the corresponding gas-water physical parameter value (mu) of the average pressureg、Bg、μw、Bw)；
(c) Obtaining the equivalent relative permeability ratio value of the water phase and the gas phase under the average pressure condition based on the equivalent phase permeability curve in the step (2)A characteristic of change with water saturation;
(d) combining the results of the steps (b) and (c), determining an average saturation value corresponding to the average pressure, and further calculating the average pressureCorresponding average gas phase equivalent relative permeabilityAnd average water phase equivalent relative permeability
(e) Selecting the next time point t in the integral range2Analysis was carried out by a similar method to obtain t2Corresponding in timeThe average equivalent relative permeability of the gas phase and the average equivalent relative permeability of the water phase … … are analogized in turn, if the number of the selected time points in the integral range is enough, the time and the average equivalent relative permeability of the gas phase and the water phase can be establishedSubstituting the relation into the following formula to realize the numerical integration of the relevant parameters and obtain the improved simulated time suitable for the gas-water two-phase seepage of the stress sensitive reservoir;
wherein t is real time and d;mean formation pressure, MPa;the gas phase equivalent relative permeability corresponding to the average pressure;the gas phase equivalent relative permeability is the average pressure.
In the step (3), the method for calculating the gas-water two-phase seepage comprehensive compression coefficient in the reservoir in the simulated time calculation formula comprises the following steps:
wherein, Ct-twoIs the gas-water two-phase comprehensive compression coefficient, MPa-1；SgThe gas phase saturation; cgIs a gas compression coefficient, MPa-1；CwIs the compressibility factor of water, MPa-1；CpIs the rock pore compression coefficient, MPa-1。
In the step (4), when the improved time curve under the root is drawn, and the gas well is produced with a fixed gas content, the abscissa isWhen the gas well gas production is not constant, the abscissa isAnd the ordinate isAbscissa under variable gas productionThe calculation can be performed using the following formula.
Wherein psitwoiSimulating pressure for the improvement corresponding to the original formation pressure; psitwowfThe improved pseudo pressure corresponding to the bottom hole flowing pressure; q. q.stwoIs the total gas-water yield; t is tsl-twoSimulating time for improved material balance corresponding to the formation linear flow phase for converting variable production conditions to fixed production conditions in days (d); n is the total number of data points.
Wherein m istwo-sThe slope of a straight line obtained by regression of data points at the formation linear flow stage on the improved time curve under the root is obtained; x is the number offIs the half-length m of the crack; phi is porosity; h is the effective thickness m of the gas layer; k is a radical ofiIs the original permeability mD at the original formation pressure conditions.
Through the steps, the inversion of the half length of the gas well fracture fractured by the produced water in the stress sensitive reservoir can be realized.
The invention has the beneficial effects that: due to the adoption of the technical method, compared with the current inversion method, the method has the following advantages and beneficial effects:
1. the method comprehensively considers the stress sensitivity and other complex seepage characteristics of the phase seepage curve, so that compared with the current mainstream crack half-length inversion method, the method is closer to the actual seepage condition of a reservoir, and the obtained crack half-length is more accurate;
2. the method adopts a semi-analytic method, is simpler and faster than a numerical analysis method;
3. the method is based on daily production data for analysis, overcomes the defect that the traditional well testing inversion method excessively depends on field well testing, does not need well shut-in testing, and obviously reduces the half-length inversion cost of the crack.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a water gas ratio and bottom hole flow pressure data for an embodiment of the present invention.
FIG. 3 is an equivalent percolation curve in an example of the present invention.
Fig. 4 is a modified under-root time curve in an embodiment of the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
Fig. 1 is a flow chart of an inversion method of the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir, which comprises the following steps:
in step (1), collecting the necessary data for collation includes: water yield qwGas production qgWater-gas ratio fwBottom hole flow pressure pwfGas well field production data, including the like; reservoir thickness h and porosity phi under original formation pressure conditionsiAbsolute permeability kiGas slip factor biAnd the like reservoir physical property parameters; fluid viscosity μ under different pressure conditionsg、μwAnd compression factor Cg、CwAnd other fluid physical parameters; end point value (S) of permeability curve corresponding to original formation pressurewci、Sgri、krgendi、krwendi) The reservoir pore throat non-isodiametric coefficient lambda, the bending coefficient η and other isodiametric curve parameters, the reservoir absolute permeability, the porosity, the stress sensitivity coefficient (α, gamma, C, D, E, F) of the end point value of the isodiametric curve and the like, wherein the water-gas ratio and the bottom hole flow pressure data in the embodiment are shown in figure 2, and part of other collected basic parameters are shown in table 1.
TABLE 1
In step (2), the equivalent relative permeability is calculated based on the following formula, and a corresponding equivalent permeability curve is drawn, and the result is shown in the attached figure 3:
wherein,andthe calculation formulas of (A) and (B) are respectively as follows:
wherein k isrgE-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Gas phase equivalent relative permeability; k is a radical ofrwE-p1<Sw>At a certain pressure (p)1) And saturation (S)w) The equivalent relative permeability of the water phase; k is a radical ofrg-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Relative permeability of the gas phase; k is a radical ofrw-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Relative permeability of the aqueous phase; biThe slip factor corresponding to the original formation pressure is MPa, B is the slip factor regression coefficient, α is the permeability stress sensitivity coefficient is MPa-1；krgendiIs the gas phase permeability endpoint value at the original formation pressure; swThe water saturation; swciIrreducible water saturation at the original formation pressure; sgriThe residual gas saturation under the original formation pressure, lambda is the capillary distribution index, η is the capillary bending coefficient, krwendiIs the water phase permeability endpoint value under the original formation pressure; c is the stress sensitivity coefficient of the gas phase infiltration endpoint value; d is the stress sensitivity coefficient of the water phase seepage endpoint value; e is the stress sensitivity coefficient of the saturation of the irreducible water; f is the residual gas saturation stress sensitivity coefficient;p is the specified formation pressure in MPa; p is a radical ofiIs the original formation pressure in MPa;
in the step (3), the improved pseudo-pressure considering the gas-water two-phase complex seepage characteristic is calculated according to the following process:
(a) utilizing the gas production q corresponding to each time point tgAnd water yield qwCalculating the ratio q of water yield to gas yield corresponding to each time pointw/qg；
(b) At time t1For example, a first pressure point p is selected within the integration range1Based on the relation between the physical parameters of gas phase and water phase and pressure, the related physical parameter value (mu) corresponding to the pressure value is calculatedg、Bg、μw、Bw)；
(c) Calculating the pressure p by using the following formula1Ratio k of equivalent relative permeability of water phase and gas phase under the conditionrwE/krgE；
(d) And (3) further determining the ratio (k) of the equivalent relative permeability of the water phase to the equivalent relative permeability of the gas phase under each pressure condition by using the equivalent relative permeability curves under different pressure conditions established in the step (2)rwE/krgE) A characteristic of change with water saturation;
(e) combining the results of the step (c) and the step (d), determining the water saturation value corresponding to the pressure point, and calculating the pressure point p by using the saturation1Corresponding gas phase equivalent relative permeability krgEAnd water phase equivalent relative permeability krwE；
(f) Selecting the next pressure point p in the integral range2And analyzing by similar method to obtain pressure point p2Corresponding gas phase equivalent relative permeability and water phase equivalent relative permeability … …Analogizing, if the number of the pressure points selected in the integral range is enough, the equivalent relative permeability k of the pressure value and the gas phase and the water phase can be establishedrgEOr krwESubstituting the relation into the following formula to realize the numerical integration of the relevant parameters and obtain the improved simulated pressure suitable for the gas-water two-phase seepage of the stress sensitive reservoir,
wherein psitwoThe improved pseudo pressure MPa/cp for considering the gas-water two-phase complex seepage characteristic of the stress sensitive reservoir; p is pressure MPa; p is a radical ofaIs a reference pressure MPa; rhogIs gas phase underground density kg/m3；ρwUnderground density of water kg/m3；ρwscGround standard density of water kg/m3；krgEIs the gas phase equivalent relative permeability; k is a radical ofrwEIs the water phase equivalent relative permeability; mu.sgIs the gas viscosity cp; mu.swIs the viscosity of water cp; q. q.sgFor ground gas production m3/d；qwWater yield m for ground3/d；BgIs the gas volume coefficient; b iswIs the volume factor of water.
In the step (3), the calculation method of the pseudo-time comprises the following steps:
(a) selecting a time point t within the integration range1Determining the pressure influence range or the average formation pressure in the reservoir by a pressure propagation distance formula or a flowing material balance methodFurther determining the corresponding gas-water physical parameter value (mu) of the average pressureg、Bg、μw、Bw)；
(c) Obtaining the equivalent relative permeability ratio value of the water phase and the gas phase under the average pressure condition based on the equivalent phase permeability curve in the step (2)A characteristic of change with water saturation;
(d) combining the results of the steps (b) and (c), determining an average saturation value corresponding to the average pressure, and further calculating the average pressureCorresponding average gas phase equivalent relative permeabilityAnd average water phase equivalent relative permeability
(e) Selecting the next time point t in the integral range2Analysis was carried out by a similar method to obtain t2The gas phase average equivalent relative permeability and the water phase average equivalent relative permeability corresponding to the moment are analogized in turn by … …, if the number of the selected time points in the integral range is enough, the time and the average gas phase and water phase equivalent relative permeability can be establishedSubstituting the relation into the following formula to realize the numerical integration of the relevant parameters and obtain the improved simulation time suitable for the gas-water two-phase seepage of the stress sensitive reservoir,
wherein,t is the real time d;is the average formation pressure MPa;the gas phase equivalent relative permeability corresponding to the average pressure;the gas phase equivalent relative permeability corresponding to the average pressure; ct-twoIs gas-water two-phase comprehensive compression coefficient MPa-1；SgThe gas phase saturation; cgIs a gas compression coefficient MPa-1；CwCompression factor MPa of water-1；CpIs the rock pore compression coefficient MPa-1，ttwoThe simulation time d for considering the improvement of the gas-water two-phase complex seepage characteristic of the stress sensitive reservoir; t is taIs a reference time d;gas phase underground density kg/m corresponding to average pressure3；The standard density of the water phase ground corresponding to the average pressure is kg/m3；The gas phase equivalent relative permeability corresponding to the average pressure;the equivalent relative permeability of the water phase corresponding to the average pressure; mu.sgIs the gas viscosity cp; mu.swIs the viscosity of water cp;the gas viscosity cp is the average pressure;the viscosity cp of water corresponding to the average pressure; ct-twoiIs the gas-water two-phase comprehensive compression coefficient MPa under the original formation pressure-1；Gas-water two-phase comprehensive compression coefficient MPa corresponding to average pressure-1。
In step (4), since the present embodiment is a constant gas production, the abscissa is taken asAnd the ordinate isThe improved under root time curve is plotted as shown in fig. 4.
Wherein psitwoiSimulating pressure for the improvement corresponding to the original formation pressure; psitwowfThe improved pseudo pressure corresponding to the bottom hole flowing pressure; q. q.stwoIs the total yield of gas-water.
In the step (5), the slope m of the straight line is obtained based on regressiontwo-sUsing a calculation model of the half-length of the crackThe half-length of the crack of the water-producing fractured gas well in the stress-sensitive reservoir is calculated to be 101.02 m.
Wherein m istwo-sThe slope of a straight line obtained by regression of data points at the formation linear flow stage on the improved time curve under the root is obtained; x is the number offIs the half-length m of the crack; phi is porosity; h is the effective thickness m of the gas layer; k is a radical ofiIs the original permeability mD at the original formation pressure conditions.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.
Claims (8)
1. A half-length inversion method for a fracture of a water-producing fractured gas well in a stress-sensitive reservoir is characterized by comprising the following steps:
(1) collecting and sorting daily production data, reservoir physical properties, fluid physical properties, gas-water phase permeability data and stress sensitive data of a gas well;
(2) comprehensively considering stress sensitivity of a phase permeation curve, stress sensitivity of absolute permeability and dynamic slippage effect, and calculating equivalent gas-water relative permeability of gas-water two-phase complex seepage characteristics under different pressure conditions;
(3) calculating improved pseudo-pressure and pseudo-time considering the gas-water two-phase complex seepage characteristics of the stress sensitive reservoir according to the following formula by using the equivalent gas-water phase seepage curve and combining with the gas well production data;
wherein psitwoThe improved pseudo pressure MPa/cp for considering the gas-water two-phase complex seepage characteristic of the stress sensitive reservoir; t is ttwoThe simulation time d for considering the improvement of the gas-water two-phase complex seepage characteristic of the stress sensitive reservoir; p is pressure MPa; p is a radical ofaIs a reference pressure MPa; rhogIs gas phase underground density kg/m3(ii) a t is the real time d; t is taIs a reference time d; rhowUnderground density of water kg/m3；ρwscGround standard density of water kg/m3；Gas phase underground density kg/m corresponding to average pressure3；The standard density of the water phase ground corresponding to the average pressure is kg/m3；krgEIs the gas phase equivalent relative permeability; k is a radical ofrwEIs the water phase equivalent relative permeability;the gas phase equivalent relative permeability corresponding to the average pressure;the equivalent relative permeability of the water phase corresponding to the average pressure; mu.sgIs the gas viscosity cp; mu.swIs the viscosity of water cp; mu.sgiAt the pressure of the original formationGas viscosity cp of (a);the gas viscosity cp is the average pressure;the viscosity cp of water corresponding to the average pressure; ct-twoiIs the gas-water two-phase comprehensive compression coefficient MPa under the original formation pressure-1；Gas-water two-phase comprehensive compression coefficient MPa corresponding to average pressure-1；
(4) Based on the improved pseudo-pressure and pseudo-time obtained by calculation, drawing and utilizing an improved time curve under the root to identify formation linear flow;
(5) and performing linear regression on data points of the formation linear flow stage, and calculating by using an inversion model according to the linear slope obtained by regression so as to realize the inversion of the half length of the fracture.
2. The method for inverting the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir as claimed in claim 1, wherein the method comprises the following steps: the necessary data to be collected and collated in step (1) includes: comprising the water yield qwGas production qgWater-gas ratio fwSleeve pressure pcOr bottom hole flow pressure pwfProduction data in situ for the gas well; reservoir thickness h and porosity phi under original formation pressure conditionsiAbsolute permeability kiGas slip factor biReservoir physical property parameters; fluid viscosity μ under different pressure conditionsg、μwAnd compression factor Cg、CwA fluid physical property parameter; end point value (S) of permeability curve corresponding to original formation pressurewci、Sgri、krgendi、krwendi) Reservoir pore throat non-isodiametric coefficient lambda and bending coefficient η facies permeability curve parameter, reservoir absolute permeability, porosity and facies permeability curve endPoint values stress sensitivity coefficients (α, γ, C, D, E, F).
3. The method for inverting the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir as claimed in claim 1, wherein the method comprises the following steps: the calculation model of the equivalent gas-water relative permeability in the step (2) is as follows:
wherein,andthe calculation formulas of (A) and (B) are respectively as follows:
wherein k isrgE-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Gas phase equivalent relative permeability; k is a radical ofrwE-p1<Sw>At a certain pressure (p)1) And saturation (S)w) The equivalent relative permeability of the water phase; k is a radical ofrg-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Relative permeability of the gas phase; k is a radical ofrw-p1<Sw>At a certain pressure (p)1) And saturation (S)w) Relative permeability of the aqueous phase; biSlip factor MPa corresponding to original formation pressure, slip factor regression coefficient, and permeability stress sensitivity coefficient MPa α-1；krgendiIs the gas phase permeability endpoint value at the original formation pressure; swThe water saturation; swciIs original toIrreducible water saturation at incipient formation pressure; sgriThe residual gas saturation under the original formation pressure, lambda is the capillary distribution index, η is the capillary bending coefficient, krwendiIs the water phase permeability endpoint value under the original formation pressure; c is the stress sensitivity coefficient of the gas phase infiltration endpoint value with the unit of MPa-1(ii) a D is the stress sensitivity coefficient of the water phase seepage endpoint value with the unit of MPa-1(ii) a E is the stress sensitivity coefficient of the saturation of the irreducible water in MPa-1(ii) a F is the residual gas saturation stress sensitivity coefficient with the unit of MPa-1(ii) a p is the specified formation pressure in MPa; p is a radical ofiIs the original formation pressure in MPa.
4. The method for inverting the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir as claimed in claim 1, wherein the method comprises the following steps: the calculation method of the pseudo pressure in the step (3) comprises the following steps:
(a) utilizing the gas production q corresponding to each time point tgAnd water yield qwCalculating the ratio q of water yield to gas yield corresponding to each time pointw/qg；
(b) At time t1For example, a first pressure point p is selected within the integration range1Based on the relation between the physical parameters of gas phase and water phase and pressure, the related physical parameter value (mu) corresponding to the pressure value is calculatedg、Bg、μw、Bw)；
(c) Calculating the pressure p by using the following formula1Ratio k of equivalent relative permeability of water phase and gas phase under the conditionrwE/krgE
(d) And (3) further determining the ratio (k) of the equivalent relative permeability of the water phase to the equivalent relative permeability of the gas phase under each pressure condition by using the equivalent relative permeability curves under different pressure conditions established in the step (2)rwE/krgE) A characteristic of change with water saturation;
(e) combining the steps (c) anddetermining the water saturation value corresponding to the pressure point as a result of the step (d), and calculating the pressure point p by using the saturation value1Corresponding gas phase equivalent relative permeability krgEAnd water phase equivalent relative permeability krwE；
(f) Selecting the next pressure point p in the integral range2And analyzing by similar method to obtain pressure point p2Corresponding gas phase equivalent relative permeability and water phase equivalent relative permeability … … are analogized in turn, if the number of the pressure points selected in the integral range is enough, the pressure value and the gas phase and water phase equivalent relative permeability k can be establishedrgEOr krwESubstituting the relation into the following formula to realize the numerical integration of the relevant parameters and obtain the improved simulated pressure suitable for the gas-water two-phase seepage of the stress sensitive reservoir;
wherein q isgFor ground gas production, m3/d；qwWater yield on the ground, m3/d；BgIs the gas volume coefficient; b iswIs the volume factor of water.
5. The method for inverting the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir as claimed in claim 1, wherein the method comprises the following steps: the calculation method of the pseudo-time in the step (3) comprises the following steps:
(a) selecting a time point t within the integration range1Determining the pressure influence range or the average formation pressure in the reservoir by a pressure propagation distance formula or a flowing material balance methodFurther determining the corresponding gas-water physical parameter value (mu) of the average pressureg、Bg、μw、Bw)；
(b) Calculating the equivalent relative permeability ratio of the water phase and the gas phase under the average pressure condition by using the following formula
(c) Obtaining the equivalent relative permeability ratio value of the water phase and the gas phase under the average pressure condition based on the equivalent phase permeability curve in the step (2)A characteristic of change with water saturation;
(d) combining the results of the steps (b) and (c), determining an average saturation value corresponding to the average pressure, and further calculating the average pressureCorresponding average gas phase equivalent relative permeabilityAnd average water phase equivalent relative permeability
(e) Selecting the next time point t in the integral range2Analysis was carried out by a similar method to obtain t2The gas phase average equivalent relative permeability and the water phase average equivalent relative permeability corresponding to the moment are analogized in turn by … …, if the number of the selected time points in the integral range is enough, the time and the average gas phase and water phase equivalent relative permeability can be establishedThe equation (b) is substituted into the following equation to realize the numerical integration of the relevant parameters and obtain the improved simulation time suitable for the gas-water two-phase seepage of the stress sensitive reservoir.
Wherein t is real time and d;mean formation pressure, MPa;the gas phase equivalent relative permeability corresponding to the average pressure;the gas phase equivalent relative permeability is the average pressure.
6. The method for inverting the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir as claimed in claim 5, wherein the method comprises the following steps: the method for calculating the gas-water two-phase seepage comprehensive compression coefficient in the reservoir in the simulated time calculation formula in the step (3) comprises the following steps:
wherein, Ct-twoIs gas-water two-phase comprehensive compression coefficient MPa-1；SgThe gas phase saturation; cgIs a gas compression coefficient MPa-1；CwCompression factor MPa of water-1；CpIs the rock pore compression coefficient MPa-1。
7. The method for inverting the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir as claimed in claim 1, wherein the method comprises the following steps: when the improved time curve under the root is drawn in the step (4), when the gas well is produced with a fixed gas content, the abscissa isAnd when the gas well gas production is not constant, the abscissaIs composed ofAnd the ordinate isAbscissa under variable gas productionThe calculation can be carried out using the following formula,
wherein psitwoiSimulating pressure for the improvement corresponding to the original formation pressure; psitwowfThe improved pseudo pressure corresponding to the bottom hole flowing pressure; q. q.stwoIs the total gas-water yield; t is tsl-twoSimulating time for improved material balance corresponding to the formation linear flow stage, wherein the time is used for converting the variable yield condition into the constant yield condition, and the unit is day; n is the total number of data points.
8. The method for inverting the half-length of a fracture of a water-producing fractured gas well in a stress-sensitive reservoir as claimed in claim 1, wherein the method comprises the following steps: in the step (5), the slope m of the straight line obtained based on the regressiontwo-sThe calculation model of the half-length of the crack is
Wherein m istwo-sThe slope of a straight line obtained by regression of data points at the formation linear flow stage on the improved time curve under the root is obtained; x is the number offIs the half-length m of the crack; phi is porosity; h is the effective thickness m of the gas layer; k is a radical ofiIs the original permeability mD at the original formation pressure conditions.
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