CN108229051B - Method for predicting recovery ratio of air foam flooding of oil reservoir - Google Patents

Method for predicting recovery ratio of air foam flooding of oil reservoir Download PDF

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CN108229051B
CN108229051B CN201810049707.XA CN201810049707A CN108229051B CN 108229051 B CN108229051 B CN 108229051B CN 201810049707 A CN201810049707 A CN 201810049707A CN 108229051 B CN108229051 B CN 108229051B
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coefficient
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尚庆华
赵习森
王玉霞
江绍静
杨永超
黄春霞
张冠华
陈龙龙
张建成
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Shaanxi Yanchang Petroleum Group Co Ltd
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Abstract

The invention belongs to the technical field of oilfield development, and particularly relates to a calculation method for predicting the recovery ratio of air foam flooding of an oil reservoir. A method for predicting the recovery ratio of air foam flooding of an oil reservoir comprises the following steps: (1) assuming that the injected fluid can gradually form three areas, namely a foam area, a liquid phase area and a gas phase area, and dividing the displacement stage into a certain stage of the displacement stage before gas breakthrough and a certain stage after gas breakthrough; (2) and respectively calculating the displacement efficiency and the sweep efficiency of each area of the foam area, the liquid phase area and the gas phase area in the current stage before or after the current stage is determined to be gas breakthrough. (3) Recovery ratio R = displacement efficiency × sweep efficiency. According to the method, the displacement fluid in the oil reservoir is divided into three areas, then the sweep efficiency and the oil displacement efficiency of each area are respectively calculated, and finally the recovery ratio of the air foam flooding is obtained, so that the feasibility and the operability are strong.

Description

Method for predicting recovery ratio of air foam flooding of oil reservoir
Technical Field
The invention belongs to the technical field of oilfield development, and particularly relates to a calculation method for predicting the recovery ratio of air foam flooding of an oil reservoir.
Background
The oil reservoir recovery rate is an important evaluation index in oil field development. The recovery effect of the oil reservoir under different driving modes can be evaluated and the recoverable reserves can be calculated through recovery prediction, and the method has important significance for oil field development planning and scheme deployment. According to the experience of a large amount of oil reservoir development at home and abroad, the factors influencing the oil reservoir recovery ratio are various, and besides the factors such as oil reservoir characteristics, natural energy, stratum fluid properties, well pattern types and the like, the factors are closely related to the development mode and the driving type.
Air foam flooding is an effective technical method for improving the recovery ratio of oil reservoirs, and has good application effects in many oil field developments at home and abroad at present. The investigation proves that the conventional method for predicting the recovery ratio of the air foam flooding mainly comprises a physical experiment method and a numerical simulation method, and a perfect and effective theoretical calculation method is lacked. The physical experiment method carries out an indoor core displacement experiment by simulating an oil reservoir and fluid conditions, calculates the predicted recovery ratio according to experimental data, has long time consumption and high required cost, and generally obtains only one-dimensional displacement recovery ratio, namely displacement efficiency, by the indoor physical experiment, and has larger recovery ratio difference with the actual oil reservoir displacement under the condition of sweep efficiency. The numerical simulation method firstly needs to establish a precise and accurate oil reservoir geological model and carries out the prediction of the recovery ratio on the basis of carrying out good fitting with the production historical data, needs a large amount of detailed and effective data information, has large workload of early preparation and later calculation and processing, and also has long time consumption.
Disclosure of Invention
The invention aims to solve the problems and provides a method for quantitatively calculating the recovery ratio by stages before and after gas breakthrough in a displacement stage.
The technical scheme of the invention is as follows:
a method for predicting the recovery ratio of air foam flooding of an oil reservoir comprises the following steps:
(1) assuming that the injected fluid can gradually form three areas, namely a foam area, a liquid phase area and a gas phase area, and dividing the displacement stage into a certain stage of the displacement stage before gas breakthrough and a certain stage after gas breakthrough;
(2) and respectively calculating the displacement efficiency and the sweep efficiency of each area of the foam area, the liquid phase area and the gas phase area in the current stage before or after the current stage is determined to be gas breakthrough.
(3) The recovery ratio R is the displacement efficiency multiplied by the sweep coefficient.
Abtfoam+Abtwater+Abtgas<AtotalWhen the sum of the swept areas of the three regions is smaller than the whole oil reservoir area, the gas is considered to be not broken through; a. thebtfoam+Abtwater+Abtgas＝AtotalWhen the sum of the swept areas of the three regions occupies the whole oil reservoir, the gas is considered to break through at the moment; when A isbtfoam+Abtwater＝AtotalWhen the sum of the swept areas of the water-based liquid phase region and the foam region occupies the whole oil reservoir, the gas phase region is considered to be completely broken through; wherein A isbtfoamIs the area swept by the foam area, AbtwaterIs the swept area of the water-based liquid phase region, AbtgasIs the swept area of the gas phase, AtotalThe whole oil reservoir area; according to definition and seepage mechanics, the area of each region can be calculated by the following formula:
Figure GDA0002897755230000021
Figure GDA0002897755230000022
Figure GDA0002897755230000023
wherein C is a coefficient related to the well pattern; when a five-point well pattern is used, C is 0.718; when an inverted seven-point well pattern is used, C is 0.743; when an inverse nine-point well pattern is adopted, C is 0.525;
②
Figure GDA0002897755230000024
and
Figure GDA0002897755230000025
respectively the simulated mobility ratio of foam and crude oil, the simulated mobility ratio of foam liquid and crude oil and the simulated mobility ratio of gas and crude oil, wherein the values of the simulated mobility ratios are respectively determined by the mobility ratio M and the permeability coefficient of variation V of two corresponding fluids under a homogeneous condition, and the simulated mobility ratios are respectively calculated according to the following formulas under a heterogeneous condition:
when V is less than or equal to 0.7,
Figure GDA0002897755230000028
wherein M is*Is a pseudo-fluidity ratio;
when V is greater than 0.7, the crystal,
Figure GDA0002897755230000026
calculating Afoam: firstly, calculating the residual foam amount by using the data of the foam half-life:
Figure GDA0002897755230000027
wherein, VleftThe residual volume of foam after a certain complete slug has elapsed time t; viThe volume of a foam slug as it is formed is assumed in the calculation to be the volume of injected air and foaming system solution at formation pressureAnd, hence, the total injected volume of fluid per slug; t is the foam half-life;
swept volume V of the foam zonefoamThe following can be calculated:
Figure GDA0002897755230000031
wherein S iswcIrreducible water saturation; sorfoamIs the residual oil saturation of the foam flooding, which is equal to the endpoint value when the relative permeability of the foam and the crude oil in the relative permeability curve of the crude oil is 0;
the swept area of the foam zone is as follows:
Figure GDA0002897755230000032
the swept area of the water-based liquid phase region, which is generated by the collapse of the foam, can be calculated from its physical significance by the following formula:
Figure GDA0002897755230000033
where φ is reservoir porosity, h is reservoir thickness, λwaterRepresents the volume ratio of the foaming system solution in each injection slug, SorwaterThe residual oil saturation of the foam liquid flooding is equal to the endpoint value when the relative permeability of the foam liquid and the crude oil in the relative permeability curve of the crude oil is 0;
the swept area of the gas phase region comes from the air which can not form foam after the fluid is injected and the swept area formed by the gas generated after the foam is broken at the front edge part, and can be expressed as follows according to the physical meaning:
Figure GDA0002897755230000034
wherein λ isgasRepresents the volume ratio of the gas in each injection slug, SorgasIs qiThe saturation of the oil displacement is equal to the end point value when the relative permeability of the gas and the crude oil is 0 in a relative permeability curve of the crude oil, R represents the reaction coefficient of the gas, and the low-temperature oxidation reaction shows that R is 0.996;
the calculation of the recovery ratio before breakthrough comprises three parts, namely the recovery ratio of a foam zone, the recovery ratio of a liquid zone and the recovery ratio of a gas zone;
wherein the foam area recovery ratio calculation process is as follows:
calculating the sweep coefficient
Evfoam＝Ezfoam·Esfoam (11)
Wherein, EsfoamIs the planar sweep coefficient, Ez, of the foam areafoamLongitudinal sweep efficiency of the foam zone
Figure GDA0002897755230000041
Figure GDA0002897755230000042
Wherein M is the fluidity ratio of foam to crude oil,
Figure GDA0002897755230000043
is the ratio of viscous force to gravity
Figure GDA0002897755230000044
In the formula utDenotes the foam flow rate, μoIs the viscosity of the crude oil in the formation, x is the distance of the reservoir in the direction of water injection, KxFor transverse permeability, Δ ρ is the density difference of the displacement fluid and the displaced fluid;
② calculating the displacement efficiency
Figure GDA0002897755230000045
In the formula, SoiIs the original oil saturation;
calculating the recovery ratio of the foam area:
RFfoam＝Edfoam×Evfoam (16)；
similarly, the liquid phase region recovery process is as follows:
Evwater＝Ezwater×Eswater (17)
wherein, EswaterIs the planar sweep coefficient, Ez, of the foam concentratewaterThe longitudinal sweep coefficient of the foam liquid is shown; ezwaterThe fluidity ratio of the foaming system solution and the crude oil is substituted into the formula (13) for calculation;
Figure GDA0002897755230000046
Figure GDA0002897755230000047
liquid phase region recovery RFwaterComprises the following steps:
RFwater＝Edwater×Evwater (20)
similarly, the gas phase zone recovery process is as follows:
Evgas＝Ezgas×Esgas (21)
wherein, EsgasIs the planar sweep coefficient of gas, EzgasIs the longitudinal sweep coefficient of the gas; ezgasThe fluidity ratio of the gas and the crude oil is substituted into the formula (13) for calculation;
Figure GDA0002897755230000051
Figure GDA0002897755230000052
recovery of gas phase region RFgasComprises the following steps:
RFgas＝Edgas×Evgas (24)
the total recovery ratio before gas breakthrough is as follows:
RF＝RFfoam+RFwater+RFgas。
the recovery ratio after breakthrough comprises three parts, namely foam zone recovery ratio, liquid zone recovery ratio and gas zone recovery ratio;
(1) calculating the volume sweep coefficient:
aiming at homogeneous oil deposit, the plane sweep coefficient Es during breakthroughbtThe following formula:
Figure GDA0002897755230000053
broken plane sweep coefficient EsafterbtThe following formula:
Figure GDA0002897755230000054
where D is a coefficient for the pattern type, when a five point pattern is used, D is 0.2749; when an inverse seven-point pattern is employed, D-0.2351; when an inverse nine-point well pattern is adopted, D is 0.201; vibtVolume of injected fluid for breakthrough;
aiming at the heterogeneous oil deposit, the plane sweep coefficient Es during breakthroughbtThe following formula:
Figure GDA0002897755230000055
broken plane sweep coefficient EsafterbtThe following formula:
Figure GDA0002897755230000056
wherein, the coefficient X is used for limiting the broken plane sweep coefficient to lead the broken plane sweep coefficient to tend to the maximum plane sweep coefficient Es under the conditions of the current fluidity ratio and the permeability variation coefficientmaxThe calculation method is as follows:
Figure GDA0002897755230000057
broken longitudinal sweep coefficient EzafterbtThe calculation method is the same as the formula (13);
volume sweep coefficient
Evafterbt＝Ezafterbt×Esafterbt (33)；
(2) Calculating dynamic oil displacement efficiency EdComprises the following steps:
Figure GDA0002897755230000061
wherein S isdIn order to displace the fluid dynamic saturation,
Figure GDA0002897755230000062
for residual oil saturation at dynamic displacement,
Figure GDA0002897755230000063
according to the theory of water saturation of the front edge of the seepage mechanics, the cumulative injection pore volume multiple PV is the reciprocal of the change rate of the water content to the water saturation, namely
Figure GDA0002897755230000064
Meanwhile, according to the seepage mechanics theory, the water content fwCan be expressed as:
Figure GDA0002897755230000065
according to the oilRelative permeability K to the foam concentrate two phasesroAnd KrwIs a function of the water saturation, which in turn can be generally expressed as:
Figure GDA0002897755230000066
wherein a and b are coefficients, can be obtained by
Figure GDA0002897755230000067
And SwLinear regression is carried out on the semilogarithmic coordinate graph;
substituting formula (37) for formula (36) and deriving to obtain
Figure GDA0002897755230000068
Figure GDA0002897755230000069
The cumulative injection pore volume multiple may be determined from the cumulative amount of injection fluid, i.e.:
Figure GDA00028977552300000610
wherein B iswIs the formation water volume coefficient, A is the oil-bearing area, h is the reservoir thickness, phi is the reservoir porosity, ρwIs the density of the foam liquid;
the fluidity ratio of the given PV number can be obtained by utilizing the formula, and the corresponding water content at the moment can be obtained by the fluidity ratio; then according to the seepage mechanics water phase flow-dividing formula, the dynamic average water saturation at the moment can be obtained
Figure GDA0002897755230000071
I.e. the dynamic saturation S of the displacement fluiddNamely:
Figure GDA0002897755230000072
wherein, muwViscosity of the foam concentrate, muoIs the formation crude oil viscosity;
the oil displacement efficiency is brought into a formula (34) of the oil displacement efficiency, and the dynamic oil displacement efficiency of the oil deposit at the moment can be obtained:
Figure GDA0002897755230000073
(3) calculated recovery ratio
According to the calculated volume sweep coefficient and oil displacement efficiency, the recovery ratio RF is calculated as follows:
RF＝Ed×Ev (43)。
the EsmaxThe calculation method of (2) is as follows:
value V at the boundary point when the permeability coefficient of variation changes from low to high is introducedcThe relationship between the fluidity ratio and the fluidity ratio can be calculated by the following formula:
Vc＝-0.063ln(M+0.1)+0.547 (30)
when the coefficient of variation of permeability V is less than VcWhen the maximum plane sweep efficiency is as follows,
Esmax＝-0.071V+0.861-0.061ln(M+0.1) (31)
when the coefficient of variation of permeability V is more than or equal to VcThe maximum plane sweep coefficient is
Figure GDA0002897755230000074
Wherein, EscThe coefficient of permeability variation is equal to VcThe plane sweep coefficient.
The invention has the technical effects that:
according to the air foam flooding mechanism, the displacement fluid in the oil reservoir is divided into three areas, and then the sweep efficiency and the flooding efficiency of each area are respectively calculated, so that the recovery ratio of the air foam flooding is finally obtained. The related parameters in the calculation formula are easy to obtain, and compared with a method for obtaining the air foam flooding recovery ratio through an indoor displacement experiment and oil reservoir numerical simulation, the method has the advantages of small workload and strong feasibility and operability. An effective technical method can be provided for evaluating and planning the development effect of the oil field.
Drawings
FIG. 1 is a schematic view of an air foam displacement recovery computing zone.
Detailed Description
In air foam flooding, the gas that makes up the foam gradually separates from the foaming system due to the instability of the foam itself. With the continuous alternating injection of gas and water-based foaming system solutions, it is assumed that the injected fluid will gradually form three zones within the formation, namely a foam zone, a liquid phase zone and a gas phase zone, due to differences in the fluid flow rate ratio within the formation. Because the gas fluidity is greater than the water-based solution fluidity and the water-based solution fluidity is greater than the foam fluidity, the foam region, the liquid phase region and the gas phase region are sequentially arranged from near to far from the injection well, as shown in fig. 1. In FIG. 1, Afoam、AwaterAnd AgasRespectively, the areas occupied by the formation of the foam region, the liquid phase region and the gas phase region, Abtfoam、AbtwaterAnd AbtgasIt means that the three regions can each expand the occupied area under the current implantation amount, atotalRepresenting the area of a complete well pattern.
According to the partition and the definition, the displacement stages are divided into before and after gas breakthrough, and then the displacement efficiency and the sweep efficiency of each region are respectively considered for calculation, and finally the recovery ratio of the air foam displacement in different stages is obtained. Before calculating the phase recovery, it is first determined at which phase the displacement is.
As shown in FIG. 1, Abtfoam+Abtwater+Abtgas<AtotalWhen the sum of the swept areas of the three regions is smaller than the whole oil reservoir area, the gas is considered to be not broken through; a. thebtfoam+Abtwater+Abtgas＝AtotalWhen the sum of the three swept areas occupies the whole reservoir, it is considered that the reservoir is fullThe gas starts to break through; when A isbtfoam+Abtwater＝AtotalWhen the sum of the swept areas of the water-based liquid phase region and the foam region occupies the whole oil reservoir, the gas phase region is considered to be completely broken through; wherein A isbtfoamIs the area swept by the foam area, AbtwaterIs the swept area of the water-based liquid phase region, AbtgasIs the swept area of the gas phase, AtotalThe whole oil reservoir area; according to definition and seepage mechanics, the area of each region can be calculated by the following formula:
Figure GDA0002897755230000081
Figure GDA0002897755230000082
Figure GDA0002897755230000083
wherein C is a coefficient related to the well pattern; when a five-point well pattern is used, C is 0.718; when an inverted seven-point well pattern is used, C is 0.743; when an inverse nine-point well pattern is adopted, C is 0.525;
②
Figure GDA0002897755230000091
and
Figure GDA0002897755230000092
respectively the simulated mobility ratio of foam and crude oil, the simulated mobility ratio of foam liquid and crude oil and the simulated mobility ratio of gas and crude oil, wherein the values of the simulated mobility ratios are respectively determined by the mobility ratio M and the permeability coefficient of variation V of two corresponding fluids under a homogeneous condition, and the simulated mobility ratios are respectively calculated according to the following formulas under a heterogeneous condition:
when V is less than or equal to 0.7,
Figure GDA0002897755230000098
wherein M is*Is a pseudo-fluidity ratio;
when V is greater than 0.7, the crystal,
Figure GDA0002897755230000093
calculating Afoam: firstly, calculating the residual foam amount by using the data of the foam half-life:
Figure GDA0002897755230000094
wherein, VleftThe residual volume of foam after a certain complete slug has elapsed time t; viThe volume of a foam slug as it is formed is assumed in the calculation to be the sum of the volume of injected air and foaming system solution at formation pressure, thus the total injected volume of fluid for each slug; t is the foam half-life; formula (6) represents a calculation method of the residual quantity of the single slug foam, and a working system of sectional injection is adopted on site, so that the residual quantity of the foam is calculated in a mode of accumulating a plurality of volumes of the foam which have passed different times. The moment of formation of each foam slug is calculated as the moment at which both fluids forming the slug have completed injection. Thus, in a physical sense, the swept volume V of the foam zonefoamThe following can be calculated:
Figure GDA0002897755230000095
wherein S iswcIrreducible water saturation; sorfoamIs the residual oil saturation of the foam flooding, which is equal to the endpoint value when the relative permeability of the foam and the crude oil in the relative permeability curve of the crude oil is 0;
after the swept volume of the foam zone was obtained, the swept area of the foam zone was as follows:
Figure GDA0002897755230000096
the swept area of the water-based liquid phase region, which is generated by the collapse of the foam, can be calculated from its physical significance by the following formula:
Figure GDA0002897755230000097
where φ is reservoir porosity, h is reservoir thickness, λwaterRepresents the volume ratio of the foaming system solution in each injection slug, SorwaterThe residual oil saturation of the foam liquid flooding is equal to the endpoint value when the relative permeability of the foam liquid and the crude oil in the relative permeability curve of the crude oil is 0;
the swept area of the gas phase region comes from the air which can not form foam after the fluid is injected and the swept area formed by the gas generated after the foam is broken at the front edge part, and can be expressed as follows according to the physical meaning:
Figure GDA0002897755230000101
wherein λ isgasRepresents the volume ratio of the gas in each injection slug, SorgasResidual oil saturation of the gas flooding is equal to the endpoint value when the relative permeability of the gas and the crude oil in a relative permeability curve of the crude oil is 0, R represents the reaction coefficient of the gas, and R is 0.996 as known from low-temperature oxidation reaction;
after the displacement phase is determined, the pre-breakthrough and post-breakthrough recovery rates are considered and calculated, respectively.
(one) Pre-breakthrough recovery
The pre-breakthrough recovery comprises three parts, namely foam zone recovery, liquid zone recovery and gas zone recovery;
(1) the foam zone recovery calculation process is as follows: because the foam stable area is far smaller than the area of the oil reservoir and the profile control plugging effect is obvious, the foam area is a circular area with the well bottom as the circle center and small radius, and the breakthrough can not be caused all the time. Before breakthrough, the injection volume multiple is equal to the sweep coefficient, so the sweep volume is equal to the volume of injected foam;
calculating the sweep coefficient
Evfoam＝Ezfoam·Esfoam (11)
Wherein, EsfoamIs the planar sweep coefficient, Ez, of the foam areafoamLongitudinal sweep efficiency of the foam zone
Figure GDA0002897755230000102
Figure GDA0002897755230000103
Wherein M is the fluidity ratio of foam to crude oil,
Figure GDA0002897755230000104
is the ratio of viscous force to gravity
Figure GDA0002897755230000105
In the formula utDenotes the foam flow rate, μoIs the viscosity of the crude oil in the formation, x is the distance of the reservoir in the direction of water injection, KxFor transverse permeability, Δ ρ is the density difference of the displacement fluid and the displaced fluid;
secondly, calculating displacement efficiency because foam can play an obvious role in plugging and profile control in air foam displacement, assuming that foam displacement is piston type displacement in a foam area, the displacement efficiency Ed of the foam displacement isfoamFor constant value, it is determined by the following formula
Figure GDA0002897755230000111
In the formula, SoiIs the original oil saturation;
calculating the recovery ratio of the foam area:
RFfoam＝Edfoam×Evfoam (16)；
(2) the liquid phase area recovery ratio calculation process is as follows:
the volume sweep coefficient of the liquid phase region is as follows:
Evwater＝Ezwater×Eswater (17)
wherein, EswaterIs the planar sweep coefficient, Ez, of the foam concentratewaterThe longitudinal sweep coefficient of the foam liquid is shown; ezwaterThe fluidity ratio of the foaming system solution and the crude oil is substituted into the formula (13) for calculation;
Figure GDA0002897755230000112
according to the leading edge theory, the average displacement fluid saturation is always equal in the range before the leading edge reaches the production well, and therefore the foam fluid dynamic displacement efficiency Ed is equal before breakthroughwaterShould be constant, is determined by
Figure GDA0002897755230000113
Liquid phase region recovery RFwaterComprises the following steps:
RFwater＝Edwater×Evwater (20)
(3) the gas phase zone recovery calculation process is as follows:
the volume sweep efficiency of the gas phase region is as follows:
Evgas＝Ezgas×Esgas (21)
wherein, EsgasIs the planar sweep coefficient, Ez, of the foam concentrategasThe longitudinal sweep coefficient of the foam liquid is shown; ezgasThe fluidity ratio of the gas and the crude oil is substituted into the formula (13) for calculation;
Figure GDA0002897755230000114
Figure GDA0002897755230000115
recovery of gas phase region RFgasComprises the following steps:
RFgas＝Edgas×Evgas (24)
the total recovery ratio before gas breakthrough is as follows:
RF＝RFfoam+RFwater+RFgas。
(II) recovery after breakthrough
(1) Calculating the volume sweep coefficient:
a: aiming at the homogeneous oil reservoir, the plane sweep coefficient Es when the oil reservoir engineering method adopts the following formula to calculate the breakthroughbtThe following formula:
Figure GDA0002897755230000121
broken plane sweep coefficient EsafterbtThe following formula:
Figure GDA0002897755230000122
where D is a coefficient for the pattern type, when a five point pattern is used, D is 0.2749; when an inverse seven-point pattern is employed, D-0.2351; when an inverse nine-point well pattern is adopted, D is 0.201; vibtVolume of injected fluid for breakthrough;
b: aiming at the heterogeneous oil reservoir, the plane wave-sum coefficient is calculated by adopting a method of correcting the mobility ratio in the homogeneous oil reservoir formula, and the pseudo-mobility ratio M is introduced and respectively comprises the pseudo-mobility ratios of foam and crude oil
Figure GDA0002897755230000123
Pseudo-fluidity ratio of foam liquid and crude oil
Figure GDA0002897755230000124
And the pseudo-fluidity ratio of the gas and the crude oil
Figure GDA0002897755230000125
Respectively calculating the plane wave sum coefficients of the foam region, the liquid phase region and the gas phase region during breakthrough
The calculation is the same as the above equations (4) and (5); plane sweep coefficient Es at break-throughbtThe following formula:
Figure GDA0002897755230000126
broken plane sweep coefficient EsafterbtThe following formula:
Figure GDA0002897755230000127
wherein the coefficients
Figure GDA0002897755230000128
Used for limiting the broken plane sweep coefficient to lead the broken plane sweep coefficient to tend to the maximum plane sweep coefficient Es under the conditions of the current fluidity ratio and the permeability coefficient of variationmaxThe calculation method is as follows:
Figure GDA0002897755230000129
calculating the maximum plane wave sum coefficient EsmaxBefore, firstly, the value V at the boundary point when the permeability variation coefficient changes from low to high is introducedcThe relationship between the fluidity ratio and the fluidity ratio can be calculated by the following formula:
Vc＝-0.063ln(M+0.1)+0.547 (30)
when the coefficient of variation of permeability V is less than VcWhen the maximum plane sweep efficiency is as follows,
Esmax＝-0.071V+0.861-0.061ln(M+0.1) (31)
when the coefficient of variation of permeability V is more than or equal to VcThe maximum plane sweep coefficient is
Figure GDA0002897755230000131
Wherein EscThe coefficient of permeability variation is equal to VcThe plane sweep coefficient.
Longitudinal sweep coefficient EzafterbtThe calculation method is the same as the formula (13);
volume sweep coefficient
Evafterbt＝Ezafterbt×Esafterbt (33)；
(2) Calculating dynamic oil displacement efficiency EdComprises the following steps:
Figure GDA0002897755230000132
wherein S isdIn order to displace the fluid dynamic saturation,
Figure GDA0002897755230000133
for residual oil saturation at dynamic displacement,
Figure GDA0002897755230000134
according to the theory of water saturation of the front edge of the seepage mechanics, the cumulative injection pore volume multiple PV is the reciprocal of the change rate of the water content to the water saturation, namely
Figure GDA0002897755230000135
Meanwhile, according to the seepage mechanics theory, the water content fwCan be expressed as:
Figure GDA0002897755230000136
according to the relative permeability K of the two phases of oil and foam liquidroAnd KrwIs a function of the water saturation, which in turn can be generally expressed as:
Figure GDA0002897755230000137
wherein a and b are coefficients, can be obtained by
Figure GDA0002897755230000138
And SwLinear regression is carried out on the semilogarithmic coordinate graph;
substituting formula (37) for formula (36) and deriving to obtain
Figure GDA0002897755230000141
Figure GDA0002897755230000142
The cumulative injection pore volume multiple may be determined from the cumulative amount of injection fluid, i.e.:
Figure GDA0002897755230000143
wherein B iswIs the formation water volume coefficient, A is the oil-bearing area, h is the reservoir thickness, phi is the reservoir porosity, ρwIs the density of the foam liquid;
the fluidity ratio of the given PV number can be obtained by utilizing the formula, and the corresponding water content at the moment can be obtained by the fluidity ratio; then according to the seepage mechanics water phase flow-dividing formula, the dynamic average water saturation at the moment can be obtained
Figure GDA0002897755230000144
I.e. the dynamic saturation S of the displacement fluiddNamely:
Figure GDA0002897755230000145
wherein, muwViscosity of the foam concentrate, muoIs the formation crude oil viscosity;
the oil displacement efficiency is brought into a formula (34) of the oil displacement efficiency, and the dynamic oil displacement efficiency of the oil deposit at the moment can be obtained:
Figure GDA0002897755230000146
(3) calculated recovery ratio
According to the calculated volume sweep coefficient and oil displacement efficiency, the recovery ratio RF is calculated as follows:
RF＝Ed×Ev (43)。
example 1
The method for predicting the recovery ratio of the air foam flooding of the oil reservoir is verified by applying the actual production data of the oil field:
the Tang 80 well region is located in Zhengji Zhengzhou of Yanan city of Shanxi province, the main oil-containing layer is a three-fold-system extended-group-length 6-oil-layer group, the average buried depth of the oil reservoir is 441 m, the average porosity is 7.9%, and the average permeability is 0.82 multiplied by 10-3μm2The pressure coefficient of an original stratum is 0.95, the temperature of an oil layer is 26-30 ℃, and the method belongs to an ultra-low permeability, low pressure and low temperature lithologic oil reservoir. And (4) determining to carry out an air foam flooding mine test in the region through oil reservoir screening and analysis. Before the mine field test, a large number of indoor tests and evaluation studies have been conducted on the area, and relatively comprehensive parameter data are obtained, as detailed in table 1.
TABLE 1 Tang 80 well indoor test parameter values (under formation conditions)
Preferred blowing agents BK-6 foaming agent Volume coefficient of formation water Bw 1.015
Frother half life T (min) 210 Irreducible water saturation Swc 32.86％
Viscosity mu of crude oilo(mPa·s) 5.84 Original oil saturation Soi 44.12％
Viscosity of foam muf(mPa·s) 105 Oil phase permeability Ko(md) 0.127
Viscosity of foam liquid muw(mPa·s) 0.875 Permeability of foam Kf(md) 0.015
Air viscosity mug(mPa·s) 0.068 Permeability of foam concentrate Kw(md) 0.079
Crude oilDensity po(kg/m3) 824 Gas phase permeability Kg(md) 0.324
Foam density ρf(kg/m3) 348 Residual oil saturation S of foam floodingorfoam 8.15％
Density of foam concentrate rhow(kg/m3) 998 Foam liquid flooding residual oil saturation Sorwater 15.88％
Air density ρg(kg/m3) 81.3 Air-driven residual oil saturation Sorgas 18.97％
On the basis of indoor comprehensive research, preferably selecting a 54-well cluster and a 55-well cluster in the area to carry out air injection foam flooding mine field test, wherein the oil-containing area of the well cluster is 0.58km2The effective thickness of the oil layer group is 10 m. The foam liquid is injected into the foam tank for 494.27m3Cumulative air injection 528.34m3And (volume under stratum condition) the benefited oil well begins to see gas, and the recovery ratio in the air foam flooding stage is calculated to be 1.79% according to the accumulated oil production data on site. When the statistical data is up, the foam liquid 5909.32m is injected in an accumulated way3Cumulative air injection 20209.24m3(volume under formation conditions), the well group is always in the gas phase, accumulated according to the siteAnd calculating the recovery ratio of the air foam flooding stage to 7.61% by using the oil production data.
According to the table 1 and the related parameters, the method for predicting the recovery ratio of the air foam flooding of the oil reservoir is used for predicting and calculating the recovery ratio of the well group in different stages of air foam flooding, and foam liquid 494.27m is injected in an accumulated mode before the gas is seen3Cumulative air injection 528.34m3(volume under formation conditions) the recovery factor was calculated to be 1.92%; the foam liquid is injected into the foam tank for 5909.32m3Cumulative air injection 20209.24m3The recovery factor (volume under formation conditions) was calculated to be 8.26%. The absolute errors of the two prediction calculation results and the field actual data calculation result are respectively 0.13% and 0.65%, and the relative errors are respectively 7.26% and 8.54%, so that the accuracy requirement that the relative error is controlled within 10% in engineering calculation is met. The accuracy and the applicability of the method for predicting the recovery ratio of the air foam flooding of the oil reservoir are explained, and a basis and a reference can be provided for evaluation of the air foam flooding effect of the oil reservoir and related planning.
The meanings represented by the respective physical quantities mentioned above have been explained, and the specific units are as follows: a. thefoam、Awater、Agas、Abtfoam、Abtwater、Abtgas、AtotalThe unit of area A is m2；Vi、Vleft、Vibt、VfoamThe units of equal volumes are all m3；μwAnd muoThe units of the equal viscosity are all mPas; Δ ρ and ρwThe units of the equal densities are all kg/m3(ii) a The unit of the spatial scales such as h and x is m; u. oftThe unit is m/d; kxUnit of (d) is md; the unit of T is min. Fluidity ratio parameter
Figure GDA0002897755230000161
M, saturation parameter Swc、Soi、Sorfoam、Sowater、Sorgas、
Figure GDA0002897755230000162
Sd、
Figure GDA0002897755230000163
Sweep coefficient Evfoam、Esfoam、Ezfoam、Evwater、Eswater、Ezwater、Esgas、Ezgas、Esbt、Esafterbt、Esmax、EscEv, Es, Ez, oil displacement efficiency Edfoam、Edwater、EdgasEd, recovery factor RFfoam、RFwater、RFgasRF, and Bw、φ、PV、Kro、KrwAnd the parameters of fw and the like are dimensionless.

Claims (5)

1. A method for predicting the recovery ratio of air foam flooding of an oil reservoir is characterized by comprising the following steps: the method comprises the following steps:
(1) assuming that the injected fluid can gradually form three areas, namely a foam area, a liquid phase area and a gas phase area, and dividing the displacement stage into a certain stage of the displacement stage before gas breakthrough and a certain stage after gas breakthrough;
wherein A isbtfoam+Abtwater+Abtgas<AtotalWhen the sum of the swept areas of the three regions is smaller than the whole oil reservoir area, the gas is considered to be not broken through; a. thebtfoam+Abtwater+Abtgas＝AtotalWhen the sum of the swept areas of the three regions occupies the whole oil reservoir, the gas is considered to break through at the moment; when A isbtfoam+Abtwater＝AtotalWhen the sum of the swept areas of the water-based liquid phase region and the foam region occupies the whole oil reservoir, the gas phase region is considered to be completely broken through; wherein A isbtfoamIs the area swept by the foam area, AbtwaterIs the swept area of the water-based liquid phase region, AbtgasIs the swept area of the gas phase, AtotalThe whole oil reservoir area;
(2) respectively calculating the displacement efficiency and the sweep efficiency of each area of the foam area, the liquid phase area and the gas phase area in the current stage before or after the current stage is determined to be gas breakthrough;
(3) the recovery ratio R is the displacement efficiency multiplied by the sweep coefficient.
2. The method for predicting reservoir air foam flooding recovery of claim 1, wherein: according to definition and seepage mechanics, the area of each region can be calculated by the following formula:
Figure FDA0002988214770000011
Figure FDA0002988214770000012
Figure FDA0002988214770000013
wherein C is a coefficient related to the well pattern; when a five-point well pattern is used, C is 0.718; when an inverted seven-point well pattern is used, C is 0.743; when an inverse nine-point well pattern is adopted, C is 0.525;
②
Figure FDA0002988214770000014
and
Figure FDA0002988214770000015
respectively the simulated mobility ratio of foam and crude oil, the simulated mobility ratio of foam liquid and crude oil and the simulated mobility ratio of gas and crude oil, wherein the values of the simulated mobility ratios are respectively determined by the mobility ratio M and the permeability coefficient of variation V of two corresponding fluids under a homogeneous condition, and the simulated mobility ratios are respectively calculated according to the following formulas under a heterogeneous condition:
when V is less than or equal to 0.7,
Figure FDA0002988214770000021
wherein M is*Is a pseudo-fluidity ratio;
when V is greater than 0.7, the crystal,
Figure FDA0002988214770000022
calculating Afoam: firstly, calculating the residual foam amount by using the data of the foam half-life:
Figure FDA0002988214770000023
wherein, VleftThe residual volume of foam after a certain complete slug has elapsed time t; viThe volume of a foam slug as it is formed is assumed in the calculation to be the sum of the volume of injected air and foaming system solution at formation pressure, thus the total injected volume of fluid for each slug; t is the foam half-life;
swept volume V of the foam zonefoamThe following can be calculated:
Figure FDA0002988214770000024
wherein S iswcIrreducible water saturation; sorfoamIs the residual oil saturation of the foam flooding, which is equal to the endpoint value when the relative permeability of the foam and the crude oil in the relative permeability curve of the crude oil is 0;
the swept area of the foam zone is as follows:
Figure FDA0002988214770000025
the swept area of the water-based liquid phase region, which is generated by the collapse of the foam, can be calculated from its physical significance by the following formula:
Figure FDA0002988214770000026
where φ is reservoir porosity, h is reservoir thickness, λwaterRepresents the volume ratio of the foaming system solution in each injection slug, SorwaterThe residual oil saturation of the foam liquid flooding is equal to the endpoint value when the relative permeability of the foam liquid and the crude oil in the relative permeability curve of the crude oil is 0;
the swept area of the gas phase region comes from the air which can not form foam after the fluid is injected and the swept area formed by the gas generated after the foam is broken at the front edge part, and can be expressed as follows according to the physical meaning:
Figure FDA0002988214770000031
wherein λ isgasRepresents the volume ratio of the gas in each injection slug, SorgasAnd the residual oil saturation of the gas flooding is equal to the endpoint value when the relative permeability of the gas and the crude oil is 0 in a relative permeability curve of the gas and the crude oil, R represents the reaction coefficient of the gas, and R is 0.996 as known from low-temperature oxidation reaction.
3. The method for predicting reservoir air foam flooding recovery of claim 2, wherein: the calculation of the recovery ratio before breakthrough comprises three parts, namely the recovery ratio of a foam zone, the recovery ratio of a liquid zone and the recovery ratio of a gas zone;
wherein the foam area recovery ratio calculation process is as follows:
calculating the sweep coefficient
Evfoam＝Ezfoam·Esfoam (11)
Wherein, EsfoamIs the planar sweep coefficient, Ez, of the foam areafoamLongitudinal sweep efficiency of the foam zone
Figure FDA0002988214770000032
Figure FDA0002988214770000033
Wherein M is the fluidity ratio of foam to crude oil,
Figure FDA0002988214770000034
is the ratio of viscous force to gravity
Figure FDA0002988214770000035
In the formula utDenotes the foam flow rate, μoIs the viscosity of the crude oil in the formation, x is the distance of the reservoir in the direction of water injection, KxFor transverse permeability, Δ ρ is the density difference of the displacement fluid and the displaced fluid;
② calculating the displacement efficiency
Figure FDA0002988214770000036
In the formula, SoiIs the original oil saturation;
calculating the recovery ratio of the foam area:
RFfoam＝Edfoam×Evfoam (16)；
similarly, the liquid phase region recovery process is as follows:
Evwater＝Ezwater×Eswater (17)
wherein, EswaterIs the planar sweep coefficient, Ez, of the foam concentratewaterThe longitudinal sweep coefficient of the foam liquid is shown; ezwaterThe fluidity ratio of the foaming system solution and the crude oil is substituted into the formula (13) for calculation;
Figure FDA0002988214770000041
Figure FDA0002988214770000042
liquid phase region recovery RFwaterComprises the following steps:
RFwater＝Edwater×Evwater (20)
similarly, the gas phase zone recovery process is as follows:
Evgas＝Ezgas×Esgas (21)
wherein, EsgasIs the planar sweep coefficient of gas, EzgasIs the longitudinal sweep coefficient of the gas; ezgasThe fluidity ratio of the gas and the crude oil is substituted into the formula (13) for calculation;
Figure FDA0002988214770000043
Figure FDA0002988214770000044
recovery of gas phase region RFgasComprises the following steps:
RFgas＝Edgas×Evgas (24)
the total recovery ratio before gas breakthrough is as follows:
RF＝RFfoam+RFwater+RFgas。
4. the method for predicting reservoir air foam flooding recovery of claim 3, wherein: the recovery ratio after breakthrough comprises three parts, namely foam zone recovery ratio, liquid zone recovery ratio and gas zone recovery ratio;
(1) calculating the volume sweep coefficient:
aiming at homogeneous oil deposit, the plane sweep coefficient Es during breakthroughbtThe following formula:
Figure FDA0002988214770000045
broken plane sweep coefficient EsafterbtThe following formula:
Figure FDA0002988214770000046
where D is a coefficient for the pattern type, when a five point pattern is used, D is 0.2749; when an inverse seven-point pattern is employed, D-0.2351; when an inverse nine-point well pattern is adopted, D is 0.201; vibtVolume of injected fluid for breakthrough;
aiming at the heterogeneous oil deposit, the plane sweep coefficient Es during breakthroughbtThe following formula:
Figure FDA0002988214770000051
broken plane sweep coefficient EsafterbtThe following formula:
Figure FDA0002988214770000052
wherein, the coefficient X is used for limiting the broken plane sweep coefficient to lead the broken plane sweep coefficient to tend to the maximum plane sweep coefficient Es under the conditions of the current fluidity ratio and the permeability variation coefficientmaxThe calculation method is as follows:
Figure FDA0002988214770000053
broken longitudinal sweep coefficient EzafterbtThe calculation method is the same as the formula (13);
volume sweep coefficient
Evafterbt＝Ezafterbt×Esafterbt (33)；
(2) Calculating dynamic oil displacement efficiency EdComprises the following steps:
Figure FDA0002988214770000054
wherein S isdIn order to displace the fluid dynamic saturation,
Figure FDA0002988214770000055
for residual oil saturation at dynamic displacement,
Figure FDA0002988214770000056
according to the theory of water saturation of the front edge of the seepage mechanics, the cumulative injection pore volume multiple PV is the reciprocal of the change rate of the water content to the water saturation, namely
Figure FDA0002988214770000057
Meanwhile, according to the seepage mechanics theory, the water content fwCan be expressed as:
Figure FDA0002988214770000058
according to the relative permeability K of the two phases of oil and foam liquidroAnd KrwIs a function of the water saturation, which in turn can be generally expressed as:
Figure FDA0002988214770000059
wherein a and b are coefficients, can be obtained by
Figure FDA0002988214770000061
And SwLinear regression is carried out on the semilogarithmic coordinate graph;
substituting formula (37) for formula (36) and deriving to obtain
Figure FDA0002988214770000062
Figure FDA0002988214770000063
The cumulative injection pore volume multiple may be determined from the cumulative amount of injection fluid, i.e.:
Figure FDA0002988214770000064
wherein B iswIs the formation water volume coefficient, A is the oil-bearing area, h is the reservoir thickness, phi is the reservoir porosity, ρwIs the density of the foam liquid;
the fluidity ratio of the given PV number can be obtained by utilizing the formula, and the corresponding water content at the moment can be obtained by the fluidity ratio; then according to the seepage mechanics water phase flow-dividing formula, the dynamic average water saturation at the moment can be obtained
Figure FDA0002988214770000065
I.e. the dynamic saturation S of the displacement fluiddNamely:
Figure FDA0002988214770000066
wherein, muwViscosity of the foam concentrate, muoIs the formation crude oil viscosity;
the oil displacement efficiency is brought into a formula (34) of the oil displacement efficiency, and the dynamic oil displacement efficiency of the oil deposit at the moment can be obtained:
Figure FDA0002988214770000067
(3) calculated recovery ratio
According to the calculated volume sweep coefficient and oil displacement efficiency, the recovery ratio RF is calculated as follows:
RF＝Ed×Ev (43)。
5. the method for predicting reservoir air foam flooding recovery of claim 4, wherein: the EsmaxThe calculation method of (2) is as follows:
value V at the boundary point when the permeability coefficient of variation changes from low to high is introducedcThe relationship between the fluidity ratio and the fluidity ratio can be calculated by the following formula:
Vc＝-0.063ln(M+0.1)+0.547 (30)
when the coefficient of variation of permeability V is less than VcWhen the maximum plane sweep efficiency is as follows,
Esmax＝-0.071V+0.861-0.061ln(M+0.1) (31)
when the coefficient of variation of permeability V is more than or equal to VcThe maximum plane sweep coefficient is
Figure FDA0002988214770000071
Wherein, EscThe coefficient of permeability variation is equal to VcThe plane sweep coefficient.
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