CN106481332B - Method for determining area's dynamic holdup inside and outside shale gas multistage pressure break horizontal well - Google Patents
Method for determining area's dynamic holdup inside and outside shale gas multistage pressure break horizontal well Download PDFInfo
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Abstract
The invention discloses a kind of methods for determining area's dynamic holdup inside and outside shale gas multistage pressure break horizontal well, comprising: establishes gas well binomial potential curve and equation by gas testing data, calculates practical flowing bottomhole pressure (FBHP) by creation data and gas well structural parameters；Consider that adsorbed gas desorption and abnormal high pressure influence, establishes the matter balance equation in the fracturing reform area and non-fracturing reform area for multistage pressure break horizontal well respectively；The dynamic holdup in fracturing reform area and non-fracturing reform area is given respectively, and the expression formula in conjunction with the channelling between fracturing reform area and the matter balance equation and twoth area in non-fracturing reform area, binomial potential curve and equation adjust dynamic holdup to be fitted practical flowing bottomhole pressure (FBHP), so that it is determined that area's dynamic holdup inside and outside pressure break horizontal well.The present invention does not need closing well test mean reservoir pressure in use, and adsorbed gas desorption and the influence of abnormal high pressure and pressure break recombination region can be considered, and can determine fracturing reform area and peripheral non-fracturing reform area dynamic holdup respectively.
Description
Technical Field
The invention belongs to the technical field of shale gas exploration and development, and particularly relates to a method for determining dynamic reserves of an inner area and an outer area of a shale gas multi-section fracturing horizontal well.
Background
The evaluation method of the shale gas well dynamic reserves is greatly different from that of the conventional gas well and mainly comprises the following steps: (1) gas reservoirs differ in their geological characteristics and development techniques. Shale gas reservoirs are autogenous and autogenous gas reservoirs, have extremely low permeability, need to be artificially built through volume fracturing modification, the gas well yield and recoverable reserves are limited by fracturing, and single-well dynamic reserves are related to the volume fracturing modification. (2) The seepage characteristics are different. Because the shale gas reservoir matrix permeability is extremely low, the gas reservoir is difficult to enter a boundary control flow stage, the dynamic reserve evaluation requirement reaches the boundary control flow stage, otherwise, the evaluated dynamic reserve is only the reserve used in a pressure fluctuation range. (3) And desorbing and diffusing the adsorbed gas. Free gas and adsorbed gas both affect the productivity of shale gas wells, and the desorption effect of the adsorbed gas needs to be considered for dynamic reserve evaluation.
Currently, the North American shale gas well is mainly produced according to a pressure release yield decreasing mode, a yield decreasing curve is mainly adopted to analyze the final recoverable reserves (EUR) of the gas well, and the North American shale gas well mainly comprises an improved Arps method, a power law index method, a diffusion index method, a Duong method and the like. The production data is fitted by adjusting coefficients in these decreasing curve models, and then the gas well production and recoverable reserves are predicted.
The decreasing curve analysis method not only requires that the bottom hole flowing pressure of the gas well is not changed greatly in the production stage, but also requires that the bottom hole flowing pressure is kept unchanged in the prediction stage. In addition, the method requires that the gas well reach a boundary control flow phase, i.e., the pressure wave reaches a physical or choked reservoir boundary, otherwise the predicted production and final recoverable reserves are high.
At present, domestic gas wells generally need to have a stable production period of 2-3 years to ensure stable market gas supply, and then are produced according to a constant pressure yield decreasing mode, for example, the stable production period of the gas wells designed by the Fuling Jordan shale gas field development scheme is 2 years. Therefore, due to the difference of production modes, the shale gas well in China is difficult to calculate the dynamic reserves of the gas well by adopting a decreasing curve analysis method at an early stage.
The material balance method is a common method used in conventional gas reservoirs to determine the dynamic reserves of a gas well, and requires an average formation pressureAnd accumulated gas production GPAnd (4) data. Calculating from the accumulated gas production and the average formation pressureThe values are then plotted on a rectangular plotAnd GPAnd (4) extrapolating the data points to the x axis by the fitting straight line to obtain the dynamic reserves of the gas well. The average formation pressure is mainly obtained through well shut-in pressure recovery well testing test interpretation of the gas well.
When the method is applied to calculating the dynamic reserves of the shale gas well, the following problems mainly exist: firstly, the influence of desorption and diffusion of shale matrix adsorbed gas cannot be considered when the dynamic reserves of the gas well are calculated; secondly, the shale matrix permeability is extremely low, and the average formation pressure is difficult to explain through the unstable well testing test of well closing pressure recovery; and thirdly, the dynamic reserves of the fracturing modified area and the dynamic reserves of the peripheral non-fracturing modified area cannot be distinguished.
According to the shale gas well dynamic reserve calculation method at home and abroad, an effective and accurate shale gas well dynamic reserve calculation method is lacked at present, and the dynamic reserve of a fracturing modification area and the dynamic reserve of a non-fracturing modification area cannot be distinguished.
Disclosure of Invention
In order to solve the problems, the invention provides a method for determining the dynamic reserves of an outer zone in a shale gas multi-zone fracturing horizontal well.
According to one embodiment of the invention, a method for determining outer zone dynamic reserves in a shale gas multi-stage fracturing horizontal well is provided, which comprises the following steps:
acquiring gas testing data, production data and gas well structural parameters of the shale gas fracturing horizontal well, establishing a gas well binomial productivity equation according to the gas testing data, and calculating actual bottom hole flowing pressure according to the production data and the gas well structural parameters;
respectively establishing a material balance equation aiming at a fracturing modification area and an uncrushed modification area of the multi-section fracturing horizontal well by considering the adsorption gas desorption and the abnormal high-pressure influence;
and respectively giving the dynamic reserves of the fracturing modified area and the non-fracturing modified area, and fitting the actual bottom hole flow pressure by combining a material balance equation of the fracturing modified area and the non-fracturing modified area, an expression of the flow channeling quantity between the fracturing modified area and the non-fracturing modified area and the binomial productivity equation to adjust the dynamic reserves so as to determine the dynamic reserves of the outer area in the fracturing horizontal well.
According to one embodiment of the invention, the step of establishing a material balance equation for a fractured modified zone and an uncracked modified zone of a multi-staged fractured horizontal well further comprises:
considering the effects of adsorption gas desorption and abnormal high pressure, establishing a shale gas reservoir substance balance equation;
dividing the single well control area of the multi-section fractured horizontal well into a fractured modified area and an uncrushed modified area according to the well pattern spacing;
and respectively establishing material balance equations of the fractured and transformed zone and the non-fractured and transformed zone based on the shale gas reservoir material balance equation.
According to an embodiment of the present invention, the step of establishing the shale gas reservoir material balance equation further comprises:
calculating the volume reduction of underground pores caused by rock skeleton compression and fluid expansion when the formation pressure changes based on the rock pore compression coefficient;
calculating the residual free gas reserve and the residual adsorbed gas reserve of the shale gas reservoir after the formation pressure is reduced based on the underground pore volume reduction and the Langmuir isothermal adsorption equation;
according to the law of conservation of material: and establishing a shale gas reservoir substance balance equation by the original free gas reserve and the original adsorbed gas reserve, namely the residual free gas reserve, the residual adsorbed gas yield and the accumulated gas yield.
According to an embodiment of the present invention, the shale gas reservoir material balance equation is:
wherein Z isa＝Za(p)，
When p ═ piWhen the temperature of the water is higher than the set temperature,p is the formation pressure, piTo the original formation pressure, GpFor cumulative yield, G is dynamic reserve, cfIs the porosity compressibility of the rock, cwIs the formation water compression coefficient, SwiIs the original water saturation of the gas reservoir, SgiFor the original gas saturation of the reservoir, phi is the effective porosity, rhoBIs shale density, VLIs the Langmuir volume, PLIs the Lane pressure, pscIs gas pressure at standard conditions, T is formation temperature, TscIs the temperature at standard conditions, z is the natural gas compression factor at pressure p, zscIs the natural gas compression factor in a standard state.
According to one embodiment of the invention, the material balance equation of the fracture transformation area is as follows:
wherein p is1To fracture the average formation pressure of the modified zone,G1moving a fracture-reforming zoneDynamic reserve, Gp1Cumulative production for gas wells, Gp2The cumulative flow rate of the non-fractured modified zone to the fractured modified zone.
According to one embodiment of the invention, the material balance equation of the non-fractured modified zone is:
wherein p is2The average formation pressure of the uncracked reconstruction zone,Gp2cumulative flow channeling from an uncracked modified zone to a fractured modified zone, G2Is the dynamic reserve of the uncracked reconstruction zone.
According to one embodiment of the invention, the step of determining the outer zone dynamic reserve in the fractured horizontal well further comprises:
given shale gas well's fracturing modification zone dynamic reserves G1Dynamic reserves G of uncracked modified zone2；
Dynamic reserve G based on fracturing modified zone1Dynamic reserves G of uncracked modified zone2Iteratively calculating the average formation pressure of the fracturing modification area by using the material balance equation of the fracturing modification area according to the daily gas production rate of the gas well;
average formation pressure p based on the fracture modification zone1And the binomial productivity equation is used for predicting the bottom hole flow pressure according to the daily gas production;
fitting the predicted and actual bottom hole flow pressures to determine a dynamic reserve of the fractured modified zone and a dynamic reserve of the non-fractured modified zone of the horizontal well.
According to an embodiment of the invention, the step of iteratively calculating the average formation pressure of the fracture reconstruction zone further comprises:
the last time step ti-1Average formation pressure value p of fracturing reconstruction area10As the current tiIterative initial value p of average formation pressure of time-step fracturing reconstruction area1If t isiIf the value is 0, the iteration initial value is the original formation pressure value;
mean formation pressure p from a fracture reformation zone1Iteratively calculating the average formation pressure p of the non-fractured modified zone from the material balance equation of the non-fractured modified zone2；
Mean formation pressure p from a fracture reformation zone1Average formation pressure p of non-fractured reconstruction zone2And calculating the current t by the cross-flow coefficient between the inner and outer regionsiChanneling flow and accumulated channeling flow from the non-fracturing reconstruction area to the fracturing reconstruction area in a time step;
average formation pressure value p based on fracturing reconstruction area1Original formation pressure piGas well cumulative gas production Gp1And the cumulative flow rate Gp2Calculating the residual error of a material balance equation of the current time step fracturing transformation area:
when the absolute value of the residual error is smaller than the given error, the iteration converges and exits; otherwise, the current average formation pressure value p is used1And as an initial value, continuously and iteratively calculating the average formation pressure value of the new fracturing reconstruction zone according to a Newton method until the error requirement is met.
According to one embodiment of the invention, the step of iteratively calculating the average formation pressure of the frac-free altered zone further comprises:
take the last time step ti-1Average formation pressure p of an uncracked modified zone20AsThis time step tiInitial value p of average formation pressure of non-fractured reconstruction area2If t isiTaking the original formation pressure as 0;
according to the current tiCurrent average formation pressure values for time-step fracture-modified and uncracked zonesp1 and p2Calculating the amount of cross flow q between the two regions2And cumulative flow rate Gp2，
Flow rate q of cross flow between two zones at current time step2Calculated by the following formula:
total accumulated flow rate between two zones Gp2Calculated by the following formula:
Gp2＝Gp20+ΔGp2，
wherein λ is a channeling coefficient, Δ Gp2For the accumulated cross flow between two zones in the current step length,Δ t is the step size of the time step, q20For the amount of cross-flow between two zones of the previous time step, Gp20The total accumulated flow rate between the two areas of the previous time step;
based on the current tiAverage formation pressure value p of time-step uncracked reconstruction area2Original formation pressure piCumulative cross-flow production Gp2Calculating the material balance equation residual error of the non-fractured modified zone,
exiting the iteration when the absolute value of the residual is less than the given error, otherwise laminating with the present averageForce value p2And as an initial value, continuously and iteratively calculating the average formation pressure value of the fractured and transformed area until the error requirement is met.
According to an embodiment of the invention, the step of fitting the predicted and actual bottom hole flow pressures to determine the dynamic reserve of the fractured modified zone and the dynamic reserve of the non-fractured modified zone of the horizontal well further comprises:
calculating a bottom hole flowing pressure based on the average formation pressure of the fracturing modification area and the binomial productivity equation;
adjusting the dynamic reserve G of the fracture modification zone by a fitting optimization algorithm1And dynamic reserve G of the non-fractured modified zone2So that the error square sum value of the calculated bottom hole flow pressure and the actual bottom hole flow pressure is in a set range, thereby determining the dynamic reserve G of the fracturing modification area1And dynamic reserve G of the non-fractured modified zone2。
The invention has the beneficial effects that:
the invention does not need to shut down a well to test the average formation pressure during use, can consider the influence of adsorbed gas desorption and an abnormal high pressure and physical property composite zone, and can respectively determine the dynamic reserves of the fracturing modification zone and the peripheral non-fracturing modification zone.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required in the description of the embodiments or the prior art:
FIG. 1 is a schematic diagram of a single well control area of a shale gas multi-staged fractured horizontal well;
FIG. 2 is a flow diagram of a method according to one embodiment of the invention;
FIG. 3 is a flow diagram of an algorithm implementation according to one embodiment of the invention;
FIG. 4 is a flow diagram for iteratively solving for an inner zone formation mean pressure according to one embodiment of the present invention;
FIG. 5 is a flow chart for iteratively solving for the average pressure of the outer zone formation according to one embodiment of the invention;
FIG. 6 is a schematic of the daily gas production and the measured bottom hole flow pressure for well A according to one embodiment of the present invention;
FIG. 7 is a graphical illustration of binomial productivity curves for well A according to one embodiment of the present invention;
FIG. 8 is a schematic diagram of a calculated bottom hole flow pressure versus measured value comparison prior to history fitting for well A in accordance with an embodiment of the present invention; and
FIG. 9 is a schematic diagram of a calculated bottom hole flow pressure versus measured value curve after history fitting for well A in accordance with an embodiment of the present invention.
Detailed Description
The following detailed description of the embodiments of the present invention will be provided with reference to the drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented. It should be noted that, as long as there is no conflict, the embodiments and the features of the embodiments of the present invention may be combined with each other, and the technical solutions formed are within the scope of the present invention.
The single-well control area of the shale gas multi-section fracturing horizontal well can be divided into a fracturing modification area (inner area) and a non-fracturing modification area (outer area) according to well pattern intervals. As shown in fig. 1, a schematic diagram of a single well control area of a horizontal well is shown, where the control area includes a fracture-modified zone 100 and an uncrushed modified zone 200, a boundary of the two zones is a fracture-modified zone boundary, and an external boundary of the uncrushed modified zone 200 is an inter-well choke boundary. The inner zone is a complex fracture network zone formed by main fracturing fractures and natural fractures after multi-section volume fracturing transformation, and the outer zone is a zone which is not fractured and transformed between adjacent wells.
Gas produced in the early production stage of the shale gas fracturing horizontal well mainly comes from the inner zone, and as the stratum pressure of the inner zone is reduced, the pressure difference between the inner zone and the outer zone is gradually amplified to form interval channeling. The flow-channeling production is related to the stratum pressure difference of the inner zone and the outer zone and the flow-channeling coefficient of the zones. When the inner zone formation pressure is reduced to the critical desorption pressure, the adsorbed gas begins to desorb and diffuse and impact the gas well productivity.
Accordingly, the present invention provides a method for determining the outer zone dynamic reserve in a shale gas multi-staged fracturing horizontal well. According to the characteristic that the shale gas fracturing horizontal well control surface is accumulated in an inner zone and an outer zone, a shale gas reservoir material balance equation considering the effects of adsorbed gas desorption and abnormal high pressure is respectively established according to the two zones, a calculation model of the gas yield and the bottom hole flow pressure of the shale gas well is established by combining a binomial productivity equation of the gas well and an expression of the flow channeling between the two zones, and the dynamic reserves of the inner zone and the outer zone of the shale gas well are finally determined by adjusting the reserves of the inner zone and the outer zone of the gas well and fitting the bottom hole flow pressure.
Fig. 2 is a flow chart of a method according to an embodiment of the present invention, fig. 3 is a flow chart of an algorithm implementation according to an embodiment of the present invention, and the present invention is described in detail below with reference to fig. 2 and 3.
Firstly, in step S110, gas test data, production data, and gas well structural parameters of the shale gas multi-stage fractured horizontal well are obtained, a gas well binomial productivity equation is established according to the gas test data, and the actual bottom hole flowing pressure is calculated according to the production data and the gas well structural parameters.
Specifically, the obtained gas testing data, production data and gas well structural parameters of the shale gas multi-section fractured horizontal well are shown in table 1. According to the oil and gas industry standard SY/T5440-plus 2000 of the people's republic of China, a gas well binomial energy production equation established by fitting gas test data is expressed as follows:
wherein A is a first-order coefficient of a gas well binomial energy production equation; b is a quadratic coefficient of a binomial energy production equation of the gas well; q is the daily gas production of the gas well, 104m3/d；p1Mean formation pressure, p, for a fracture reformation zonewfThe bottom hole flowing pressure is MPa corresponding to the gas well when the yield is q. As can be seen from the formula (1-1), as long as the average formation pressure p of the fracture modification zone is given1And after the daily gas production of the gas well, the predicted bottom hole flow pressure of the gas well can be calculated according to the formula. Average formation pressure p of fracturing reformation area1This can be calculated in the following steps of the present invention.
Next, in step S120, material balance equations for the fractured and non-fractured modified zones of the multi-staged fractured horizontal well are established, respectively, taking into account the adsorbed gas desorption and the abnormal high pressure effects. The step specifically includes the following steps.
In step S1201, a shale gas reservoir material balance equation is established in consideration of the adsorbed gas desorption and the abnormal high pressure effect. In the step, when a shale gas reservoir substance balance equation is established, the influence of desorption and diffusion of free gas and adsorbed gas needs to be comprehensively considered. In addition, for abnormally high pressure shale gas reservoirs, rock elastic energy effects also need to be considered. Because the pore compressibility of the rock at the initial stage of development of the abnormal high-pressure gas reservoir is approximately in the same order of magnitude as that of the natural gas, the elastic driving energy of the abnormal high-pressure gas reservoir cannot be ignored, otherwise, the evaluated dynamic reserves are higher. The shale gas reservoir substance balance equation considering the influence of the abnormal high pressure and the adsorption gas desorption is established by analyzing the influence of the abnormal high pressure and the adsorption gas desorption on the shale gas reservoir substance balance equation according to the mass conservation principle.
Assuming that the original free gas reserve of the gas reservoir is GfThe local layer pressure is defined by PiThe decrease in subsurface pore volume due to rock skeleton compression and fluid expansion when reduced to P is expressed as:
wherein G isfFor the original free gas reserve of the gas reservoir, 104m3；BgiIs the natural gas volume coefficient at the original formation pressure; sgiThe original gas saturation of the gas reservoir; swiThe original water saturation of the gas reservoir; c. CfIs effective pore compressibility, MPa-1；cwIs the formation water compression coefficient, MPa-1；ΔVeFor volume change of subsurface pores caused by formation pressure drop, 104m3。
Since e is when x → 0x1+ x, equation (2-1) can be simplified as:
equation (2-2) represents the change in subsurface pore volume caused by the pressure drop in the abnormally high pressure gas reservoir formation.
Because natural gas in the shale gas reservoir exists in a free gas and adsorption gas mode, the adsorption gas accounts for 20-85%. The shale adsorbed gas content can be described by the langmuir isothermal adsorption equation as follows:
wherein V (p) represents the gas content of the shale saturated adsorption gas when the pressure is p, and m3/t；VLIs the Langmuir volume, which represents the maximum saturated adsorbed gas content of the shale as the formation pressure approaches infinity, m3/t；PLIs Lane pressure, representing 50% V in the Lane's isothermal adsorption curveLCorresponding pressure, MPa. The lower the Lane pressure, the less readily the adsorbed gas will desorb during production.
Based on equation (2-3), the total adsorbed gas volume of the shale gas reservoir at any pressure can be expressed as:
where ρ isBIs shale density, t/m3；VBIs the total volume of shale, m3。
Based on equation (2-4), the original formation pressure is piThe total free gas and adsorbed gas reserves can be expressed as:
the local formation pressure is defined by piThe accumulated gas production when p is reduced to GpThe reduction of the pore volume of the shale gas reservoir can be calculated by the following formula (2-6):
the remaining free gas reserve can be calculated by the following formula:
remaining adsorbed gas inventory:
according to the law of conservation of material: the original free gas reserve + original adsorbed gas reserve-residual free gas reserve + residual adsorbed gas yield + accumulated gas yield-can be obtained as follows:
b in the formula (2-9)gBy conversion with a compression factor z, the formula (2-9) can be arranged as follows:
if order:
then the formula (2-10) can be arranged as:
the equations (2-12) are shale gas reservoir material balance equations considering the effects of adsorbed gas desorption and abnormal high pressure.
In step S1202, the single well control area of the multi-section fractured horizontal well is divided into a fractured and transformed zone and an uncracked and transformed zone according to the well pattern spacing, and the zones are as shown in fig. 1.
In step S1203, material balance equations for the fractured and reformed zones and the non-fractured and reformed zones are respectively established based on the shale gas reservoir material balance equations. Specifically, the material balance equation of the fracture transformation zone established based on the material balance equation (2-12) is as follows:
wherein p is1Mean formation pressure, G, for fracturing a modified zone1Dynamic reserves for fracture modification zone, Gp1Cumulative production for gas wells, Gp2The cumulative flow rate of the non-fractured modified zone to the fractured modified zone.
The material balance equation of the non-fractured modified zone established based on the material balance equation (2-12) is as follows:
wherein p is2Mean formation pressure, G, for an uncracked modified zone2Is the dynamic reserve of the uncracked reconstruction zone.
Finally, in step S130, the dynamic reserves of the fractured and transformed zone and the non-fractured and transformed zone are respectively given, and the dynamic reserves are adjusted to fit the actual bottom hole flow pressure by combining the material balance equation of the fractured and transformed zone and the non-fractured and transformed zone, the expression of the flow rate channeling between the two zones, and the binomial productivity equation, so as to determine the dynamic reserves of the inner and outer zones of the fractured horizontal well.
In this step, the determination of the dynamic reserve of the outer zone in the horizontal well comprises in particular the following steps. First, in step S1301, an estimated value of dynamic reserve of a given shale gas horizontal well fracturing reformation zone is G10And the estimated value of the dynamic reserve of the non-fractured modified zone is G20These two dynamic reserves are estimates, not final values.
In step S1302, an estimate G based on fracture modification zone dynamic reserves10Estimate G of dynamic reserves in uncracked modified zone20And iteratively calculating the average formation pressure of the fractured and transformed region according to the daily gas production of the gas well by using a material balance equation of the fractured and transformed region, a material balance equation of the non-fractured and transformed region, a gas well productivity equation and an expression of the flow rate between the two regions.
Specifically, iteratively calculating the average formation pressure of the fracture modification zone may be performed through several steps as shown in fig. 4. Firstly, the last time step ti-1Average formation pressure value p of inner fracturing reconstruction zone10As the current time step tiAverage formation pressure p of inner fracturing reconstruction zone1The initial value of the iteration. If t isiWhen the value is 0, the initial value of the iteration is the original formation pressure value pi。
Then, according to the average formation pressure p of the fracturing reconstruction area1Iteratively calculating the average formation pressure p of the non-fractured modified zone from the material balance equation of the non-fractured modified zone2。
Iteratively calculating average formation pressure p of an uncracked reconstruction region2Including several steps as shown in fig. 5. Firstly, take the last time step ti-1Average formation pressure p of inner non-fractured reconstruction zone20As the current time step tiInitial value p of average formation pressure of inner non-fractured reconstruction area2If t isiThe initial value of the iteration is taken as the original formation pressure pi。
Then, based on the current tiCurrent average formation pressure values p of a fractured and rebuilt area and an un-fractured rebuilt area in time step1And p2Calculating the amount of cross flow q between the two regions at the current time step according to the following formula2And cumulative flow rate Gp2. Wherein the flow rate q of the cross flow between the two regions at the current time step is calculated2Expression (c):
calculating the total cumulative flow rate G between two zonesp2The expression of (a) is:
Gp2＝Gp20+ΔGp2， (2-16)
wherein,λ is the cross flow coefficient, Δ t is the step length of time, q20For the amount of cross-flow between two zones of the previous time step, Gp20Total accumulated cross flow, Δ G, between two zones for the last time stepp2The accumulated flow rate between the two areas in the current step length is shown.
Then, based on the current tiAverage formation pressure value p of non-fractured reconstruction area in time step2Original formation pressure piCumulative cross-flow production Gp2And calculating the material balance equation residual error of the non-fractured modified area. The residual error is:
when the absolute value of the residual error is smaller than the given error, exiting iteration; otherwise, the current average formation pressure value p is used2And as an iteration initial value, continuously and iteratively calculating the average formation pressure value of the fractured and transformed zone until the average formation pressure value meets the error requirement.
Based on the calculation, the average formation pressure value p of the non-fractured reconstruction area can be obtained2. Next, the average formation pressure p is determined according to the fracturing reconstruction zone1Average formation pressure p of non-fractured reconstruction zone2And calculating the current time-step flow rate and the accumulated flow rate from the non-fractured modified zone to the fractured modified zone by using the interval flow rate coefficient. The current time-step flow rate and the accumulated flow rate can be calculated by the average formation pressure value of the non-fractured reconstruction area.
Next, based on average formation pressure value p of the fracturing modification area1Original formation pressure piGas well cumulative gas production Gp1And cumulative flow rate Gp2And calculating the residual error of the material balance equation of the fracturing transformation area in the current time step. The residual error is:
when the absolute value of the residual error is smaller than the given error, the iteration converges and exits; otherwise, the current average formation pressure value p is used1And as an iteration initial value, continuously iterating and calculating the average formation pressure value of the new fracturing reconstruction zone according to a Newton method until the average formation pressure value meets the error requirement.
In step S1303, the average formation pressure value p of the fracture reconstruction zone based on the above obtained values1And a binomial productivity equation for predicting the bottom hole flowing pressure according to the daily gas production. In particular, given that other parameters are known, provided that an estimate G of the dynamic reserve of a given fracture modification zone is given10And estimate G of the dynamic reserves of the uncracked frac zone20The daily gas production rate of the gas well can be obtained through the production data, and then the corresponding bottom hole flowing pressure is calculated according to the daily gas production rate of the gas well and the productivity equation.
In step S1304, the predicted and actual bottom hole flow pressures are fitted to determine the dynamic reserves of the horizontal well fracture-modified zone and the dynamic reserves of the non-fracture-modified zone. Specifically, in the step, the bottom hole flow pressure is calculated based on the average formation pressure of the fracturing modification area and a binomial productivity equation (1-1), and the dynamic reserve G of the fracturing modification area is adjusted through a fitting optimization algorithm1And dynamic reserves G of the non-fractured modified zone2So that the error square sum value of the calculated bottom hole flow pressure and the actual bottom hole flow pressure is in a set range, and the dynamic reserve G of the fracturing modification area is determined1And dynamic reserves G of the non-fractured modified zone2。
TABLE 1
The invention is illustrated below by means of a specific example. Taking a shale gas well A of the Lomaxi group of the Sichuan basin reservoir as an example, the main parameters of the well are shown in Table 1.
After the well finishes gas testing in 12 months from 2012, the well adopts a 5-inch half casing for 9 months of test production, then a 2-inch half oil pipe is put into the well for production, and 9 times of bottom hole pressure and temperature gradient tests are cumulatively carried out in the period. Fig. 6 shows the daily gas production and the measured bottom hole flow pressure during the gas testing and production period of the well.
Before calculating the dynamic reserves, the well binomial productivity equation is evaluated according to the gas testing data. According to the oil and gas industry standard SY/T5440-2000 of the people's republic of China, a binomial productivity equation of the gas well is established by fitting gas test data, and the result is shown in FIG. 7. The coefficients of the well A binomial productivity equation are respectively A-21.107 and B-2.9494.
According to the method of the invention, an algorithm program is established, the parameters in the table 1 and the production data such as the daily gas production in the graph of 6 are input, and estimated values G of the internal and external dynamic reserves are respectively given10、G20，G102.5 million square, G203 billion square. The calculated bottom hole flow pressure is shown in figure 8. Adjusting dynamic reserves G by fitting optimization algorithm1And G2The calculated bottom hole flow pressure and the actual bottom hole flow pressure are fitted, and the final fitting result is shown in fig. 9. The current inner zone of the fitted well A has a dynamic reserve of 1.83 million and the outer zone has a reserve of 0.4 million, the extent of mobilization of the outer zone is low.
The substance balance equation established in the invention considers the influence of adsorption gas desorption and rock pore compression coefficient, and on the basis, the dynamic reserve evaluation method based on production dynamic data is established by integrating the substance balance equation and the gas well productivity equation. The method can consider the influences of shale gas adsorption and desorption and rock pore compression coefficients on a shale gas reservoir substance balance equation during calculation, and does not need to shut in the average formation pressure of pressure recovery evaluation during calculation. The calculation result is suitable for various applications such as reasonable production allocation of shale gas wells, development technical policy and development scheme optimization.
Although the embodiments of the present invention have been described above, the above description is only for the convenience of understanding the present invention, and is not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A method for determining an outer zone dynamic reserve in a shale gas multi-staged fracturing horizontal well, comprising:
acquiring gas testing data, production data and gas well structural parameters of a shale gas multi-section fractured horizontal well, establishing a gas well binomial productivity equation according to the gas testing data, and calculating actual bottom hole flowing pressure according to the production data and the gas well structural parameters;
respectively establishing a material balance equation aiming at a fracturing modification area and an uncrushed modification area of the multi-section fracturing horizontal well by considering the adsorption gas desorption and the abnormal high-pressure influence;
respectively giving estimated values of dynamic reserves of the fractured modified zone and the non-fractured modified zone, and fitting the actual bottom hole flow pressure by combining a material balance equation of the fractured modified zone and the non-fractured modified zone, an expression of a flow channeling amount between the two zones and the estimated value of the dynamic reserves adjusted by the binomial productivity equation, so as to determine the dynamic reserves of the fractured modified zone and the non-fractured modified zone as the dynamic reserves of an inner zone and an outer zone of a fracturing horizontal well;
wherein, the expression of the flow rate is as follows:
wherein q is2Is the amount of cross-flow between two zones, λ is the cross-flow coefficient, p1Mean formation pressure value, p, for the fracture modified zone2The average formation pressure value of the uncracked reconstruction zone.
2. The method of claim 1, wherein the step of establishing a material balance equation for a fractured and non-fractured modified zone of a multi-staged fractured horizontal well further comprises:
considering the effects of adsorption gas desorption and abnormal high pressure, establishing a shale gas reservoir substance balance equation;
dividing the single well control area of the multi-section fractured horizontal well into a fractured modified area and an uncrushed modified area according to the well pattern spacing;
and respectively establishing material balance equations of the fractured and transformed zone and the non-fractured and transformed zone based on the shale gas reservoir material balance equation.
3. The method of claim 2, wherein the step of establishing the shale gas reservoir material balance equation further comprises:
calculating the volume reduction of underground pores caused by rock skeleton compression and fluid expansion when the formation pressure changes based on the rock pore compression coefficient;
calculating the residual free gas reserve and the residual adsorbed gas reserve of the shale gas reservoir after the formation pressure is reduced based on the underground pore volume reduction and the Langmuir isothermal adsorption equation;
according to the law of conservation of material: and establishing a shale gas reservoir substance balance equation by the original free gas reserve and the original adsorbed gas reserve, namely the residual free gas reserve, the residual adsorbed gas yield and the accumulated gas yield.
4. The method of claim 2 or 3, wherein the shale gas reservoir material balance equation is:
wherein Z isa＝Za(p)，
When p ═ piWhen the temperature of the water is higher than the set temperature,p is the formation pressure, piTo the original formation pressure, GpFor cumulative yield, G is dynamic reserve, cfIs the porosity compressibility of the rock, cwIs the formation water compression coefficient, SwiIs the original water saturation of the gas reservoir, SgiFor the original gas saturation of the reservoir, phi is the effective porosity, rhoBIs shale density, VLIs the Langmuir volume, PLIs the Lane pressure, pscIs gas pressure at standard conditions, T is formation temperature, TscIs the temperature at standard conditions, z is the natural gas compression factor at pressure p, zscIs the natural gas compression factor in a standard state.
5. The method of claim 4, wherein the material balance equation for the fracture modification zone is:
wherein p is1To fracture the average formation pressure of the modified zone,G1dynamic reserves for fracture modification zone, Gp1Cumulative production for gas wells, Gp2The cumulative flow rate of the non-fractured modified zone to the fractured modified zone.
6. The method of claim 4, wherein the material balance equation for the non-fractured modified zone is:
wherein p is2The average formation pressure of the uncracked reconstruction zone,Gp2cumulative flow channeling from an uncracked modified zone to a fractured modified zone, G2Is the dynamic reserve of the uncracked reconstruction zone.
7. The method of claim 5 or 6, wherein the step of determining the outer zone dynamic reserve within the fractured horizontal well further comprises:
given shale gas multi-stage fracturing horizontal well fracturing transformation zone dynamic reserve estimation value G10Estimate G of dynamic reserves in uncracked modified zone20；
Estimated value G based on dynamic reserves of fracturing reconstruction zone10Estimate G of dynamic reserves in uncracked modified zone20Equation of mass balance for fracture modified zone, uncrackedIteratively calculating the average formation pressure of the fracturing modification area by the material balance equation of the fracturing modification area according to the daily gas yield of the gas well;
average formation pressure p based on the fracture modification zone1And the binomial productivity equation is used for predicting the bottom hole flow pressure according to the daily gas production;
fitting the predicted and actual bottom hole flow pressures to determine a dynamic reserve of the fractured modified zone and a dynamic reserve of the non-fractured modified zone of the horizontal well.
8. The method of claim 7, wherein the step of iteratively calculating the average formation pressure of the fracture modification zone further comprises:
the last time step ti-1Average formation pressure value p of fracturing reconstruction area10As the current tiIterative initial value p of average formation pressure of time-step fracturing reconstruction area1If t isiIf the value is 0, the iteration initial value is the original formation pressure value;
mean formation pressure p from a fracture reformation zone1Iteratively calculating the average formation pressure p of the non-fractured modified zone from the material balance equation of the non-fractured modified zone2；
Mean formation pressure p from a fracture reformation zone1Average formation pressure p of non-fractured reconstruction zone2And calculating the current t by the internal and external area cross flow coefficientiChanneling flow and accumulated channeling flow from the non-fracturing reconstruction area to the fracturing reconstruction area in a time step;
average formation pressure value p based on fracturing reconstruction area1Original formation pressure piGas well cumulative gas production Gp1And the cumulative flow rate Gp2Calculating the residual error of a material balance equation of the current time step fracturing transformation area:
when the absolute value of the residual error is less than a given errorThe iteration converges and the iteration exits, otherwise, the current average formation pressure value p is used1And as an initial value, continuously and iteratively calculating the average formation pressure value of the new fracturing reconstruction zone according to a Newton method until the error requirement is met.
9. The method of claim 8, wherein the step of iteratively calculating the average formation pressure of the frac-free altered zone further comprises:
take the last time step ti-1Average formation pressure p of an uncracked modified zone20As the current time step tiInitial value p of average formation pressure of non-fractured reconstruction area2If t isiTaking the original formation pressure as 0;
according to the current tiCurrent average formation pressure values p of time step fracturing modified area and non-fracturing modified area1And p2Calculating the cross flow q between the inner and outer regions2And cumulative flow rate Gp2，
Total accumulated cross flow G between inner and outer zonesp2Calculated by the following formula:
Gp2＝Gp20+ΔGp2，
wherein, Δ Gp2The accumulated flow rate between the inner zone and the outer zone in the current step length,Δ t is the step size of the time step, q20Is the amount of cross flow between the inner and outer zones of the last time step, Gp20The total accumulated flow rate between the inner area and the outer area of the previous time step;
based on the current tiAverage formation pressure value p of time-step uncracked reconstruction area2Original formation pressure piAnd cumulative flow cross-over production G between inner and outer regionsp2Calculating the material balance equation residual error of the non-fractured modified zone:
when the absolute value of the residual error is less thanWhen the error is determined, the iteration is exited, otherwise, the current average formation pressure value p is used2And as an initial value, continuously and iteratively calculating the average formation pressure value of the fractured and transformed area until the error requirement is met.
10. The method of claim 9, wherein the step of fitting the predicted and actual bottom hole flow pressures to determine the dynamic reserve of the fractured modified zone and the dynamic reserve of the non-fractured modified zone of the horizontal well further comprises:
calculating a bottom hole flowing pressure based on the average formation pressure of the fracturing modification area and the binomial productivity equation;
adjusting an estimate G of the dynamic reserve of the fracture modification zone by a fitting optimization algorithm10And an estimate G of the dynamic reserve of the non-fractured modified zone20So that the error square sum value of the calculated bottom hole flow pressure and the actual bottom hole flow pressure is in a set range, thereby determining the dynamic reserve G of the fracturing modification area1And dynamic reserve G of the non-fractured modified zone2。
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