CN107130959A - A kind of methane output Forecasting Methodology - Google Patents
A kind of methane output Forecasting Methodology Download PDFInfo
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- CN107130959A CN107130959A CN201710372453.0A CN201710372453A CN107130959A CN 107130959 A CN107130959 A CN 107130959A CN 201710372453 A CN201710372453 A CN 201710372453A CN 107130959 A CN107130959 A CN 107130959A
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Abstract
The invention discloses a kind of methane output Forecasting Methodology, comprise the following steps：Set up the geological model that coal bed gas is preserved and migrated；The mathematical modeling of coalbed methane reservoir is set up in the geological model, in the mathematical modeling, the Dynamic Permeability in coal seam is obtained according to the variable quantity of matrix of coal desorption compression deformability and matrix of coal porosity；The mathematical modeling is solved using numerical method, numerical model is obtained；The numerical model is solved, methane output and pressure distribution is obtained.The present invention improves the degree of accuracy of Forecasting Methodology by accumulating the synthesis improvement of constriction coefficient to the cleat in coal compressed coefficient and coal body, further, the present invention considers near wellbore zone coal dust influence, nearly well coal dust conversion pollutes epidermis for coal dust, it is adaptable to easily goes out coal dust, geological conditions and understands not clear enough coal bed gas well.
Description
Technical field
The present invention relates to the production technique field of coal bed gas, more particularly to a kind of methane output Forecasting Methodology.
Background technology
Coal bed gas is a kind of from the Unconventional gas for being born from storage, and its development and utilization is to improving energy resource structure, environment
Protection and safety of coal mines are respectively provided with significance.Based on existing Coal-seam Gas Recovery Technologies, numerous business are there has been
Change or the personal coal bed gas numerical simulation software researched and developed.
Coal dust is blocked and self-regulation effect is influenceed in two big factors of coal seam permeability, coal bed gas well development process, special
It is not initial stage of development, the easy output coal dust of ature of coal blocks coal seam aerogenesis passage near wellbore zone, causes permeability reduction, still,
Existing coal bed gas numerical simulation software does not consider both influence factors, and the penetration rate model of use is not accounted for
Coal dust blocks the influence to permeability, lacks the synthesis improvement that constriction coefficient is accumulated to the cleat in coal compressed coefficient and coal body.
The content of the invention
In order to solve the above-mentioned technical problem, the invention provides a kind of methane output Forecasting Methodology, self-regulation has been used
Effect improves penetration rate model, and prediction side is improved by the synthesis improvement that constriction coefficient is accumulated to the cleat in coal compressed coefficient and coal body
The degree of accuracy of method.
In order to reach the object of the invention, what the technical scheme of the embodiment of the present invention was realized in：
The invention provides a kind of methane output Forecasting Methodology, including：
Set up the geological model that coal bed gas is preserved and migrated；
The mathematical modeling of coalbed methane reservoir is set up in the geological model, in the mathematical modeling, according to matrix of coal
The variable quantity of desorption compression deformability and matrix of coal porosity obtains the Dynamic Permeability in coal seam；
The mathematical modeling is solved using numerical method, numerical model is obtained；
The numerical model is solved, methane output and pressure distribution is obtained.
Further, it is assumed that p is reservoir pressure, unit is MPa；Pr is matrix of coal critical desorption pressures, and unit is MPa,
As p ＞ prWhen：
Wherein：K is the dynamic absolute permeability in crack, and unit is 10-3μm2；KoFor the original permeability in coal seam, unit
For 10-3μm2；CfFor pore volume compressibility, unit is 1/MPa；V is the Poisson's ratio of coal petrography；p0Primitively it is laminated for coal seam
Power, unit is MPa；
As p≤prWhen：
Matrix of coal desorbs compression deformability Δ ε：
Wherein：ρcFor matrix of coal density, unit is t/m3；R is ideal gas constant, R=8.314J/ (molK)；E is
Young's modulus of elasticity, unit is MPa；V0For the molal volume under gas standard situation；T is temperature, and unit is K；
The variable quantity of the matrix of coal porosity is：
Wherein：φ is the dynamic aperture porosity in coal seam；φoFor the primary porosity in coal seam；M represents matrix of coal denaturation amount
First characterisitic parameter, unit is MPa；Ks represents the second characterisitic parameter of matrix of coal denaturation amount, and unit is MPa；The coal seam
Dynamic Permeability is：
Wherein,For initial pore volume compressibility；VLFor Lan Shi volumes；B=1/PL, PLFor blue formula pressure.
Further, in the mathematical modeling, nearly well coal dust conversion is coal dust pollution epidermis sd, it is dirty by coal dust
Contaminate epidermis sd, pressure break epidermis sfWith perforation epidermis spSum calculates skin factor sall, i.e.,：
sall=sd+sf+sp；
Wherein, sdFor pollution epidermis；sfFor pressure break epidermis；spFor perforation epidermis；xfFor fracture half-length, unit is m；rwFor
Wellbore radius, unit is m；K is the dynamic absolute permeability in crack, and unit is 10-3μm2；KsUnder the influence of being blocked by coal dust
Permeability, unit for μm2；rsFor pollution radius, unit is m；εVFor the rock volume coefficient of strain；For primary porosity；Rc
It is particle in unit volume coal petrography with liquid discharge rate, unit is kg/s；λ is coal petrography liquefaction coefficient；Q is Liquid output, and unit is
kg/s； Kd1、Kd2For field deposition rate constant；vgljThe critical flow velocity rolled for pulverized coal particle, unit is m/s.
Further, the mathematical modeling includes fundamental differential, the solution of matrix of coal micro-pore system of fissure system
Adsoption equation, subsidiary equation, definite condition are inhaled, wherein,
The fundamental differential of the fissure system includes gas phase fundamental differential and aqueous phase fundamental differential, its
In,
Gas phase fundamental differential is
Aqueous phase fundamental differential is
Wherein, qmdesItem is desorbed for coal bed gas, unit is kg/s；qgFor gas production, unit is kg/s；qwFor aquifer yield, list
Position is kg/s；SwFor water saturation；SgFor gas saturation；K is the absolute permeability in crack；KrgFor gas phase in crack
Relative permeability；KrwFor the relative permeability of aqueous phase in crack； μgFor the viscosity of gas；μwFor the viscosity of water；ρgFor gas
Density；ρwFor the density of water；φ is fracture aperture；pgFor gaseous pressure；pwFor aqueous phase pressure；
The desorption adsoption equation of the matrix of coal micro-pore system includes：
Wherein, FGFor matrix unit geometrical factor, zero dimension；σ is Warren the and Root form factors of matrix of coal block,
Unit is m-2；D is diffusion coefficient, and unit is m2/d；VmAccumulated for matrix of coal block, unit is m3；VeFor on fissure-plane with freedom
Gas pressure is in the adsorbed gas content of poised state, and unit is m3；τ is adsorption time constant, and unit is s；
The subsidiary equation includes：
Sg+Sw=1 (3)
pcgw(Sw)=pg-pw(4)；
Wherein, pcgwFor capillary force, unit is Mpa.
Further, in the gas phase fundamental differential and aqueous phase fundamental differential,
The gas production qgFor：
The aquifer yield qwFor：
Wherein, h is reservoir thickness, and unit is m；PwfFor flowing bottomhole pressure (FBHP), unit is Mpa；rwFor wellbore radius, unit is
m；reFor effective radius re, unit is m；S is skin factor.
Further, for square net system, the effective radius reFor：
re=0.208 Δ x；
For rectangular grid system, the effective radius reFor：
Wherein, Δ x, Δ y are illustrated respectively in the mesh spacing in plane both direction.
Further, the mathematical modeling is solved by finite difference calculus, obtains numerical model.
Further, the numerical model is solved using implicit pressure explicit saturation method.
Technical scheme, has the advantages that：
The methane output Forecasting Methodology that the present invention is provided, compression deformability and matrix of coal hole are desorbed according to matrix of coal
The variable quantity of degree obtains the Dynamic Permeability in coal seam, is changed by the synthesis that constriction coefficient is accumulated to the cleat in coal compressed coefficient and coal body
Enter to improve the degree of accuracy of Forecasting Methodology；
Further, the present invention considers near wellbore zone coal dust influence, and nearly well coal dust conversion pollutes epidermis for coal dust,
Understand not clear enough coal bed gas well suitable for easily going out coal dust, geological conditions.
Brief description of the drawings
Accompanying drawing described herein is used for providing a further understanding of the present invention, constitutes the part of the application, this hair
Bright schematic description and description is used to explain the present invention, does not constitute inappropriate limitation of the present invention.In the accompanying drawings：
Fig. 1 is a kind of schematic flow sheet of methane output Forecasting Methodology of the embodiment of the present invention；
Fig. 2 is the permeability saturation curve schematic diagram of the embodiment of the present invention；
Fig. 3 is the capillary pressure curve schematic diagram of the embodiment of the present invention；
Fig. 4 is the initial reservoir pressure distribution schematic diagram of the embodiment of the present invention；
Fig. 5 is the pressure distribution schematic diagram after the simulation 300 days of the embodiment of the present invention；
Fig. 6 is the methane output distribution schematic diagram after the simulation 1300 days of the embodiment of the present invention.
Embodiment
For the object, technical solutions and advantages of the present invention are more clearly understood, below in conjunction with accompanying drawing to the present invention
Embodiment be described in detail.It should be noted that in the case where not conflicting, embodiment and embodiment in the application
In feature can mutually be combined.
A kind of reference picture 1, methane output Forecasting Methodology according to embodiments of the present invention, comprises the following steps：
Step 101：Set up the geological model that coal bed gas is preserved and migrated；
Specifically, according to the actual conditions of studied bed gas reservoir, D geology model as shown in Figure 1, input are built
Relevant parameter, the relevant parameter includes mesh spacing, reservoir thickness h, porosity φ and permeability KoDeng geologic parameter, and
By carrying out difference discrete to the permeability saturation curve shown in Fig. 2, the relative infiltration of gas phase under different gas saturation is obtained
Aqueous phase relative permeability under rate and different water cut saturation degree.
It should be noted that the geological model that coal bed gas is stored up and migrated can be summarized as follows：
(1) coal seam reservoirs have typical crack-hole dual pore structure, are by the micro-pore system in matrix of coal block
The diplopore slot sytem constituted with fissure system；
(2) there is gas and water two-phase fluid in coal seam reservoirs；
(3) micropore in matrix of coal block is the major reservoir spaces of coal bed gas, and coal bed gas is mainly with adsorbed state preservation
In on the inner surface of micropore.Micropore very little, water can not enter wherein, so only existing single phase gas in micro-pore system.
Fissure system is both the reservoir space of gas and water, is also the seepage channel of gas and water two-phase fluid；
(4) coal seam gas is from coal seam reservoirs migration and production experience seepage flow, desorption and spreads three phases, wherein,
Seepage flow：When coal bed gas well drainage and step-down, coal bed gas and water in fissure system are under barometric gradient effect to ooze
Manifold formula is to Wellbore Flow.Darcy laws are obeyed in this flowing；
Desorption：Because gas and water is from crack output, coal seam reservoirs pressure is caused to decline, in matrix of coal block surface micropore slot sytem
The coal bed gas of absorption is desorbed so that the coal bed gas content i.e. coal bed gas adsorbed in matrix of coal block surface micropore slot sytem is dense
Degree reduction.This coal bed gas content or coal bed gas concentration Ke are described Yong Lan Miaoer equations；
Diffusion：With the reduction of coal bed gas concentration in matrix of coal block surface micropore gap, the internal capillary gap system of matrix of coal block
Coal bed gas concentration in coal bed gas concentration gradient, i.e. its internal capillary slot sytem is formed between system and surface micropore slot sytem relative
It is higher, and coal bed gas concentration is relatively low in its surface micropore gap.In the presence of concentration gradient, in internal capillary slot sytem
Coal bed gas by micro-pore system along concentration gradient reduce direction from inside to surface occur diffusion And Movement, be considered as herein
Quasi-stable state is migrated, and is controlled by Fick First Laws.
(5) migration process of gas and water is isothermal in coal seam reservoirs.
(6) gas in fissure system is free gas, shows as actual gas characteristic；Water is compressible fluid.
In micro-pore system, selective absorption and diffusion phenomena are not present in various gas components.
(7) desorption on substrate block surface is very fast, it is sufficient to maintain the balance between free gas and adsorbed gas.In coal
Adsorbed gas inside substrate block is in non-equilibrium state with free gas.
Specifically, by taking certain block mouthful coal bed gas well as an example, the major parameter of the geological model of structure is as follows：
Permeability KoFor 0.08mD；Original formation pressure PoFor 4MPa；Critical desorption pressures PrFor 2.3MPa；Porosity φ
For 0.01；Fracture half-length LfFor 30m；Desorption time trFor 3.6d；Lan Shi pressure PLFor 2MPa；Lan Shi volumes VLFor 30m3/t；Ton
Coal air content QgFor 8m3/t。
Emphasis of the present invention considers the influence of self-regulation effect and coal dust, it is thus necessary to determine that relevant parameter, such as Young springform
E, Poisson's ratio ν of coal petrography etc. are measured, so as to the influence of accurate description self-regulation effect and coal dust.
Step 102：The mathematical modeling of coalbed methane reservoir is set up in the geological model, in the mathematical modeling, root
The Dynamic Permeability in coal seam is obtained according to the variable quantity of matrix of coal desorption compression deformability and matrix of coal porosity；
Further, according to coal bed gas adsorption -diffusion model, the mathematical modeling of coal bed gas numerical simulation, the number are set up
Learn fundamental differential of the model including fissure system, the desorption adsoption equation of matrix of coal micro-pore system, subsidiary equation, side
Boundary's condition.
The fundamental differential of the fissure system includes gas phase fundamental differential and aqueous phase fundamental differential, gas
Phase fundamental differential is：
Aqueous phase fundamental differential is：
Subsidiary equation is：
Sg+Sw=1 (3)
pcgw(Sw)=pg-pw (4)
Wherein, qmdesItem is desorbed for coal bed gas, unit is kg/s；qgFor gas production, unit is kg/s；qwFor aquifer yield, list
Position is kg/s；SwFor water saturation；SgFor gas saturation；pcgwFor capillary force, unit is Mpa；K is absolute for crack
Permeability；KrgFor the relative permeability of gas phase in crack；KrwFor the relative permeability of aqueous phase in crack；μgFor the viscosity of gas；
μwFor the viscosity of water；ρgFor the density of gas；ρwFor the density of water；φ is fracture aperture；pgFor gaseous pressure；pwFor aqueous phase
Pressure.
Exchange the processing of item gas desorption quantity：
Gas in fissure system is that the gas in free gas, matrix micropores gap is then mainly adsorbed gas.In matrix
In, the gas only in the matrix micropores gap of fissure-plane, desorption is sufficiently fast, and poised state is in free gas；
And gas is in nonequilibrium condition with the free gas in crack in the matrix micropores gap away from crack.
The adsorbed gas content Ke for being in poised state with free gas is tried to achieve Yong Lan Miaoer models：
Wherein, VLFor Lan Shi volumes；PLFor blue formula pressure；PgFor free gas pressure；VeIt is flat to be in free gas
The adsorbed gas content of weighing apparatus state.
In the presence of there is between surface gas concentration difference inside substrate block, in substrate block internal capillary gap
Gas will migrate in the method for diffusion to outside, and enter in fissure system, can be considered a source item to handle.By non-equilibrium
Quasi-stable state condition considers, according to Fick First Laws, the rate of change and matrix of coal block of the average air content of matrix of coal block to the time
Average air content and the difference of adsorption gas content are directly proportional, and are diffused into the unit interval by the desorption of unit matrix of coal
Gas flow to fissure system is directly proportional to the rate of change of matrix of coal block average gas contents, i.e. matrix of coal micro-pore system
Desorbing adsoption equation is：
Wherein, FGFor matrix unit geometrical factor, zero dimension is (for plate shaped, FGFor 2；Cylinder, FGFor 4；It is spherical,
FGFor 6)；σ is Warren the and Root form factors of matrix of coal block, and unit is m-2；D is diffusion coefficient, and unit is m2/d；VmFor
Matrix of coal block is accumulated, and unit is m3；VeIt is single to be in the adsorbed gas content of poised state on fissure-plane with free gas pressure
Position is m3；τ is adsorption time constant, and unit is s.
What deserves to be explained is, Warren and Root form factors, diffusion coefficient D, the matrix of coal block product of σ matrix of coal blocks
Vm, adsorption time constant, τ, matrix unit geometrical factor FGIt can be obtained ahead of time, wherein σ and FGCan be pre- according to actual conditions
First set；D、Vm, τ can be measured by laboratory experiment.
Solve above-mentioned equation group, in addition it is also necessary to give boundary condition and primary condition according to specific circumstances.Boundary condition and
Primary condition is referred to as definite condition.
Boundary condition in coalbed methane reservoir numerical simulation is divided into Outer Boundary Conditions and the major class of internal boundary condition two, wherein
Outer Boundary Conditions refer to coal seam reservoirs external boundary state in which, and internal boundary condition refers to coal seam gas production well state in which.
The Outer Boundary Conditions include outer closure border and outer constant-pressure boundary.This Forecasting Methodology for outer closure border and
Outer constant-pressure boundary is all applicable.The numerical solution (needing to set virtual grid) of closed boundary is complex, and in the persimmon village
South block coal bed gas well is applied to closed boundary.If there is lasting water source supply on border, that is, constant-pressure boundary, it is no then for envelope
Close border.Moreover, under the conditions of well pattern, adjacent well is interfered, outer closure condition is also considered as.Outer Boundary Conditions are using envelope
Close boundary condition.
Closed boundary condition：Closing on external boundary E, no fluid flows through, then can be expressed as：
In the presence of having coal seam gas production well, due to well radius compared with inter-well distance very little, it is possible to it is seen
Work is point sink, is handled as internal boundary condition.In the methane output Forecasting Methodology, using constant-pressure boundary condition.
When the flowing bottomhole pressure (FBHP) of given well, being solved by following equation increases a yield in yield, the differential equation
.According to fur coat than formula, the gas and water yield of coal bed gas well is respectively：
Wherein, qgFor gas production；qwFor aquifer yield, unit is kg/s；K be crack absolute permeability, unit for μm2；
KrgFor the relative permeability of gas phase in crack, unit for μm2；KrwFor the relative permeability of aqueous phase in crack, unit for μm2；μg
For the viscosity of gas, unit is mPas；μwFor the viscosity of water, unit is mPas；ρgFor the density of gas, unit is kg/
m3；ρwFor the density of water, unit is kg/m3；pgFor gaseous pressure, unit is Mpa；pwFor aqueous phase pressure, unit is Mpa；H is
Reservoir thickness, unit is m；PwfFor flowing bottomhole pressure (FBHP), unit is Mpa；rwFor wellbore radius, unit is m； reFor effective radius re,
Unit is m, effective radius reIt is relevant with mesh spacing, square net system： re=0.208 Δ x；Rectangular grid system：
Skin factor s is nondimensional, is that the nearly well stream of influence enters dynamic principal element, specifically, skin factor s leads to
The s crossed in formula (11)allCalculated：
sall=sd+sf+sp (11)
Wherein, sdEpidermis is polluted for coal dust；sfFor pressure break epidermis；spFor perforation epidermis.
It should be noted that near wellbore zone due to construction pressure break, and barometric gradient it is larger the reason for, coal dust amount compared with
Greatly, coal dust can block coal-bed methane seepage passage, hinder coal bed gas product.Nearly well coal dust mainly influences nearly well permeability, according to stifled
Radius is filled in, is converted as coal dust pollution epidermis sd, in coal dust pollution epidermis sdIn, RcItem is the influence device to hole for considering coal dust
The chocking-up degree in road, is represented with discharge rate；By perforating parameter, s is determined using existing conventional platep。
Wherein,
Wherein, xfFor fracture half-length, unit is m；rwFor wellbore radius, unit is m；K is the absolute permeability in crack, single
Position for μm2；KCFor by coal dust etc. block under the influence of permeability, unit for μm2；rsFor pollution radius, unit is m；εVFor rock
Bulk strain coefficient；For primary porosity；RcIt is particle in unit volume coal petrography with liquid discharge rate, unit is kg/s；λ
For coal petrography liquefaction coefficient；Q is Liquid output, and unit is kg/s；Kd1、Kd2Respectively first surface sedimentation rate constant and the second table
Face sedimentation rate constant；vgljThe critical flow velocity rolled for pulverized coal particle, unit is m/s.
Primary condition：
To the pressure distribution and saturation distribution being scheduled in the initial time coalbed methane reservoir of cbm development, it can represent
For：
P (x, y) |T=0=Pij(x, y) (16)
Sw(x, y) |t=0=Swij(x, y) (17)
Wherein, Pij(X, y) be primary condition under give diverse location corresponding to pressure；Swij(x, y) is initial strip
The water saturation corresponding to diverse location given under part, i, j represents the position residing for the grid in plane both direction
Put.
The processing of some other parameters in equation：
In formula：ρgFor gas density, unit is kg/m3；γgFor specific gravity of gas；Z is compressibility factor；P is reservoir pressure,
Unit is Pa；T is temperature, and unit is K.
In formula：φ is the dynamic aperture porosity in coal seam；φoFor the primary porosity in coal seam；p0For coal seam original formation pressure,
Unit is MPa；M represents the first characterisitic parameter of matrix of coal denaturation amount, and unit is MPa；Ks represents the second of matrix of coal denaturation amount
Characterisitic parameter, unit is MPa；Δ ε is Coal matrix shrinkage amount.
As p ＞ prWhen, Pr is critical desorption pressures,
In formula：K is the absolute permeability of the Dynamic Permeability, i.e. crack in coal seam, and unit is 10-3μm2；KoFor the original in coal seam
Beginning permeability, unit is 10-3μm2；CfFor pore volume compressibility, unit is 1/MPa；V is the Poisson's ratio of coal petrography.
As p≤prWhen,
Can obtain matrix of coal desorption compression deformability according to Zhao Ming chapters pertinent literature is：
Wherein：ρcFor matrix of coal density, unit is t/m3；R is ideal gas constant, R=8.314J/ (molK)；E is
Young's modulus of elasticity, unit is MPa；V0For the molal volume under gas standard situation；P is reservoir pressure, and unit is MPa；pr
For matrix of coal critical desorption pressures, unit is MPa；VLFor Lan Shi volumes；B=1/PL, PLFor blue formula pressure.
According to P＆M models, drop in formation pressure can be obtained, the variable quantity of matrix of coal porosity is：
Wherein,
According to pore volume compressibility CfDefinition can obtain：
Due to initial pore volume compressibilityIt is represented by：
Formula (25) can be further simplified shown as：
It is theoretical according to Ji-Quan Shi, shown in the penetration rate model such as formula (28) that can obtain coal seam
Wherein, σ and σ0Stress respectively before reservoir conditions change and after change, unit is MPa.
Stress variation is accordingly：
Formula (27) and formula (29) are substituted into formula (28) the permeability formula in coal seam can be obtained and be：
Step 103, using numerical method the mathematical modeling is solved, obtain numerical model.
The numerical method applied in engineering has finite difference calculus, FInite Element, the calculus of variations and finite boundary member method etc..
In an embodiment of the present invention, the number of coal bed gas migration rule in description coal seam reservoirs is set up by finite difference calculus
It is worth model, i.e. DIFFERENCE EQUATIONS.
Under the conditions of uniform grid, block centered difference grid is employed, to the left end of gas and water two-phase partial differential equation
To space difference, right-hand vector carries out time difference, can obtain following difference equation：
Gas equation difference equation：
Water equation difference equation：
Wherein, subscript i, j represent the location of grid in plane both direction, and subscript n represents n-th of time
Step, Δ xi、ΔyiIt is illustrated respectively in the mesh spacing in plane both direction.
Vi,j=h Δs xiΔyj
For reduced equation, Differetial Operators are introduced：
After simplification, gas equation is as follows：
It is further simplified as：
Similarly, the aqueous phase difference equation after must can simplifying is：
It resulting in the DIFFERENCE EQUATIONS of gas and water two-phase, Δ TgΔPgRepresent the gas phase differential in xy both directions
Writing a Chinese character in simplified form after operator merging；ΔTwΔPwImplication represent by xy both directions aqueous phase differential operator merge after writing a Chinese character in simplified form.
Contain four known variables P altogether in two equationsg、Pw、SgAnd Sw, but it is independent actually there was only two
Variable, remaining variables can be handled as the function of the two independent variables.It is by P in the solution procedure of the modelgWith
SwSolved as independent variable.
Step 104, the solution numerical model, obtain methane output and pressure distribution.
Left end term coefficient conductivity T in DIFFERENCE EQUATIONSgAnd TwIt is to solve for variable gaseous pressure and water phase saturation
Function, so the DIFFERENCE EQUATIONS is nonlinear., it is necessary to first use necessarily when being solved for nonlinear difference equation group
Method is linearized, and it is converted into linear DIFFERENCE EQUATIONS, is then solved again with some way iteration.
In an embodiment of the present invention, the numerical model is solved using implicit pressure explicit saturation method (IMPES) method, that is, selected
Gaseous pressure and water phase saturation are that coefficient and yield are explicitly handled in independent variable, difference equation, pressure and saturation degree
Implicitly handled.Show full method using hidden pressure in IMPES methods alternately to solve, so equation left end reaches in the calculation
Western term coefficient takes a time step value, and equation right-hand vector presses Taylor series expansion, takes single order a small amount of.Merged by equation,
To each knots removal water saturation, the pressure equation of a variable of only pressure increment is obtained, then all sections of simultaneous
Point pressure equation solution.Solve to substitute into equation after pressure and explicitly obtain saturation degree increment.Solution is as follows：
Equation left end expansion：
δ x=xn+1-xn, i.e. δ x represent x from the n-th time step to the period of the (n+1)th time step in change；
In IMPES methods, it will be assumed that during being produced in whole oil reservoir, capillary pressure is not at any time all the time
Between change, and capillary pressure pcIt is δ p for constantc=0；
Porosity φ is the linear function of pressure, i.e.,
It can thus be concluded that：
Darcy expansion is made to gas equation left end now, can be obtained：
The expansion of water equation left end darcy can be similarly obtained, can be obtained：
Equation right-hand vector is deployed：
δ(ρgSgφ)=Sgφδρg+ρgφδ(Sg)+ρgSgδφ (42)
δ(ρwSwφ)=Swφδρw+ρwφδ(Sw)+ρwSwδφ (43)
Because density and porosity are all the functions of pressure, two formulas can do following deformation again above：
δ(ρgSgφ)=SgφCgδPg-ρgφδSw+ρgSgCpδPg (44)
δ(ρwSwφ)=SwφCwδPg+ρwφδSw+ρwSwCpδPg (45)
Wherein, CgFor the derivative of density of gas phase pressure；CwFor derivative of the aqueous phase densities to pressure；CpIt is porosity to pressure
Derivative.
The diffusion desorption item expansion of equation left end：
First, according to Fick First Laws, gas spreads into crack in matrix of coal micropore under description plan stable condition
The differential equation of process is as follows：
In order to obtain adsorbed gas content in n+1 moment matrixs of coalExpression formula, to the differential equation carry out separation change
Measure and integrate.
It is assumed that in the time out of n → n+1 iteration steps, the gas content of matrix of coal adsorption is normal under average pressure
Number, is taken asThen：
Solve：
Order：
So
Here it is the final expression formula of description matrix of coal micropore Adsorption on Surface gas volume.
Here, by the average desorption rate in n → n+1 iteration steps from unit volume matrix of coal desorption gas into crack
It is defined as：
It can be obtained by above-mentioned formula：
In formula,It is the average content of adsorbed gas inside n moment matrix of coal,It is n, n+1 moment respectively
The content of the matrix of coal adsorption gas of balance is maintained with free gas pressure in crack, its expression formula is：
Now, linearisation expansion is carried out to above formula using fully implicit method.From tnTo tn+1In the iterative process of time step,
So：
Nonlinear System of Equations is linearized：
The expansion result of above-mentioned left end and right-hand vector is substituted into, and pressure term is moved on to the equation left side, saturation degree is moved
To equation right-hand member, that is, obtain the aobvious full DIFFERENCE EQUATIONS of the hidden pressure of complete gas and water two-phase：
The stability of difference equation, convergence：
When explicit difference equation meets following formula：
Difierence equation is stable, according to difference equation compatibility and the relation of stability, it can be noted that, to physics
Upper significant reservoir simulation problems, the solution of boundary value problem is usually smooth, as long as its difference equation meets stability and wanted
Ask, difference equation is exactly convergent.When spatial mesh size goes to zero, solution of difference equation converges on the former differential equation
Solution.
Whether difference equation is stable, i.e., Δ t and Δ x sizes are proposed to limit, in fact, when Δ t, Δ x are excessive
When, truncated error will be made to become very big so that the approximate solution that difference method is obtained differs larger with the true solution of the differential equation, because
It is smaller that this should be noted that a Δ t, Δ x suitably take when being solved with implied format and explicit form, can thus meet error
It is required that, difference equation is just stablized, and also just restrains.
First, Δ t, Δ x have to meet relational expression be exactlyThis is the relative size to both
One limitation, only meet require, can restrain.Secondly in order to not make truncated error very big, Δ t, Δ x two are caused
Person meets respectively suitably to be taken small, and this is suitably not specifically limited, and should be selected according to specific oil reservoir situation, such as in example
According to the size of bed gas reservoir in, it is 20 meters to choose Δ x, and oil reservoir size now is at more than 200 meters.
Equation solution：
The gas and water equation that simultaneous is obtained, is eliminated, and obtains the relational expression for variable on pressure increment：
According to above formula, to each node, we obtain one only with pressure increment δ PgFor the pressure equation of variable,
Solution is contacted to the pressure equation of all nodes, you can obtain change value of pressure.For three-dimensional problem, its pressure equation is
Matrix number is a pentadiagonal matrix.This is the typical coefficient matrix structure of Numerical Simulation of Reservoir Problem.The characteristics of IMPES methods
Each element for being the matrix is a simple real number, therefore is solved fairly simple.
Obtain δ PgAfterwards, in its generation, is returned in Primordial Qi water equation, just can obtains δ Sw, so as to obtain the saturation degree of gas.
Parameter, derivative and boundary condition treatment：
Parameter on auxiliary magnet is all handled accordingly, showed with the node parameter values corresponding to them.
Absolute permeability is calculated by harmonic-mean, i.e.,：
Absolute permeability takes the value of a time step in time.
Flow coefficientIn except absolute permeability using harmonic-mean calculate in addition to, remaining is according to upstream
Value is weighed, i.e.,：
Others are by that analogy.
Gas phase permeability saturation curve and aqueous phase permeability saturation curve are as shown in Fig. 2 capillary pressure curve such as Fig. 3 institutes
Show, the abscissa in Fig. 2 and Fig. 3 is water saturation, relative permeability and capillary pressure can be obtained using linear interpolation method
Value：
In order that calculating process is stable, derivative term may be taken as secant between the last iterative value and the n-th time step
Slope, calculation formula is as follows：
K need not be used during calculatingrgLocal derviation calculation formula.
For block centered difference grid, the processing of Outer Boundary Conditions is by fictionalizing row's net at outer boundary mesh
Lattice are realized.
When border is known pressure saturation degree, is handled, be represented by using linear interpolation method：
In formula, P1And S1Borderline pressure and intensity value are represented respectively.
When border is closed boundary, then make virtual grid equal with intensity value with the pressure on boundary mesh.
Pwi,j=Pwi+1,j=Pwi,j+1
Pgi,j=Pgi+1,j=Pgi,j+1 (69)
Swi,j=Swi+1,j=Swi,j+1
Sgi,j=Sgi+1,j=Sgi,j+1
In an embodiment of the present invention, the distribution of geological model initial reservoir pressure, after operation a period of time for calculating
Pressure distribution and coal bed gas daily output curve as shown in Figure 4, Figure 5 and Figure 6.Flowing bottomhole pressure (FBHP) data can voluntarily be set,
Can also be using the actual flowing bottomhole pressure (FBHP) in scene.The flowing bottomhole pressure (FBHP) voluntarily set is produced to produce system optimization design and future
Amount prediction.The actual flowing bottomhole pressure (FBHP) in scene be for the ease of history matching, so as to obtain the geologic parameters such as permeability, porosity and
The coal bed gas characterisitic parameters such as Lan Shi pressure, Lan Shi volumes.
It should be noted that the methane output Forecasting Methodology of the application present invention, including data acquisition, data processing, number
According to key steps such as input, numerical simulation computing, data outputs.Original formation pressure, initial saturation degree, original permeability, phase
Collection in worksite and experiment are needed to the creation data such as the geologic parameters such as permeability curve and flowing bottomhole pressure (FBHP), gas production, aquifer yield
Room is obtained, and the data such as relative permeability and capillary pressure need difference discrete just to apply.
The methane output Forecasting Methodology that the present invention is provided, compression deformability and matrix of coal hole are desorbed according to matrix of coal
The variable quantity of degree obtains the Dynamic Permeability in coal seam, is changed by the synthesis that constriction coefficient is accumulated to the cleat in coal compressed coefficient and coal body
Enter to improve the degree of accuracy of Forecasting Methodology；
Further, the present invention considers near wellbore zone coal dust influence, and nearly well coal dust conversion pollutes epidermis for coal dust,
History matching, capability forecasting and the optimization of production system can be more precisely used for, it is adaptable to easily go out coal dust, geological conditions
Not clear enough the coal bed gas well of solution.
One of ordinary skill in the art will appreciate that all or part of step in the above method can be instructed by program
Related hardware is completed, and described program can be stored in computer-readable recording medium, such as read-only storage, disk or CD
Deng.Alternatively, all or part of step of above-described embodiment can also use one or more integrated circuits to realize, accordingly
Each module/unit in ground, above-described embodiment can be realized in the form of hardware, it would however also be possible to employ software function module
Form is realized.The present invention is not restricted to the combination of the hardware and software of any particular form.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the invention, for the skill of this area
For art personnel, the present invention can have various modifications and variations.Within the spirit and principles of the invention, that is made is any
Modification, equivalent substitution, improvement etc., should be included in the scope of the protection.
Claims (8)
1. a kind of methane output Forecasting Methodology, it is characterised in that including：
Set up the geological model that coal bed gas is preserved and migrated；
The mathematical modeling of coalbed methane reservoir is set up in the geological model, in the mathematical modeling, is desorbed according to matrix of coal
The variable quantity of compression deformability and matrix of coal porosity obtains the Dynamic Permeability in coal seam；
The mathematical modeling is solved using numerical method, numerical model is obtained；
The numerical model is solved, methane output and pressure distribution is obtained.
2. according to the method described in claim 1, it is characterised in that assuming that p is reservoir pressure, unit is MPa；prFor matrix of coal
Critical desorption pressures, unit is MPa,
As p ＞ prWhen：
<mrow>
<mi>K</mi>
<mo>=</mo>
<msub>
<mi>K</mi>
<mn>0</mn>
</msub>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mn>3</mn>
<msub>
<mi>C</mi>
<mi>f</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mi>v</mi>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>v</mi>
</mrow>
</mfrac>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>-</mo>
<msub>
<mi>p</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>20</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein：K is the dynamic absolute permeability in crack, and unit is 10-3μm2；KoFor the original permeability in coal seam, unit is 10-3μ
m2；CfFor pore volume compressibility, unit is 1/MPa；V is the Poisson's ratio of coal petrography；p0For coal seam original formation pressure, unit
For MPa；
As p≤prWhen：
Matrix of coal desorbs compression deformability Δ ε：
<mrow>
<mi>&Delta;</mi>
<mi>&epsiv;</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&rho;</mi>
<mi>c</mi>
</msub>
<msub>
<mi>RTV</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>EV</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<msubsup>
<mo>&Integral;</mo>
<msub>
<mi>p</mi>
<mi>r</mi>
</msub>
<mi>p</mi>
</msubsup>
<mi>d</mi>
<mo>&lsqb;</mo>
<mi>l</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>b</mi>
<mi>p</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>21</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein：ρcFor matrix of coal density, unit is t/m3；R is ideal gas constant, R=8.314J/ (molK)；E is Young
Modulus of elasticity, unit is MPa；V0For the molal volume under gas standard situation；T is temperature, and unit is K；
The variable quantity of the matrix of coal porosity is：
<mrow>
<mi>&phi;</mi>
<mo>-</mo>
<msub>
<mi>&phi;</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>M</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>-</mo>
<msub>
<mi>p</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mfrac>
<msub>
<mi>K</mi>
<mi>s</mi>
</msub>
<mi>M</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mi>&Delta;</mi>
<mi>&epsiv;</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>22</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein：φ is the dynamic aperture porosity in coal seam；φoFor the primary porosity in coal seam；M represents the first spy of matrix of coal denaturation amount
Property parameter, unit is MPa；Ks represents the second characterisitic parameter of matrix of coal denaturation amount, and unit is MPa；The dynamic in the coal seam is oozed
Rate is thoroughly：
<mrow>
<mi>K</mi>
<mo>=</mo>
<msub>
<mi>K</mi>
<mn>0</mn>
</msub>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mn>3</mn>
<msub>
<mi>C</mi>
<mrow>
<mi>f</mi>
<mn>0</mn>
</mrow>
</msub>
<mo>&lsqb;</mo>
<mn>1</mn>
<mfrac>
<mrow>
<mo>(</mo>
<mi>M</mi>
<mo>-</mo>
<msub>
<mi>K</mi>
<mi>s</mi>
</msub>
<mo>)</mo>
<msub>
<mi>&rho;</mi>
<mi>c</mi>
</msub>
<msub>
<mi>bRTV</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>EV</mi>
<mn>0</mn>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>b</mi>
<mi>p</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>{</mo>
<mo>-</mo>
<mfrac>
<mi>v</mi>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>v</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>-</mo>
<msub>
<mi>p</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mo>&lsqb;</mo>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>b</mi>
<mi>p</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>ln</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>bp</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<msub>
<mi>&rho;</mi>
<mi>c</mi>
</msub>
<msub>
<mi>RTV</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mn>3</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>V</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<mo>}</mo>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>30</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,For initial pore volume compressibility；VLFor Lan Shi volumes；B=1/PL, PLFor blue formula pressure.
3. according to the method described in claim 1, it is characterised in that in the mathematical modeling, nearly the conversion of well coal dust is coal
Powder pollution epidermis sd, epidermis s is polluted by coal dustd, pressure break epidermis sfWith perforation epidermis spSum calculates skin factor sall, i.e.,：
sall=sd+sf+sp；
<mrow>
<msub>
<mi>s</mi>
<mi>f</mi>
</msub>
<mo>=</mo>
<mo>-</mo>
<mi>l</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>x</mi>
<mi>f</mi>
</msub>
<mrow>
<mn>2</mn>
<msub>
<mi>r</mi>
<mi>w</mi>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>s</mi>
<mi>d</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mi>K</mi>
<msub>
<mi>K</mi>
<mi>C</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>ln</mi>
<mfrac>
<msub>
<mi>r</mi>
<mi>w</mi>
</msub>
<msub>
<mi>r</mi>
<mi>s</mi>
</msub>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
1
Wherein, sdFor pollution epidermis；sfFor pressure break epidermis；spFor perforation epidermis；xfFor fracture half-length, unit is m；rwFor pit shaft half
Footpath, unit is m；K is the dynamic absolute permeability in crack, and unit is 10-3μm2；KsFor the permeability under the influence of being blocked by coal dust,
Unit for μm2；rsFor pollution radius, unit is m；εVFor the rock volume coefficient of strain；For primary porosity；RcFor unit body
Particle is with liquid discharge rate in product coal petrography, and unit is kg/s；λ is coal petrography liquefaction coefficient；Q is Liquid output, and unit is kg/s；Kd1、
Kd2For field deposition rate constant；vgljThe critical flow velocity rolled for pulverized coal particle, unit is m/s.
4. according to the method described in claim 1, it is characterised in that the mathematical modeling includes the Basic Differential side of fissure system
Desorption adsoption equation, subsidiary equation, the definite condition of journey, matrix of coal micro-pore system, wherein,
The fundamental differential of the fissure system includes gas phase fundamental differential and aqueous phase fundamental differential, wherein,
Gas phase fundamental differential is
<mrow>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>KK</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<msub>
<mi>&rho;</mi>
<mi>g</mi>
</msub>
</mrow>
<msub>
<mi>&mu;</mi>
<mi>g</mi>
</msub>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mi>g</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>KK</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<msub>
<mi>&rho;</mi>
<mi>g</mi>
</msub>
</mrow>
<msub>
<mi>&mu;</mi>
<mi>g</mi>
</msub>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mi>g</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>q</mi>
<mrow>
<mi>m</mi>
<mi>d</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>q</mi>
<mi>g</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&rho;</mi>
<mi>g</mi>
</msub>
<msub>
<mi>S</mi>
<mi>g</mi>
</msub>
<mi>&phi;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Aqueous phase fundamental differential is
<mrow>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>KK</mi>
<mrow>
<mi>r</mi>
<mi>w</mi>
</mrow>
</msub>
<msub>
<mi>&rho;</mi>
<mi>w</mi>
</msub>
</mrow>
<msub>
<mi>&mu;</mi>
<mi>w</mi>
</msub>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mi>w</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>KK</mi>
<mrow>
<mi>r</mi>
<mi>w</mi>
</mrow>
</msub>
<msub>
<mi>&rho;</mi>
<mi>w</mi>
</msub>
</mrow>
<msub>
<mi>&mu;</mi>
<mi>w</mi>
</msub>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>p</mi>
<mi>w</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>q</mi>
<mi>w</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>&rho;</mi>
<mi>w</mi>
</msub>
<msub>
<mi>S</mi>
<mi>w</mi>
</msub>
<mi>&phi;</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, qmdesItem is desorbed for coal bed gas, unit is kg/s；qgFor gas production, unit is kg/s；qwFor aquifer yield, unit is
kg/s；SwFor water saturation；SgFor gas saturation；K is the absolute permeability in crack；KrgOozed for the relative of gas phase in crack
Saturating rate；KrwFor the relative permeability of aqueous phase in crack；μgFor the viscosity of gas；μwFor the viscosity of water；ρgFor the density of gas；ρw
For the density of water；φ is fracture aperture；pgFor gaseous pressure；pwFor aqueous phase pressure；
The desorption adsoption equation of the matrix of coal micro-pore system includes：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mi>m</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<mi>&sigma;</mi>
<mi>D</mi>
<mo>&lsqb;</mo>
<msub>
<mi>V</mi>
<mi>m</mi>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>g</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mi>&tau;</mi>
</mfrac>
<mo>&lsqb;</mo>
<msub>
<mi>V</mi>
<mi>m</mi>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>g</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>q</mi>
<mrow>
<mi>m</mi>
<mi>d</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>F</mi>
<mi>G</mi>
</msub>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>V</mi>
<mi>m</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, FGFor matrix unit geometrical factor, zero dimension；σ is Warren the and Root form factors of matrix of coal block, and unit is
m-2；D is diffusion coefficient, and unit is m2/d；VmAccumulated for matrix of coal block, unit is m3；VeFor on fissure-plane with free gas pressure
Adsorbed gas content in poised state, unit is m3；τ is adsorption time constant, and unit is s；
The subsidiary equation includes：
Sg+Sw=1 (3)
pcgw(Sw)=pg-pw(4)；
Wherein, pcgwFor capillary force, unit is Mpa.
5. method according to claim 4, it is characterised in that in the gas phase fundamental differential and aqueous phase Basic Differential
In equation,
The gas production qgFor：
<mrow>
<msub>
<mi>q</mi>
<mi>g</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;KK</mi>
<mrow>
<mi>r</mi>
<mi>g</mi>
</mrow>
</msub>
<msub>
<mi>&rho;</mi>
<mi>g</mi>
</msub>
<mi>h</mi>
</mrow>
<mrow>
<msub>
<mi>&mu;</mi>
<mi>g</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mi>n</mi>
<mfrac>
<msub>
<mi>r</mi>
<mi>e</mi>
</msub>
<msub>
<mi>r</mi>
<mi>w</mi>
</msub>
</mfrac>
<mo>+</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>g</mi>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>w</mi>
<mi>f</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
The aquifer yield qwFor：
<mrow>
<msub>
<mi>q</mi>
<mi>w</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<msub>
<mi>&pi;KK</mi>
<mrow>
<mi>r</mi>
<mi>w</mi>
</mrow>
</msub>
<msub>
<mi>&rho;</mi>
<mi>w</mi>
</msub>
<mi>h</mi>
</mrow>
<mrow>
<msub>
<mi>&mu;</mi>
<mi>w</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mi>n</mi>
<mfrac>
<msub>
<mi>r</mi>
<mi>e</mi>
</msub>
<msub>
<mi>r</mi>
<mi>w</mi>
</msub>
</mfrac>
<mo>+</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>w</mi>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>w</mi>
<mi>f</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, h is reservoir thickness, and unit is m；PwfFor flowing bottomhole pressure (FBHP), unit is Mpa；rwFor wellbore radius, unit is m；reFor
Effective radius re, unit is m；S is skin factor.
6. method according to claim 5, it is characterised in that for square net system, the effective radius reFor：
re=0.208 Δ x；
For rectangular grid system, the effective radius reFor：
<mrow>
<msub>
<mi>r</mi>
<mi>e</mi>
</msub>
<mo>=</mo>
<mn>0.14</mn>
<msqrt>
<mrow>
<msup>
<mi>&Delta;x</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mi>&Delta;y</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>;</mo>
</mrow>
Wherein, Δ x, Δ y are illustrated respectively in the mesh spacing in plane both direction.
7. according to the method described in claim 1, it is characterised in that the mathematical modeling is asked by finite difference calculus
Solution, obtains numerical model.
8. according to the method described in claim 1, it is characterised in that the numerical model is solved using implicit pressure explicit saturation method.
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