CN111415031A - Method for predicting productivity of coal-bed gas well - Google Patents

Method for predicting productivity of coal-bed gas well Download PDF

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CN111415031A
CN111415031A CN202010102007.XA CN202010102007A CN111415031A CN 111415031 A CN111415031 A CN 111415031A CN 202010102007 A CN202010102007 A CN 202010102007A CN 111415031 A CN111415031 A CN 111415031A
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肖芝华
孙政
武男
石军太
林文姬
侯伟
闫霞
张雷
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Petrochina Co Ltd
China United Coalbed Methane National Engineering Research Center Corp Ltd
Petrochina Coalbed Methane Co Ltd
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Abstract

The invention discloses a method for predicting the productivity of a coal-bed gas well. The method comprises the steps of calculating the yield of the coal-bed gas well by distinguishing the conditions that a desorption area and a non-desorption area exist in a reservoir, assuming the position of the front edge of a pressure wave or simultaneously assuming the position of the front edge of the desorption area, respectively using a substance conservation principle and a productivity equation, and gradually adjusting assumed parameters in an iterative comparison mode until the difference of the yields calculated by the two methods meets the preset precision requirement, so that the correct position of the front edge of the pressure wave and the position of the front edge of the desorption area are determined, and the productivity of the coal-bed gas well is calculated.

Description

Method for predicting productivity of coal-bed gas well
Technical Field
The invention relates to the technical field of coal bed gas exploitation, in particular to a method for predicting the productivity of a coal bed gas well.
Background
The coal bed gas reservoir belongs to a double-pore medium and comprises a matrix system and a fracture system, and the gas-water distribution characteristics and the seepage mechanism of the coal bed gas reservoir are different from those of the conventional sandstone gas reservoir, so that the conventional gas reservoir energy production prediction method cannot be applied to the coal bed gas reservoir. The coalbed methane reservoir mainly contains adsorbed gas, and a small amount of free gas is added, so that the gas production depends on the desorption of the gas and the seepage capability in cracks, and the coalbed methane well productivity predicted by the existing analytic method is always greatly different from the actual coalbed methane well productivity.
Disclosure of Invention
In view of the problem that the prediction result of the coal bed gas productivity is greatly different from the actual productivity in the prior art, the invention provides the method for predicting the coal bed gas productivity, so as to overcome the problem.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for predicting the productivity of a coal-bed gas well comprises the following steps:
the method comprises the following steps: assuming a pressure wave location r of the reservoirp(ii) a If the reservoir has a desorption zone, the pressure wave front position r is assumed at the same timepAnd the position r of the front edge of the desorption regiond；
Step two: on the basis of the assumption, calculating the water yield according to a substance conservation principle and recording the water yield as a first water yield, and if an analysis area exists, calculating the gas yield according to the substance conservation principle and recording the gas yield as a first gas yield;
step three: based on the assumption, calculating the water yield according to a capacity equation and recording as a second water yield, and if an analysis area exists, simultaneously calculating the gas yield according to the capacity equation and recording as the second gas yield;
step four: comparing the first and second water yields by adjusting the pressure wave position rpDetermining the position r of the front edge of the pressure wave to ensure that the difference between the first water yield and the second water yield reaches the preset precision requirementp(ii) a If the reservoir layer has an analytic region, adjusting the pressure wave front position rpAnd the position r of the front edge of the desorption regiondEnabling the first gas production rate and the second gas production rate and the difference between the first water production rate and the second water production rate to simultaneously meet the preset precision requirement, and determining the pressure wave front edge position rpAnd the position r of the front edge of the desorption regiond；
Step five: passing the finally determined position r of the front edge of the desorption zonedOr the position r of the front edge of the desorption zonedAnd pressure wave position rpAnd calculating the yield of the coal-bed gas well.
Optionally, in step four, if a desorption zone is present, the first gas production is first compared with the second gas production by adjusting the position r of the front of the desorption zonedMaking the difference between the two reach the preset precision requirement, and determining the front edge position r of the desorption areadThen, the first and second water yields are compared, and the pressure wave position r is adjustedpDetermining the pressure wave position r by making the difference between the two reach the preset precision requirementp。
Optionally, in the second step, a calculation formula for calculating the first water yield according to the principle of conservation of substances is as follows:
Figure BDA0002387170480000021
the calculation formula for calculating the first gas production according to the substance conservation principle is as follows:
Figure BDA0002387170480000022
wherein r is the distance from the wellbore, rwIs the radius of the shaft, h is the thickness of the producing zone, t is the production time, phi (t) is the porosity of the coal bed, Sw(t) is the saturation of the water content, Bw(t) is the compressibility of the aqueous phase, P (t) is the pore fluid pressure, VLIs L angmuir volume constant, PLIs L angmuir pressure constant, Sg(t) is the saturation of the gas content, Bg(t) is a gas phase compression factor.
Optionally, the pressure distribution of the coal seam is obtained by adopting the following formula:
Figure BDA0002387170480000023
Figure BDA0002387170480000024
in the formula, PeAs boundary pressure, PdIs the critical desorption pressure, PwfIs the bottom hole flowing pressure reIs the boundary position;
considering the influence of the matrix water-containing pores on the production energy prediction, the formula for describing the gas desorption characteristics of the real coal rock is obtained as follows:
Figure BDA0002387170480000025
in the formula, SmwWater saturation in the coal matrix; if the calculation takes into account the influence of the matrix water-containing pores on the production prediction, then in step two, V in the formula for the first gas production will be calculatedLIs replaced by (1-S)mw)VL。
Optionally, in step three, the calculation formula for calculating the second water yield according to the capacity equation is as follows:
Figure BDA0002387170480000031
the calculation formula for calculating the second gas production according to the capacity equation is as follows:
Figure BDA0002387170480000032
in the formula, mwaterFor the aqueous phase, mgasIs a gas phase pseudo pressure, muwThe viscosity of the aqueous phase.
Optionally, in the formula for calculating the second water production, the water pseudo pressure is calculated using the following formula:
Figure BDA0002387170480000033
in the formula for calculating the second gas production, the gas pseudo pressure is calculated by the following formula:
Figure BDA0002387170480000034
in the formula, Kw(P) is the water phase permeability, Kg(P) is the gas phase permeability, μgIs the gas phase viscosity and Z is the gas deviation factor.
Optionally, in the method, if the coal-bed gas well is subjected to fracture reformation, in order to convert the elliptical seepage problem into the linear flow problem, the following relational expression is adopted to perform coordinate transformation on the calculation process:
x＝Lf×chξ×cosη，
y＝Lf×shξ×sinη，
wherein x and y are rectangular coordinates, LfHalf-length of the crack, ξ is an elliptical coordinate;
the following relationship is obtained:
Ra＝Lf×chξd，
Rb＝Lf×shξd，
Rpa＝Lf×chξp，
Rpb＝Lf×shξpd，
wherein Ra, Rb, Rpa and Rpb are respectively the long axis position and the short axis position of the desorption zone front of the fracturing vertical well and the long axis position and the short axis position of the pressure wave front, and ξ d and ξ p are respectively the desorption zone front and the pressure wave front under the condition of linear flow.
Optionally, if the coal-bed gas well is subjected to fracturing modification, calculating the first water yield by using the following formula according to the substance conservation principle:
Figure BDA0002387170480000041
according to the principle of conservation of substances, the first gas production is calculated by adopting the following formula:
Figure BDA0002387170480000042
wherein h is the thickness of the pay zone, ξwIs the wellbore radius in the case of linear flow, t is the production time, phi (t) is the coal bed porosity, Sw(t) is the saturation of the water content, Bw(t) is the compressibility of the aqueous phase, P (t) is the pore fluid pressure, VLIs L angmuir volume constant, PLIs L angmuir pressure constant, Sg(t) is the saturation of the gas content, Bg(t) is a gas phase compression factor.
Optionally, if the coal-bed gas well is subjected to fracturing modification, calculating a second water yield by using the following formula according to a capacity equation:
Figure BDA0002387170480000043
calculating a second gas production rate according to a capacity equation by adopting the following formula:
Figure BDA0002387170480000044
in the formula, mwaterFor the aqueous phase, mgasFor gas phase to simulate pressure, PeRepresenting the pressure at the coal seam boundary, PwfIndicating the bottom hole flow pressure, muwIs waterPhase viscosity.
Optionally, in the first step, whether the desorption zone exists in the reservoir is judged according to the relation between the bottom hole flowing pressure and the critical desorption pressure.
In conclusion, the beneficial effects of the invention are as follows:
the method comprises the steps of calculating the yield of the coal-bed gas well by distinguishing the conditions that an analytic area and a non-analytic area exist in a reservoir, assuming the position of the front edge of a pressure wave or simultaneously assuming the position of the front edge of a desorption area, respectively using a substance conservation principle and a capacity equation, and gradually adjusting assumed parameters in an iterative comparison mode until the difference of the yields calculated by the two methods meets the preset precision requirement, so that the correct position of the front edge of the pressure wave and the position of the front edge of the desorption area are determined, and the capacity of the coal-bed gas well is calculated.
Drawings
FIG. 1 is a schematic flow chart of a method for predicting productivity of a coal-bed gas well according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the effect of gas desorption on pressure transmission during the production of coalbed methane;
FIG. 3 is a schematic diagram illustrating a pressure profile that may occur during the analysis of a coalbed methane reservoir production process in accordance with the present invention;
FIG. 4 is a schematic diagram of pressure expansion of a coal-bed gas well in the case of no fracturing and no fracturing.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present application. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present application, it is to be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meaning of the above terms in the present application can be understood in a specific case by those of ordinary skill in the art.
The technical conception of the invention is as follows: the method comprises the steps of calculating the yield of the coal-bed gas well by distinguishing the conditions that the reservoir has an analysis area and a non-analysis area, assuming the position of the front edge of a pressure wave or simultaneously assuming the position of the front edge of a desorption area, and respectively utilizing a substance conservation principle and a capacity equation, and gradually adjusting assumed parameters in an iterative comparison mode until the difference of the yields calculated by the two methods meets the preset precision requirement, so that the correct position of the front edge of the pressure wave and the position of the front edge of the desorption area are determined, and the capacity of the coal-bed gas well is calculated.
Due to the existence of the critical desorption pressure of the coal seam, the coal seam in the production process can be divided into a desorption area and a non-desorption area, namely, the pressure of the coal seam in the area is lower than or higher than the critical desorption pressure. Whether the desorption area can be efficiently expanded or not is closely related to a pressure transmission mechanism in the production process, and the gas production capacity of the coal-bed gas well is directly influenced.
In coal bed gas exploitation, along with pressure reduction, adsorbed gas in a coal bed matrix system is gradually desorbed, and a cross flow enters a fracture, so that a fluid flowing mechanism in the fracture generates complex phase state conversion of single-phase water-gas-water two-phase-single-phase gas, and the pressure propagation speed is further reduced. For example, when the reservoir pressure is slightly lower than the critical desorption pressure, as shown in fig. 2(a), a small amount of desorption gas enters the fracture, and a continuous gas column cannot be formed due to a small amount of gas, and the flowing capability is lacked, so that the flowing mechanism in the fracture still belongs to single-phase water flow. But these gases may be present in the crevices in the form of separate bubbles. These static bubbles cling to the fracture surfaces, occupy a portion of the flow path, reduce the effective flow area of the fluid, impair the fluid flow capacity, and result in a reduced pressure transfer rate. When the reservoir pressure is further reduced, as shown in fig. 2(b), a large amount of desorbed gas enters the fracture, more and more bubbles gradually gather to form large-bubble continuous gas flow, and the flow mechanism in the fracture changes single-phase water into gas-water two-phase flow. Due to the occurrence of the gas-water two-phase interface, the pressure of the gas-water two-phase capillary tube needs to be overcome in the transmission process of the pressure of the storage layer, so that the transmission of pressure waves is slower.
For any one coal reservoir unit, when the pressure of the coal reservoir unit is higher than the critical desorption pressure, single-phase water seepage flows in the unit; when the pressure is lower than the critical desorption pressure, the desorbed gas continuously flows into the cracks, a small amount of desorbed gas can change the single-phase water seepage into the unsaturated single-phase water seepage, and a large amount of desorbed gas can change the single-phase water seepage into the gas-water two-phase seepage. The analysis on the seepage mechanism of the coal reservoir unit is carried out, the pressure distribution form can be various for the whole coal bed, the corresponding coal reservoir seepage mechanism becomes complex, and the coal reservoir seepage mechanism can be single-phase water seepage, gas-water two-phase flow or the combination of a plurality of seepage mechanisms. In view of this, previously existing capacity models do not well consider the pressure transfer process to have an extremely important impact on coalbed methane well production. The present application analyzes the pressure distribution of coal bed gas potential during production and the corresponding seepage conditions to reveal the pressure transfer mechanism at different production stages, as shown in fig. 3.
As shown in FIG. 3, the pressure profile at the beginning of gas well production may be generally represented by curve ①, it can be seen that the coal bed pressure in this case is entirely above the critical desorption pressure, while the pressure front has not yet reached the boundary, as production proceeds, the difference in the field drainage regime may occur as the pressure front transitions from ① to ② as the bottom stream pressure drops to a lesser magnitude, the pressure drop curve transitions from ① to ③ as the gas well accelerates drainage, for the pressure drop curve ② the difference from curve ① is that the pressure front reaches the boundary, for the pressure drop curve ③, it can be seen from the graph that a portion of the pressure in the bottom zone is below the critical desorption pressure, which is in the desorption zone, while another portion of the coal bed pressure is still above the desorption critical pressure, which is not in the desorption zone, which gas desorption occurs, which is in the desorption zone, which is in the single phase flow, which is in the near-phase flow zone, which the desorption of the coal bed gas is still above the critical desorption pressure, which is in the initial zone, which the desorption zone is still above the critical desorption zone, which is in the single phase flow of the gas, which is in the gas well, which is in the production process, the single phase flow profile of the single phase flow of the gas, which is different from which the single phase flow of the gas well, which the gas is not in the single phase flow, which the single phase flow is produced, which is not the gas flow, which is produced, which is the single phase flow profile is different from which the single phase flow, which the single phase flow of the single phase flow, which is not the single phase flow of the single phase flow, which is different from the single phase flow of the single.
As production continues, either pressure profile ② or ③ will gradually change to curve ④, i.e., a portion of the area near the bottom of the well will have a pressure less than the critical desorption pressure, while the pressure front has reached the gas reservoir boundary. in this case, a portion of the coal reservoir will be in the desorption zone, and a portion will be in the non-desorption zone, i.e., the production of the coal gas well during this production phase will be determined by both the gas-water two-phase seepage from the near well region and the single-phase water seepage from the far well region.
According to the analysis, the fluid flow mechanism of the coal bed gas under different pressure distribution conditions has difference, and the difference can influence the production dynamics of the gas well. In the existing coal-bed gas well analytic productivity prediction model, the influence of the pressure transmission process on the productivity of the coal-bed gas well is not fully reflected. In view of the above, according to the content shown in the above figure, the invention divides the coal bed gas well production process into 5 stages, covers the whole production process of the coal bed gas well, and describes the slow evolution physical process of the coal bed gas reservoir fluid flow mechanism from single-phase water-gas-water two-phase-single-phase gas. Based on the method, the seepage mechanism in the coal seam is analyzed, and a productivity prediction equation is gradually established to form a novel productivity prediction model.
As shown in fig. 1, a schematic flow chart of a method for predicting productivity of a coal-bed gas well according to an embodiment of the present invention is provided, where the method includes:
the method comprises the following steps: assuming a pressure wave location r of the reservoirp(ii) a If the reservoir has a desorption zone, the pressure wave front position r is assumed at the same timepAnd the position r of the front edge of the desorption regiond。
In the first step, whether the reservoir has the desorption region or not can be judged according to the relation between the bottom hole flowing pressure and the critical desorption pressure. The critical desorption pressure is a limit, and when the coal bed pressure is higher than the critical desorption pressure, the coal bed does not generate gas desorption; and when the pressure is lower than the critical desorption pressure, gas desorption occurs in the coal bed.
Step two: on the assumption, the water yield is calculated according to the principle of conservation of substances and recorded as a first water yield, if an analysis area exists, the gas yield is calculated according to the principle of conservation of substances and recorded as a first gas yield, namely: and calculating the first yield of the coal bed gas by adopting a material conservation principle according to the assumed numerical value.
Step three: based on the assumption, calculating the water yield according to a capacity equation and recording as a second water yield, if an analysis area exists, simultaneously calculating the gas yield according to the capacity equation and recording as the second gas yield, namely: and calculating the second yield of the coal bed gas by adopting a productivity equation according to the assumed numerical value.
Step four: based on the above calculation, for the case where no analysis region exists, the first water production amount and the second water production amount are compared, and the pressure wave position r is adjustedpThe difference between the first water yield and the second water yield reaches the preset precision requirement, so that the position r of the front edge of the pressure wave is determinedp. If the reservoir has an analytic region, the position r of the front edge of the pressure wave is adjustedpAnd the position r of the front edge of the desorption regiondThe first gas production rate and the second gas production rate and the difference between the first water production rate and the second water production rate simultaneously reach the preset precision requirement (for example, within 5 percent of the difference), and the pressure wave front edge position r is determinedpAnd the position r of the front edge of the desorption regiond。
In the method, for the case of no analytical zone, the first water yield calculated by the material conservation equation method is enlarged as the pressure drop zone is enlarged, and the second water yield calculated by the capacity equation is reduced as the pressure drop zone is enlarged. Therefore, the calculated yield error of the two methods is reduced along with the expansion of the pressure drop area, and finally the accuracy requirement is necessarily met, so that the method has good convergence. Similarly, for the condition that the desorption zone exists, the first gas production rate calculated by the material conservation equation method is enlarged along with the enlargement of the desorption zone, and the second gas production rate calculated by the capacity equation is reduced along with the enlargement of the desorption zone, so that the gas production rate error calculated by the material conservation equation method and the capacity equation is reduced along with the enlargement of the desorption zone, and finally, the preset precision requirement is necessarily met, and the good convergence of the method is reflected.
Step five: passing the finally determined position r of the front edge of the desorption zonedOr the position r of the front edge of the desorption zonedAnd pressure wave position rpAnd calculating the yield of the coal-bed gas well so as to obtain the accurate production prediction of the coal-bed gas well.
In the second step of the method, a calculation formula for calculating the first water yield according to the substance conservation principle is specifically as follows:
Figure BDA0002387170480000091
the calculation formula for calculating the first gas production according to the substance conservation principle is as follows:
Figure BDA0002387170480000092
wherein r is the distance from the wellbore, rwIs the radius of the shaft, h is the thickness of the producing zone, t is the production time, phi (t) is the porosity of the coal bed, Sw(t) is the saturation of the water content, Bw(t) is the compressibility of the water phase, i.e., the ratio of the volume of the same number of moles of water under coal bed conditions (coal bed pressure and coal bed temperature) to the volume under ground standard conditions (20 degrees C., one atmosphere), P (t) is the pore fluid pressure, VLIs L angmuir volume constant, PLIs L angmuir pressure constant, Sg(t) is the saturation of the gas content, Bg(t) is a gas phase compression factor.
The above equation is obtained by integrating the micro-rings of the coal seam by using the principle of conservation of material, and referring to fig. 4(a), in the method, the bottom hole flow pressure and the production zone parameters of the coal-bed gas well, as well as the basic fluid properties such as the thickness of the production zone, the critical desorption pressure, the absolute permeability, the gas-water relative permeability curve, the gas viscosity, the gas compression coefficient, the gas compression factor, the water viscosity and the like are known or measurable, and only the positions of the front edge of the analysis zone and the front edge of the pressure wave in the mining area are unknown. It is noted that in the formula for calculating the first water production, the integral term of water production uses the location r of the pressure wave frontpAnd in the formula for calculating the first gas production rate, the integral term of the gas production rate uses the front edge position r of the desorption regiondThe reason is that the produced gas is formed in the pressure reduction process only in the desorption region, and the pressure wave and the region outside the desorption region do not contribute to the produced gas.
In one embodiment of the present application, in stepIn the fourth step, if the desorption zone exists, the first gas production rate and the second gas production rate are compared firstly, and the position r of the front edge of the desorption zone is adjusteddSo that the difference between the two reaches the preset precision requirement, and determining the front edge position r of the desorption regiondThen, the first water yield and the second water yield are compared, and the pressure wave position r is adjustedpSo that the difference between the two reaches the preset precision requirement, and the pressure wave position r is determinedp。
In this application, the gas production comparison is used to determine the front of the desorption zone, i.e. rd(ii) a The water production is compared afterwards, and it is used to determine the pressure wave front, rp. The idea of the prediction method is to ask for the gas production and the water production through the pressure transmission (including the desorption area expansion and the pressure wave expansion) of the coal-bed gas well. The pressure fluctuation range is the part of the coal bed with pressure lower than the original formation pressure; the desorption area is the part of the coal bed with the pressure lower than the critical desorption pressure. The expansion of the desorption area contributes to both gas production and water production; moreover, the pressure sweep range includes the desorption region, so we need to determine the desorption region first and then determine the pressure sweep range, i.e. compare the gas production first and then the water production.
In one embodiment of the present application, in calculating the first gas production rate, the pressure distribution of the coal seam is obtained by using the following formula:
Figure BDA0002387170480000101
Figure BDA0002387170480000102
in the formula, PeAs boundary pressure, PdIs the critical desorption pressure, PwfIs the bottom hole flowing pressure. Considering the influence of the matrix water-containing pores on the production energy prediction, the formula for describing the gas desorption characteristics of the real coal rock is obtained as follows:
Figure BDA0002387170480000111
in the formula, SmwWater saturation in the coal matrix; if the calculation takes into account the influence of the matrix water-containing pores on the production prediction, then in step two, V in the formula for the first gas production will be calculatedLIs replaced by (1-S)mw)VL。
The above process takes into account the effect of different gas-water distribution characteristics in the coal matrix on the gas desorption capacity when calculating the first gas production rate.
Since the Gibbs free energy in the gas adsorption and desorption processes in the solid-gas system is equal, the gas adsorption process and the desorption process are completely reversible, so the desorption characteristics of the solid-gas system in the invention can be described by the following formula:
Figure BDA0002387170480000112
in the formula, VLIs L angmuir volume constant, m3/m3(ii) a P is pore fluid pressure, MPa; pLIs L angmumir pressure constant, MPa, V is the unit volume adsorption capacity of coal and rock, m3/m3。
In a solid-liquid system, the gas desorption process has more energy for gas nucleation than the gas adsorption process, so that the gas desorption is difficult. Meanwhile, the further aggregation of the gas after nucleation is restricted by the capillary force of gas and water phases, so that the difficulty of gas desorption is further increased. The applicant has conducted intensive research on the gas desorption characteristics of the solid-liquid system, and two aspects of theoretical means and indoor experiments show that the desorption amount of the gas-liquid system is very little and can be ignored, so that the desorption characteristics of the solid-liquid system in the invention can be described by the following formula:
V≈0 (2)
in this application, it is believed that some of the matrix pores in the coal bed are saturated with water and the remainder are saturated with gas. The different coal reservoirs are different in water content degree, namely different in water content pore size. The desorption formula of the solid-liquid system finds that the gas in the pores of the hydrous coal rock matrix is difficult to be effectively desorbed. The water cut of the coal bed matrix pores can be represented by water saturation, and the water cut can be represented by the valueObtained by means of nuclear magnetic resonance. Therefore, the coal bed of the saturated water part meets the desorption rule of the solid-liquid system, the saturated gas part meets the desorption rule of the solid-gas system, and finally the gas desorption characteristic formula suitable for representing the real coal rock, namely the formula for describing the gas desorption characteristic of the real coal rock is obtained. In the formula, SmwWhich represents the water saturation of the coal matrix, represents the volume of water in the coal bed matrix system as a percentage of the total pore volume of the matrix system, and is used herein to represent the percentage of "water-containing pores" as a percentage of the total pores. When S ismwWhen the number is 1, all pores are 'water-containing pores', and the analytical formula is degraded into a solid-liquid analytical characteristic formula (2); when S ismwWhen the value is 0, all pores are "water-free pores", and the above analytical formula is degenerated to the solid-gas analytical characteristic formula (1).
In an embodiment of the present application, in step three, the calculation formula for calculating the second water yield according to the capacity equation is specifically as follows:
Figure BDA0002387170480000121
the calculation formula for calculating the second gas production according to the capacity equation is specifically as follows:
Figure BDA0002387170480000122
in the formula, mwaterFor the aqueous phase, mgasIs a gas phase pseudo pressure, muwIs the viscosity of the aqueous phase reIs the boundary position.
Wherein, the water phase simulated pressure is calculated by adopting the following formula:
Figure BDA0002387170480000123
in the formula for calculating the second gas production, the gas pseudo pressure is calculated using the following formula:
Figure BDA0002387170480000124
in the formula, Kw(P) is the water phase permeability, Kg(P) is the gas phase permeability, μgFor gas phase viscosity, Z is a gas deviation factor, representing the ratio of the volume of the same number of moles of gas in the real state (taking into account intermolecular forces) to the volume in the ideal state (taking into account intermolecular forces).
In an embodiment of the present application, considering the influence of the coal-bed gas well after fracturing reformation, referring to fig. 4(b), in order to convert the elliptical seepage problem into the linear flow problem, the following relation is used to perform coordinate transformation on the calculation process:
x＝Lf×chξ×cosη，
y＝Lf×shξ×sinη，
wherein x and y are rectangular coordinates, LfHalf the crack length, ξ is an elliptical coordinate.
Thus, by coordinate transformation, the following relation is obtained:
Ra＝Lf×chξd，
Rb＝Lf×shξd，
Rpa＝Lf×chξp，
Rpb＝Lf×shξpd，
wherein Ra, Rb, Rpa and Rpb are respectively the long axis position and the short axis position of the desorption zone front of the fracturing vertical well and the long axis position and the short axis position of the pressure wave front, and ξ d and ξ p are respectively the desorption zone front and the pressure wave front under the condition of linear flow.
Finally, according to the principle of conservation of materials, a formula for calculating the first water yield of the coal-bed gas well after fracturing modification is obtained as follows:
Figure BDA0002387170480000131
according to the principle of conservation of materials, the formula for calculating the first gas production rate of the coal-bed gas well after fracturing modification is obtained as follows:
Figure BDA0002387170480000132
wherein h is the thickness of the pay zone, ξwIs the wellbore radius in the case of linear flow, t is the production time, phi (t) is the coal bed porosity, Sw(t) is the saturation of the water content, Bw(t) is the compressibility of the aqueous phase, P (t) is the pore fluid pressure, VLIs L angmuir volume constant, PLIs L angmuir pressure constant, Sg(t) is the saturation of the gas content, Bg(t) is the water phase compressibility.
According to the capacity equation, a formula for calculating the second water yield after the coal-bed gas well is fractured and transformed is obtained as follows:
Figure BDA0002387170480000133
according to the capacity equation, a formula for calculating the second gas production rate after the coal-bed gas well is subjected to fracturing transformation is obtained as follows:
Figure BDA0002387170480000141
in the formula, mwaterFor the aqueous phase, mgasFor gas phase to simulate pressure, PeRepresenting the pressure at the coal seam boundary, PwfIndicating the bottom hole flow pressure, muwThe viscosity of the aqueous phase.
And respectively calculating the gas production and the water production through the calculation formula with the fracturing fracture, further determining the positions of the pressure wave front edge and the desorption area front edge, and finally determining the gas production and the water production of the coal-bed gas well. The specific solving steps are similar to those for solving the non-fractured vertical well, and are not described in detail herein.
While the foregoing is directed to embodiments of the present invention, other modifications and variations of the present invention may be devised by those skilled in the art in light of the above teachings. It should be understood by those skilled in the art that the foregoing detailed description is for the purpose of better explaining the present invention, and the scope of the present invention should be determined by the scope of the appended claims.

Claims (10)

1. The method for predicting the productivity of the coal-bed gas well is characterized by comprising the following steps:
the method comprises the following steps: assuming a pressure wave location r of the reservoirp(ii) a If the reservoir has a desorption zone, the pressure wave front position r is assumed at the same timepAnd the position r of the front edge of the desorption regiond；
Step two: on the basis of the assumption, calculating the water yield according to a substance conservation principle and recording the water yield as a first water yield, and if a desorption area exists, calculating the gas yield according to the substance conservation principle and recording the gas yield as a first gas yield;
step three: based on the assumption, calculating the water yield according to a capacity equation and recording as a second water yield, and if an analysis area exists, simultaneously calculating the gas yield according to the capacity equation and recording as the second gas yield;
step four: comparing the first and second water yields by adjusting the pressure wave position rpDetermining the position r of the front edge of the pressure wave to ensure that the difference between the first water yield and the second water yield reaches the preset precision requirementp(ii) a If the reservoir layer has an analytic region, adjusting the pressure wave front position rpAnd the position r of the front edge of the desorption regiondEnabling the first gas production rate and the second gas production rate and the difference between the first water production rate and the second water production rate to simultaneously meet the preset precision requirement, and determining the pressure wave front edge position rpAnd the position r of the front edge of the desorption regiond；
Step five: passing the finally determined position r of the front edge of the desorption zonedOr the position r of the front edge of the desorption zonedAnd pressure wave position rpAnd calculating the yield of the coal-bed gas well.
2. The method of claim 1, wherein in step four, if a desorption zone is present, the first gas production is first compared with the second gas production by adjusting the position r of the front edge of the desorption zonedTo make the difference between the two reach the pre-determined valueSetting precision requirements; at the position r of the front edge of the desorption zonedThen, the first and second water yields are compared, and the pressure wave position r is adjustedpDetermining the pressure wave position r by making the difference between the two reach the preset precision requirementp。
3. The method according to claim 1, wherein in the second step, the calculation formula for calculating the first water yield according to the principle of conservation of substances is as follows:
Figure FDA0002387170470000011
the calculation formula for calculating the first gas production according to the substance conservation principle is as follows:
Figure FDA0002387170470000012
wherein r is the distance from the wellbore, rwIs the radius of the shaft, h is the thickness of the producing zone, t is the production time, phi (t) is the porosity of the coal bed, Sw(t) is the saturation of the water content, Bw(t) is the compressibility of the aqueous phase, P (t) is the pore fluid pressure, VLIs L angmuir volume constant, PLIs L angmuir pressure constant, Sg(t) is the saturation of the gas content, Bg(t) is a gas phase compression factor.
4. The method of claim 3, wherein the pressure profile of the coal seam is obtained using the following equation:
Figure FDA0002387170470000021
Figure FDA0002387170470000022
in the formula, PeAs boundary pressure, PdIs the critical desorption pressure, PwfIs the bottom hole flowing pressure reIs the boundary position;
considering the influence of the matrix water-containing pores on the production energy prediction, the formula for describing the gas desorption characteristics of the real coal rock is obtained as follows:
Figure FDA0002387170470000023
in the formula, SmwWater saturation in the coal matrix; if the calculation takes into account the influence of the matrix water-containing pores on the production prediction, then in step two, V in the formula for the first gas production will be calculatedLIs replaced by (1-S)mw)VL。
5. The method of claim 4, wherein in step three, the second water yield is calculated according to the capacity equation as follows:
Figure FDA0002387170470000024
the calculation formula for calculating the second gas production according to the capacity equation is as follows:
Figure FDA0002387170470000025
in the formula, mwaterFor the aqueous phase, mgasIs a gas phase pseudo pressure, muwThe viscosity of the aqueous phase.
6. The method of claim 5, wherein in the formula for calculating the second water production, the water pseudo pressure is calculated using the formula:
Figure FDA0002387170470000031
in the formula for calculating the second gas production, the gas pseudo pressure is calculated by the following formula:
Figure FDA0002387170470000032
in the formula, Kw(P) is the water phase permeability, Kg(P) is the gas phase permeability, μgIs the gas phase viscosity and Z is the gas deviation factor.
7. The method of claim 1, wherein in order to convert the elliptical seepage problem to a linear flow problem if the coal bed gas well is frac reformed, the calculation is coordinate transformed using the following relationship:
x＝Lf×chξ×cosη，
y＝Lf×shξ×sinη，
wherein x and y are rectangular coordinates, LfHalf-length of the crack, ξ is an elliptical coordinate;
the following relationship is obtained:
Ra＝Lf×chξd，
Rb＝Lf×shξd，
Rpa＝Lf×chξp，
Rpb＝Lf×shξpd，
wherein Ra, Rb, Rpa and Rpb are respectively the long axis position and the short axis position of the desorption zone front of the fracturing vertical well and the long axis position and the short axis position of the pressure wave front, and ξ d and ξ p are respectively the desorption zone front and the pressure wave front under the condition of linear flow.
8. The method of claim 7, wherein if the coal bed gas well is frac modified, the first water production is calculated according to the principles of conservation of material using the formula:
Figure FDA0002387170470000033
according to the principle of conservation of substances, the first gas production is calculated by adopting the following formula:
Figure FDA0002387170470000034
wherein h is the thickness of the pay zone, ξwIs the wellbore radius in the case of linear flow, t is the production time, phi (t) is the coal bed porosity, Sw(t) is the saturation of the water content, Bw(t) is the compressibility of the aqueous phase, P (t) is the pore fluid pressure, VLIs L angmuir volume constant, PLIs L angmuir pressure constant, Sg(t) is the saturation of the gas content, Bg(t) is a gas phase compression factor.
9. The method of claim 8, wherein if the coalbed methane well is fractured and reformed, calculating the second water production according to the capacity equation by using the following formula:
Figure FDA0002387170470000041
calculating a second gas production rate according to a capacity equation by adopting the following formula:
Figure FDA0002387170470000042
in the formula, mwaterFor the aqueous phase, mgasFor gas phase to simulate pressure, PeRepresenting the pressure at the coal seam boundary, PwfIndicating the bottom hole flow pressure, muwThe viscosity of the aqueous phase.
10. The method as claimed in claim 1, wherein in step one, the presence of a desorption zone in the reservoir is determined based on the relationship between the bottom hole flowing pressure and the critical desorption pressure.
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