CN110162737A - The analogy method and its device of unconventional porous media gas flowing - Google Patents
The analogy method and its device of unconventional porous media gas flowing Download PDFInfo
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Abstract
The invention discloses the analogy methods and its device of a kind of unconventional porous media gas flowing, it is related to oil and gas development numerical simulation technology field, the following steps are included: the porosity based on the porous media of joint network structure in gas reservoir, the porosity of the porous media of matrix structure in gas reservoir, the permeability of the porous media of joint network structure in gas reservoir, the permeability of the porous media of matrix structure in gas reservoir, the gas density of matrix structure in gas reservoir, the gas density of joint network structure in gas reservoir, the aerodynamic force viscosity of matrix structure in gas reservoir, the aerodynamic force viscosity etc. of joint network structure obtains the flow equation group of unconventional gas reservoir individual well gas production in gas reservoir；Etc..The application can carry out efficiently healthy and strong numerical simulation for gas flowing in unconventional porous media, overcome the problems, such as that non-conservation and the robustness of conventional method are poor, it is particularly suitable for " dessert " regional prediction, to instruct the determination of drilling well position in engineering, it is ensured that the high-efficiency mining of gas in the success of drilling well and gas reservoir.
Description
Technical field
The present invention relates to oil and gas development numerical simulation technology field, in particular to a kind of unconventional porous media gas flowing
Analogy method and its device.
Background technique
With the worsening shortages of conventional oil natural gas resource, unconventional oil and gas due to its recoverable reserves is huge and increasingly
Paid attention to.However, exploiting difficulty and cost since unconventional petroleum resources are normally in complicated porous media
Much higher than conventional gas and oil resource.If not precisely prediction unconventional oil and gas rich region (" dessert " region) in advance, it is more likely that
So that the well head bored is in non-" dessert " region, to cause the exploitative significant wastage of drilling well.Therefore, for unconventional
Oil gas before exploitation it is necessary to carry out accurate " dessert " regional prediction, that this is just depended on is accurate, efficient, robustness is strong numerical value
Analogy method.
For nontraditional reservoir, the double osmole types of diplopore are more common, available analysis in some simple cases
Numerical solution under solution and more complex operating condition.For unconventional gas reservoir, effective method for numerical simulation there is no at present, reason is such as
Under: (1) oil in oil reservoir be incompressible fluid, density is constant, be accordingly used in the equation of numerical simulation be it is linear, be easy to
Obtain analytic solution and the stronger numerical solution of robustness；(2) natural gas in gas reservoir is compressible fluid, and density is with pressure, temperature
Degree has complicated non-linear relation, cause equation for simulating be it is nonlinear, analytic solution can not be acquired, numerical solution
Robustness is greatly reduced.Based on above-mentioned two o'clock reason, traditional method for numerical simulation will lead to no physical significance or inaccurate
It is true as a result, cannot be used directly for the numerical simulation that gas flows in unconventional gas reservoir.Therefore, the need based on Practical Project exploitation
It wants, it is necessary to develop a kind of efficient healthy and strong method for numerical simulation suitable for unconventional gas reservoir, fills up current method blank, from
It and is preferably " dessert " regional prediction in engineering, and then achieve the purpose that efficient gas production.
The invention proposes the efficient healthy and strong method for numerical simulation for gas flowing in unconventional porous media, overcome
The problem of non-conservation and the robustness difference of conventional method is further used for dessert prediction, can instruct drilling well position in engineering
Determination, it is ensured that the high-efficiency mining of gas in the success of drilling well and gas reservoir.
Summary of the invention
In order to overcome the drawbacks described above of the prior art, the technical problem to be solved is that provide one kind for the embodiment of the present invention
The analogy method and its device of unconventional porous media gas flowing, can be flowed for gas in unconventional porous media into
The efficiently healthy and strong numerical simulation of row, overcomes the problems, such as that the non-conservation of conventional method and robustness are poor, is particularly suitable for " dessert " region
Prediction, to instruct the determination of drilling well position in engineering, it is ensured that the high-efficiency mining of gas in the success of drilling well and gas reservoir.
The specific technical solution of the embodiment of the present invention is:
A kind of analogy method of unconventional porous media gas flowing, comprising the following steps:
Hole based on the porous media of matrix structure in the porosity of the porous media of joint network structure in gas reservoir, gas reservoir
The permeability of the porous media of joint network structure in rate, gas reservoir, the permeability of the porous media of matrix structure in gas reservoir, base in gas reservoir
The gas density of joint network structure in the gas density of matter structure, gas reservoir, the aerodynamic force viscosity of matrix structure in gas reservoir, in gas reservoir
The gas pressure of matrix structure in the aerodynamic force viscosity of joint network structure, gas reservoir, in gas reservoir joint network structure gas pressure, gas reservoir
The gas velocity vectors of joint network structure, the form factor of seam net, bottom pressure in the gas velocity vectors of interior matrix structure, gas reservoir
Obtain the flow equation group of unconventional gas reservoir individual well gas production；
The flow equation group of the unconventional gas reservoir individual well gas production is carried out discrete to obtain discrete equation on staggered-mesh
Group；
It is adopted equal to remaining gaseous mass in last moment gas reservoir with from gas reservoir according to the gas gross mass at each moment
The sum of gaseous mass out obtains mass-conservation equation, and then obtains the n-th moment Medium Culture gaseous mass, the (n+1)th moment base again
Gaseous mass, the gaseous mass of extraction in gaseous mass, the n-th moment seam net interior gaseous mass in matter, the (n+1)th moment seam is netted；
Medium Culture gaseous mass is inscribed when obtaining each according to conservation of mass principle and seam nets the balance side of interior gaseous mass
Journey group；
Matrix average pressure, seam net average pressure in the discrete equation group is modified to obtain revised equation
Group；
Based on it is each when inscribe Medium Culture gaseous mass and seam net in gaseous mass equilibrium equation group, the n-th moment matrix
Gas in interior gaseous mass, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam net interior gaseous mass, the (n+1)th moment seam is netted
The mass balance relational expression of gas in quality, the gaseous mass of extraction obtain the mass balance relational expression of Medium Culture gas, seam is netted；
It is closed according to the mass balance that revised equation group, the mass balance relational expression of Medium Culture gas, seam net interior gas
It is that formula obtains additional equation, additional equation is solved to obtain the average pressure of Medium Culture, stitches the average pressure in net.
Preferably, the governing equation group of unconventional gas reservoir individual well gas production is specific as follows:
Gas density and pressure, there are following relationships for temperature:
The flow equation group of unconventional gas reservoir individual well gas production is obtained according to above-mentioned formula, specific as follows:
Wherein, φ indicates the porosity of porous media, and k indicates the permeability of porous media, and ρ indicates gas density, and μ is indicated
Aerodynamic force viscosity, p indicate that gas pressure, u indicate that gas velocity vectors, subscript M indicate matrix structure in gas reservoir, subscript F table
Show joint network structure in gas reservoir, δwIndicate pithead position flag parameters, value be 0 indicate no well head, be 1 to indicate well head, pbhTable
Show that bottom pressure, α indicate the form factor of seam net, Lx indicates crack in the average headway in the direction x, and Ly indicates crack in the direction y
Average headway, CwIndicate well head constant, rwIndicate well head radius, re=0.20788h indicates that equivalent well head radius, h indicate well
The size of gas reservoir grid, k where mouthfulMThe matrix permeability and k of local gas reservoir where indicating well headFLocal gas where indicating well head
The seam net permeability of hiding, W indicate that molecular weight gas, R indicate universal gas constant, and T is to indicate gas temperature, kxxM、kyyMIt indicates
Two components of matrix permeability tensor, kxxF、kyyFIndicate two components of seam net permeability tensor.
Preferably, the flow equation group of the unconventional gas reservoir individual well gas production is carried out on staggered-mesh in step discrete
Obtain in discrete equation group, the two equations can be carried out on staggered-mesh with finite difference calculus it is discrete, obtain it is following from
Dissipate equation group:
Wherein,
Wherein, i, j indicate any one grid node, i.e., are i-th of node, in the direction y are j-th of node in the direction x；
kxxM、kyyMRespectively indicate two components of matrix permeability tensor in two directions；kxxF、kyyFRespectively indicate seam net permeability
Two components of tensor in two directions；Δ t indicates time step, and Δ x indicates that spatial mesh size in the x direction, Δ y indicate
Spatial mesh size in y-direction, u and v indicate that two components of velocity vector u, nx indicate that the grid number in the direction x, ny indicate the side y
To grid number, subscript n indicates current time step, and n+1 indicates next time step.
Preferably, remaining gaseous mass in last moment gas reservoir is equal to according to the gas gross mass at each moment in step
It is obtained in mass-conservation equation with from the sum of the gaseous mass produced in gas reservoir, detailed process is as follows:
And then obtain again the n-th moment Medium Culture gaseous mass, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam net in
Gaseous mass, the (n+1)th moment stitch gaseous mass in net, in the gaseous mass of extraction, specific as follows:
Wherein, mM (n)Indicate the n-th moment Medium Culture gaseous mass, mM (n+1)Indicate the (n+1)th moment Medium Culture gaseous mass, mF (n)Indicate that the n-th moment seam nets interior gaseous mass, mF (n+1)Indicate that the (n+1)th moment seam nets interior gaseous mass, mQ (n+1)When indicating (n+1)th
The gaseous mass of extraction is carved,Indicate the average value of Medium Culture gas pressure when (n+1)th time step,Indicate (n+1)th
Seam nets the average value of interior gas pressure when a time step,Indicate being averaged for Medium Culture gas pressure when (n+1)th time step
Value,Indicate the average value of gas pressure in seam net when (n+1)th time step.
Preferably, Medium Culture gaseous mass is inscribed when step obtains each according to conservation of mass principle and seam nets interior gas
In the equilibrium equation group of quality, each moment matrix and seam net need to meet following mass balance relationship:
Wherein,
Wherein, mTIndicate that each moment leaves the gaseous mass that matrix enters seam net；mMIndicate Medium Culture gaseous mass, mF
Indicate that the n-th moment seam nets interior gaseous mass, mQIndicate the gaseous mass of extraction, subscript n indicates current time step, and n+1 is indicated
Next time step.
Preferably, matrix average pressure, the seam net average pressure in the discrete equation group are modified in step
Into revised equation group, detailed process is as follows:
Wherein,It indicates to be i-th of node, in the direction y be at j-th of node in the direction x in former discrete equation group
Matrix pressure,It indicates to be i-th of node, in the direction y be the seam net at j-th of node in the direction x in former discrete equation group
Pressure,Indicate former discrete equation group mesostroma average pressure,It indicates to stitch net average pressure, p in former discrete equation groupMi,j
It is i-th of node, in the direction y is the matrix pressure at j-th of node, p in the direction x after indicates amendmentFi,jIt indicates after correcting in x
Direction is i-th of node, in the direction y is the seam network pressure power at j-th of node,Indicate revised matrix average pressure,Indicate revised seam net average pressure.
Preferably, step based on it is each when inscribe Medium Culture gaseous mass and seam net in gaseous mass equilibrium equation
Group, the n-th moment Medium Culture gaseous mass, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam net interior gaseous mass, (n+1)th
Gas in moment seam nets interior gaseous mass, the gaseous mass of extraction obtains the mass balance relational expression of Medium Culture gas, seam is netted
In mass balance relational expression, the mass balance relational expression of gas, seam net the mass balance relational expression of interior gas such as in actual substrate
Under:
Preferably, the gas in step is netted according to revised equation group, the mass balance relational expression of Medium Culture gas, seam
Mass balance relational expression obtain additional equation, solved to obtain the average pressure of Medium Culture, in seam net to additional equation
In average pressure, revised equation group is substituted into the mass balance relational expression of Medium Culture gas, the quality of the interior gas of seam net is put down
Weighing apparatus relational expression obtains additional equation, and additional equation is specific as follows:
Above-mentioned additional equation is solved to obtain the average pressure of Medium Culture, stitches the average pressure in net.
Preferably, to the source item S=- δ in the flow equation group of unconventional gas reservoir individual well gas productionwCwpF(pF-pbh) carry out office
Portion's linear optimization, willSubstitute the source of discrete form
?Therefore, one of equation changes in discrete equation group are as follows:
A kind of simulator of unconventional porous media gas flowing, including memory and processor store in memory
Computer program, the computer program are performed the steps of when being executed by the processor as any of the above-described described non-
The analogy method of Conventional porous dielectric gas flowing.
Technical solution of the present invention have it is following significant the utility model has the advantages that
It should present application addresses be unsatisfactory for the conservation of mass and main diagonal dominance in conventional method and the non-physical simulation of bring
As a result the problem of serious distortion, the simulation robustness and precision for the flowing of unconventional porous media gas greatly improved, make
It obtains and the gas production process progress analog simulation of unconventional gas reservoir is possibly realized.With method provided in the application, success
Realize " dessert " prediction of unconventional gas reservoir, this method have the advantages that it is healthy and strong with it is high-precision, can effectively be mentioned in engineering
High drilling well hit rate improves gas production efficiency.
Referring to following description and accompanying drawings, only certain exemplary embodiments of this invention is disclosed in detail, specifies original of the invention
Reason can be in a manner of adopted.It should be understood that embodiments of the present invention are not so limited in range.In appended power
In the range of the spirit and terms that benefit requires, embodiments of the present invention include many changes, modifications and are equal.For a kind of reality
The feature that the mode of applying is described and/or shown can be made in one or more other embodiments in a manner of same or similar
With, be combined with the feature in other embodiment, or substitution other embodiment in feature.
Detailed description of the invention
Attached drawing described here is only used for task of explanation, and is not intended to limit model disclosed by the invention in any way
It encloses.In addition, shape and proportional sizes of each component in figure etc. are only schematical, it is used to help the understanding of the present invention, and
It is not the specific shape and proportional sizes for limiting each component of the present invention.Those skilled in the art under the teachings of the present invention, can
Implement the present invention to select various possible shapes and proportional sizes as the case may be.
Fig. 1 is the step flow chart of the analogy method of unconventional porous media gas flowing in the embodiment of the present invention；
Fig. 2 is unconventional gas reservoir gas production design conditions schematic diagram in the embodiment of the present invention；
Fig. 3 is the seam network pressure power at conventional method well head；
Fig. 4 is that conventional method gaseous mass conservation examines schematic diagram；
Fig. 5 is that gaseous mass conservation examines schematic diagram in the embodiment of the present invention；
Fig. 6 is to stitch network pressure power in the embodiment of the present invention at revised well head with the schematic diagram of gas production number of days；
Fig. 7 a is the schematic diagram of pithead position 1；
Fig. 7 b is the schematic diagram of pithead position 2；
Fig. 7 c is the schematic diagram of pithead position 3；
Fig. 7 d is the schematic diagram of pithead position 4；
Fig. 8 is the schematic diagram that the seam network pressure power in the embodiment of the present invention at different pithead positions changes over time；
The signal that Fig. 9 changes over time for residual gas quality in the gas reservoir at pithead positions different in the embodiment of the present invention
Figure；
Figure 10 is the signal that the accumulative extraction gaseous mass in the embodiment of the present invention at different pithead positions changes over time
Figure.
Specific embodiment
With reference to the drawings and the description of the specific embodiments of the present invention, details of the invention can clearly be understood.But
It is the specific embodiment of invention described herein, purpose for explaining only the invention, and cannot understand in any way
At being limitation of the present invention.Under the teachings of the present invention, technical staff is contemplated that based on any possible change of the invention
Shape, these are regarded as belonging to the scope of the present invention.It should be noted that when element is referred to as " being set to " another yuan
Part, it can directly on the other element or there may also be elements placed in the middle.When an element is considered as " connection "
Another element, it can be directly to another element or may be simultaneously present centering elements.Term " installation ",
" connected ", " connection " shall be understood in a broad sense, for example, it may be mechanical connection or electrical connection, are also possible to inside two elements
Connection, can be directly connected, can also indirectly connected through an intermediary, for the ordinary skill in the art,
The concrete meaning of above-mentioned term can be understood as the case may be.Term as used herein " vertical ", " horizontal ",
"upper", "lower", "left", "right" and similar statement for illustrative purposes only, are not meant to be the only embodiment.
Unless otherwise defined, all technical and scientific terms used herein and the technical field for belonging to the application
The normally understood meaning of technical staff is identical.The term used in the description of the present application is intended merely to description tool herein
The purpose of the embodiment of body, it is not intended that in limitation the application.Term as used herein "and/or" includes one or more
Any and all combinations of relevant listed item.
In order to carry out efficiently healthy and strong numerical simulation for gas flowing in unconventional porous media, conventional method is overcome
Non-conservation and robustness difference problem, " dessert " regional prediction is particularly suitable for, to instruct in engineering drilling well position really
It is fixed, it is ensured that the high-efficiency mining of gas in the success of drilling well and gas reservoir proposes a kind of unconventional porous media gas in this application
The analogy method of body flowing, as shown in Figure 1, the analogy method of the unconventional porous media gas flowing may include following step
It is rapid:
S101: based on the porous media of matrix structure in the porosity of the porous media of joint network structure in gas reservoir, gas reservoir
The permeability of the porous media of joint network structure in porosity, gas reservoir, the permeability of the porous media of matrix structure, gas reservoir in gas reservoir
The gas density of joint network structure in the gas density of interior matrix structure, gas reservoir, in gas reservoir matrix structure aerodynamic force viscosity, gas
The aerodynamic force viscosity of joint network structure in hiding, the gas pressure of matrix structure in gas reservoir, the gas pressure of joint network structure in gas reservoir,
Gas velocity vectors of matrix structure in gas reservoir, the gas velocity vectors of joint network structure, the form factor of seam net, shaft bottom in gas reservoir
Pressure obtains the flow equation group of unconventional gas reservoir individual well gas production.
In this step, the governing equation group of unconventional gas reservoir individual well gas production is specific as follows:
Due to the compressibility of gas, gas density and pressure, there are following relationships for temperature:
It brings formula (3)-(8) into formula (1) and (2) obtains the flow equation group of unconventional gas reservoir individual well gas production, specifically
It is as follows:
Wherein, φ indicates the porosity of porous media, and k indicates the permeability of porous media, and ρ indicates gas density, and μ is indicated
Aerodynamic force viscosity, p indicate that gas pressure, u indicate that gas velocity vectors, subscript M indicate matrix structure in gas reservoir, subscript F table
Show joint network structure in gas reservoir, δwIndicate pithead position flag parameters, value be 0 indicate no well head, be 1 to indicate well head, pbhTable
Show that bottom pressure, α indicate the form factor of seam net, Lx indicates crack in the average headway in the direction x, and Ly indicates crack in the direction y
Average headway, CwIndicate well head constant, rwIndicate well head radius, re=0.20788h indicates that equivalent well head radius, h indicate well
The size of gas reservoir grid, k where mouthfulMThe matrix permeability and k of local gas reservoir where indicating well headFLocal gas where indicating well head
The seam net permeability of hiding, W indicate that molecular weight gas, R indicate universal gas constant, and T is to indicate gas temperature, kxxM、kyyMIt indicates
Two components of matrix permeability tensor, kxxF、kyyFIndicate two components of seam net permeability tensor.
S102: to the flow equation group of the unconventional gas reservoir individual well gas production carried out on staggered-mesh it is discrete obtain it is discrete
Equation group.
In this step, with finite difference calculus to two equations in the flow equation group of unconventional gas reservoir individual well gas production
Carried out on staggered-mesh discrete, to obtain following discrete equation group, the purpose of following discrete equation groups is to solve base
Matter pressure pMAnd pF:
Wherein,
Wherein, i, j indicate any one grid node, i.e., are i-th of node, in the direction y are j-th of node in the direction x；
kxxM、kyyMRespectively indicate two components of matrix permeability tensor in two directions；kxxF、kyyFRespectively indicate seam net permeability
Two components of tensor in two directions；Δ t indicates time step, and Δ x indicates that spatial mesh size in the x direction, Δ y indicate
Spatial mesh size in y-direction, u and v indicate that two components of velocity vector u, nx indicate that the grid number in the direction x, ny indicate the side y
To grid number, subscript n indicates current time step, and n+1 indicates next time step.
Fig. 2 is unconventional gas reservoir gas production design conditions schematic diagram in the embodiment of the present invention, as shown in Fig. 2, shown in Fig. 2
In unconventional gas reservoir, above-mentioned discrete equation group is solved, calculating parameter is shown in Table 1.Simulate the well head pressure variation feelings of gas production 100 days
Condition.Fig. 3 is the seam network pressure power at conventional method well head, and as shown in Figure 3: well head pressure is negative value, illustrates the gas production from gas reservoir
Process is mistakenly simulated, because of either gas production or gas injection, pressure can not reach vacuum state.In fact, true
Gas production process should be that seam network pressure power at well head is greater than bottom pressure, i.e. pF>pbh(pbh=202650Pa in table 1).Cause
This, has obtained non-physical result using the calculation method of traditional S01 and S102 step, it is clear that it is actual to be unable to true reappearance
Gas production process.
1 calculating parameter of table
Note: 1md=9.8692327 × 10-16m2。
S103: according to the gas gross mass at each moment be equal in last moment gas reservoir remaining gaseous mass with from gas reservoir
The sum of the gaseous mass of middle extraction obtains mass-conservation equation, and then when obtaining the n-th moment Medium Culture gaseous mass, (n+1)th again
Carve Medium Culture gaseous mass, the n-th moment stitched gaseous mass in net, the (n+1)th moment seam nets interior gaseous mass, the gas matter of extraction
Amount.
In order to find and analyze the defect of the prior art, examines calculate gas gross mass and Theoretical gas in this application
The difference of gross mass.For theoretically, the sum of residual gas quality and extraction gaseous mass in entire gas production process in gas reservoir
It should remain unchanged, that is, meet general adaptating law --- the conservation of mass of nature.That is, when meeting the conservation of mass, it is any
Gas gross mass when the gas gross mass at moment should be equal to initial time non-gas production in gas reservoir, i.e. Theoretical gas gross mass are as follows:
Wherein, mM0Indicate the gaseous mass that initial time Medium Culture contains, mF0Indicate the gas contained in initial time seam net
Weight,Indicate the density that Medium Culture gas is carved at the beginning,Indicate that seam nets the density that interior gas is carved at the beginning,
VMi,jIndicate the volume of Medium Culture gas, VFi,jIndicate that seam nets the volume of interior gas,Indicate the gas pressure of Medium Culture,
Indicate the gas pressure in seam net.
In calculating gas production process, remaining gas in last moment gas reservoir is equal to according to the gas gross mass at each moment
Quality and the sum of the gaseous mass produced from gas reservoir obtain mass-conservation equation, and detailed process is as follows:
And then obtain again the n-th moment Medium Culture gaseous mass, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam net in
Gaseous mass, the (n+1)th moment stitch gaseous mass in net, in the gaseous mass of extraction, specific as follows:
Wherein, mM (n)Indicate the n-th moment Medium Culture gaseous mass, mM (n+1)Indicate the (n+1)th moment Medium Culture gaseous mass, mF (n)Indicate that the n-th moment seam nets interior gaseous mass, mF (n+1)Indicate that the (n+1)th moment seam nets interior gaseous mass, mQ (n+1)Indicate extraction
Gaseous mass,Indicate the average value of Medium Culture gas pressure when (n+1)th time step,Indicate (n+1)th time step
When seam net in gas pressure average value,Indicate the average value of Medium Culture gas pressure when (n+1)th time step,Table
Seam nets the average value of interior gas pressure when showing (n+1)th time step.
According to the calculating parameter in table 1, respectively obtain in entire calculating process, the theoretical gross mass (formula (13)) of gas with
Calculate gross mass (formula (14)), Fig. 4 be conventional method gaseous mass conservation examine schematic diagram, as shown in Figure 4, it is clear that calculating matter
Amount is not obviously inconsistent with Theoretical Mass, in the entire gas production process of simulation, calculates quality well below Theoretical Mass, illustrates counting
Artificial quality has occurred during calculating to lose, mass conservation law is no longer abided by.This be cause to obtain in the prior art it is non-
Physical result and can not one of the practical gas production of real simulation the reason of flowing this defect.Further analysis equation (11) and equation
(12) coefficient in, as shown in table 2, it is known that equation group is unsatisfactory for main diagonally dominant codition.According to the knowledge of linear algebra, only
Having equation group to meet main diagonal dominance just can guarantee the convergence solution that can centainly acquire physical significance, otherwise may cause and does not restrain
Or the solution of non-physical meaning.Therefore, find that not can guarantee main diagonal dominance in the technology is also that it calculates failure in application
Another major reason.
The main Research On Diagonal Dominance of 2 conventional method of table is examined
Note: data are shown
In this application, in order in view of the above technology the problem of non-conservation of mass, the problem known to formula (14) be by
Incorrect matrix average pressureWith seam net average pressureIt is caused, it is therefore desirable to which that the two average pressures are repaired
Just.
S104: matrix average pressure, the seam net average pressure in the discrete equation group are modified after obtaining amendment
Equation group, and then correct every bit instantaneous pressure, detailed process is as follows:
Wherein,It indicates to be i-th of node, in the direction y be at j-th of node in the direction x in former discrete equation group
Matrix pressure,It indicates to be i-th of node, in the direction y be the seam net at j-th of node in the direction x in former discrete equation group
Pressure,Indicate former discrete equation group mesostroma average pressure,It indicates to stitch net average pressure, p in former discrete equation groupMi,j
It is i-th of node, in the direction y is the matrix pressure at j-th of node, p in the direction x after indicates amendmentFi,jIt indicates after correcting in x
Direction is i-th of node, in the direction y is the seam network pressure power at j-th of node,Indicate revised matrix average pressure,Indicate revised seam net average pressure.
By above-mentioned revised equation group as it can be seen that correct p in order to obtainMAnd pF, it is necessary to acquire correct average pressureWith
S105: inscribing Medium Culture gaseous mass when obtaining each according to conservation of mass principle and seam nets the flat of interior gaseous mass
Weigh equation group.
In this step, from the conservation of mass: each moment Medium Culture gaseous mass and seam are netted interior gaseous mass and need to be expired
It is enough lower mass balance relationship:
Wherein,Wherein, mT
Indicate that each moment leaves the gaseous mass that matrix enters seam net；mMIndicate Medium Culture gaseous mass, mFIndicate that the n-th moment stitched net
Interior gaseous mass, mQIndicate the gaseous mass of extraction, subscript n indicates current time step, and n+1 indicates next time step.
S106: based on it is each when inscribe Medium Culture gaseous mass and seam net in the equilibrium equation group of gaseous mass, the n-th moment
In Medium Culture gaseous mass, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam net interior gaseous mass, the (n+1)th moment seam is netted
The mass balance of gas is closed in gaseous mass, the gaseous mass of extraction obtain the mass balance relational expression of Medium Culture gas, seam is netted
It is formula.
In this step, by the mass balance relational expression of formula (17) to (24) available Medium Culture gas, seam net
The mass balance relational expression of gas, specific as follows:
S107: the quality for netting interior gas according to revised equation group, the mass balance relational expression of Medium Culture gas, seam is flat
Weighing apparatus relational expression obtains additional equation, is solved to obtain the average pressure of Medium Culture to additional equation, stitches the average pressure in net.
In this step, revised equation group is substituted into the mass balance relational expression of Medium Culture gas, seam nets interior gas
Mass balance relational expression obtain additional equation, additional equation is specific as follows:
Above-mentioned additional equation is solved to obtain the correct average pressure of Medium CultureAverage pressure in seam netWhen acquiring the correct average pressure of Medium CultureAverage pressure in seam netAfter, it can be by the two parameters
In generation, is back to revised equation group, i.e. formula (15) and formula (16), thus correct matrix pressure p after being correctedMi,jWith seam net
Pressure pFi,j；Pass through matrix pressure p correct after amendmentMi,jWith seam net pressure pFi,jReasonable discrete equation group is solved,
Correctly to simulate unconventional porous media gas flowing, thus the actual gas reservoir gas production process of true reappearance.
In a preferred embodiment, aiming at the problem that being unsatisfactory for main diagonal dominance, to unconventional gas reservoir single well
Source item S=- δ in the flow equation group of gaswCwpF(pF-pbh) local linear optimization is carried out, it willSubstitute the source item of discrete formTherefore, one of equation in discrete equation group, i.e. equation (12) change are as follows:
Above-mentioned technical proposal in the application is used to calculate gas recovery shown in Fig. 2 and table 1, Fig. 5 is that the present invention is real
It applies gaseous mass conservation in example and examines schematic diagram, as shown in Figure 5, it is known that the calculating gross mass of gas is entirely up to 800 days
It is consistent with theoretical calculation gross mass always in gas production simulation process, it is shown that good conservation of mass characteristic, in addition seen from table 3
The property of main diagonal dominance has also obtained meeting well.Fig. 6 is to stitch network pressure power in the embodiment of the present invention at revised well head
With the schematic diagram of gas production number of days, Fig. 6 shows that the seam network pressure power at well head is consistently greater than bottom pressure, and with gas production process
It carries out monotonic decreasing finally to tend to be steady, has reproduced the actual pressure variation in engineering well.Therefore, this series of results is said
What bright the application was proposed, which meets the conservation of mass and the new algorithm of main diagonal dominance, has good robustness and very high precision,
The gas flowing law being suitble in the unconventional porous media of simulation can be utilized for dessert prediction.
Fig. 7 a is the schematic diagram of pithead position 1, and Fig. 7 b is the schematic diagram of pithead position 2, and Fig. 7 c is the signal of pithead position 3
Figure, Fig. 7 d is the schematic diagram of pithead position 4, and as shown in Fig. 7 a to 7d, listed 4 kinds of typical well head arrangements, are used in figure
Method in the application has carried out numerical simulation, obtains seam network pressure power at well head, residual gas quality, accumulative extraction gas in gas reservoir
These three key results of weight.Fig. 8 is that the seam network pressure power in the embodiment of the present invention at different pithead positions changes over time
Schematic diagram, as shown in figure 8, it shows that the seam network pressure power of pithead position 1 and 2 is identical, the seam network pressure power of pithead position 3 and 4 is identical,
But it is both rear to be apparently higher than the above two.Pithead position 1 and 2 stitches the decline of network pressure power faster in the same time, when illustrating unit
It is interior to produce more gas, it is more advantageous to and improves gas production efficiency.Fig. 9 is in the embodiment of the present invention at different pithead positions
The schematic diagram that residual gas quality changes over time in gas reservoir, Figure 10 are accumulative at different pithead positions in the embodiment of the present invention
The schematic diagram that changes over time of extraction gaseous mass, show in Fig. 9 in same time less gas reservoir residual gas quality and
The more accumulative gas productions shown in Figure 10 also all illustrate that the certain gas production efficiency of pithead position 1 and 2 is higher than 3 He of pithead position
4, therefore the two positions are gas production " dessert ".Meanwhile the above results also illustrate that well head is located at " sweet tea with when " dessert " is interior
Still on gas production efficiency without influence, this just gives the raising gas production working efficiency in engineering at edge (position 2) at point " center (position 1)
Convenience is brought, as long as well head is beaten in " dessert " area inside, is scheduled on " dessert " district center without one.In addition, even if well head
It is located close to the perimeter in " dessert " area, as shown in Figure 7 c, gas production efficiency can also be greatly reduced, as shown in Fig. 8 to Figure 10, because
Pay attention to well head cannot being beaten outside " dessert " area as far as possible in this Practical Project.
The analogy method of unconventional porous media gas flowing is when calculating matrix and seam network pressure power in the application, using flat
Equal pressure carries out pressure correction to both to promote the conservation of mass of algorithm；Secondly, according to gas in unconventional porous media
The mass transport feature of flowing lists the mass balance relationship of gas in matrix and seam net for each moment respectively；And it will
The mass balance relational expression of gas is in revised equation group brings the mass balance relational expression of Medium Culture gas into, seam is netted to obtain
To calculating matrix average pressure and stitching the additional equation group of net average pressure, correct mean pressure is acquired by solving equation group
Power, to finally realize pressure correction and meet the conservation of mass；Finally also using source item local linearization the well head in equation
Gas production item carries out local linearization, to ensure that main diagonal dominance.Present application addresses be unsatisfactory for quality in conventional method for this
Conservation and main diagonal dominance and the problem of bring non-physical analog result serious distortion, greatly improved for unconventional porous
The simulation robustness and precision of dielectric gas flowing, so that becoming for the gas production process progress analog simulation of unconventional gas reservoir can
Energy.With method provided in the application, be successfully realized " dessert " prediction of unconventional gas reservoir, this method have it is healthy and strong and
High-precision advantage can effectively improve drilling well hit rate in engineering, improve gas production efficiency.
It also proposed a kind of simulator of unconventional porous media gas flowing, including memory and processing in the application
Device stores computer program in memory, the computer program when being executed by the processor, perform the steps of as
The analogy method of any of the above-described unconventional porous media gas flowing.
In the present embodiment, the memory may include the physical unit for storing information, usually by information
It is stored again with the media using the methods of electricity, magnetic or optics after digitlization.Memory described in present embodiment again may be used
To include: to store the device of information, such as RAM, ROM in the way of electric energy；The device of information is stored in the way of magnetic energy, it is such as hard
Disk, floppy disk, tape, core memory, magnetic bubble memory, USB flash disk；Using the device of optical mode storage information, such as CD or DVD.
Certainly, there are also memories of other modes, such as quantum memory, graphene memory etc..In the present embodiment, described
Processor can be implemented in any suitable manner.For example, the processor can take such as microprocessor or processor with
And storage can be by computer-readable Jie of the computer readable program code (such as software or firmware) of (micro-) processor execution
Matter, logic gate, switch, specific integrated circuit (Application Specific Integrated Circuit, ASIC), can
The form etc. of programmed logic controller and insertion microcontroller.The server that this specification embodiment provides, processor
The concrete function realized with memory, can contrast explanation with the aforementioned embodiments in this specification.
All the embodiments in this specification are described in a progressive manner, the highlights of each of the examples are with
The difference of other embodiments, the same or similar parts between the embodiments can be referred to each other.Above-described embodiment is only
Illustrate technical concepts and features of the invention, its object is to those skilled in the art can understand the contents of the present invention
And implement accordingly, it is not intended to limit the scope of the present invention.Equivalence changes made by all Spirit Essences according to the present invention
Or modification, it should be covered by the protection scope of the present invention.
Claims (10)
1. a kind of analogy method of unconventional porous media gas flowing, which comprises the following steps:
Based on the porosity of the porous media of matrix structure, gas in the porosity of the porous media of joint network structure in gas reservoir, gas reservoir
The permeability of porous media of joint network structure in hiding, the permeability of the porous media of matrix structure in gas reservoir, matrix knot in gas reservoir
The gas density of joint network structure in the gas density of structure, gas reservoir, in gas reservoir matrix structure aerodynamic force viscosity, gas reservoir inseam net
The gas pressure of matrix structure in the aerodynamic force viscosity of structure, gas reservoir, base in the gas pressure, gas reservoir of joint network structure in gas reservoir
The gas velocity vectors of joint network structure, the form factor of seam net, bottom pressure obtain in the gas velocity vectors of matter structure, gas reservoir
The flow equation group of unconventional gas reservoir individual well gas production；
The flow equation group of the unconventional gas reservoir individual well gas production is carried out discrete to obtain discrete equation group on staggered-mesh；
It is produced equal to remaining gaseous mass in last moment gas reservoir and from gas reservoir according to the gas gross mass at each moment
The sum of gaseous mass obtains mass-conservation equation, and then obtains the n-th moment Medium Culture gaseous mass, the (n+1)th moment Medium Culture again
Gaseous mass, the gaseous mass of extraction in gaseous mass, the n-th moment seam net interior gaseous mass, the (n+1)th moment seam is netted；
Medium Culture gaseous mass is inscribed when obtaining each according to conservation of mass principle and seam nets the equilibrium equation group of interior gaseous mass；
Matrix average pressure, seam net average pressure in the discrete equation group is modified to obtain revised equation group；
Based on it is each when inscribe Medium Culture gaseous mass and seam net in the equilibrium equation group of gaseous mass, the n-th moment Medium Culture gas
Weight, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam net interior gaseous mass, the (n+1)th moment stitched gaseous mass in net,
The mass balance relational expression of gas in the gaseous mass of extraction obtains the mass balance relational expression of Medium Culture gas, seam is netted；
The mass balance relational expression of interior gas is netted according to revised equation group, the mass balance relational expression of Medium Culture gas, seam
Additional equation is obtained, additional equation is solved to obtain the average pressure of Medium Culture, stitches the average pressure in net.
2. the analogy method of unconventional porous media gas flowing according to claim 1, which is characterized in that unconventional
The governing equation group of gas reservoir individual well gas production is specific as follows:
Gas density and pressure, there are following relationships for temperature:
The flow equation group of unconventional gas reservoir individual well gas production is obtained according to above-mentioned formula, specific as follows:
Wherein, φ indicates the porosity of porous media, and k indicates the permeability of porous media, and ρ indicates gas density, and μ indicates gas
Dynamic viscosity, p indicate that gas pressure, u indicate that gas velocity vectors, subscript M indicate that matrix structure in gas reservoir, subscript F indicate gas
Joint network structure in hiding, δwIndicate pithead position flag parameters, value be 0 indicate no well head, be 1 to indicate well head, pbhIndicate well
Bottom pressure, α indicate the form factor of seam net, and Lx indicates crack in the average headway in the direction x, and Ly indicates crack in the flat of the direction y
Equal spacing, CwIndicate well head constant, rwIndicate well head radius, re=0.20788h indicates that equivalent well head radius, h indicate well head institute
In the size of gas reservoir grid, kMThe matrix permeability and k of local gas reservoir where indicating well headFLocal gas reservoir where indicating well head
Net permeability is stitched, W indicates that molecular weight gas, R indicate universal gas constant, and T is to indicate gas temperature, kxxM、kyyMIndicate matrix
Two components of permeability tensor, kxxF、kyyFIndicate two components of seam net permeability tensor.
3. the analogy method of unconventional porous media gas flowing according to claim 2, which is characterized in that in step
To the flow equation group of the unconventional gas reservoir individual well gas production carried out on staggered-mesh it is discrete obtain in discrete equation group, use
Finite difference calculus can carry out the two equations discrete on staggered-mesh, obtain following discrete equation group:
Wherein,
Wherein, i, j indicate any one grid node, i.e., are i-th of node, in the direction y are j-th of node in the direction x；kxxM、
kyyMRespectively indicate two components of matrix permeability tensor in two directions；kxxF、kyyFRespectively indicate seam net permeability tensor
Two components in two directions；Δ t indicates time step, and Δ x indicates that spatial mesh size in the x direction, Δ y are indicated in y
Spatial mesh size on direction, u and v indicate that two components of velocity vector u, nx indicate that the grid number in the direction x, ny indicate the direction y
Grid number, subscript n indicates current time step, and n+1 indicates next time step.
4. the analogy method of unconventional porous media gas flowing according to claim 3, which is characterized in that in step
It is equal to remaining gaseous mass and the gas produced from gas reservoir in last moment gas reservoir according to the gas gross mass at each moment
Quality sum obtains in mass-conservation equation, and detailed process is as follows:
And then the n-th moment Medium Culture gaseous mass, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam are obtained again and nets interior gas
Quality, the (n+1)th moment stitch gaseous mass in net, in the gaseous mass of extraction, specific as follows:
Wherein, mM (n)Indicate the n-th moment Medium Culture gaseous mass, mM (n+1)Indicate the (n+1)th moment Medium Culture gaseous mass, mF (n)Table
Show that the n-th moment seam nets interior gaseous mass, mF (n+1)Indicate that the (n+1)th moment seam nets interior gaseous mass, mQ (n+1)Indicate that the (n+1)th moment adopted
Gaseous mass out,Indicate the average value of Medium Culture gas pressure when (n+1)th time step,Indicate (n+1)th
Seam nets the average value of interior gas pressure when time step,Indicate the average value of Medium Culture gas pressure when (n+1)th time step,Indicate the average value of gas pressure in seam net when (n+1)th time step.
5. the analogy method of unconventional porous media gas flowing according to claim 4, which is characterized in that in step
Medium Culture gaseous mass is inscribed when obtaining each according to conservation of mass principle and seam is netted in the equilibrium equation group of interior gaseous mass, often
One moment matrix and seam net need to meet following mass balance relationship:
Wherein,
Wherein, mTIndicate that each moment leaves the gaseous mass that matrix enters seam net；mMIndicate Medium Culture gaseous mass, mFIt indicates
N-th moment seam nets interior gaseous mass, mQIndicate the gaseous mass of extraction, subscript n indicates current time step, and n+1 indicates next
Time step.
6. the analogy method of unconventional porous media gas flowing according to claim 5, which is characterized in that in step
Matrix average pressure, seam net average pressure in the discrete equation group is modified to obtain in revised equation group, is had
Body process is as follows:
Wherein,It indicates to be i-th of node, in the direction y be the matrix at j-th of node in the direction x in former discrete equation group
Pressure,It indicates to be i-th of node, in the direction y be the seam network pressure power at j-th of node in the direction x in former discrete equation group,Indicate former discrete equation group mesostroma average pressure,It indicates to stitch net average pressure, p in former discrete equation groupMi,jIt indicates
It is i-th of node, in the direction y is the matrix pressure at j-th of node, p in the direction x after amendmentFi,jIt indicates after correcting in the direction x
It is the seam network pressure power at j-th of node for i-th of node, in the direction y,Indicate revised matrix average pressure,Table
Show revised seam net average pressure.
7. the analogy method of unconventional porous media gas flowing according to claim 6, which is characterized in that in step
Based on it is each when inscribe Medium Culture gaseous mass and seam net in gaseous mass equilibrium equation group, the n-th moment Medium Culture gas matter
Gaseous mass, extraction in amount, the (n+1)th moment Medium Culture gaseous mass, the n-th moment seam net interior gaseous mass, the (n+1)th moment seam is netted
Gaseous mass obtain Medium Culture gas mass balance relational expression, seam net in gas mass balance relational expression in, specific base
The mass balance relational expression of gas, the mass balance relational expression of the interior gas of seam net are as follows in matter:
8. the analogy method of unconventional porous media gas flowing according to claim 7, which is characterized in that in step
It is obtained according to the mass balance relational expression that revised equation group, the mass balance relational expression of Medium Culture gas, seam net interior gas
Additional equation is solved to obtain the average pressure of Medium Culture, be stitched in the average pressure in netting to additional equation, will be revised
The mass balance relational expression of gas obtains additional equation in equation group substitutes into the mass balance relational expression of Medium Culture gas, seam is netted,
Additional equation is specific as follows:
Above-mentioned additional equation is solved to obtain the average pressure of Medium Culture, stitches the average pressure in net.
9. the analogy method of unconventional porous media gas flowing according to claim 3, which is characterized in that very
Advise the source item S=- δ in the flow equation group of gas reservoir individual well gas productionwCwpF(pF-pbh) local linear optimization is carried out, it willSubstitute the source item of discrete formTherefore, one of equation changes in discrete equation group are as follows:
10. a kind of simulator of unconventional porous media gas flowing, which is characterized in that including memory and processor, deposit
Computer program is stored in reservoir, the computer program performs the steps of right such as and want when being executed by the processor
Seek the analogy method of any unconventional porous media gas flowing in 1 to 9.
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