CN114330155B - Prediction method considering spontaneous imbibition oil-water relative permeability of core under ionic water concentration - Google Patents
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Abstract
The invention discloses a prediction method of oil-water relative permeability under the spontaneous imbibition of a core by considering the concentration of ionized water, which aims at solving the problems that the oil-water relative permeability in spontaneous imbibition is difficult to accurately obtain in the existing spontaneous imbibition research approach and method, and accurately calculates the oil-water relative permeability under the spontaneous imbibition by combining the physical parameters of the core and the property parameters of fluid through a theoretical model, and accurately draws an oil-water relative permeability curve and a standardized oil-water relative permeability curve in the spontaneous imbibition process of the core. The prediction method provided by the invention is accurate and reliable, has the advantages of short period, strong repeatability, wide application range, economy, practicability and the like, and provides a reliable means for further researching the spontaneous imbibition action mechanism and effectively guiding the oil reservoir development.
Description
Technical Field
The invention belongs to the technical field of oil reservoir exploration and development, and particularly relates to a prediction method of spontaneous imbibition oil-water relative permeability of a core by considering ionic water concentration.
Background
Along with the continuous increase of oil and gas requirements, the decrease of conventional oil and gas productivity and the application and popularization of new technology for exploration and development, unconventional oil and gas gradually become a new field of global oil exploration and development, and a great breakthrough is made, and dense oil is one of unconventional energy sources and is another new hot spot for global unconventional oil and gas exploration and development after shale gas. Compact oil is regarded as 'dinner' in the field of Chinese unconventional oil and gas, and is called 'black gold' abroad, so that the economic value of the compact oil is seen. The total amount of the compact oil geological resources (106.7-111.5) multiplied by 10 8 t in China is a more realistic petroleum succession resource in the future. However, the compact oil reservoir generally has the characteristics of low pores (phi < 10%), low permeability (k < 1.0X10 -3μm2), small pore throats (d < 1.0 mu m) and the like, and is easy to form a spontaneous imbibition area under the action of strong capillary force. Spontaneous imbibition widely exists in the fields of engineering application and natural science, and the definition of the oil-water relative permeability of the spontaneous imbibition has important significance for researching imbibition mechanism, oil reservoir numerical simulation calculation and oil reservoir development scheme design.
At present, research on spontaneous imbibition mainly comprises two approaches of an indoor experiment and a numerical simulation method. The indoor experiment is mainly focused on the change relation between the spontaneous imbibition amount/spontaneous imbibition recovery ratio and time/dimensionless time of crude oil, and the oil-water relative permeability under the spontaneous imbibition effect of the core cannot be obtained; the existing spontaneous imbibition numerical simulation method mainly comprises the following steps: firstly, establishing a imbibition mathematical model based on a mass conservation equation, an experimental phase permeation curve, a J function, a poiseuille equation and the like, wherein most of the mathematical models mainly study the relation between spontaneous imbibition quantity/spontaneous imbibition recovery ratio and time/dimensionless time of crude oil, and comparing and analyzing with experimental results, only a small number of the mathematical models establish the relative oil-water permeability in the displacement process based on the poiseuille equation, and the accurate calculation of the relative oil-water permeability in the spontaneous imbibition is obviously lacking under the assumption that the matrix permeability is K=S w -1 or the matrix contact surface is not considered; based on experimental data, the relative permeability of a wet phase (water phase) is obtained through fitting theoretical calculation and comparison of experimental test results, but the method needs to assume parameter values for a plurality of times, and has the problems of complex calculation steps, multiple resolvability and the like. The prediction method in the patent CN105676309A, CN110306960A needs to obtain the oil-water relative permeability through experiments and does not consider the influence of the concentration of the ionized water; the prediction method in patent CN109884269A, CN111305805A, CN111460651A, CN112163360a cannot calculate or predict the relative permeability of oil and water; the calculation method in CN110398450a can only obtain relative permeability of wet phase (water phase), and the average water saturation of the front edge needs to be imbibed in the calculation process, but the average water saturation of the front edge is difficult to obtain accurately, and the influence of the concentration of the ionized water is not considered.
Disclosure of Invention
The invention aims to provide a prediction method for oil-water relative permeability under the spontaneous imbibition effect of a core by considering the concentration of ionized water, aiming at solving the problem that the relative permeability of oil-water in spontaneous imbibition is difficult to accurately obtain in the existing spontaneous imbibition research route and method, and further researching the spontaneous imbibition effect mechanism and effectively guiding the development process of a compact oil reservoir.
In order to achieve the above purpose, the method for predicting the oil-water relative permeability under the spontaneous imbibition effect of the ion water concentration core comprises the following steps:
1. Collecting core physical parameters and fluid properties, including: oil phase viscosity mu o, water phase viscosity mu w, formation water mineralization c 2, ionic water mineralization c 1, oil-water interfacial tension sigma, contact angle theta, core length l, core diameter d, core porosity phi, core irreducible water saturation S wi, core residual oil saturation S or, core maximum pore diameter lambda max, core minimum pore diameter lambda min.
2. According to the maximum pore diameter lambda max, the minimum pore diameter lambda min, the core irreducible water saturation S wi and the core residual oil saturation S or, the maximum effective pore diameter lambda emax and the minimum effective pore diameter lambda emin of the core are calculated, and the calculation formula is as follows: And/>
According to the core porosity phi, the core maximum effective pore diameter lambda emax and the core minimum effective pore diameter lambda emin, calculating the core aperture fractal dimension D m, wherein the calculation formula is as follows: Where d E is a euclidean constant, d E =2 in the two-dimensional plane, d E =3 in the three-dimensional space.
Calculating a core tortuosity fractal dimension D T according to the core length l, the core porosity phi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin and the core aperture fractal dimension D m, wherein the calculation formula is as follows: Where τ is core tortuosity,/> Lambda eav is the average diameter of the core,
3. Obtaining a relational expression between a imbibition time t 'and a critical effective capillary diameter lambda ec, wherein the imbibition time t' is obtained by substituting an oil phase in a capillary in a core by an imbibition water phase just completely according to oil phase viscosity mu o, water phase viscosity mu w, oil-water interface tension sigma, a contact angle theta, core length l and core tortuosity fractal dimension D T: and a plot of the imbibition time t' versus the critical effective capillary diameter lambda ec is drawn.
The oil phase and water phase imbibition speed of the core is calculated according to the oil phase viscosity mu o, the water phase viscosity mu w, the formation water mineralization degree c 2, the ionic water mineralization degree c 1, the oil-water interfacial tension sigma, the contact angle theta, the core length l, the core porosity phi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin, the core aperture fractal dimension D m, the core tortuosity fractal dimension D T and the critical effective capillary diameter lambda ec, and the calculation formula of the oil phase imbibition speed q o of the core is as follows:
The calculation formula of the core water phase imbibition speed q w is as follows: /(I) Wherein R is an ideal gas constant term, T is temperature, V w is the molar volume of the water phase, lambda e is the effective diameter of the capillary, mu w-o is the difference between the viscosity of the water phase and the viscosity of the oil phase, S is the imbibition contact area of the core,L' is the length of the core immersed in the ionized water, i is the ratio of the cross-sectional areas at the two ends of the core immersed in the ionized water, j is the ratio of the side area of the core immersed in the ionized water, x is the distance of the oil-water interface in the capillary bundle with the length of the core l moving in the capillary
T is the imbibition time.
4. The whole core water phase saturation S w is calculated according to the core length l, the core irreducible water saturation S wi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin, the capillary effective diameter lambda e, the critical effective capillary diameter lambda ec, the core aperture fractal dimension D m and the core tortuosity fractal dimension D T, and the calculation formula is as follows:
5. The calculation formula of the spontaneous imbibition oil-water relative permeability of the core is calculated according to oil phase viscosity mu o, water phase viscosity mu w, formation water mineralization c 2, ionized water mineralization c 1, oil-water interfacial tension sigma, contact angle theta, core length l, core maximum effective pore diameter lambda emax, core minimum effective pore diameter lambda emin, distance x of oil-water interface moving in capillary bundle with core length l, capillary effective diameter lambda e, critical effective capillary diameter lambda ec, core aperture fractal dimension D m and core tortuosity fractal dimension D T, wherein the calculation formula of spontaneous imbibition oil-water relative permeability k rw of the core is as follows:
The calculation formula of the spontaneous imbibition oil phase relative permeability k ro of the core is as follows: /(I) And combining the water phase saturation S w of the whole core, and accurately acquiring an oil-water relative permeability curve in the spontaneous imbibition process of the core.
6. According to the core irreducible water saturation S wi, the core residual oil saturation S or and the core standardized water saturation S w *, calculating the water saturation S w', wherein the relation is as follows: and the relative permeability of spontaneous imbibition oil and water of the rock core is standardized, and the calculation formula of the standardized treatment is as follows: /(I) Wherein α, β, m, n are constants, depending on the rock wettability and its pore structure; and finally, drawing a standardized oil-water relative permeability curve in the spontaneous imbibition process of the core.
The beneficial effects of the invention are as follows:
Aiming at the problem that the oil-water relative permeability in spontaneous imbibition is difficult to accurately obtain in the existing spontaneous imbibition research approach and method, the oil-water relative permeability curve under the spontaneous imbibition effect is accurately calculated and obtained through a theoretical model by combining the physical parameters of the core and the fluid property parameters. The prediction method provided by the invention is accurate and reliable, has the advantages of short period, strong repeatability, wide application range, economy, practicability and the like, and provides a reliable means for further researching the spontaneous imbibition action mechanism and effectively guiding the oil reservoir development.
Drawings
Fig. 1 is a model of spontaneous imbibition flow of a single capillary tube.
Fig. 2 is a schematic view of a capillary bundle model of a core.
Fig. 3 is a core 1# capillary pressure curve of example 1.
FIG. 4 is a plot of core 1# imbibition time t' versus critical effective capillary diameter lambda ec for example 1.
Fig. 5 is a graph of oil-water relative permeability during spontaneous imbibition of core # 1 in example 1.
FIG. 6 is a graph of normalized oil-water relative permeability during spontaneous imbibition of core # 1 in example 1.
Fig. 7 is a graph of core 2# capillary pressure in example 2.
Fig. 8 is a plot of core 2# imbibition time t' versus critical effective capillary diameter lambda ec for example 2.
Fig. 9 is a graph of oil-water relative permeability during spontaneous imbibition of core #2 in example 2.
Fig. 10 is a normalized oil-water relative permeability curve during spontaneous imbibition of core # 2 in example 2.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, but the scope of the present invention is not limited to these examples.
The invention relates to a method for predicting the relative permeability of oil and water under the action of spontaneous imbibition based on single capillary stress analysis and combining fractal theory and capillary bundle model characteristics.
As shown in fig. 1, capillary force F c＝S'·pc for inducing fluid suction in a hydrophilic capillary with radius r, penetration force F Π =s' ·pi caused by different ionized water in stratum, shearing friction force F f＝C·[x'τw+(L'-x')τo on capillary wall, fluid gravity F g＝S'·[x'ρw+(L'-x)ρo ] g·sin α in capillary, wherein: s' is the capillary cross-sectional area; Is capillary pressure; /(I) Is osmotic pressure; c is the circumference of the capillary; l' is the capillary length; Is water phase shearing force; /(I) Is oil phase shearing force; x' is the distance that the oil-water interface moves in the capillary; r is the capillary radius; r is an ideal gas constant term; t is the temperature; v w is the molar volume of the aqueous phase; c 2 is the formation water mineralization and c 1 is the ionic water mineralization; mu w is the aqueous phase viscosity; mu o is the viscosity of the oil phase; sigma is the oil-water interfacial tension; θ is the contact angle; ρ w is the aqueous phase density; ρ o is the oil phase density; alpha is the capillary inclination angle or the reservoir inclination angle; all take international units.
The single-phase viscous incompressible fluid in the capillary tube meets Newton's second law ma = Σf, and under the action of neglecting inertia force, the imbibition dynamics equation is as follows:
the capillary line imbibition speed v and the time t required by the oil-water interface moving in the capillary tube with the distance x' are obtained by the arrangement, namely:
Wherein: mu w-o is the difference between the aqueous phase viscosity and the oil phase viscosity; ρ w-o is the difference between the density of the aqueous phase and the density of the oil phase.
Because the influence of gravity is small, the gravity is ignored to obtain the following calculation formula:
Considering the existence of bound water and residual oil in the capillary, assuming that the bound water exists in an immobilized boundary layer with the thickness of h w, the residual oil is also equivalent to the immobilized boundary layer with the thickness of h o being attached to the inner wall of the capillary, and the effective radius r e of the capillary is as follows:
wherein: s wi' is capillary irreducible water saturation; s or' is the capillary residual oil saturation.
Substituting the effective radius r e of the capillary into a calculation formula of the capillary line imbibition speed v and the moving distance x' of the oil-water interface in the capillary, and converting the effective radius r e of the capillary into the effective diameter lambda e of the capillary to obtain the following calculation formula:
Wherein: lambda is the capillary diameter.
The pores in the reservoir core are mutually communicated to form a curved channel, so that the capillary bundles of the core, which are provided with pores mutually communicated to form capillary bundles with unequal diameters, are schematically shown in fig. 2.
According to the distance x' of the oil-water interface moving in the capillary, the calculation formula of the distance x of the oil-water interface moving in the capillary bundle with the core length of l is as follows: distance of oil-water interface in capillary tube bundle actually moving in capillary tube/> Actual capillary length in capillary bundleWherein: d T is the fractal dimension of the tortuosity of the core,Τ is the tortuosity of the core,Lambda eav is the average capillary diameter,Lambda emax is the maximum effective pore diameter of the core, lambda emin is the minimum effective pore diameter of the core,
Lambda max is the maximum pore diameter of the core, lambda min is the minimum pore diameter of the core, S wi is the irreducible water saturation of the core (S wi＝Swi'),Sor can be considered as the saturation of the residual oil of the core (S or＝Sor');Dm can be considered as the fractal dimension of the pore diameter of the core,/>)D E is euclidean constant, in two dimensions, da E =2, 1<D m <2; whereas in three dimensions d E = 3, 1<D m <3; phi is the core porosity.
Based on fractal theory, combining capillary bundle model, core cross-sectional area: the effective diameter number of the capillary is accumulated on the core imbibition contact surface: /(I) The core imbibition capillary effective diameter varies from lambda e to lambda e+dλe by an amount: /(I)Wherein: s S is the rock cross-sectional area; n S is the accumulated pore number of the core imbibition contact surface; s is the core imbibition contact areaL' is the length of the core immersed in the ionized water, i is the ratio of the cross-sectional areas at the two ends of the core immersed in the ionized water, and j is the ratio of the side areas of the core immersed in the ionized water.
Based on fractal theory and combined with capillary bundle model, the whole core is immersed into the seepage liquid to calculate the effective pore volume V' t:
The volume V' w of the aqueous phase in the core is:
Similarly, the volume V' o of the oil phase in the core is:
The saturation degree of each phase of the oil and water of the whole rock core can be obtained: (or S o＝1-Sw), considering the condition of bound water, the saturation degree of each phase of the whole core oil-water is: /(I) S o＝1-Sw, wherein: s w is the water phase saturation of the whole core,S o is the overall core oil phase saturation.
According to capillary line imbibition speed v, capillary force p c, osmotic force p П, actual capillary length L in capillary bundle, and distance X of oil-water interface in capillary bundle in actual movement in capillary, effective actual capillary imbibition speed v e of capillary in capillary bundle is calculated as follows:
The total volume flow of each phase in the core is the sum of the flow through each capillary in the capillary bundle, and according to capillary model analysis and research, the total flow of the core water phase is the integral from the critical capillary diameter lambda ec to the maximum effective pore diameter lambda emax of the core, namely the water phase imbibition speed q w is:
similarly, the oil phase imbibition rate q o is:
The total imbibition q t when imbibition of the aqueous phase to the outlet end (x=l) is the integral from the core minimum effective pore diameter λ emin to the core maximum effective pore diameter λ emax, namely:
relative permeability refers to the ratio of the effective permeability of each phase to the absolute permeability (single phase fluid), namely:
wherein: k rw is the relative permeability of the spontaneous imbibition water phase of the core, and k ro is the relative permeability of the spontaneous imbibition oil phase of the core. And combining the water phase saturation S w of the whole core, and accurately acquiring an oil-water relative permeability curve in the spontaneous imbibition process of the core.
The critical effective capillary diameter lambda ec is defined in the capillary bundle (core) as the effective capillary diameter of the capillary tube that is exactly completely displaced by the previously imbibed fluid (water phase) within time t'. The calculation formula between the imbibition time t' of the original fluid (oil phase) in the capillary just completely replaced by imbibition fluid (water phase) and the critical effective capillary diameter lambda ec is as follows:
From the core-bound water saturation S wi, core residual saturation S or, core normalized water saturation S w * (typically equally divided into ten parts within [0,1.0 ]), the water saturation S w' is calculated as: and the relative permeability of spontaneous imbibition oil and water of the rock core is standardized, and the calculation formula of the standardized treatment is as follows: /(I) Wherein α, β, m, n are constants, depending on the rock wettability and its pore structure; and finally, drawing a standardized oil-water relative permeability curve in the spontaneous imbibition process of the core, wherein the standardized curve can provide an important theoretical basis for researching the spontaneous imbibition mechanism of the oil reservoir and effectively guiding development.
Example 1
1. Taking an oilfield core 1# and measuring the core porosity phi by adopting a saturated water weighing method based on the measured core diameter d and core length l. The oil field core is subjected to mercury intrusion test to obtain a capillary pressure curve, and a maximum pore diameter lambda max, a minimum pore diameter lambda min, a residual oil saturation (residual mercury saturation can be regarded as residual oil saturation in a mercury intrusion curve) S or and a core bound water saturation (unsaturated mercury pore volume can be regarded as core bound water saturation in the mercury intrusion curve) S wi of the core can be obtained according to the capillary pressure curve, as shown in fig. 3. Fluid physical property tests are carried out on underground crude oil and formation water to obtain oil phase viscosity mu o, water phase viscosity mu w, oil-water interfacial tension sigma and formation water mineralization degree c 2; diluting formation water 3 times by distilled water to obtain the mineralization degree c 1 of the ionized water. And obtaining the contact angle theta of the core surface by using the core 1# and underground crude oil and formation water. The results are shown in Table 1.
TABLE 1 statistical table of fluid properties and core 1# physical parameters
2. According to the maximum pore diameter lambda max, the minimum pore diameter lambda min, the core irreducible water saturation S wi and the core residual oil saturation S or, the maximum effective pore diameter lambda emax and the minimum effective pore diameter lambda emin of the core are calculated, and the calculation formula is as follows: And/> The calculation result was λ emax＝5.5491μm、λemin =0.0188 μm.
According to the core porosity phi, the core maximum effective pore diameter lambda emax and the core minimum effective pore diameter lambda emin, calculating the core aperture fractal dimension D m, wherein the calculation formula is as follows: Where D E is the euclidean constant, D E =2, and the calculation result is D m = 1.6979.
Calculating a core tortuosity fractal dimension D T according to the core length l, the core porosity phi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin and the core aperture fractal dimension D m, wherein the calculation formula is as follows: Where τ is core tortuosity,/> Lambda eav is the average diameter of the core,The calculation result is D T = 1.1788.
3. Calculating different time t' and critical effective capillary diameter lambda ec according to oil phase viscosity mu o, water phase viscosity mu w, oil-water interfacial tension sigma, contact angle theta, core length l and core tortuosity fractal dimension D T, wherein the calculation formula is as follows:
Wherein t 'is the imbibition time when the original fluid (oil phase) in the single capillary tube in the capillary tube bundle is just completely replaced by the imbibition fluid (water phase), and a curve between the imbibition time t' and the critical effective capillary lambda ec is drawn, and the result is shown in fig. 4.
The oil phase and water phase imbibition speed of the core is calculated according to the oil phase viscosity mu o, the water phase viscosity mu w, the formation water mineralization degree c 2, the ionic water mineralization degree c 1, the oil-water interfacial tension sigma, the contact angle theta, the core length l, the core porosity phi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin, the core aperture fractal dimension D m, the core tortuosity fractal dimension D T and the critical effective capillary diameter lambda ec, and the calculation formula of the oil phase imbibition speed q o of the core is as follows:
The calculation formula of the core water phase imbibition speed q w is as follows: /(I) Wherein R is an ideal gas constant term, T is temperature, V w is the molar volume of the water phase, lambda e is the effective diameter of the capillary, mu w-o is the difference between the viscosity of the water phase and the viscosity of the oil phase, S is the imbibition contact area of the core,L' is the length of the core immersed in the ionized water, i is the ratio of the cross-sectional areas at the two ends of the core immersed in the ionized water, j is the ratio of the side surface area of the core immersed in the ionized water, x is the distance of the oil-water interface in the capillary bundle with the length of the core l moving in the capillary,
T is the imbibition time.
4. The whole core water phase saturation S w is calculated according to the core length l, the core irreducible water saturation S wi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin, the capillary effective diameter lambda e, the critical effective capillary diameter lambda ec, the core aperture fractal dimension D m and the core tortuosity fractal dimension D T, and the calculation formula is as follows:
5. The calculation formula of the spontaneous imbibition oil-water relative permeability of the core is calculated according to the oil phase viscosity mu o, the water phase viscosity mu w, the formation water mineralization degree c 2, the ionized water mineralization degree c 1, the oil-water interfacial tension sigma, the contact angle theta, the core length l, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin, the distance x of the oil-water interface moving in the capillary, the capillary effective diameter lambda e, the critical effective capillary diameter lambda ec, the core aperture fractal dimension D m and the core tortuosity fractal dimension D T, wherein the calculation formula of the spontaneous imbibition water relative permeability k rw of the core is as follows: The calculation formula of the spontaneous imbibition oil phase relative permeability k ro of the core is as follows: /(I) By combining the water phase saturation S w of the whole core, the oil-water relative permeability curve of the core in the spontaneous imbibition process is accurately obtained, and the result is shown in figure 5.
6. From the core-bound water saturation S wi, the core residual saturation S or, the normalized water saturation for a given core S w * (typically in ten equal parts in [0,1.0 ]), the water saturation S w' is calculated as: And the relative permeability of spontaneous imbibition oil and water of the rock core is standardized, and the calculation formula of the standardized treatment is as follows: wherein α, β, m, n are constants, depending on the rock wettability and its pore structure; finally, a normalized oil-water relative permeability curve in the spontaneous imbibition process of the core is drawn, and the result is shown in fig. 6.
Example 2
1. And taking an oilfield core No. 2, and measuring the core porosity phi by adopting a saturated water weighing method based on the measured core diameter d and core length l. The oil field core is subjected to mercury intrusion test to obtain a capillary pressure curve, and a core maximum pore diameter lambda max, a core minimum pore diameter lambda min, a core residual oil saturation S or and a core irreducible water saturation S wi can be obtained according to the capillary pressure curve, as shown in fig. 7. Fluid physical property tests are carried out on underground crude oil and formation water to obtain oil phase viscosity mu o, water phase viscosity mu w, oil-water interfacial tension sigma and formation water mineralization degree c 2; diluting formation water by 4 times by distilled water to obtain the mineralization degree c 1 of the ionized water. And obtaining the contact angle theta of the core surface by using the core 2# and underground crude oil and formation water. The results are shown in Table 2.
Table 2 fluid properties and core 2# physical parameter statistics
Step 2 and step 5 are the same as in example 1, and a curve between the imbibition time t' and the critical effective capillary lambda ec is obtained, and the result is shown in fig. 8; and meanwhile, an oil-water relative permeability curve and a standardized oil-water relative permeability curve in the spontaneous imbibition process of the core are obtained and drawn, and the results are shown in fig. 9 and 10.
Because the core of the oil reservoir (particularly hypotonic, ultra hypotonic and compact reservoir) has higher capillary pressure, the core has stronger capability of spontaneously sucking wet phase fluid; meanwhile, the oil-water relative permeability curve is widely applied to oil field development, but the oil-water relative permeability curve in the spontaneous imbibition process of the core is difficult to obtain through experiments. The invention provides a prediction method for spontaneous imbibition oil-water relative permeability of a rock core under ionic water concentration based on single capillary stress analysis and combining analysis theory and capillary tube bundle model characteristics. According to the embodiment of the invention, parameters such as physical properties and fluid properties of a core are acquired, effective physical parameters of the core, fractal dimension of core aperture and fractal dimension of tortuosity are calculated according to the acquired parameters, critical effective capillary diameter, oil-water imbibition speed and water phase saturation of the core are determined according to the calculated related parameters, and finally an oil-water relative permeability curve and a standardized oil-water relative permeability curve in the spontaneous imbibition process of the core are acquired through calculation of the oil-water relative permeability and standardized treatment. The method can simply, rapidly and accurately determine the relative permeability of oil and water in the spontaneous imbibition process of the core according to parameters such as physical properties of the core, fluid properties and the like, and further effectively guide the efficient development process of the oil reservoir.
Claims (1)
1. The prediction method for the oil-water relative permeability under the spontaneous imbibition effect of the ionic water concentration core is characterized by comprising the following steps of:
(1) Collecting core physical parameters and fluid properties, including: oil phase viscosity mu o, water phase viscosity mu w, formation water mineralization c 2, ionic water mineralization c 1, oil-water interfacial tension sigma, contact angle theta, core length l, core diameter d, core porosity phi, core irreducible water saturation S wi, core residual oil saturation S or, core maximum pore diameter lambda max, core minimum pore diameter lambda min;
(2) According to the maximum pore diameter lambda max, the minimum pore diameter lambda min, the core irreducible water saturation S wi and the core residual oil saturation S or, the maximum effective pore diameter lambda emax and the minimum effective pore diameter lambda emin of the core are calculated, and the calculation formula is as follows: And/>
According to the core porosity phi, the core maximum effective pore diameter lambda emax and the core minimum effective pore diameter lambda emin, calculating the core aperture fractal dimension D m, wherein the calculation formula is as follows: Where d E is a euclidean constant, d E =2 in the two-dimensional plane, d E =3 in the three-dimensional space;
Calculating a core tortuosity fractal dimension D T according to the core length l, the core porosity phi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin and the core aperture fractal dimension D m, wherein the calculation formula is as follows: Where τ is core tortuosity,/> Lambda eav is the average diameter of the core,
(3) Obtaining a relational expression between a imbibition time t 'and a critical effective capillary diameter lambda ec, wherein the imbibition time t' is obtained by substituting an oil phase in a capillary in a core by an imbibition water phase just completely according to oil phase viscosity mu o, water phase viscosity mu w, oil-water interface tension sigma, a contact angle theta, core length l and core tortuosity fractal dimension D T: drawing a curve between the imbibition time t' and the critical effective capillary diameter lambda ec;
The oil phase and water phase imbibition speed of the core is calculated according to the oil phase viscosity mu o, the water phase viscosity mu w, the formation water mineralization degree c 2, the ionic water mineralization degree c 1, the oil-water interfacial tension sigma, the contact angle theta, the core length l, the core porosity phi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin, the core aperture fractal dimension D m, the core tortuosity fractal dimension D T and the critical effective capillary diameter lambda ec, and the calculation formula of the oil phase imbibition speed q o of the core is as follows:
The calculation formula of the core water phase imbibition speed q w is as follows: /(I) Wherein R is an ideal gas constant term, T is temperature, V w is the molar volume of the water phase, lambda e is the effective diameter of the capillary, mu w-o is the difference between the viscosity of the water phase and the viscosity of the oil phase, S is the imbibition contact area of the core,L' is the length of the core immersed in the ionized water, i is the ratio of the cross-sectional areas at the two ends of the core immersed in the ionized water, j is the ratio of the side area of the core immersed in the ionized water, x is the distance of the oil-water interface in the capillary bundle with the length of the core l moving in the capillary
T is imbibition time;
(4) The whole core water phase saturation S w is calculated according to the core length l, the core irreducible water saturation S wi, the core maximum effective pore diameter lambda emax, the core minimum effective pore diameter lambda emin, the capillary effective diameter lambda e, the critical effective capillary diameter lambda ec, the core aperture fractal dimension D m and the core tortuosity fractal dimension D T, and the calculation formula is as follows:
(5) The calculation formula of the spontaneous imbibition oil-water relative permeability of the core is calculated according to oil phase viscosity mu o, water phase viscosity mu w, formation water mineralization c 2, ionized water mineralization c 1, oil-water interfacial tension sigma, contact angle theta, core length l, core maximum effective pore diameter lambda emax, core minimum effective pore diameter lambda emin, distance x of oil-water interface moving in capillary bundle with core length l, capillary effective diameter lambda e, critical effective capillary diameter lambda ec, core aperture fractal dimension D m and core tortuosity fractal dimension D T, wherein the calculation formula of spontaneous imbibition oil-water relative permeability k rw of the core is as follows:
The calculation formula of the spontaneous imbibition oil phase relative permeability k ro of the core is as follows: /(I) Combining the water phase saturation S w of the whole core, accurately acquiring an oil-water relative permeability curve in the spontaneous imbibition process of the core;
(6) According to the core irreducible water saturation S wi, the core residual oil saturation S or and the core standardized water saturation S w *, calculating the water saturation S w', wherein the relation is as follows: and the relative permeability of spontaneous imbibition oil and water of the rock core is standardized, and the calculation formula of the standardized treatment is as follows: /(I) Wherein α, β, m, n are constants, depending on the rock wettability and its pore structure; and finally, drawing a standardized oil-water relative permeability curve in the spontaneous imbibition process of the core. /(I)
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