CN108868745B - Oil reservoir flow field matching evaluation method - Google Patents

Oil reservoir flow field matching evaluation method Download PDF

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CN108868745B
CN108868745B CN201810746492.7A CN201810746492A CN108868745B CN 108868745 B CN108868745 B CN 108868745B CN 201810746492 A CN201810746492 A CN 201810746492A CN 108868745 B CN108868745 B CN 108868745B
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谷建伟
刘若凡
王鹏润
张烈
赵亮
张圆圆
隋顾磊
王小蕊
任燕龙
周鑫
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China University of Petroleum East China
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Abstract

The invention discloses a method for evaluating the matching performance of an oil reservoir flow field, which comprises the following steps: dividing the flow field into three types, namely a control parameter field, an oil phase displacement parameter field and a water phase displacement parameter field; converting the field parameters of the control parameter, the field parameters of the oil phase displacement parameter and the field parameters of the water phase displacement parameter to a numerical interval of [0,1 ]; evaluating the overall matching performance of the flow field; and evaluating the matching performance of the flow field distribution. The flow field matching performance calculated by the method fully considers the flow field characteristics in the ultra-high water cut period, and provides reliable basis for oilfield deployment decision.

Description

Oil reservoir flow field matching evaluation method
Technical Field
The invention belongs to the technical field of quantitative characterization of an oil reservoir flow field, and particularly relates to an oil reservoir flow field matching evaluation method.
Background
The research of the oil reservoir flow field is still in the initial stage, and the application degree of the research result in the actual production is lower. At present, the domestic flow field research mainly has the following characteristics: first, the flow field characterization indicators are different for different scholars. At present, different scholars have different viewpoints in flow field description, and the scholars adopt different index screening methods to characterize the oil reservoir flow field. In addition, most scholars divide the flow field indexes into static indexes and dynamic indexes, but the static indexes and the dynamic indexes are combined in a weighting mode when the flow field is characterized, and the combination is obviously inaccurate. Second, flow field follow-up studies are less. In the aspect of flow fields, most researches focus on the characterization of the flow fields, and the main idea is to select a membership function to normalize index data by a fuzzy mathematical method on the basis of index screening, determine the weight of each index by means of an analytic hierarchy process, and finally couple all indexes into a comprehensive index. However, different types of indexes are coupled, so that the deviation is great, and the follow-up research on flow field characterization is less.
Disclosure of Invention
In view of the above, the invention provides an oil reservoir flow field matching evaluation method.
In order to solve the technical problem, the invention discloses a method for evaluating the matching property of an oil reservoir flow field, which comprises the following steps:
step 1, dividing flow fields into three types, namely a control parameter field for representing the control capability distribution of an oil reservoir injection-production system, an oil phase displacement parameter field for representing the distribution state of residual oil and a water phase displacement parameter field for representing the state of movable water;
step 2, converting the parameters of the control parameter field, the parameters of the oil phase displacement parameter field and the parameters of the water phase displacement parameter field into a numerical interval of [0,1 ];
step 3, evaluating the overall matching performance of the flow field: respectively evaluating the matching of the control parameter field and the oil phase displacement parameter field and the matching of the control parameter field and the water phase displacement parameter field by adopting a cosine similarity measurement method;
and 4, evaluating the flow field distribution matching.
Optionally, the control parameter field in step 1 comprises pressure, pressure gradient and streamline density; the oil phase displacement parameter field comprises the recoverable reserves abundance of the residual oil and the oil phase flow coefficient; the water phase displacement parameter field comprises a water passing multiple and a water phase flow coefficient.
Optionally, (i) said pressure is calculated by numerical simulation;
(ii) the pressure gradient is calculated by the following method:
the pressure gradient is calculated according to the pressure distribution, and the specific algorithm is that the pressure gradients in the X direction and the Y direction are respectively calculated, and then the pressure gradient values in the two directions are combined into a total pressure gradient according to a parallelogram rule;
for any unit body i of the oil reservoir, the calculation formula of the displacement pressure gradient in the X direction is as follows:
Figure GDA0003112200930000021
in the formula, Pgi(x)The pressure gradient of the unit body i in the X direction is expressed, and the pressure gradient is MPa/m; piRepresents the pressure at cell i, MPa; deltaxiRepresents the grid step length of the unit body i in the X direction, m;
similarly, the simplified calculation formula of the displacement pressure gradient in the Y direction of any unit body j of the oil reservoir is as follows:
Figure GDA0003112200930000022
in the formula, Pgj(y)The pressure gradient of the unit body j in the Y direction is expressed, and the pressure gradient is MPa/m; deltayiRepresenting the grid step length m of the unit body j in the Y direction;
synthesizing the displacement pressure gradient in the direction of X, Y at the unit body i according to a parallelogram rule to obtain the total pressure gradient of the unit body;
Figure GDA0003112200930000023
in the formula, Pg(i)Represents the total pressure gradient of the unit body, MPa/m;
(iii) the streamline density is calculated by the following formula (4):
Figure GDA0003112200930000024
in the formula, NiThe streamline density of the unit body i is decimal; n is a radical ofslThe total number of times of flow-through of the streamline of the unit body i is decimal.
Alternatively, (i) the remaining oil recoverable abundance is calculated by the following equation:
Figure GDA0003112200930000025
in the formula, FdoriThe recoverable reserve abundance of the residual oil is unit i, g/cm2；ФiPorosity, decimal fraction of unit body i; soi(t) is the residual oil saturation, decimal number, of the unit body i at the time t; sorResidual oil saturation, decimal, for unit i; h isiIs the effective thickness of unit body i, cm; rhooiDensity of ground crude oil in g/cm of unit i3；BoiVolume coefficient of crude oil in cm for unit body i3/cm3；
(ii) The oil phase flow coefficient is calculated by the following formula:
Figure GDA0003112200930000031
in the formula, LdoiIs the oil phase flow coefficient of unit i, μm2·cm/mPa·s；KiEffective permeability of Unit cell i, μm2；kroi(swi(t)) is the relative permeability, decimal, of the oil phase of unit cell i at time t; u. ofoiThe viscosity of the oil phase, mPas, of the unit i.
Alternatively, (i) the fold water passage is prepared by the following method:
the oil-water relative permeability is a function of saturation, expressed for unit volume i as:
Figure GDA0003112200930000032
the volume of unit cell i is expressed as:
Vi＝△xi△yi△zi (8)
the pore volume of unit i is:
PVi＝φ△xi△yi△zi (9)
the cumulative amount of oil extracted from unit cell i under surface conditions is expressed as:
NPi＝ρo(Swi(t)-Swc)/Bo (10)
in the formula, Swi(t) is the water saturation and decimal of the unit body i at the time t; swcIrreducible water saturation, decimal;
the oil yield at a certain moment of the unit body i is as follows:
Figure GDA0003112200930000033
neglecting capillary forces and gravity, the water-oil volume flow is calculated by darcy's law in the x-direction:
Figure GDA0003112200930000034
Figure GDA0003112200930000035
therefore, it is not only easy to use
Figure GDA0003112200930000036
In the same way
Figure GDA0003112200930000041
Figure GDA0003112200930000042
The water to oil yield ratio under surface conditions is therefore:
Figure GDA0003112200930000043
the accumulated water yield of the unit body at a certain moment is as follows:
Figure GDA0003112200930000044
substituting equations (7), (11), (17) into (18) yields:
Figure GDA0003112200930000045
cumulative water injection amount WIiComprises the following steps:
WIi＝WPi+ρwPVi(Swi(t)-Swc)/Bw (20)
the water passing multiple is therefore:
Figure GDA0003112200930000046
in the formula, RwiThe water passing times and decimal numbers of the unit bodies i at the time t;
(ii) the water phase flow coefficient is calculated by the following method:
Figure GDA0003112200930000047
in the formula, LdwiIs the water phase flow coefficient of the unit body i, mum2·cm/mPa·s；krwi(swi(t)) relative permeability of aqueous phase of unit cell i at time tTransmittance, decimal fraction; u. ofwiThe aqueous phase viscosity, mPas, of the unit i.
Optionally, the step 2 of converting the control parameter field parameter, the oil phase displacement parameter field parameter, and the water phase displacement parameter field parameter to the [0,1] value interval specifically includes:
step 2.1, controlling a parameter field:
step 2.1.1, pressure gradient: and calculating the membership degree by adopting a simplified half-raised trapezoidal membership function after the logarithm of the pressure gradient is obtained:
Figure GDA0003112200930000051
in the formula, Pgi is the pressure gradient at the unit body i, and is MPa/m; l (Pgi) is a membership function for Pgi; pgmax and Pgmin respectively represent the maximum value and the minimum value of Pgi, MPa/m;
step 2.1.2, streamline density: after logarithm of the streamline density is taken, the membership degree is calculated by adopting a simplified half-raised trapezoidal membership function:
Figure GDA0003112200930000052
in the formula, NiThe streamline density and decimal number at the unit body i are shown; l (N)i) Is NiA membership function of; nmax and Nmin represent NiMaximum and minimum, decimal;
step 2.1.3, pressure: the degree of membership is calculated using a simplified half-raised trapezoidal membership function:
Figure GDA0003112200930000053
in the formula, Pi is the pressure at the unit body i, MPa; l (Pi) is a membership function of Pi; p max and Pmin represent the maximum value and the minimum value of Pi, and Mpa respectively;
step 2.2, oil phase displacement parameter field:
step 2.2.1, the recoverable reserves abundance of the residual oil:
Figure GDA0003112200930000054
in the formula, Fdori is the recoverable reserve abundance of the residual oil at the unit body i, g/cm2(ii) a L (Fdori) is a membership function of Fdori; fdormax and Fdormin represent the maximum and minimum values of Fdori, g/cm2；
Step 2.2.2, oil phase flow coefficient:
Figure GDA0003112200930000055
in the formula, LdoiIs the oil phase flow coefficient at unit cell i, μm2·cm/mPa·s；L(Ldoi) Membership functions for fcoi; ldomax、LdominEach represents LdoiMaximum and minimum of, μm2·cm/mPa·s；
Step 2.3, water phase displacement parameter field:
step 2.3.1, water passing multiple:
Figure GDA0003112200930000061
in the formula, RwiThe number of the water passing times and the decimal number of the unit body i are shown; l (R)wi) Is RwiA membership function of; rwmax、RwminEach represents RwiMaximum and minimum, decimal;
step 2.3.2, the flow coefficient of the water phase is as follows:
Figure GDA0003112200930000062
in the formula, LdwiIs the flow coefficient of the water phase at the unit cell i, mum2·cm/mPa·s；L(Ldwi) Is LdwiA membership function of; ldwmax、LdwminAre respectively provided withRepresents LdwiMaximum and minimum of, μm2·cm/mPa·s；
The weights of the three indexes of the control parameter field are as follows:
ωK＝(0.539,0.296,0.164)T (30)
the weights of the two indexes of the oil phase displacement parameter field are as follows:
ωo＝(0.667,0.333)T (31)
the weights of two indexes of the water-phase displacement parameter field are as follows:
ωw＝(0.667,0.333)T (32)。
optionally, respectively evaluating the matching between the control parameter field and the oil-phase displacement parameter field and the matching between the control parameter field and the water-phase displacement parameter field by using a cosine similarity measurement method specifically includes:
if the oil reservoir has n unit bodies in total, the control parameter field and the displacement parameter field both have n elements, and the data of the control parameter field and the displacement parameter field are expressed in a vector form: control parameter field vector KZ ═ (KZ)1,kz2…kzn) And displacement parameter field direction QT ═ (QT)1,qt2…qtn)；
Judging the similarity degree between the two vectors according to the included angle of the vectors; if the included angle theta between the control parameter field vector and the displacement parameter field vector is 0 degrees, the two vectors are in the same direction, the similarity degree is the highest and is 1; if the included angle is 180 degrees, the two vectors are opposite in direction, the similarity degree is the lowest and is 0; the smaller the included angle is, the higher the similarity degree is, the larger the included angle is, the lower the similarity degree is; the "matching distance" of KZ and QT is thus represented by the angle θ; representing the similarity of the two by cos theta, namely the matching degree;
according to the geometric meaning of the vector inner product, the inner product of the vector KZ and the vector QT is equal to the product of the projection of the vector KZ on the vector QT and the modular length of the vector QT, as shown in formula (33);
KZ·QT＝|QT||KZ|cosθ (33)
calculating the cosine of the included angle of the vector according to the formula (33) and showing the cosine of the included angle in the formula (34);
Figure GDA0003112200930000071
on the basis of flow field characterization, the oil phase matching degree of the whole flow field and the water phase matching degree of the whole flow field are calculated according to a formula (34).
Optionally, the evaluation of the flow field distribution matching property specifically includes: calculating the matching distance between the control parameter field intensity and the displacement parameter field intensity of the unit body i according to an absolute value distance formula by taking the unit body i as a research object, as shown in a formula (35);
dist(kzi,qti)＝|kzi-qti| (35)
in the formula, kziThe field intensity and decimal of a control parameter of the unit body grid i are represented; qtiRepresenting the field strength and decimal of the displacement parameter of the unit body grid i; dist (kz)i,qti) Representing the absolute value distance, decimal, of the unit cell grid i;
constructing a Gaussian matching degree function according to the absolute value distance as shown in a formula (36), and converting the distance into the matching degree;
Figure GDA0003112200930000072
in the formula, Sim (kz)i,qti) Representing the Gaussian matching degree and decimal of the unit body grid i; dist (kz)i,qti) Representing the absolute value distance of the unit cell grid i; kziThe field intensity and decimal of a control parameter of the unit body grid i are represented;
and (3) calculating the matching degree of the oil phase and the water phase of any unit body according to the formula (35) and the formula (36), thereby obtaining the distribution of the matching degree of the oil phase and the matching degree of the water phase.
Compared with the prior art, the invention can obtain the following technical effects:
1) the invention divides the flow field into a control parameter field for representing the control capability of the injection and production system and a displacement parameter field for representing the displacement condition of the oil reservoir, and the displacement parameter field can be divided into an oil phase and a water phase.
2) The invention calculates the matching of the control parameter field and the displacement parameter field from the whole angle and the distribution angle respectively. In the aspect of integration, the control parameter field and the displacement parameter field are regarded as integration, and the matching performance of the control parameter field and the displacement parameter field is calculated by adopting a cosine similarity measurement method. In the aspect of distribution, the unit bodies are taken as research objects, the matching of each unit body is researched by adopting a Gaussian matching measurement method, and the matching degree distribution is obtained.
Of course, it is not necessary for any one product in which the invention is practiced to achieve all of the above-described technical effects simultaneously.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of the calculation of the pressure gradient in the X direction;
FIG. 2 is a schematic diagram of the Y-direction pressure gradient calculation;
FIG. 3 is a schematic diagram of a unit body;
FIG. 4 is a graph of Gaussian match versus distance absolute values in accordance with the present invention;
FIG. 5 is a plot of relative permeability for a library 53 of the present invention;
FIG. 6 is a control parameter field of the library 53 of the present invention;
FIG. 7 is a library 53 of the present invention oil phase displacement parameter fields;
FIG. 8 is a library 53 of the present invention for an aqueous phase displacement parameter field;
FIG. 9 illustrates the overall matching of the flow field of the library 53 of the present invention;
FIG. 10 is a graph of the oil phase matching degree distribution of library 53 of the present invention;
FIG. 11 is a graph of the water phase matching degree distribution of the library 53 of the present invention.
Detailed Description
The following embodiments are described in detail with reference to the accompanying drawings, so that how to implement the technical features of the present invention to solve the technical problems and achieve the technical effects can be fully understood and implemented.
The invention discloses an oil reservoir flow field matching evaluation method, which comprises the following steps:
step 1, dividing flow fields into three types, namely a control parameter field for representing the control capability distribution of an oil reservoir injection-production system, an oil phase displacement parameter field for representing the distribution state of residual oil and a water phase displacement parameter field for representing the movable water state. The following indices were screened for these three parameter fields:
(1) control parameter field: pressure, pressure gradient, and streamline density;
the three indexes represent the control capability distribution of the injection and production system on the oil reservoir.
Pressure (1)
The pressure can be calculated from the numerical simulation results.
Gradient of pressure-
The pressure gradient can be calculated according to the pressure distribution, and the specific algorithm is to calculate the pressure gradients in the X direction and the Y direction respectively and then synthesize the pressure gradients in the two directions into a total pressure gradient according to a parallelogram rule.
For any unit cell i of the reservoir, the pressure distribution along the X direction is shown in fig. 1. Here, the calculation formula of the displacement pressure gradient in the X direction is:
Figure GDA0003112200930000091
in the formula, Pgi(x)The pressure gradient of the unit body i in the X direction is expressed, and the pressure gradient is MPa/m; piRepresents the pressure at cell i, MPa; deltaxiRepresents the grid step size, m, of the unit cell i in the X direction.
Similarly, as shown in fig. 2, the simplified calculation formula of the displacement pressure gradient in the Y direction of any unit body j of the oil reservoir is as follows:
Figure GDA0003112200930000092
in the formula, Pgj(y)Denotes the pressure gradient, MP, of the unit cell j in the Y directiona/m；ΔyiRepresents the grid step size, m, of the unit cell j in the Y direction.
According to the parallelogram rule, as shown in FIG. 3, the X, Y-directional displacement pressure gradient at unit i is synthesized as the total pressure gradient of the unit.
Figure GDA0003112200930000093
In the formula, Pg(i)Represents the total pressure gradient of the unit body, MPa/m;
(iii) streamline density
The streamline represents the fluid flowing path in the stratum under the current injection and production conditions, and directly reflects the control degree distribution of the external injection and production conditions on the residual oil, so that the streamline can be used as the representation index of a control parameter field.
The basic idea of the streamline numerical simulation is to implicitly solve the pressure field and velocity field distribution of a research area according to an IMPES method, and then carry out streamline tracing from a water injection well to a production well to obtain streamline distribution.
The determination of the number of the flow lines requires that the volume flow of each flow line is specified, then the number of the flow lines is determined according to the flow, and the number of the flow lines generated by the water injection well depends on the injection quantity.
If the flow line has an entry point and an exit point in a grid of unit cells, the flow line flows through the unit cell once. Therefore, the ratio of the total flow line passing times of each grid to the grid area can be calculated according to the number of the flow lines, namely the flow line density:
Figure GDA0003112200930000094
in the formula, NiThe streamline density of the unit body i is decimal; n is a radical ofslThe total number of times of flow-through of the streamline of the unit body i is decimal.
(2) Oil phase displacement parameter field: the recoverable reserve abundance of the residual oil and the oil phase flow coefficient;
and for the oil phase displacement parameter field, two indexes of the recoverable reserve abundance of the residual oil and the oil phase flow coefficient are respectively screened out from the two aspects of the residual oil quantity and the fluidity of the residual oil.
Residual oil recoverable reserve abundance
Figure GDA0003112200930000101
In the formula, FdoriThe recoverable reserve abundance of the residual oil is unit i, g/cm2；ФiPorosity, decimal fraction of unit body i; soi(t) is the residual oil saturation, decimal number, of the unit body i at the time t; sorResidual oil saturation, decimal, for unit i; h isiIs the effective thickness of unit body i, cm; rhooiDensity of ground crude oil in g/cm of unit i3；BoiVolume coefficient of crude oil in cm for unit body i3/cm3。
Oil phase flow coefficient
Figure GDA0003112200930000102
In the formula, LdoiIs the oil phase flow coefficient of unit i, μm2·cm/mPa·s；KiEffective permeability of Unit cell i, μm2；kroi(swi(t)) is the relative permeability, decimal, of the oil phase of unit cell i at time t; u. ofoiThe viscosity of the oil phase of the unit body i is mPa.s;
(3) water phase displacement parameter field: water passing multiple and water phase flow coefficient:
the water phase displacement parameter field characterization is similar to the oil phase displacement parameter field characterization, and should be considered from the perspective of both the degree of water displacement and the flowability of the water.
Water passing multiple
The oil-water relative permeability is a function of saturation and can be expressed for unit volume i as:
Figure GDA0003112200930000103
the volume of unit cell i can be expressed as:
Vi＝△xi△yi△zi (8)
the pore volume of unit i is:
PVi＝φ△xi△yi△zi (9)
the cumulative amount of oil extracted from unit cell i under surface conditions can be expressed as:
NPi＝ρo(Swi(t)-Swc)/Bo (10)
in the formula, Swi(t) is the water saturation and decimal of the unit body i at the time t; swcFractional number to irreducible water saturation.
The oil yield at a certain moment of the unit body i is as follows:
Figure GDA0003112200930000111
neglecting capillary forces and gravity, the water-oil volume flow is calculated by darcy's law in the x-direction:
Figure GDA0003112200930000112
Figure GDA0003112200930000113
therefore, it is not only easy to use
Figure GDA0003112200930000114
In the same way
Figure GDA0003112200930000115
Figure GDA0003112200930000116
The water to oil yield ratio under surface conditions is therefore:
Figure GDA0003112200930000117
the accumulated water yield of the unit body at a certain moment is as follows:
Figure GDA0003112200930000118
substituting equations (7), (11), (17) into (18) yields:
Figure GDA0003112200930000119
cumulative water injection amount WIiComprises the following steps:
WIi＝WPi+ρwPVi(Swi(t)-Swc)/Bw (20)
the water passing multiple is therefore:
Figure GDA00031122009300001110
in the formula, RwiIs the water passing multiple and decimal of the unit body i at the time t.
Water phase flow coefficient
Figure GDA0003112200930000121
In the formula, LdwiIs the water phase flow coefficient of the unit body i, mum2·cm/mPa·s；krwi(swi(t)) the relative permeability, decimal fraction, of the aqueous phase of the unit cell i at time t; u. ofwiIn unit body iAqueous phase viscosity, mPa · s;
and determining the index membership degree through fuzzy mathematics on the basis of index screening.
Because the unit and the magnitude of different indexes are different, in order to facilitate comparison and analysis, membership functions of different indexes need to be determined first, and therefore index parameters are converted into a numerical value interval of [0,1 ].
(1) Controlling a parameter field
Pressure gradient
It can be known from indoor physical simulation experiments that the displacement pressure gradient is larger, the displacement efficiency is larger, but the displacement efficiency is increased gradually along with the increase of the displacement pressure gradient, so that the degree of membership is calculated by taking the logarithm of the pressure gradient and then adopting a simplified half-ascending trapezoidal membership function:
Figure GDA0003112200930000122
in the formula, PgiThe pressure gradient at the unit body i is MPa/m; l (Pg)i) Is PgiA membership function of; pgmax and Pgmin represent PgiMaximum and minimum values of (d), MPa/m.
Density of flow line-
The greater the streamline density is, the stronger the control ability of the flow field to the fluid is, but the increasing amplitude of the control ability of the flow field to the fluid is gradually reduced along with the increase of the streamline density, so that the logarithm of the streamline density is taken, and then the membership degree is calculated by adopting a simplified half-raised trapezoidal membership function:
Figure GDA0003112200930000123
in the formula, Ni is the streamline density and decimal number of the unit body i; l (Ni) is a membership function for Ni; nmax and Nmin represent the maximum and minimum values and decimal fraction of Ni, respectively.
③ pressure
The greater the pressure, the greater the control parameter field strength, so a simplified half-raised trapezoidal membership function is selected to calculate the degree of membership:
Figure GDA0003112200930000124
in the formula, Pi is the pressure at the unit body i, MPa; l (Pi) is a membership function of Pi; p max and Pmin represent the maximum and minimum values of Pi, MPa, respectively.
(2) Oil phase displacement parameter field
The oil phase displacement parameter field is similar to the control parameter field index normalization, which is not described herein, and the normalization formula is as follows:
the recoverable reserves abundance of the residual oil:
Figure GDA0003112200930000131
in the formula, Fdori is the recoverable reserve abundance of the residual oil at the unit body i, g/cm2(ii) a L (Fdori) is a membership function of Fdori; fdormax and Fdormin represent the maximum and minimum values of Fdori, g/cm2。
Oil phase flow coefficient:
Figure GDA0003112200930000132
in the formula, LdoiIs the oil phase flow coefficient at unit cell i, μm2·cm/mPa·s；L(Ldoi) Membership functions for fcoi; ldomax、LdominEach represents LdoiMaximum and minimum of, μm2·cm/mPa·s。
(3) Water phase displacement parameter field
Water passing multiple:
Figure GDA0003112200930000133
in the formula, RwiThe number of the water passing times and the decimal number of the unit body i are shown; l (R)wi) Is RwiMembership function of；Rwmax、RwminEach represents RwiMaximum and minimum, decimal.
Water phase flow coefficient
Figure GDA0003112200930000134
In the formula, LdwiIs the flow coefficient of the water phase at the unit cell i, mum2·cm/mPa·s；L(Ldwi) Is LdwiA membership function of; ldwmax、LdwminEach represents LdwiMaximum and minimum of, μm2·cm/mPa·s。
And determining the weight of each index in each parameter field by an analytic hierarchy process expert scoring method.
TABLE 1 control parameter field weight analysis
Figure GDA0003112200930000135
The weights of the three indexes of the control parameter field determined according to the scores are as follows:
ωK＝(0.539,0.296,0.164)T (30)
TABLE 2 oil phase displacement parameter field weight analysis
Figure GDA0003112200930000141
The weights of the two indexes of the oil phase displacement parameter field determined according to the scoring are as follows:
ωo＝(0.667,0.333)T (31)
TABLE 3 aqueous phase displacement parameter field weight analysis
Figure GDA0003112200930000142
The weights of the two indexes of the water phase displacement parameter field determined according to the scoring are as follows:
ωw＝(0.667,0.333)T (32)
three parameter fields can be coupled out according to the weight of each index.
The flow field matching is briefly analyzed on the basis of flow field characterization, and the following results are obtained: the more similar the control parameter field and the oil phase displacement parameter field are, the more matched are. This is because the more similar the two, meaning the more oil left in the areas where the injection and production system has strong control, the less oil left in the areas where the injection and production system has poor control, in which case the injection and production system is matched to the displacement conditions of the reservoir. Similarly, the more similar the control parameter field and the aqueous displacement parameter field, the more mismatched the fields. Therefore, the matching evaluation problem of the control parameter field and the displacement parameter field can be converted into a similarity measurement problem of the control parameter field and the displacement parameter field.
Step 2, evaluating the overall matching performance of the flow field:
the invention adopts a cosine similarity measurement method to evaluate the matching of the control parameter field and the oil phase displacement parameter field and the matching of the control parameter field and the water phase displacement parameter field respectively. Assuming that the oil reservoir has n unit bodies, the control parameter field and the displacement parameter field both have n elements, and data of the control parameter field and the displacement parameter field are expressed in a vector form: control parameter field vector KZ ═ (KZ)1,kz2…kzn) And displacement parameter field direction QT ═ (QT)1,qt2…qtn)。
According to the size of the included angle of the vectors, the similarity degree between the two vectors can be judged. If the included angle theta between the control parameter field vector and the displacement parameter field vector is 0 degrees, the two vectors are in the same direction, the similarity degree is the highest and is 1; if the included angle is 180 degrees, the two vectors are opposite in direction, the similarity degree is the lowest and is 0; the smaller the angle, the higher the degree of similarity, and the larger the angle, the lower the degree of similarity. The "matching distance" of KZ and QT can thus be expressed by the angle θ. The similarity of the two, i.e. the degree of matching, can be expressed by cos θ.
The inner product of the vector KZ and the vector QT is equal to the product of the projection of the vector KZ on the vector QT and the modular length of the vector QT, according to the geometric meaning of the inner product of the vectors, as shown in equation (33).
KZ·QT＝|QT||KZ|cosθ (33)
The cosine of the angle of the vector calculated according to equation (33) is shown in equation (34).
Figure GDA0003112200930000151
On the basis of flow field representation, the oil phase matching degree of the whole flow field and the water phase matching degree of the whole flow field can be calculated according to a formula (34).
Step 3, evaluating the flow field distribution matching performance:
the unit i is used as a research object, and the matching distance between the control parameter field intensity and the displacement parameter field intensity of the unit i can be calculated according to an absolute value distance formula, as shown in formula (35).
dist(kzi,qti)＝|kzi-qti| (35)
In the formula, kziThe field intensity and decimal of a control parameter of the unit body grid i are represented; qtiRepresenting the field strength and decimal of the displacement parameter of the unit body grid i; dist (kz)i,qti) The absolute distance, decimal, of the unit cell grid i is shown.
And constructing a Gaussian matching degree function according to the absolute value distance as shown in a formula (36), and converting the distance into the matching degree.
Figure GDA0003112200930000152
In the formula, Sim (kz)i,qti) Representing the Gaussian matching degree and decimal of the unit body grid i; dist (kz)i,qti) Representing the absolute value distance of the unit cell grid i; kziThe field intensity and decimal of a control parameter of the unit body grid i are represented;
as can be seen from fig. 4, in the [0,1] interval, the gaussian matching degree decreases monotonically with the increase of the absolute value distance, so the gaussian matching degree function can be used as a similarity measurement method for studying the matching of the flow field.
The matching degree of the oil phase and the water phase of any unit body can be calculated according to the formula (35) and the formula (36), so that the distribution of the matching degree of the oil phase and the matching degree of the water phase is obtained.
Example 1
The following is a description with specific experimental data and results:
(1) block related data
The actual oil reservoir model of the Tandong 12 g53 unit is taken as an example for illustration, and the outline of the model is as follows:
the oil-water relative permeability curve and the physical property data of the Tando 12 g53 unit are shown in FIG. 5 and Table 1.
TABLE 4 library 53 Unit physical Property data sheet
Figure GDA0003112200930000161
The reclamation east 12 oil reservoirs are produced from 2006 and 12 months, and undergo capacity construction in three periods of 2007, 2008 and 2009, wherein the g53 injection and production unit is put into operation in 2009. The comprehensive water content of the injection-production unit reaches 77.5 percent in 2016, 9 months and g 53.
(2) Flow field characterization
If the number of unit cells is too large, a local enlargement of the area may be selected, for example, in this example, the grid of unit cells is 210 × 60, but the library 53 unit cells are only a small portion of the total reservoir, so the area of unit cells 45-87, 9-37 is selected for local enlargement.
The pressure gradient, streamline density, pressure index data are normalized according to equations (23) to (25), and then these three indices are coupled into a control parameter field according to equation (30).
The residual oil recoverable abundance and the oil phase flow coefficient are normalized according to the formulas (26) and (27), and then the two indexes are coupled into an oil phase displacement parameter field according to the formula (31).
The water flow multiple and the water phase flow coefficient are normalized according to the formulas (28) and (29), and then the two indexes are coupled into a water phase displacement parameter field according to the formula (32). The calculated control parameter field, oil phase displacement parameter field and water phase displacement parameter field are shown in fig. 6-9.
As can be seen from fig. 6, the control parameter field has stronger control capability between injection wells and production wells, and weaker control capability in the residual oil enrichment zone; as can be seen from fig. 7, the oil phase displacement parameter field is weaker around the water well and stronger in the remaining oil concentration distribution area; as can be seen from fig. 8, the aqueous phase displacement parameter field is stronger around the water well and weaker around the oil well.
(3) Evaluation of flow field overall matching
And respectively calculating the matching degree of the control parameter field and the oil phase displacement parameter field and the matching degree of the control parameter field and the water phase displacement parameter field according to a formula (34), namely the oil phase matching degree and the water phase matching degree. The calculation result is shown in fig. 9, the calculated overall oil phase matching degree of the flow field is 0.799, the calculated overall water phase matching degree is 0.936, and for an oil reservoir with a plurality of small layers, the matching performance of the plurality of small layers can be rapidly compared by adopting an overall matching evaluation method, and the small layer needing to be adjusted is screened out.
(4) Evaluation of flow field distribution matching
According to the formula (35) and the formula (36), respectively calculating the distribution of the oil phase matching degree and the water phase matching degree, as shown in fig. 10 and fig. 11, analyzing the distribution conditions of the oil phase matching degree and the water phase matching degree, wherein the oil phase matching degree is higher, and the injection-production adaptability of a lower area with water phase matching is better; on the contrary, the injection-production system in the region with lower oil phase matching degree and higher water phase matching degree has poorer adaptability.
To sum up, the patent can evaluate the matching performance of the flow field from the whole and distribution angles respectively, the whole matching performance evaluation can quickly compare the matching performance of a plurality of small layers, the distribution matching performance evaluation can be started from the local part, the flow field matching performance of each area of the flow field is determined, and the combination of the whole matching performance evaluation and the distribution matching performance evaluation can make the oil reservoir development and adjustment more targeted.
While the foregoing description shows and describes several preferred embodiments of the invention, it is to be understood, as noted above, that the invention is not limited to the forms disclosed herein, but is not to be construed as excluding other embodiments and is capable of use in various other combinations, modifications, and environments and is capable of changes within the scope of the inventive concept as expressed herein, commensurate with the above teachings, or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. The method for evaluating the matching performance of the oil reservoir flow field is characterized by comprising the following steps of:
step 1, dividing flow fields into three types, namely a control parameter field for representing the control capability distribution of an oil reservoir injection-production system, an oil phase displacement parameter field for representing the distribution state of residual oil and a water phase displacement parameter field for representing the state of movable water;
the control parameter field in the step 1 comprises pressure, pressure gradient and streamline density; the oil phase displacement parameter field comprises the recoverable reserves abundance of the residual oil and the oil phase flow coefficient; the water phase displacement parameter field comprises a water passing multiple and a water phase flow coefficient;
(i) the pressure is calculated through a numerical simulation result;
(ii) the pressure gradient is calculated by the following method:
the pressure gradient is calculated according to the pressure distribution, and the specific algorithm is that the pressure gradients in the X direction and the Y direction are respectively calculated, and then the pressure gradient values in the two directions are combined into a total pressure gradient according to a parallelogram rule;
for any unit body i of the oil reservoir, the calculation formula of the displacement pressure gradient in the X direction is as follows:
Figure FDA0003112200920000011
in the formula, Pgi(x)The pressure gradient of the unit body i in the X direction is expressed, and the pressure gradient is MPa/m; piRepresents the pressure at cell i, MPa; deltaxiRepresents the grid step length of the unit body i in the X direction, m;
similarly, the simplified calculation formula of the displacement pressure gradient in the Y direction of any unit body j of the oil reservoir is as follows:
Figure FDA0003112200920000012
in the formula, Pgj(y)The pressure gradient of the unit body j in the Y direction is expressed, and the pressure gradient is MPa/m; deltayiRepresenting the grid step length m of the unit body j in the Y direction;
synthesizing the displacement pressure gradient in the direction of X, Y at the unit body i according to a parallelogram rule to obtain the total pressure gradient of the unit body;
Figure FDA0003112200920000013
in the formula, Pg(i)Represents the total pressure gradient of the unit body, MPa/m;
(iii) the streamline density is calculated by the following formula (4):
Figure FDA0003112200920000014
in the formula, NiThe streamline density of the unit body i is decimal; n is a radical ofslThe number of total streamline flows of the unit body i is decimal;
step 2, converting the parameters of the control parameter field, the parameters of the oil phase displacement parameter field and the parameters of the water phase displacement parameter field into a numerical interval of [0,1 ];
step 3, evaluating the overall matching performance of the flow field: respectively evaluating the matching of the control parameter field and the oil phase displacement parameter field and the matching of the control parameter field and the water phase displacement parameter field by adopting a cosine similarity measurement method;
and 4, evaluating the flow field distribution matching.
2. The method for evaluating the matching property of the oil reservoir flow field according to claim 1, wherein (i) the recoverable reserve abundance of the residual oil is calculated by the following formula:
Figure FDA0003112200920000021
in the formula, FdoriThe recoverable reserve abundance of the residual oil is unit i, g/cm2；ФiPorosity, decimal fraction of unit body i; soi(t) is the residual oil saturation, decimal number, of the unit body i at the time t; sorResidual oil saturation, decimal, for unit i; h isiIs the effective thickness of unit body i, cm; rhooiDensity of ground crude oil in g/cm of unit i3；BoiVolume coefficient of crude oil in cm for unit body i3/cm3；
(ii) The oil phase flow coefficient is calculated by the following formula:
Figure FDA0003112200920000022
in the formula, LdoiIs the oil phase flow coefficient of unit i, μm2·cm/mPa·s；KiEffective permeability of Unit cell i, μm2；kroi(swi(t)) is the relative permeability, decimal, of the oil phase of unit cell i at time t; u. ofoiThe viscosity of the oil phase, mPas, of the unit i.
3. The method for evaluating the matching property of the oil reservoir flow field according to claim 2, wherein (i) the water passing multiple is prepared by the following method:
the oil-water relative permeability is a function of saturation, expressed for unit volume i as:
Figure FDA0003112200920000023
the volume of unit cell i is expressed as:
Vi＝△xi△yi△zi (8)
the pore volume of unit i is:
PVi＝φ△xi△yi△zi (9)
the cumulative amount of oil extracted from unit cell i under surface conditions is expressed as:
NPi＝ρo(Swi(t)-Swc)/Bo (10)
in the formula, Swi(t) is the water saturation and decimal of the unit body i at the time t; swcIrreducible water saturation, decimal; the oil yield at a certain moment of the unit body i is as follows:
Figure FDA0003112200920000031
neglecting capillary forces and gravity, the water-oil volume flow is calculated by darcy's law in the x-direction:
Figure FDA0003112200920000032
Figure FDA0003112200920000033
therefore, it is not only easy to use
Figure FDA0003112200920000034
In the same way
Figure FDA0003112200920000035
Figure FDA0003112200920000036
The water to oil yield ratio under surface conditions is therefore:
Figure FDA0003112200920000037
the accumulated water yield of the unit body at a certain moment is as follows:
Figure FDA0003112200920000038
substituting equations (7), (11), (17) into (18) yields:
Figure FDA0003112200920000039
cumulative water injection amount WIiComprises the following steps:
WIi＝WPi+ρwPVi(Swi(t)-Swc)/Bw (20)
the water passing multiple is therefore:
Figure FDA0003112200920000041
in the formula, RwiThe water passing times and decimal numbers of the unit bodies i at the time t;
(ii) the water phase flow coefficient is calculated by the following method:
Figure FDA0003112200920000042
in the formula, LdwiIs the water phase flow coefficient of the unit body i, mum2·cm/mPa·s；krwi(swi(t)) the relative permeability, decimal fraction, of the aqueous phase of the unit cell i at time t; u. ofwiThe aqueous phase viscosity, mPas, of the unit i.
4. The method for evaluating the matching performance of the oil reservoir flow field according to claim 3, wherein the step 2 of converting the parameters of the control parameter field, the oil phase displacement parameter field and the water phase displacement parameter field into the numerical value interval of [0,1] specifically comprises the following steps:
step 2.1, controlling a parameter field:
step 2.1.1, pressure gradient: and calculating the membership degree by adopting a simplified half-raised trapezoidal membership function after the logarithm of the pressure gradient is obtained:
Figure FDA0003112200920000043
in the formula, PgiThe pressure gradient at the unit body i is MPa/m; l (Pg)i) Is PgiA membership function of; pgmax、PgminEach represents PgiMaximum and minimum values of (2), MPa/m;
step 2.1.2, streamline density: after logarithm of the streamline density is taken, the membership degree is calculated by adopting a simplified half-raised trapezoidal membership function:
Figure FDA0003112200920000044
in the formula, NiThe streamline density and decimal number at the unit body i are shown; l (N)i) Is NiA membership function of; nmax and Nmin represent NiMaximum and minimum, decimal;
step 2.1.3, pressure: the degree of membership is calculated using a simplified half-raised trapezoidal membership function:
Figure FDA0003112200920000045
in the formula, PiThe pressure at the unit body i, MPa; l (P)i) Is PiA membership function of; pmax、PminEach represents PiMaximum and minimum values of, Mpa;
step 2.2, oil phase displacement parameter field:
step 2.2.1, the recoverable reserves abundance of the residual oil:
Figure FDA0003112200920000051
in the formula, FdoriIs the recoverable reserve abundance of the residual oil at unit body i, g/cm2；L(Fdori) Is FdoriA membership function of; fdormax、FdorminEach represents FdoriMaximum and minimum of (2), g/cm2；
Step 2.2.2, oil phase flow coefficient:
Figure FDA0003112200920000052
in the formula, LdoiIs the oil phase flow coefficient at unit cell i, μm2·cm/mPa·s；L(Ldoi) Membership functions for fcoi; ldomax、LdominEach represents LdoiMaximum and minimum of, μm2·cm/mPa·s；
Step 2.3, water phase displacement parameter field:
step 2.3.1, water passing multiple:
Figure FDA0003112200920000053
in the formula, RwiThe number of the water passing times and the decimal number of the unit body i are shown; l (R)wi) Is RwiA membership function of; rwmax、RwminEach represents RwiMaximum and minimum, decimal;
step 2.3.2, the flow coefficient of the water phase is as follows:
Figure FDA0003112200920000054
in the formula, LdwiIs the flow coefficient of the water phase at the unit cell i, mum2·cm/mPa·s；L(Ldwi) Is LdwiA membership function of; ldwmax、LdwminEach represents LdwiMaximum and minimum of, μm2·cm/mPa·s；
The weights of the three indexes of the control parameter field are as follows:
ωK＝(0.539,0.296,0.164)T (30)
the weights of the two indexes of the oil phase displacement parameter field are as follows:
ωo＝(0.667,0.333)T (31)
the weights of two indexes of the water-phase displacement parameter field are as follows:
ωw＝(0.667,0.333)T (32)。
5. the method for evaluating the matching property of the oil reservoir flow field according to claim 4, wherein the step of respectively evaluating the matching property of the control parameter field and the oil phase displacement parameter field and the matching property of the control parameter field and the water phase displacement parameter field by adopting a cosine similarity measurement method specifically comprises the following steps:
if the oil reservoir has n unit bodies in total, the control parameter field and the displacement parameter field both have n elements, and the data of the control parameter field and the displacement parameter field are expressed in a vector form: control parameter field vector KZ ═ (KZ)1,kz2…kzn) And displacement parameter field direction QT ═ (QT)1,qt2…qtn)；
Judging the similarity degree between the two vectors according to the included angle of the vectors; if the included angle theta between the control parameter field vector and the displacement parameter field vector is 0 degrees, the two vectors are in the same direction, the similarity degree is the highest and is 1; if the included angle is 180 degrees, the two vectors are opposite in direction, the similarity degree is the lowest and is 0; the smaller the included angle is, the higher the similarity degree is, the larger the included angle is, the lower the similarity degree is; the "matching distance" of KZ and QT is thus represented by the angle θ; representing the similarity of the two by cos theta, namely the matching degree;
according to the geometric meaning of the vector inner product, the inner product of the vector KZ and the vector QT is equal to the product of the projection of the vector KZ on the vector QT and the modular length of the vector QT, as shown in formula (33);
KZ·QT＝|QT||KZ|cosθ (33)
calculating the cosine of the included angle of the vector according to the formula (33) and showing the cosine of the included angle in the formula (34);
Figure FDA0003112200920000061
on the basis of flow field characterization, the oil phase matching degree of the whole flow field and the water phase matching degree of the whole flow field are calculated according to a formula (34).
6. The method for evaluating the matching property of the oil reservoir flow field according to claim 5, wherein the evaluation of the matching property of the flow field distribution is specifically as follows: calculating the matching distance between the control parameter field intensity and the displacement parameter field intensity of the unit body i according to an absolute value distance formula by taking the unit body i as a research object, as shown in a formula (35);
dist(kzi,qti)＝|kzi-qti| (35)
in the formula, kziThe field intensity and decimal of a control parameter of the unit body grid i are represented; qtiRepresenting the field strength and decimal of the displacement parameter of the unit body grid i; dist (kz)i,qti) Representing the absolute value distance, decimal, of the unit cell grid i;
constructing a Gaussian matching degree function according to the absolute value distance as shown in a formula (36), and converting the distance into the matching degree;
Figure FDA0003112200920000062
in the formula, Sim (kz)i,qti) Representing the Gaussian matching degree and decimal of the unit body grid i; dist (kz)i,qti) Representing the absolute value distance of the unit cell grid i; kziThe field intensity and decimal of a control parameter of the unit body grid i are represented;
and (3) calculating the matching degree of the oil phase and the water phase of any unit body according to the formula (35) and the formula (36), thereby obtaining the distribution of the matching degree of the oil phase and the matching degree of the water phase.
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