CN108507920A - A kind of analogy method of water-oil phase relative permeability - Google Patents
A kind of analogy method of water-oil phase relative permeability Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 96
- 230000035699 permeability Effects 0.000 title claims abstract description 83
- 239000011148 porous material Substances 0.000 claims abstract description 213
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 123
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- 239000011435 rock Substances 0.000 claims abstract description 21
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- 238000009736 wetting Methods 0.000 claims description 23
- 238000006073 displacement reaction Methods 0.000 claims description 22
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- 239000011159 matrix material Substances 0.000 claims description 13
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- FFBHFFJDDLITSX-UHFFFAOYSA-N benzyl N-[2-hydroxy-4-(3-oxomorpholin-4-yl)phenyl]carbamate Chemical compound OC1=C(NC(=O)OCC2=CC=CC=C2)C=CC(=C1)N1CCOCC1=O FFBHFFJDDLITSX-UHFFFAOYSA-N 0.000 claims description 11
- 238000004364 calculation method Methods 0.000 claims description 6
- 210000000867 larynx Anatomy 0.000 claims description 4
- 238000009738 saturating Methods 0.000 claims 2
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- 239000012071 phase Substances 0.000 description 153
- 238000002474 experimental method Methods 0.000 description 6
- 239000000243 solution Substances 0.000 description 6
- QSHDDOUJBYECFT-UHFFFAOYSA-N mercury Chemical compound [Hg] QSHDDOUJBYECFT-UHFFFAOYSA-N 0.000 description 4
- 229910052753 mercury Inorganic materials 0.000 description 4
- 238000011161 development Methods 0.000 description 3
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- 238000003825 pressing Methods 0.000 description 2
- 239000008346 aqueous phase Substances 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000000205 computational method Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000008595 infiltration Effects 0.000 description 1
- 238000001764 infiltration Methods 0.000 description 1
- 238000002347 injection Methods 0.000 description 1
- 239000007924 injection Substances 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
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- 229920006395 saturated elastomer Polymers 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
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Abstract
The present invention provides a kind of analogy methods of water-oil phase relative permeability comprising following steps：The pore throat data of rock sample are obtained, the pore throat data include the frequency distribution data of pore radius and the frequency distribution data of throat radius；Based on the pore throat data, pore network is built；Water-oil phase fluid-flow analogy criterion is established in the pore network；According to the two-phase fluid flow simulating criterion, implement the flow simulating of two-phase fluid in the pore network, to obtain the pore network water phase relative permeability data and pore network oil relative permeability data under different aperture network water saturation.Technical solution provided by the invention is calculated by carrying out pore network simulation according to pore throat data, is capable of the water-oil phase relative permeability data of quick obtaining rock sample to be measured, it is possible thereby to draw out corresponding water-oil phase permeability saturation curve.
Description
Technical field
The present invention relates to a kind of analogy methods of core sample water-oil phase distribution character, more particularly to a kind of to be based on constant speed
The analogy method for pressing the water-oil phase relative permeability of mercury, belongs to oil recovery technique field.
Background technology
Two-phase relative permeability is to describe the important parameter of water-oil phase seepage flow in oil reservoir, by analyzing water-oil phase phase
Many Production developments of oil reservoir during waterflooding development can be reflected by oozing curve, while in reservoir engineering calculating and Numerical-Mode
It is required for water-oil phase mutually to ooze data during quasi-.
The acquisition methods of water-oil phase permeability saturation curve are specifically divided into mainly by experimental method as stable state at present
Method and cold store enclosure.The analysis object faced with reservoir physics becomes increasingly complex, such as low permeability reservoir and shale, experiment point
Analysis method exposes following deficiency：Experimental period is long or certain rock samples are difficult to carry out stable state and non-stable phase flow experiment,
The water-oil phase phase percolation curve that the caused measurement error of length experimental period also leads to obtain simultaneously is unreliable.
Therefore, it is urgently to be resolved hurrily as art technology how to provide a kind of analogy method of water-oil phase relative permeability
Technical problem.
Invention content
In order to solve the above technical problems, the purpose of the present invention is to provide a kind of simulation sides of water-oil phase relative permeability
Method.This method is based on pore throat data, is calculated by carrying out pore network simulation, is capable of the water-oil phase of quick obtaining rock sample to be measured
Relative permeability data.
In order to achieve the above objectives, the present invention provides a kind of analogy methods of water-oil phase relative permeability comprising with
Lower step：
The pore throat data of rock sample are obtained, the pore throat data include the frequency distribution data and throat radius of pore radius
Frequency distribution data；
Based on the pore throat data, pore network is built；
Water-oil phase fluid-flow analogy criterion is established in the pore network；
According to the two-phase fluid flow simulating criterion, implement the flow simulating of two-phase fluid in the pore network,
It is opposite to obtain pore network water phase relative permeability data under different aperture network water saturation and pore network oil phase
Permeability data.
In the above-mentioned methods, it is preferable that be based on the pore throat data, structure pore network includes following procedure：
Based on the frequency distribution data of the pore radius, assignment processing is carried out to the hole in the pore network；
Based on the frequency distribution data of the throat radius, assignment processing is carried out to the venturi in the pore network.
In the above-mentioned methods, it is preferable that the frequency distribution data based on the pore radius, in the pore network
It includes following procedure that hole, which carries out assignment processing,：
Process 1：Based on the frequency distribution data of the pore radius, the histogram frequency distribution diagram of pore radius is built；
Process 2：On the basis of the histogram frequency distribution diagram of the pore radius, random generation one is fallen in the histogram
The data currently generated at random are assigned to corresponding hole (" the corresponding hole " by the data in middle hole radius distribution value
It is primarily referred to as choosing that hole being assigned when pore network is assigned) it is used as its radius value, and count assignment hole
The number that various radius values occur in gap, once the number that the random radius value being currently generated occurs in assignment hole is more than
The radius frequency of corresponding hole (i.e. foregoing " corresponding hole "), it is determined that the random radius value being currently generated
In vain, a new random radius value is regenerated, until no longer there is the random radius value being currently generated in assignment before
The number occurred in hole is more than this phenomenon of the radius frequency of the hole.
In technical solution provided by the invention, before model calculates, need to the pore network model assignment automatically generated,
Each hole assigns random pore radius value.The radius frequency of corresponding hole can be according to phase in the histogram
The ordinate of hole is answered to determine.
In the above-mentioned methods, it is preferable that the frequency distribution data based on the throat radius, in the pore network
It includes following procedure that venturi, which carries out assignment processing,：
Process 1：Based on the frequency distribution data of the throat radius, the histogram frequency distribution diagram of throat radius is built；
Process 2：On the basis of the histogram frequency distribution diagram of the throat radius, random generation one is fallen in the histogram
The data currently generated at random are assigned to corresponding venturi (" the corresponding venturi " by the data in middle throat radius Distribution Value
It is primarily referred to as choosing that venturi being assigned when pore network is assigned) it is used as its radius value, and count assignment larynx
The number that various radius values occur in road, once the random radius value being currently generated is in the number occurred in assignment venturi before
More than the radius frequency of corresponding venturi (i.e. foregoing " corresponding venturi "), it is determined that random half be currently generated
Diameter value is invalid, regenerates a new random radius value, until no longer there is the random radius value being currently generated before
The number occurred in assignment venturi is more than this phenomenon of the radius frequency of corresponding venturi.
To in pore network hole and venturi carry out assignment after, you can structure meet pore constriction radius frequency distribution
Pore network.Other parameters in pore network can also carry out assignment according to the method described above.
In the above-mentioned methods, it is preferable that water-oil phase fluid-flow analogy criterion is established in the pore network includes
Following procedure：
Displacing front of the pore network in displacement process is obtained, from all venturis being connected with the displacing front
In select the maximum venturi of net pressure as optimal venturi；
By the optimal venturi, and the current state of all holes being connected with the optimal venturi is updated to by non-profit
The state that wetting phase is full of, meanwhile, the current state of the pressure field of the pore network is updated.
In the above-mentioned methods, it is preferable that it includes following mistake to obtain displacing front of the pore network in displacement process
Journey：
All holes that by non-wetted phase are full of of the pore network in displacement process are obtained, these holes constitute
Hole group；
Displacing front of the pore network in displacement process can be obtained according to the hole group.
In the above-mentioned methods, it is preferable that the current state of the pressure field of the pore network is updated including following
Process：
Matrix division shown in an equations simultaneousness accepted way of doing sth 1 for the sum of flow by each hole, and to the Matrix division
It is solved to get to new pressure field
In the equation group shown in formula 1,AndWherein, Ni
The hole collection that expression and hole i are connected directly by venturi around it, rijThe radius of venturi between expression hole i and hole j,
LijThe length of venturi, μ between expression hole i and hole jijThe viscosity of venturi, P between expression hole i and hole jnIndicate hole n
Capillary force, bnIndicate hole n by flow.
In a specific embodiment, the current state of the pressure field of the pore network is updated including following
Process：
First, it is assumed that fluid is incompressible, according to mass conservation law, pass through on the timing node of a flowing stage in office
The sum of volume flow of hole i is 0, as shown in Equation 7
In formula 7, NiThe hole collection that expression and hole i are connected directly by venturi around it, QijExpression formula as depicted in figure 8
In formula 8, rijThe radius of venturi between expression hole i and hole j；LijVenturi between expression hole i and hole j
Length；pcCapillary pressure is indicated, depending on the state parameter of sign the window gap i and hole j of the front, when two hole states
When parameter is identical, the flowing in venturi at this time corresponds to single-phase flow, and capillary pressure directly takes 0；PiIndicate the pressure at hole i；Pj
Indicate the pressure at hole j；μijThe viscosity of venturi between expression hole i and hole j；Negative sign before formula is indicated relative to hole
Fluid flows out for gap i；
Then, the equations simultaneousness of the sum of the flow of each hole is formed into equation group, equation group is as shown in Equation 1：
In formula 1,And
The coefficient matrix of equation group shown in formula 1For symmetric positive definite matrix, therefore
Equation group centainly has solution, solves the Matrix division and can be obtained new pore network pressure field.
As shown in figure 4, in a specific embodiment, water-oil phase fluid flowing mould is established in the pore network
Quasi- criterion includes following procedure：
Process 1：When displacement to a certain stage, which is obtained according to the hole group for the hole composition being full of by non-wetted phase
" displacing front " of section；Wherein, the hole being full of by non-wetted phase is the hole occupied completely by oil phase；
Process 2：All venturis being connected with " displacing front " are marked, for example, yellowly can be marked
Or chain-dotted line form, but not limited to this, these out labeled venturis indicate that venturi is in boundary and faces drive state；
Process 3：It is elected to be optimal venturi from the selection maximum venturi of net pressure in labeled venturi out；The present invention is to quilt
The venturi being marked is analyzed, and is found due to being that row replaces type displacement (i.e. non-wetted phase displacement wetting phase, that is, oil at this time
Driven water-replacing), capillary force shows as resistance, therefore the net pressure in these venturis for being extracted is equal to this displacement stage hole net
The pressure difference that network pressure field acts on venturi both ends subtracts the corresponding hollow billet resistance of venturi, it is clear that the net pressure of venturi is bigger, non-
The easier such venturi of intrusion of wetting phase, therefore the maximum venturi of net pressure in above-mentioned labeled venturi out can be elected to be most
Excellent venturi；
Process 4：The state of the optimal venturi is updated to the shape being full of by non-wetted phase by facing drive state in boundary
State, while the state that the state for all holes being connected with the optimal venturi is full of by wetted phase being updated to non-wetted
The state being mutually full of；
Process 5：The current state of the pressure field of the pore network is updated, process is as follows：
First, it is assumed that fluid is incompressible, according to mass conservation law, pass through on the timing node of a flowing stage in office
The sum of volume flow of hole i is 0, as shown in Equation 7
In formula 7, NiThe hole collection that expression and hole i are connected directly by venturi around it, QijExpression formula as depicted in figure 8
In formula 8, rijThe radius of venturi between expression hole i and hole j；LijVenturi between expression hole i and hole j
Length；pcCapillary pressure is indicated, depending on the state parameter of sign the window gap i and hole j of the front, when two hole states
When parameter is identical, the flowing in venturi at this time corresponds to single-phase flow, and capillary pressure directly takes 0；PiIndicate the pressure at hole i；Pj
Indicate the pressure at hole j；μijThe viscosity of venturi between expression hole i and hole j；Negative sign before formula is indicated relative to hole
Fluid flows out for gap i；
Then, the equations simultaneousness of the sum of the flow of each hole is formed into equation group, equation group is as shown in Equation 1：
In formula 1,And
The coefficient matrix of equation group shown in formula 1For symmetric positive definite matrix, therefore should
Equation group centainly has solution, solves the Matrix division and can be obtained new pore network pressure field.
In the above-mentioned methods, it is preferable that according to the two-phase fluid flow simulating criterion, implement in the pore network
The flow simulating of two-phase fluid, to obtain the pore network water phase relative permeability data under different aperture network water saturation
Include following procedure with pore network oil relative permeability data：
Process 1：The pore network is obtained respectively in displacement process, complete water filled network volume and completely quilt
The network volume that oil is full of；The water filled network volume completely includes the volume and completely of complete water filled hole
The volume of water filled venturi, the network volume being initially filled with oil completely include the hole being initially filled with oil completely volume and
The volume for the venturi being initially filled with oil completely；Wherein,
In the pore network, the shape of the hole is spherical shape, and the calculation formula of volume is as shown in Equation 2
R is the radius of hole in formula 2；
In the pore network, the shape of the venturi is cylinder, and the calculation formula of volume is as shown in Equation 3
VVenturi=π r2L formulas 3
R is the radius of venturi circular cross-section in formula 2, and L is the length of venturi；
Process 2：According to formula shown in formula 4 to the water filled network volume completely and the net being initially filled with oil completely
Network volume carries out normalizing percentage processing, to obtain the water saturation and oil saturation of the pore network
In formula 4, SwkIt indicates to soak phase saturation, S in pore networkokIndicate non-wetted phase saturation in pore network, ri
Indicate the radius of venturi i, LiIndicate the length of venturi i, RjIndicate the radius of hole j.
Process 3：The total flow Q of the pore network under constraint water state is obtained respectivelysumo(Swi), instantaneous oil phase flow
Qsumo(Swk) and instantaneous water phase flow Qsumw(Swk), according to formula shown in formula 5 and formula 6, different aperture network is obtained respectively and is contained
The water phase relative permeability and oil relative permeability of pore network under water saturation
In formula 5, Krw(Swk) indicate the water phase relative permeability under different wetting phase saturation, μ in pore networkwIndicate water
The viscosity of phase, μoIndicate the viscosity of oil phase, Q 'sumw(Swk) indicate in pore network water phase flow under different wetting phase saturation
First derivative, Qsumo(Swi) indicate to fetter the total flow of the pore network under water state；
In formula 6, Kro(Swk) indicate the oil relative permeability under different non-wetted phase saturations, K in pore networko
(Swk) indicate the water phase relative permeability under different wetting phase saturation, K in pore networkoi(Swi) indicate under constraint water state
Oil relative permeability, Q 'sumo(Swk) indicate the first derivative of oil phase flow under different wetting phase saturation in pore network,
Qsumo(Swi) indicate to fetter the total flow of the pore network under water state.
The instantaneous oil phase flow Q of the pore networksumo(Swk) and instantaneous water phase flow Qsumw(Swk) be primarily referred to as it is a certain
When inscribe the oil phase flow Q of the pore networksumo(Swk) and water phase flow Qsumw(Swk)。
In the above-mentioned methods, it is preferable that in the instantaneous oil phase flow Q for obtaining pore networksumo(Swk) and instantaneous aqueous phase stream
Measure Qsumw(Swk) before, this method further includes building the step of individual oil phase analog network and individual water phase analog network respectively
Suddenly, building process is as described below：
Based on the pore network, oil phase pore network and water phase pore network therein are distinguished；
Respectively based on the oil phase pore network and water phase pore network distinguished, in addition virtual venturi is to get to list
Only oil phase analog network and individual water phase analog network；Wherein, in pore network described in the radius ratio of the virtual venturi
Venturi radius it is 10 times small.
In the above-mentioned methods, the shape of hole is spherical shape in the pore network, and the shape of the venturi is cylinder, institute
The shape for stating virtual venturi is also cylinder.
In technical solution provided by the invention, it can be easy to calculate the total flow of pore network according to pressure field,
However, individually oil phase or water phase pore network and imperfect (as shown in Figure 6), therefore in the oil phase flow of calculating pore network
Before water phase flow, need to build virtual network to it.Specific way is as described above：With individual oil phase or water phase hole
Based on network, and throat radius become smaller 10 times virtual venturi (as shown in Figures 7 and 8 the venturi for playing slash line) i.e.
Form complete pore network.After forming complete pore network, then calculates its corresponding flow and pore network just can be obtained
Oil phase flow and water phase flow.
In the above-mentioned methods, it is preferable that this method further includes according to the hole under the different aperture network water saturation
It is bent to draw water-oil phase relative permeability for gap network water phase relative permeability data and pore network oil relative permeability data
The step of line.
In the above-mentioned methods, it is preferable that the drafting of the water-oil phase permeability saturation curve includes following procedure：It utilizes
Interpolation method is by the pore network water phase relative permeability data and pore network oil phase phase under different aperture network water saturation
Smooth curve is connected into get to water-oil phase permeability saturation curve to permeability data.
In the above-mentioned methods, it is preferable that the drafting of the water-oil phase permeability saturation curve includes following procedure：
According to formula shown in formula 9, formula 10 and formula 11, (formula shown in formula 9- formulas 10 indicates typical water-oil phase phase osmole
Type), by discrete pore network water phase relative permeability data and pore network oil relative permeability data connection at smooth
Curve simultaneously carries out process of fitting treatment
In formula 9, SwDIndicate standardized water saturation, SWIndicate water saturation, SWiIndicate irreducible water saturation,
SorIndicate residual oil saturation；
The K in formula 10rw(Sw) indicate that the water phase relative permeability under different wetting phase saturation in pore network, a indicate
The relative permeability of water, S under residual oil saturationwDIndicate that standardized water saturation, m indicate to depend on reservoir rock hole
The index of structure and wetability.
Kro(Sw)=b (1-SwD)n
The K in formula 11ro(Sw) indicate that the oil relative permeability under different wetting phase saturation in pore network, b indicate
Oily relative permeability, S under irreducible water saturationwDIndicate that standardized water saturation, n indicate to depend on reservoir rock hole
The index of gap structure and wetability.
Beneficial effects of the present invention：
Technical solution provided by the invention can pass through development on the basis of the pore throat data that constant speed Mercury-injection test obtains
Pore network simulation calculates, the water-oil phase relative permeability of quick obtaining rock sample to be measured, and on this basis can be into one
Step obtains water-oil phase phase percolation curve.
Description of the drawings
Fig. 1 is the pore radius curve of frequency distribution figure of rock sample；
Fig. 2 is the pore radius histogram frequency distribution diagram of rock sample；
Fig. 3 is the throat radius histogram frequency distribution diagram of rock sample；
Fig. 4 is the flow diagram that water-oil phase fluid-flow analogy criterion is established in pore network；
Fig. 5 is the structure diagram of pore network；
Fig. 6 is the schematic diagram that oil phase pore network and water phase pore network are distinguished from pore network；
Fig. 7 is individual oil phase hole analog network；
Fig. 8 is individual water phase hole analog network；
Fig. 9 is water-oil phase permeability saturation curve；
Figure 10 is the comparison diagram of the analogue value and experiment value of relative permeability.
Specific implementation mode
In order to which technical characteristic, purpose and the advantageous effect to the present invention are more clearly understood, now to the skill of the present invention
Art scheme carry out it is described further below, but should not be understood as to the present invention can practical range restriction.
The application embodiment provides a kind of analogy method of water-oil phase relative permeability, and this method includes following step
Suddenly：
Step S101：Constant speed pressure mercury experiment is carried out to rock sample to be analyzed, to obtain pore throat data (Fig. 1-3 institutes of rock sample
It is shown as the pore radius and throat radius distributed data that certain middle and high infiltration rock core constant speed pressure mercury obtains), pore throat data include hole half
The frequency distribution data of diameter and the frequency distribution data of throat radius.
Step S102：Based on the pore throat data, pore network is built
Process 1：Based on the frequency distribution data of the pore radius, the hole in the pore network is carried out at assignment
Reason, process are as follows：
Based on the frequency distribution data of the pore radius, the histogram frequency distribution diagram of pore radius is built.
On the basis of the histogram frequency distribution diagram of pore radius, random generation one falls the pore radius in the histogram
The data currently generated at random are assigned to corresponding hole as its radius value, and count assignment hole by the data in Distribution Value
The number that various radius values occur in gap, once the number that the random radius value being currently generated occurs in assignment hole is more than
The radius frequency of the calculated corresponding hole in front, it is determined that the random radius value being currently generated is invalid, regenerates one
A new random radius value, until no longer there is the random radius value being currently generated in the number occurred in assignment hole before
The radius frequency of the corresponding hole calculated more than front.
By taking the frequency distribution data for pressing the pore radius of certain block rock core of mercury acquisition by constant speed as an example, to pore radius
The pretreatment of frequency distribution data illustrates：
Pore radius curve of frequency distribution figure shown in FIG. 1 is converted to corresponding column frequency distribution data figure first
(as shown in Figure 2)；
Then, based on column frequency distribution data figure shown in Fig. 2, the random number generated in 8 to 25 will be with
The number that machine generates is assigned to corresponding hole as its radius value, and counts the number that various radius values occur in assignment hole,
Once the random radius value this time generated is more than prior calculated phase in the number previously occurred in assignment hole
The radius frequency for the hole answered then assert that the random radius value this time generated is invalid, regenerates a random number until not going out
The now above phenomenon, below to realize the program code of this part：
Process 2：With reference to the operation of the above process 1, the frequency distribution data (as shown in Figure 3) based on the throat radius,
Assignment processing is carried out to the venturi in the pore network, process is as follows：
Based on the frequency distribution data of the throat radius, the histogram frequency distribution diagram of throat radius is built.
On the basis of the histogram frequency distribution diagram of throat radius, random generation one falls the throat radius in the histogram
The data currently generated at random are assigned to corresponding venturi as its radius value, and count assignment larynx by the data in Distribution Value
The number that various radius values occur in road, once the random radius value being currently generated is in the number occurred in assignment venturi before
The radius frequency of the corresponding venturi calculated more than front, it is determined that the random radius value being currently generated is invalid, gives birth to again
At a new random radius value, until no longer there is the above phenomenon.
After each parameter completes assignment in realizing to pore network, i.e., structure obtains meeting pore constriction radius frequency distribution
Pore network.
Step S103：Water-oil phase fluid-flow analogy criterion is established in the pore network
Process 1：Displacing front of the pore network in displacement process is obtained, from the institute being connected with the displacing front
Have and selects the maximum venturi of net pressure in venturi as optimal venturi.
It is described in detail below in conjunction with pore network schematic diagram shown in Fig. 4：
When displacement to a certain stage, according to the hole formed by hole of the non-wetted phase full of (being occupied completely by oil phase)
Gap group can obtain " displacing front " in this stage.Later, all venturis being connected with " displacing front " can be marked,
For example, can mark and be.These out labeled venturis indicate to face drive state in boundary.Next, by the stage
All labeled venturis out, which extract, to be analyzed, due to being that for type displacement, (" row replaces type displacement " indicates non-to row at this time
Wetting phase displacement wetting phase, that is, oily driven water-replacing), capillary force shows as resistance.Therefore in these venturis for being extracted
Net pressure is equal to the pressure difference that this displacement stage pore network pressure field acts on venturi both ends and subtracts the corresponding hollow billet resistance of venturi
Power, it is clear that the net pressure of venturi is bigger, the non-wetted easier such venturi of intrusion of phase, therefore can face these and drive in yellow venturi
The maximum venturi of net pressure is elected to be optimal venturi.
Process 2：By the optimal venturi, and the current state of all holes being connected with the optimal venturi is updated to
The state being full of by non-wetted phase
The state of optimal venturi is updated to the state occupied by non-wetted phase by facing drive state in boundary before, together
When, state that the state for the hole being connected with optimal venturi is updated to be occupied by non-wetted phase.
Process 3：The current state of the pressure field of the pore network is updated
It is possible, firstly, to assume that fluid is incompressible, according to mass conservation law, on the timing node of a flowing stage in office
The sum of volume flow by hole i is 0, as shown in Equation 7
In formula 7, NiThe hole collection that expression and hole i are connected directly by venturi around it, flow QijExpression formula such as
Shown in formula 8
In formula 8, rijThe radius of venturi between expression hole i and hole j；LijVenturi between expression hole i and hole j
Length；Negative sign indicates that fluid flows out for hole i；pcIndicate capillary pressure, the sign window gap i of the front and hole
The state parameter of gap j is determined, and when two hole state parameters are identical, the flowing in venturi at this time corresponds to single-phase flow, capillary force
Directly take 0.
Secondly, the equations simultaneousness of the sum of the flow of each hole is formed into equation group, as shown in Equation 1
In formula 1,And
The coefficient matrix of equation groupFor symmetric positive definite matrix, thus equation group one
Surely there is solution, solve the Matrix division and can be obtained new pore network pressure field.
Step S104：According to the two-phase fluid flow simulating criterion, implement two-phase fluid in the pore network
Flow simulating, to obtain pore network water phase relative permeability data and the pore network under different aperture network water saturation
Oil relative permeability data
Process 1：The pore network is obtained respectively in displacement process, complete water filled network volume and completely quilt
The network volume that oil is full of；The water filled network volume completely includes the volume and completely of complete water filled hole
The volume of water filled venturi, the network volume being initially filled with oil completely include the hole being initially filled with oil completely volume and
The volume for the venturi being initially filled with oil completely；Wherein,
In the pore network, the hole is spherical structure, and the calculation formula of volume is as shown in Equation 2
R indicates the radius of hole in formula 2；
In the pore network, the venturi is cylindrical structure, and the calculation formula of volume is as shown in Equation 3
VVenturi=π r2L formulas 3
R indicates that the radius of venturi circular cross-section, L indicate the length of venturi in formula 2.L can pass through the image method of micron CT
Holes between length obtain, also belong to one of rock sample pore throat data of initial acquisition.
With pore network schematic diagram shown in fig. 5, this process is described in detail：
When pore network displacement proceeds to a certain moment (as shown in Figure 5), the state of hole and venturi can be carried out
It distinguishes.Distinguish the hole being occupied by the water completely, the venturi being occupied by the water completely, the hole, completely oily occupied completely by oil
Venturi is occupied, the network volume for being occupied by the water and being occupied completely by oil completely is calculated separately out；Wherein, the net being occupied by the water completely
Network volume includes two branches, is the hole being occupied by the water completely and the venturi being occupied by the water completely respectively；Net is occupied by oil completely
Network volume also includes two parts, is by the hole that occupies of oil and to occupy venturi by oil completely completely respectively.
According to formula shown in formula 4 to the water filled network volume completely and the network volume being initially filled with oil completely
Normalizing percentage processing is carried out, the water saturation and oil saturation of pore network at this time are obtained
In formula, SwkIt indicates to soak phase saturation, S in pore networkokIndicate non-wetted phase saturation in pore network, riTable
Show the radius of venturi i, LiIndicate the length of venturi i, RjIndicate the radius of hole j.
Process 3：The total flow Q of constraint water state lower opening gap network is obtained respectivelysumo(Swi), instantaneous oil phase flow Qsumo
(Swk) and instantaneous water phase flow Qsumw(Swk), according to formula shown in formula 5 and formula 6, it is aqueous full that different aperture network is obtained respectively
With the water phase relative permeability and oil relative permeability of the lower pore network of degree
In formula 5, Krw(Swk) indicate the water phase relative permeability under different wetting phase saturation, μ in pore networkwIndicate water
The viscosity of phase, μoIndicate the viscosity of oil phase, Q 'sumw(Swk) the water phase flow under different wetting phase saturation in pore network of table four
First derivative, Qsumo(Swi) indicate to fetter the total flow of the pore network under water state；
In formula 6, Kro(Swk) indicate the oil relative permeability under different non-wetted phase saturations, K in pore networko
(Swk) indicate the water phase relative permeability under different wetting phase saturation, K in pore networkoi(Swi) indicate under constraint water state
Oil relative permeability, Q 'sumo(Swk) indicate the first derivative of oil phase flow under different wetting phase saturation in pore network,
Qsumo(Swi) indicate to fetter the total flow of the pore network under water state.
Wherein, it can be easy to calculate the total flow of pore network according to pressure field, and individually oil phase or water phase hole
Gap network is simultaneously imperfect, therefore before the oil phase flow and water phase flow for calculating pore network, needs to build each list
Only analog network, specific way can be as shown in Figure 6 to 8：First, the oil phase pore network in pore network is distinguished
With water phase pore network (as shown in Figure 6)；Then, respectively using the oil phase pore network and water phase pore network distinguished as base
Plinth, in addition (venturi for playing slash line in figure indicates virtual venturi, the larynx in the radius ratio pore network of virtual venturi to virtual venturi
The radius in road is 10 times small), that is, form complete individually oil phase hole analog network (as shown in Figure 7) and individual water phase hole
Analog network (as shown in Figure 8)；Finally, its corresponding flow is calculated to get to the oil phase flow and water phase flow of pore network.
Step S105：According under different aperture network water saturation pore network water phase relative permeability data and hole
Gap network oil relative permeability data draw water-oil phase permeability saturation curve
According to the model (as shown in formula 9, formula 10 and formula 11) of typical water-oil phase relative permeability, by discrete hole net
Network water phase relative permeability data and pore network oil relative permeability data connection at smooth curve and carry out process of fitting treatment,
The parameter in the model of typical water-oil phase relative permeability is obtained to get to smooth water-oil phase permeability saturation curve
In formula 9, SwDIndicate zero dimension water saturation, SWIndicate water saturation, SWiIndicate irreducible water saturation,
SorIndicate residual oil saturation；
The K in formula 10rw(Sw) indicate that the water phase relative permeability under different wetting phase saturation in pore network, a indicate
The relative permeability of water, S under residual oil saturationwDIndicate that standardized water saturation, m indicate to depend on reservoir rock hole
The index of structure and wetability.
Kro(Sw)=b (1-SwD)n
The K in formula 11ro(Sw) indicate that the oil relative permeability under different wetting phase saturation in pore network, b indicate
Oily relative permeability, S under irreducible water saturationwDIndicate that standardized water saturation, n indicate to depend on reservoir rock hole
The index of gap structure and wetability.
The pore network for meeting pore constriction radius frequency distribution can be obtained by program above, opened based on this
Flow simulating of the water-oil phase fluid in pore network is opened up, it is available as schemed mutually to ooze computational methods according to the pore network of foundation
Discrete data point is mutually oozed shown in 9, finally, smooth water-oil phase permeability saturation curve is can be obtained with Exponential Model
Model.
Kro(Sw)=0.7268 (1-SwD)1.4645。
In order to verify accurate calculating of the model for relative permeability, selection standard 100Md Berea cores carry out laboratory
Calibration experiment, first saturated water, then the process of oily expelling water is carried out, Figure 10 is model predication value and Experimental comparison's value, and error is 8.3%
Within, it is seen that there is preferable consistency.
Claims (10)
1. a kind of analogy method of water-oil phase relative permeability comprising following steps：
The pore throat data of rock sample are obtained, the pore throat data include the frequency distribution data of pore radius and the frequency of throat radius
Distributed data；
Based on the pore throat data, pore network is built；
Water-oil phase fluid-flow analogy criterion is established in the pore network；
According to the two-phase fluid flow simulating criterion, implement the flow simulating of two-phase fluid in the pore network, to obtain
Take pore network water phase relative permeability data and pore network oil phase under different aperture network water saturation are opposite to permeate
Rate data.
2. according to the method described in claim 1, wherein, being based on the pore throat data, structure pore network includes following procedure：
Based on the frequency distribution data of the pore radius, assignment processing is carried out to the hole in the pore network；
Based on the frequency distribution data of the throat radius, assignment processing is carried out to the venturi in the pore network.
3. requiring the method described in 2 according to power, wherein the frequency distribution data based on the pore radius, to the hole net
It includes following procedure that hole in network, which carries out assignment processing,：
Process 1：Based on the frequency distribution data of the pore radius, the histogram frequency distribution diagram of pore radius is built；
Process 2：On the basis of the histogram frequency distribution diagram of the pore radius, random generation one is fallen in the histogram mesoporous
The data currently generated at random are assigned to corresponding hole as its radius value, and counted by the data in gap radius distribution value
The number that various radius values occur in assignment hole, once time that the random radius value being currently generated occurs in assignment hole
Radius frequency of the number more than corresponding hole, it is determined that the random radius value being currently generated is invalid, regenerates one newly
Random radius value, until no longer there is the random radius value being currently generated and being more than in the number occurred in assignment hole before
This phenomenon of the radius frequency of corresponding hole.
4. according to the method described in claim 2, wherein, based on the frequency distribution data of the throat radius, to the hole
It includes following procedure that venturi in network, which carries out assignment processing,：
Process 1：Based on the frequency distribution data of the throat radius, the histogram frequency distribution diagram of throat radius is built；
Process 2：On the basis of the histogram frequency distribution diagram of the throat radius, random generation one falls the larynx in the histogram
The data currently generated at random are assigned to corresponding venturi as its radius value, and counted by the data in road radius distribution value
The number that various radius values occur in assignment venturi, once the random radius value being currently generated occurs in assignment venturi before
Number be more than corresponding venturi radius frequency, it is determined that the random radius value being currently generated is invalid, regenerates one
A new random radius value, until no longer there is the random radius value being currently generated in the number occurred in assignment venturi before
More than this phenomenon of the radius frequency of corresponding venturi.
5. according to the method described in claim 1, wherein, it is accurate that water-oil phase fluid-flow analogy is established in the pore network
It include then following procedure：
Displacing front of the pore network in displacement process is obtained, is selected from all venturis being connected with the displacing front
Go out the maximum venturi of net pressure as optimal venturi；
By the optimal venturi, and the current state of all holes being connected with the optimal venturi is updated to by non-wetted phase
The state being full of, meanwhile, the current state of the pressure field of the pore network is updated.
6. according to the method described in claim 5, wherein, packet is updated to the current state of the pressure field of the pore network
Include following procedure：
Matrix division shown in an equations simultaneousness accepted way of doing sth 1 for the sum of flow by each hole, and the Matrix division is carried out
It solves to get to new pressure field
In the equation group shown in formula 1,AndWherein, Ni
The hole collection that expression and hole i are connected directly by venturi around it, rijThe radius of venturi between expression hole i and hole j,
LijThe length of venturi, μ between expression hole i and hole jijThe viscosity of venturi, P between expression hole i and hole jnIndicate hole n
Capillary force, bnIndicate hole n by flow.
7. method according to claim 5 or 6, wherein obtain displacing front of the pore network in displacement process
Including following procedure：
All holes that by non-wetted phase are full of of the pore network in displacement process are obtained, can be obtained according to these holes
Take displacing front of the pore network in displacement process.
8. according to the method described in claim 1, wherein, according to the two-phase fluid flow simulating criterion, in the hole net
The flow simulating for implementing two-phase fluid in network, to obtain, the pore network water phase under different aperture network water saturation is opposite to ooze
Saturating rate data and pore network oil relative permeability data include following procedure：
Process 1：The pore network is obtained respectively in displacement process, complete water filled network volume and is filled completely by oil
Full network volume；The water filled network volume completely includes the volume of complete water filled hole and completely by water
The volume for the venturi being full of, the network volume being initially filled with oil completely include the hole being initially filled with oil completely volume and completely
The volume for the venturi being initially filled with oil；Wherein,
In the pore network, the shape of the hole is spherical shape, and the calculation formula of volume is as shown in Equation 2
R indicates the radius of hole in formula 2；
In the pore network, the shape of the venturi is cylinder, and the calculation formula of volume is as shown in Equation 3
VVenturi=π r2L formulas 3
R indicates that the radius of venturi circular cross-section, L indicate the length of venturi in formula 2；
Process 2：According to formula shown in formula 4 to the water filled network volume completely and the network body being initially filled with oil completely
Product carries out normalizing percentage processing, to obtain the water saturation and oil saturation of the pore network
In formula 4, SwkIt indicates to soak phase saturation, S in pore networkokIndicate non-wetted phase saturation in pore network, riIt indicates
The radius of venturi i, LiIndicate the length of venturi i, RjIndicate the radius of hole j；
Process 3：The total flow Q of the pore network under constraint water state is obtained respectivelysumo(Swi), instantaneous oil phase flow Qsumo
(Swk) and instantaneous water phase flow Qsumw(Swk), according to formula shown in formula 5 and formula 6, it is aqueous full that different aperture network is obtained respectively
With the water phase relative permeability and oil relative permeability of the lower pore network of degree
In formula 5, Krw(Swk) indicate the water phase relative permeability under different wetting phase saturation, μ in pore networkwIndicate water phase
Viscosity, μoIndicate the viscosity of oil phase, Q 'sumw(Swk) the water phase flow under different wetting phase saturation in pore network of table four single order
Derivative, Qsumo(Swi) indicate to fetter the total flow of the pore network under water state；
In formula 6, Kro(Swk) indicate the oil relative permeability under different non-wetted phase saturations, K in pore networko(Swk) indicate
Water phase relative permeability in pore network under different wetting phase saturation, Koi(Swi) indicate to fetter the oil phase phase under water state
To permeability, Q 'sumo(Swk) indicate the first derivative of oil phase flow under different wetting phase saturation in pore network, Qsumo(Swi)
Indicate the total flow of the pore network under constraint water state.
9. according to the method described in claim 1, wherein, this method further includes according to the different aperture network water saturation
Under pore network water phase relative permeability data and pore network oil relative permeability data, draw that water-oil phase is opposite to be oozed
The step of saturating rate curve.
10. according to the method described in claim 9, wherein, the drafting of the water-oil phase permeability saturation curve includes following
Process：
It is according to formula shown in formula 9, formula 10 and formula 11, the pore network water phase under different aperture network water saturation is opposite
Permeability data and pore network oil relative permeability data are fitted to smooth curve
In formula 9, SwDIndicate standardized water saturation, SWIndicate water saturation, SWiIndicate irreducible water saturation, SorTable
Show residual oil saturation；
The K in formula 10rw(Sw) indicate that the water phase relative permeability under different wetting phase saturation in pore network, a indicate remaining
The relative permeability of water, S under oily saturation degreewDIndicate that standardized water saturation, m indicate to depend on reservoir rock pore structure
With the index of wetability；
Kro(Sw)=b (1-SwD)n
The K in formula 11ro(Sw) indicate that the oil relative permeability under different wetting phase saturation in pore network, b are indicated in beam
Tie up relative permeability oily under water saturation, SwDIndicate that standardized water saturation, n indicate to depend on reservoir rock hole knot
The index of structure and wetability.
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