CN110984972A - Method for calculating gas-water permeability of coal bed gas in different production stages - Google Patents
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Abstract
The application discloses a method for calculating gas-water permeability of coal bed gas in different production stages, which comprises the following steps: according to different mining stages, the production stage is divided into the following four stages: a single-phase water flow stage, a near wellbore zone unsaturated single-phase flow stage, a near wellbore zone gas-water two-phase flow stage and a single-phase gas flow stage; and calculating the permeability according to the effective stress effect, the coal matrix shrinkage effect caused by gas desorption, the coal matrix shrinkage effect caused by water desorption and the restriction of the Kelvenberg effect on the permeability by combining an empirical model of the permeability and the pressure. The invention provides a gas-water permeability calculation model comprehensively considering the four-effect influence in the drainage and production process of the coal-bed gas well for the first time aiming at four production stages of the coal-bed gas well, so that the dynamic permeability of the coal-bed gas well can be predicted more accurately and quickly.
Description
Technical Field
The application relates to the technical field of mining, in particular to a method for calculating gas-water permeability of coal bed gas in different production stages.
Background
The coal bed gas is hydrocarbon gas which is stored in a coal bed, takes methane as a main component, is adsorbed on the surface of coal matrix particles as a main component, is partially dissociated in coal pores or is dissolved in coal bed water, and is an associated mineral resource of coal. Coal reservoir permeability is a critical parameter affecting coalbed methane production. In the actual coal bed gas exploitation process, the permeability of the reservoir coal rock is found to be reduced along with the production of gas and the increase of the effective stress of the coal bed, but the reservoir physical property changes complicatedly due to the uniqueness of the coal rock body and the drainage and exploitation mode. In the process of coal bed gas well extraction, the physical properties of a coal reservoir are influenced by various factors and are in dynamic change. Scholars at home and abroad make a great deal of theoretical and experimental researches on the dynamic change of the permeability of the coal bed gas, and the scholars summarize that the dynamic change of the permeability of the coal bed gas are mainly limited by an effective stress effect, a matrix shrinkage effect and a Kelvin Berger effect. The effective stress effect refers to the effect that the effective stress born by the coal body is increased due to the drainage and pressure reduction, and the physical property of the coal body is reduced due to the compaction of the coal body. Along with the water and gas extraction of the coal bed gas well, the working fluid level in the production shaft can be continuously reduced, the pressure of pore fluid is gradually reduced, the effective stress borne by the coal body framework is increased, the pore volume is reduced, the crack tends to be closed, and the permeability of the coal rock is gradually reduced. The matrix shrinkage effect refers to the effect of matrix shrinkage and reservoir physical property improvement caused by desorption of the adsorbed coal bed gas when the reservoir pressure is less than the critical desorption pressure. The clinkerberg effect is an effect in which gas molecules having the same average spread of free flow of gas molecules as the channel spread collide with the channel wall at a low permeability, thereby promoting darcy flow.
The change rule of the physical property of the coal reservoir in the mining process is still a difficult problem at present, the pace of the exploration and development of the coal bed gas in China is severely restricted, and the change rule is an important problem to be solved urgently at present. However, previous researches do not fully report a key mechanism influencing dynamic permeability of a coal reservoir, and do not perform too fine and deep quantitative characterization on the phase permeability rule of each production stage of the coal-bed gas well.
Disclosure of Invention
In view of the above problems, the present invention provides a method for calculating gas-water permeability of coal bed gas in different production stages, so as to solve or at least partially solve the above existing technical problems.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the invention provides a method for calculating gas-water permeability of coal bed gas in different production stages, which comprises the following steps:
according to different mining stages, the production stage is divided into the following four stages: a single-phase water flow stage, a near wellbore zone unsaturated single-phase flow stage, a near wellbore zone gas-water two-phase flow stage and a single-phase gas flow stage;
and calculating the permeability according to the effective stress effect, the coal matrix shrinkage effect caused by gas desorption, the coal matrix shrinkage effect caused by water desorption and the restriction of the Kelvenberg effect on the permeability by combining an empirical model of the permeability and the pressure.
Further, the calculating the permeability comprises:
calculation of gas-water permeability of a coalbed methane well of a coal reservoir during said single-phase water flow phase, and/or
Calculating the gas-water permeability of the coal-bed gas well in the unsaturated single-phase flow stage of the near wellbore zone of the coal reservoir, and/or
Calculating the gas-water permeability of the coal-bed gas well in the gas-water two-phase flow stage of the near wellbore area of the coal reservoir, and/or
And calculating the gas-water permeability of the coal-bed gas well when the coal reservoir is in the single-phase gas flowing stage.
Further, the calculation of the gas-water permeability of the coal-bed gas well in the single-phase water flow stage of the coal reservoir comprises the following steps:
step 301, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in formula (1): σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 302, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in formula (2):
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
the coal matrix internal gasCoal matrix expansion amount caused by gas adsorption when body pressure is balanced with external gas pressure
Model simplification can be assumed:
in formula (3): epsilonLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage and expansion due to gas desorption can be simplified as follows:
in formula (4):
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 303, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the single-phase water flowing stage:
in formula (5): k is the permeability, k0Is the initial permeability, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time and t is the time.
Further, the calculation of the gas-water permeability of the coal-bed gas well in the near-wellbore region unsaturated single-phase flow stage of the coal reservoir comprises the following steps:
step 401, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in the formula (6), σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 402, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in the formula (7), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
the coal matrix expansion amount caused by gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure
Can be performed as a hypothesisModel simplification:
in formula (8), εLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage and expansion due to gas desorption can be simplified as follows:
in the formula (9), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 403, solving the strain amount under coal matrix shrinkage caused by pore water drainage
In the formula (10), C1Is the concentration of water molecules adsorbed by the first layer, C2Is the concentration of water molecules adsorbed by the first layer, CsIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient, ρ is the density of the coal matrix, V0Is the volume change of the coal matrix caused by the adsorption of 1 mol of water molecules;
step 404, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the near-wellbore region unsaturated single-phase flow stage:
in formula (11): k is the permeability, k0Is the initial permeability, B is the gas slip coefficient,
is the mean pressure, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time, t is the time, rho is the density of the coal matrix, V0Is the volume change of coal matrix, C, due to the adsorption of 1 mol of water moleculessIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient.
Further, the calculation of the gas-water permeability of the coal-bed gas well in the near-wellbore gas-water two-phase flow stage and the single-phase gas flow stage of the coal reservoir comprises the following steps:
step 501, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in the formula (12), σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the storageLayer pressure, p0Is the original reservoir pressure;
step 502, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in the formula (13), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
the coal matrix expansion amount caused by gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure
Model simplification can be assumed:
in formula (14), epsilonLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage and expansion due to gas desorption can be simplified as follows:
in the formula (15), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 503, solving the strain amount under the coal matrix shrinkage caused by the drainage of pore water
In the formula (16), C1Is the concentration of water molecules adsorbed by the first layer, C2Is the concentration of water molecules adsorbed by the second layer, CsIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient, ρ is the density of the coal matrix, V0Is the volume change of the coal matrix caused by the adsorption of 1 mol of water molecules;
step 504, establishing a quantitative equation of the influence of the gas slippage effect on the permeability of the coal reservoir:
in formula (17): kgIs the gas permeability, K∞Is the clinberg permeability, B is the gas slip coefficient;
505, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the near-wellbore region gas-water two-phase flow stage:
in formula (18): k is the permeability, k0Is the initial permeability, B is the gas slip coefficient,
is the mean pressure, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time, t is the time, rho is the density of the coal matrix, V0Is the volume change of coal matrix, C, due to the adsorption of 1 mol of water moleculessIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient.
The invention has the beneficial effects that:
① the method of the invention considers the strain mechanism of coal matrix shrinkage caused by water discharge, which plays a key role in the accurate inversion of coal reservoir dynamic permeability, combines the strain mechanism of coal matrix shrinkage caused by water discharge with the empirical model of permeability and pressure, realizes the prejudgment of coal reservoir dynamic permeability in the drainage and mining process, and further realizes the rapid and accurate monitoring of coal formation dynamic permeability change in the drainage and mining process;
② the method of the invention not only can prejudge the change rule of the dynamic permeability of the coal reservoir, but also can determine the influence degree of different water-containing conditions of the coal matrix pore on the dynamic permeability of the reservoir in an inversion way, thereby laying theoretical support for realizing the reasonable development of the coal-bed gas well.
The foregoing description is only an overview of the technical solutions of the present application, and the present application can be implemented according to the content of the description in order to make the technical means of the present application more clearly understood, and the following detailed description of the present application is given in order to make the above and other objects, features, and advantages of the present application more clearly understandable.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the application. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
FIG. 1 is a schematic diagram illustrating the coal bed methane production staging and phase change characterization in one embodiment of the present application;
FIG. 2 illustrates a micro-schematic of a single-phase drainage cleat flow during a single-phase water flow phase of a coal-bed gas well in an embodiment of the present application;
FIG. 3 illustrates a single phase water flow phase permeability plot for a coal bed gas well in one embodiment of the present application;
FIG. 4 shows a microscopic gas-water two-phase cleat flow diagram of a non-saturated single-phase flow phase of a coal-bed gas well according to an embodiment of the present application;
FIG. 5 is a graph illustrating a phase-permeability curve of a non-saturated single-phase flow of a coalbed methane well according to an embodiment of the present application;
FIG. 6 is a microscopic view of gas-water two-phase shear flow during the gas-water two-phase flow phase of a coal bed gas well in one embodiment of the present application;
FIG. 7 is a plot of two-phase flow phasic permeability for coalbed methane well gas water in one embodiment of the present application;
FIG. 8 illustrates a micro-schematic of a single-phase gas production cleat flow for a single-phase gas phase of a coal-bed gas well in an embodiment of the present application;
Detailed Description
Exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
The embodiment of the invention discloses a method for calculating gas-water permeability of coal bed gas in different production stages, which comprises the following steps:
according to the difference of mining stages, the production stage is divided into the following four stages: a single-phase water flow stage, a near wellbore zone unsaturated single-phase flow stage, a near wellbore zone gas-water two-phase flow stage and a single-phase gas flow stage; as shown in fig. 1, in the initial drainage and mining period, the coal seam produces mainly water and simultaneously produces a small amount of free gas and dissolved gas; when the coal bed is reduced to be below the critical desorption pressure, the coal bed methane molecules are quickly desorbed and then diffused into the cracks, and the gas yield is gradually increased and the water yield is gradually reduced; along with the increase of the produced water yield and the further increase of the production pressure difference, the water saturation in the coal bed is relatively reduced, the coal bed is mainly used for producing gas and gradually reaches a gas production peak, and the water yield is relatively stabilized at a lower level.
And calculating the permeability according to the effective stress effect, the coal matrix shrinkage effect caused by gas desorption, the coal matrix shrinkage effect caused by water desorption and the restriction of the Kelvenberg effect on the permeability by combining the permeability and an empirical model of pressure. In the single-phase flow stage at the initial stage of coal bed gas drainage and mining, the effective stress borne by a coal reservoir is continuously increased, so that the width of a crack is narrowed, and the permeability is reduced; when the reservoir pressure is reduced to be lower than the critical desorption pressure, the coal bed gas starts to be desorbed, the coal matrix shrinkage effect is gradually enhanced, the crack is widened, and the permeability is rebounded; in the later period of drainage and production, the pressure of the reservoir is reduced to a lower level, the Krringenberg effect of gas under the low-pressure condition is more obvious, and the permeability of the coal reservoir is favorably improved. The method is combined with an empirical model of permeability and pressure to predict the permeability change, and comprehensively considers the restriction of 4 effects of stress sensitivity, matrix shrinkage caused by gas desorption, matrix shrinkage caused by water desorption and Kelincolnberg effect on the physical property of the coal reservoir in the drainage and mining process, so that the dynamic permeability of the reservoir in the drainage and mining process is predicted.
In one embodiment, calculating the gas-water permeability of the coal bed gas at different production stages comprises:
the method comprises the steps of calculating the gas-water permeability of the coal-bed gas well when the coal reservoir is in a single-phase water flowing stage, and/or calculating the gas-water permeability of the coal-bed gas well when the coal reservoir is in a near-wellbore zone unsaturated single-phase flowing stage, and/or calculating the gas-water permeability of the coal-bed gas well when the coal reservoir is in a near-wellbore zone gas-water two-phase flowing stage, and/or calculating the gas-water permeability of the coal reservoir when the coal reservoir is in a single-phase gas flowing stage.
In a preferred embodiment, the calculation of the gas-water permeability of the coalbed methane well of the coal reservoir in the single-phase water flow phase comprises the steps of:
step 301, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in formula (1): σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 302, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in formula (2):
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
coal matrix swelling amount due to gas adsorption when internal gas pressure of coal matrix is balanced with external gas pressure
Is a time variable, cannotHowever, the solution can be made under the assumption that ① coal samples are homogeneous bodies, ② coal samples have constant external pressure, and the following equation is established, thereby simplifying the model:
in formula (3): epsilonLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage expansion due to gas desorption can be simplified as follows:
in formula (4):
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 303, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the single-phase water flowing stage:
in formula (5): k is the permeability, k0Is the initial permeability, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time and t is the time.
As shown in fig. 2 and 3, in the initial period of production, the pressure of each point of the reservoir is higher than the critical desorption pressure, and the gas is mainly in the adsorption state in the coal matrix block. In the initial state, only a small amount of free gas is present in the cutting, and it can be considered as being approximately saturated with water. Meanwhile, because the coal bed gas reservoir belongs to a low-pressure gas reservoir, the content of dissolved gas in water is extremely low and can be ignored. When the gas well is put into initial production, the cleat is saturated by single-phase water, so the flow characteristic at this stage is single-phase water flow, namely the drainage and depressurization stage of the coal bed gas. The main purpose of the stage is to reduce the reservoir pressure and promote the desorption of the adsorbed gas in the coal rock matrix block and the cutting of the gas to form gas. At this stage of production, the relative permeability of the aqueous phase was always 1. The coal rock is susceptible to stress sensitivity, namely the permeability of a coal reservoir is reduced along with the reduction of the reservoir pressure, so that the relative permeability of the water phase in the whole region is always 1 in the stage, and the effective permeability of the water phase in a near well region is lower than that in a far well region.
In one embodiment, the calculation of the gas-water permeability of the coal-bed gas well in the unsaturated single-phase flow stage of the near wellbore zone of the coal reservoir comprises the following steps:
step 401, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in the formula (6), σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 402, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in the formula (7)，
The coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
coal matrix swelling amount due to gas adsorption when internal gas pressure of coal matrix is balanced with external gas pressure
The time variable is a time variable and cannot be solved, but the following assumptions can be made that ① coal samples are homogeneous bodies and ② external pressure of the coal samples is constant, the following equation is established, and model simplification is further realized:
in formula (8), εLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage expansion due to gas desorption can be simplified as follows:
in the formula (9), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 403, solving the strain amount under coal matrix shrinkage caused by pore water drainage
In the formula (10), C1Is the concentration of water molecules adsorbed by the first layer, C2Is the concentration of water molecules adsorbed by the first layer, CsIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient, ρ is the density of the coal matrix, V0Is the volume change of the coal matrix caused by the adsorption of 1 mol of water molecules;
step 404, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the near-wellbore region unsaturated single-phase flow stage:
in formula (11): k is the permeability, k0Is the initial permeability, B is the gas slip coefficient,
is the mean pressure, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time, t is the time, rho is the density of the coal matrix, V0Is the volume change of coal matrix, C, due to the adsorption of 1 mol of water moleculessIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient.
As shown in fig. 4 and 5, as the bottom hole flow pressure continues to decrease with further production, the pressure drop funnel continues to expand outward, and the sweep range of the coal bed gas well continues to expand. Meanwhile, the pressure of the near-well area is continuously reduced and gradually approaches the critical desorption pressure, when the pressure of the near-well area is lower than the critical desorption pressure, the adsorbed gas in the near-well area in the initial state can be desorbed and continuously enters the coal-rock cleat, the cleat and the wall surface of the coal bed exist in the form of micro bubbles, but the small bubbles are independent, a relatively large gas column is not formed, the gas phase saturation is small, and continuous gas flow is not formed, so that the reservoir seepage flow still flows in a single-phase manner. However, the seepage capability of the single-phase water in the near-well area is reduced to a certain extent at this time, because the desorbed micro bubbles cannot flow, but exist in the seepage channels and occupy a part of the seepage channels of the single-phase water. If the phase permeability curve is used for explanation, it can be considered that gas enters the cleat, so that the smaller the water phase permeability is, the gas phase permeability in the interval is still 0, and the water phase permeability is less than 1.
In one embodiment, the calculation of the gas-water permeability of the coal-bed gas well of the coal reservoir in the near-wellbore gas-water two-phase flow phase and the single-phase gas flow phase comprises the following steps:
step 501, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in the formula (12), σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 502, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in the formula (13), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
coal matrix swelling amount due to gas adsorption when internal gas pressure of coal matrix is balanced with external gas pressure
The time variable is a time variable and cannot be solved, but the following assumptions can be made that ① coal samples are homogeneous bodies and ② external pressure of the coal samples is constant, the following equation is established, and model simplification is further realized:
in formula (14), epsilonLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage expansion due to gas desorption can be simplified as follows:
in the formula (15), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 503, solving the strain amount under the coal matrix shrinkage caused by the drainage of pore water
In the formula (16), C1Is the concentration of water molecules adsorbed by the first layer, C2Is the concentration of water molecules adsorbed by the second layer, CsIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient, ρ is the density of the coal matrix, V0Is the volume change of the coal matrix caused by the adsorption of 1 mol of water molecules;
step 504, establishing a quantitative equation of the influence of the gas slippage effect on the permeability of the coal reservoir:
in formula (17): kgIs the gas permeability, K∞Is the clinberg permeability, B is the gas slip coefficient;
505, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the near-wellbore area gas-water two-phase flow stage:
formula (18)) The method comprises the following steps: k is the permeability, k0Is the initial permeability, B is the gas slip coefficient,
is the mean pressure, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time, t is the time, rho is the density of the coal matrix, V0Is the volume change of coal matrix, C, due to the adsorption of 1 mol of water moleculessIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient.
As shown in fig. 6 and 7, the fluid flow mechanism of the near wellbore zone belongs to gas-water two-phase flow, and the gas phase and the water phase flow simultaneously in the coal seam cutting. On the basis of unsaturated single-phase flow, small bubbles are aggregated and form large bubbles along with further desorption of adsorbed gas in the matrix, the saturation of the gas phase is gradually increased, and finally gas phase flow is formed. Because the gas phase and the water phase in the cleavage process interfere with each other in a blocking way, especially the existence of the two-phase interface action (such as interfacial force, dynamic wetting, Jamin effect and the like) further increases the flow resistance, and the effective permeability is less than 1, namely Krw + Krg < 1. In the gas-water two-phase flow stage of coal bed gas exploitation, gas in the matrix system is continuously desorbed, so that gas in the process of cutting is supplemented, the duration of the stage is longer, and the two-phase flow region is continuously expanded to a far well region.
As shown in fig. 8, when the reservoir pressure between wells is reduced below the critical desorption pressure, the matrix pores at each point of the reservoir continuously supply gas to the cleats, so as to achieve dynamic balance between gas supply and gas production. At this point, the saturation of the water contained in the coal seam is close to the saturation of the irreducible water, and single-phase gas flows in the coal seam in the cutting process. In the flowing stage, the gas well water yield is found to be extremely small and negligible, and the gas production is in a stable yield stage. The pressure propagation medium in the flowing stage of the single-phase gas is the single-phase gas, the pressure of the whole area is less than the critical desorption pressure, the desorbed gas enters the cleft and supplements the pressure of the cleft, and the gas-phase permeability is less than 1 due to the existence of the bound water film on the cleft wall surface.
To sum up, the invention discloses a method for calculating gas-water permeability of coal bed gas in different production stages, which comprises the following steps: according to the difference of mining stages, the production stage is divided into the following four stages: a single-phase water flow stage, a near wellbore zone unsaturated single-phase flow stage, a near wellbore zone gas-water two-phase flow stage and a single-phase gas flow stage; and calculating the permeability according to the effective stress effect, the coal matrix shrinkage effect caused by gas desorption, the coal matrix shrinkage effect caused by water desorption and the restriction of the Kelvenberg effect on the permeability by combining an empirical model of the permeability and the pressure. The invention provides a gas-water permeability calculation model comprehensively considering the four-effect influence in the drainage and production process of the coal-bed gas well for the first time aiming at four production stages of the coal-bed gas well, so that the dynamic permeability of the coal-bed gas well can be predicted more accurately and quickly.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes, substitutions or improvements within the technical scope of the present invention, and all such changes, substitutions or improvements are included in the scope of the present invention.
In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the application may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
Claims (5)
1. A method for calculating gas-water permeability of coal bed gas in different production stages is characterized by comprising the following steps:
according to different mining stages, the production stage is divided into the following four stages: a single-phase water flow stage, a near wellbore zone unsaturated single-phase flow stage, a near wellbore zone gas-water two-phase flow stage and a single-phase gas flow stage;
and calculating the permeability according to the effective stress effect, the coal matrix shrinkage effect caused by gas desorption, the coal matrix shrinkage effect caused by water desorption and the restriction of the Kelvenberg effect on the permeability by combining an empirical model of the permeability and the pressure.
2. The method for calculating gas-water permeability of coal bed methane at different production stages according to claim 1, wherein the calculating the permeability comprises:
calculating the gas-water permeability of the coal-bed gas well when the coal reservoir is in the single-phase water flowing stage; and/or
Calculating the gas-water permeability of the coal-bed gas well in the unsaturated single-phase flow stage of the near wellbore region of the coal reservoir; and/or
Calculating the gas-water permeability of the coal bed gas well in the gas-water two-phase flow stage of the near wellbore area of the coal reservoir; and/or
And calculating the gas-water permeability of the coal-bed gas well when the coal reservoir is in the single-phase gas flowing stage.
3. The method for calculating gas-water permeability of coal bed methane in different production stages according to claim 2, wherein the calculation of the gas-water permeability of the coal bed methane when the coal reservoir is in the single-phase water flow stage comprises the following steps:
step 301, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in formula (1): σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 302, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in formula (2):
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
the coal matrix expansion amount caused by gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure
Model simplification can be assumed:
in formula (3): epsilonLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage and expansion due to gas desorption can be simplified as follows:
in formula (4):
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 303, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the single-phase water flowing stage:
in formula (5): k is the permeability, k0Is the initial permeability, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time and t is the time.
4. The method for calculating the gas-water permeability of the coal-bed gas in different production stages according to claim 2, wherein the calculation of the gas-water permeability of the coal-bed gas reservoir in the near-wellbore zone unsaturated single-phase flow stage comprises the following steps:
step 401, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in the formula (6), σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 402, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in the formula (7), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion caused by corresponding gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure, t is time, and tau is diffusion time;
the coal matrix expansion amount caused by gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure
Model simplification can be assumed:
in formula (8), εLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage and expansion due to gas desorption can be simplified as follows:
in the formula (9), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is introduced by gas adsorption under the condition of original gas pressureThe expansion amount of the coal matrix is increased,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 403, solving the strain amount under coal matrix shrinkage caused by pore water drainage
In the formula (10), C1Is the concentration of water molecules adsorbed by the first layer, C2Is the concentration of water molecules adsorbed by the first layer, CsIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient, ρ is the density of the coal matrix, V0Is the volume change of the coal matrix caused by the adsorption of 1 mol of water molecules;
step 404, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the near-wellbore region unsaturated single-phase flow stage:
in formula (11): k is the permeability, k0Is the initial permeability, B is the gas slip coefficient,
is the mean pressure, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time, t is the time, rho is the density of the coal matrix, V0Is the volume change of coal matrix, C, due to the adsorption of 1 mol of water moleculessIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient.
5. The method for calculating gas-water permeability of different production stages of coal-bed gas according to claim 2, wherein the calculation of the gas-water permeability of the coal-bed gas reservoir in the near wellbore gas-water two-phase flow stage and the single-phase gas flow stage comprises the following steps:
step 501, constructing a stress characterization model of the influence of stress sensitivity on the coal reservoir:
in the formula (12), σ is the effective horizontal stress, σ0Is the effective horizontal stress under the original condition, v is the Poisson's ratio, p is the reservoir pressure, p is0Is the original reservoir pressure;
step 502, establishing a strain model under coal matrix shrinkage caused by gas desorption:
in the formula (13), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
caused by gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressureThe coal matrix swelling capacity, t is time, and tau is diffusion time;
the coal matrix expansion amount caused by gas adsorption when the internal gas pressure of the coal matrix is balanced with the external gas pressure
Model simplification can be assumed:
in formula (14), epsilonLIs the Langmuir expansion coefficient, pLIs the pressure coefficient, p∞Is the final pressure value;
then, the model of coal matrix shrinkage and expansion due to gas desorption can be simplified as follows:
in the formula (15), the reaction mixture is,
the coal matrix expansion amount caused by gas adsorption under the non-equilibrium condition,
is the coal matrix expansion amount caused by gas adsorption under the original gas pressure condition,
is the coal matrix expansion caused by gas adsorption under the final gas pressure condition, t is the time, τ is the diffusion time;
step 503, solving the strain amount under the coal matrix shrinkage caused by the drainage of pore water
In the formula (16), C1Is the concentration of water molecules adsorbed by the first layer, C2Is the concentration of water molecules adsorbed by the second layer, CsIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient, ρ is the density of the coal matrix, V0Is the volume change of the coal matrix caused by the adsorption of 1 mol of water molecules;
step 504, establishing a quantitative equation of the influence of the gas slippage effect on the permeability of the coal reservoir:
in formula (17): kgIs the gas permeability, K∞Is the clinberg permeability, B is the gas slip coefficient;
505, establishing a coal-bed gas well gas-water permeability characteristic model of the coal reservoir in the near-wellbore region gas-water two-phase flow stage:
in formula (18): k is the permeability, k0Is the initial permeability, B is the gas slip coefficient,
is the mean pressure, cfIs the compressibility of the coal-rock cleat, v is the Poisson's ratio, p is the reservoir pressure0Is the original reservoir pressure, E is the coal rock modulus of elasticity,
is the coal matrix expansion caused by gas adsorption under the original gas pressure condition, tau is the diffusion time, t is the time, rho is the density of the coal matrix,V0is the volume change of coal matrix, C, due to the adsorption of 1 mol of water moleculessIs the number of adsorption sites of water molecules, K, on 1 kg of coal substrate1Is the equilibrium constant, K, under adsorption of the first layer2Is the equilibrium constant under adsorption of the second layer, agIs the water activity coefficient.
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