CN114428934B - Oil-water relative permeability curve characterization method based on trigonometric function - Google Patents
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Abstract
The invention provides an oil-water relative permeability curve characterization method based on a trigonometric function, which comprises the following steps: step 1, selecting typical oil-water relative permeability curve data capable of reflecting oil reservoir characteristics; step 2, carrying out standardized treatment on the water saturation S w in the oil-water relative permeability curve data, and defining the water saturation as X; step 3, the natural logarithm is calculated for the ratio K ro/Krw of the relative permeability of the oil phase and the relative permeability of the water phase, and then divided by pi, and the arctangent function value is calculated, and is defined as Y; and step 4, establishing a linear function relation between Y and X, and determining a function expression of a relation curve of relative permeability ratio and water saturation of the oil phase and the water phase based on the trigonometric function. The oil-water relative permeability curve characterization method based on the trigonometric function performs mathematical characterization on a complex nonlinear relation between the relative permeability ratio of the oil phase to the water phase and the water saturation, so that the oil reservoir water flooding development effect and trend are accurately predicted, and the development and production practice of an oil field are guided.
Description
Technical Field
The invention relates to the technical field of oilfield development, in particular to an oil-water relative permeability curve characterization method based on a trigonometric function.
Background
The oil-water relative permeability curve is the comprehensive reflection of oil-water two-phase seepage characteristics in the rock gaps, and is the most basic rule followed by the oil-water two-phase in the seepage process. The oil-water permeability curve is important data in oil production prediction of oil reservoir engineering. The oil-water relative permeability curve is effectively characterized, and the method has important guiding significance for optimizing an oil field development scheme, improving the oil field recovery ratio and improving the oil field development effect.
At present, the traditional oil-water relative permeability characterization method mainly uses an exponential function characterization method, wherein the function characterization form is simple, but the error is larger, and the precision is poorer. Particularly, in a low water saturation region, a complex nonlinear relation between the relative permeability of oil and water and the water saturation cannot be accurately represented, so that early oil yield of oil field development cannot be accurately predicted, and optimization of an integral development scheme of the oil field and improvement of final recovery efficiency are affected.
In application number: the Chinese patent application CN201310116446.6 relates to a representation method of oil-water relative permeability curve under different displacement pressure gradient conditions, and belongs to the technical field of petroleum development oil reservoir engineering. The method comprises the following steps: (1) Applying different displacement pressure gradients to a group of cores with the same or similar permeability to obtain the permeability experimental data of each core, then making a corresponding permeability curve of each core according to the permeability experimental data, and then carrying out normalization treatment on the corresponding permeability curve of each core to obtain a corresponding oil-water relative permeability curve of each core; (2) Fitting a water phase maximum relative permeability, oil displacement efficiency and pressure gradient statistical rule according to the data of the phase permeability experiment, namely solving the water phase maximum relative permeability and residual oil saturation under different pressure gradients; (3) And solving a characteristic curve equation of the oil-water relative permeability curve corresponding to each core. The patent mainly characterizes the change of the oil-water relative permeability curve relative to the conventional oil-water relative permeability curve under different displacement pressure gradients, and does not relate to the characterization of the relationship between the oil-water relative permeability ratio and the water saturation in the conventional oil-water relative permeability curve.
In application number: in CN 201810257741.6's chinese patent application, a method for characterizing oil phase relative permeability curve based on harris model is related, comprising: selecting typical oil-water relative permeability curve data capable of reflecting physical characteristics of a block or an oil reservoir; carrying out standardization treatment on the relative oil phase permeability and the water saturation, and judging the relationship between the standardized relative oil phase permeability and the water saturation; constructing a function expression of a relation curve of oil phase relative permeability and water saturation based on a Harris model; and solving coefficients in a function expression for constructing a relation curve of oil phase relative permeability and water saturation by using a least square method. The patent mainly characterizes the relation between a single oil phase relative permeability curve and water saturation based on a Harris model, does not characterize the relation between the water phase relative permeability curve and the water saturation, and does not relate to the characterization of the relation between the oil phase relative permeability ratio and the water saturation in the oil-water relative permeability curve.
In order to accurately characterize the nonlinear relationship between the oil-water relative permeability and the water saturation, the selection of a reasonable mathematical model is particularly important. Therefore, the invention discloses a novel oil-water relative permeability curve characterization method based on a trigonometric function, and solves the technical problems.
Disclosure of Invention
The invention aims to provide an oil-water relative permeability curve characterization method which is constructed based on a trigonometric function and can accurately characterize a complex nonlinear relationship between the relative permeability ratio of an oil phase to a water phase and the water saturation.
The aim of the invention can be achieved by the following technical measures: the invention provides an oil-water relative permeability curve characterization method based on a trigonometric function, which comprises the following steps: step 1, selecting typical oil-water relative permeability curve data capable of reflecting physical characteristics of a block oil reservoir; step 2, carrying out standardized treatment on the water saturation S w in the oil-water relative permeability curve data, and defining the water saturation as X; step 3, the natural logarithm is calculated for the ratio K ro/Krw of the relative permeability of the oil phase and the relative permeability of the water phase, and then divided by pi, and the arctangent function value is calculated, and is defined as Y; and 4, establishing a linear function relation between Y and X, and determining a function expression of a relation curve of relative permeability ratio and water saturation of the oil phase and the water phase based on a trigonometric function.
The aim of the invention can be achieved by the following technical measures:
In step 1, data were selected including water saturation S w, oil phase relative permeability K ro, water phase relative permeability K rw, and water content f w.
In step 2, the water saturation S w in the oil-water relative permeability curve data is normalized and defined as X, and the normalized water saturation is expressed as:
wherein:
S w, water saturation and dimensionless;
s wc, irreducible water saturation, dimensionless;
S or, residual oil saturation, dimensionless;
S wn, normalized water saturation and dimensionless.
In step 3, the natural logarithm of the ratio K ro/Krw of the relative permeability of oil and water to the relative permeability of water phase is calculated and divided by pi, and the arctangent function value is calculated and defined as Y, so that the method can be obtained:
wherein:
K ro -oil phase relative permeability, dimensionless;
K rw -relative permeability of aqueous phase, dimensionless.
In step 4, judging that the Y and the X have a better linear relation, and establishing a linear function relation expression between the Y and the X:
Y＝aX+b (3)
wherein:
a. b-coefficient to be determined;
and (3) carrying out linear fitting solution on the coefficients in the formula (3), and determining the numerical values of the coefficients a and b.
In step 4, according to the values of a and b, a functional expression of a relation curve of relative permeability ratio of oil phase to water phase and water saturation is established based on a trigonometric function:
wherein, K ro is the relative permeability of the oil phase, and the dimensionless property is provided;
k rw -relative permeability of aqueous phase, dimensionless;
S wn, normalized water saturation and dimensionless.
According to the oil-water relative permeability curve characterization method based on the trigonometric function, a complex nonlinear relation between the oil phase relative permeability ratio and the water saturation is converted into a relatively simple linear relation by performing trigonometric function processing on the oil-water relative permeability experimental parameter, and fitting solution is performed on each term coefficient in the linear function expression, so that high-precision mathematical characterization of the oil-water relative permeability curve is realized. The invention carries out mathematical characterization on the oil-water relative permeability curve based on the trigonometric function, lays a foundation for the derivation of oil reservoir engineering, water flooding theory and oil reservoir numerical simulation calculation method, further accurately predicts the oil reservoir water flooding development effect and trend, and guides the development and production practice of the oil field.
Drawings
FIG. 1 is a flowchart of an embodiment of a method for characterizing an oil-water relative permeability curve based on trigonometric functions according to the present invention;
FIG. 2 is a graph showing the linear relationship between the permeability parameters Y and X of the oil water phase in an embodiment of the present invention;
FIG. 3 is a graph showing the comparison of the water content calculated by the trigonometric function-based oil-water relative permeability curve characterization method and the water content calculated by the conventional exponential function method in an embodiment of the present invention.
Detailed Description
The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of preferred embodiments, as illustrated in the accompanying drawings.
As shown in fig. 1, fig. 1 is a flowchart of the oil-water relative permeability curve characterization method based on trigonometric functions according to the present invention.
In step 101, typical oil-water relative permeability curve data reflecting physical characteristics of a block reservoir is selected. In one embodiment, the typical oil-water relative permeability curve data (table 1) of a certain block of the victory oil field is selected, so that the oil-water two-phase comprehensive seepage characteristic of the oil reservoir of the block can be accurately reflected.
TABLE 1 data sheet of oil-water relative permeability for a block of the victory oil field
The flow proceeds to step 102.
In step 102, the water saturation S w in the oil-water relative permeability curve data is normalized and defined as X, and the normalized water saturation is expressed as:
wherein:
S w, water saturation and dimensionless;
s wc, irreducible water saturation, dimensionless;
S or, residual oil saturation, dimensionless;
S wn, the normalized water saturation, dimensionless;
The flow proceeds to step 103.
In step 103, the natural logarithm is obtained for the ratio K ro/Krw of the relative oil-water permeability to the relative water permeability, which is divided by pi, and the arctangent function value is obtained, which is defined as Y, to obtain:
wherein:
K ro -oil phase relative permeability, dimensionless;
k rw -relative permeability of aqueous phase, dimensionless;
As can be seen from table 1, the irreducible water saturation S wc = 0.173, the residual oil saturation S or = 1-0.715 = 0.285, and the treated oil-water relative permeability parameters X and Y (table 2) can be obtained according to formulas (1) and (2).
And judging the curve form between the treated oil-water relative permeability parameters X and Y.
The flow proceeds to step 104.
In step 104, the processed oil-water relative permeability parameters Y and X have a better linear relationship (fig. 2), and a linear functional relationship expression between Y and X is established:
Y＝aX+b (3)
wherein:
a. b-the coefficient to be determined.
Linear fitting of Y to X yields the coefficient a= -2.4460, b= 1.4561, i.e.
TABLE 2 oil-water relative permeability parameter Table after treatment of a block of the victory oil field
| X | Y |
| 0.251 | 0.850 |
| 0.286 | 0.768 |
| 0.328 | 0.668 |
| 0.376 | 0.547 |
| 0.439 | 0.381 |
| 0.496 | 0.229 |
| 0.548 | 0.086 |
| 0.625 | -0.108 |
| 0.685 | -0.249 |
| 0.740 | -0.356 |
| 0.777 | -0.428 |
| 0.819 | -0.498 |
Finally, based on the trigonometric function, a functional expression of a relation curve of the relative permeability ratio of the oil phase to the water phase and the water saturation is established:
according to the steps, the oil-water relative permeability curve based on trigonometric function characterization is realized.
According to the characterization method of the traditional oil-water relative permeability curve, the function expression of the relation curve of the relative permeability ratio of the oil phase to the water phase and the water saturation is as follows:
and respectively utilizing a trigonometric function to establish a relative permeability ratio and water saturation functional relation expression of the oil phase and the water phase and utilizing a traditional relative permeability ratio and water saturation functional relation expression of the oil phase and the water phase to calculate a water content formula:
wherein:
f w -water content, dimensionless;
mu w -viscosity of the formation water, mPa.s;
Mu o -viscosity of crude oil, mPa.s;
On the basis, the water content curves calculated by the two characterization methods can be compared with actual experimental results (figure 3), the oil-water relative permeability curve characterization method based on the trigonometric function can greatly improve the fitting precision of the water content compared with the traditional oil-water relative permeability characterization method, lay a foundation for the derivation of oil reservoir engineering, water flooding theory and oil reservoir numerical simulation calculation method, improve the prediction precision of the oil reservoir water flooding development effect and trend, and guide the efficient development of oil fields.
The oil-water relative permeability curve characterization method based on the trigonometric function in the invention carries out mathematical characterization on the complex nonlinear relation between the relative permeability ratio of the oil phase and the water saturation, lays a foundation for the derivation of oil reservoir engineering, water flooding theory and oil reservoir numerical simulation calculation method, further accurately predicts the oil reservoir water flooding development effect and trend, and guides the development and production practice of the oil field.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but although the present invention has been described in detail with reference to the foregoing embodiment, it will be apparent to those skilled in the art that modifications may be made to the technical solution described in the foregoing embodiment, or equivalents may be substituted for some of the technical features thereof. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Other than the technical features described in the specification, all are known to those skilled in the art.
Claims (4)
1. The oil-water relative permeability curve characterization method based on the trigonometric function is characterized by comprising the following steps of:
Step 1, selecting typical oil-water relative permeability curve data capable of reflecting physical characteristics of a block oil reservoir;
Step 2, carrying out standardized treatment on the water saturation S w in the oil-water relative permeability curve data, and defining the water saturation as X;
step 3, the natural logarithm is calculated for the ratio K ro/Krw of the relative permeability of the oil phase and the relative permeability of the water phase, and then divided by pi, and the arctangent function value is calculated, and is defined as Y;
Step 4, establishing a linear function relation between Y and X, and determining a function expression of a relation curve of relative permeability ratio and water saturation of an oil phase and a water phase based on a trigonometric function;
In step 4, judging that the Y and the X have a better linear relation, and establishing a linear function relation expression between the Y and the X:
Y＝aX+b(3)
wherein:
a. b-coefficient to be determined;
Carrying out linear fitting solution on the coefficients in the formula (3), and determining the numerical values of the coefficients a and b;
in step 4, according to the values of a and b, a functional expression of a relation curve of relative permeability ratio of oil phase to water phase and water saturation is established based on a trigonometric function:
wherein, K ro is the relative permeability of the oil phase, and the dimensionless property is provided;
k rw -relative permeability of aqueous phase, dimensionless;
S wn, normalized water saturation and dimensionless.
2. The method for characterizing an oil-water relative permeability curve based on trigonometric function as recited in claim 1, wherein in step 1, the selected data includes water saturation S w, oil phase relative permeability K ro, water phase relative permeability K rw and water content f w.
3. The method for characterizing an oil-water relative permeability curve based on trigonometric function as recited in claim 1, wherein in step 2, the water saturation S w in the oil-water relative permeability curve data is normalized and defined as X, and the normalized water saturation is expressed as:
wherein:
S w, water saturation and dimensionless;
s wc, irreducible water saturation, dimensionless;
S or, residual oil saturation, dimensionless;
S wn, normalized water saturation and dimensionless.
4. The method for characterizing an oil-water relative permeability curve based on trigonometric function as recited in claim 1, wherein in step 3, the ratio K ro/Krw of the oil-water relative permeability to the water phase relative permeability is calculated as a natural logarithm, divided by pi, and an arctangent function value is calculated, which is defined as Y, to obtain:
wherein:
K ro -oil phase relative permeability, dimensionless;
K rw -relative permeability of aqueous phase, dimensionless.
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| CN105510203A (en) * | 2015-11-18 | 2016-04-20 | 中国石油新疆油田分公司勘探开发研究院 | Method for determination of sandstone oil reservoir oil-water relative permeability under different temperature gradients |
| CN108226010A (en) * | 2018-03-07 | 2018-06-29 | 中国矿业大学 | A kind of assay method of fluid permeance property in porous media |
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| CN105510203A (en) * | 2015-11-18 | 2016-04-20 | 中国石油新疆油田分公司勘探开发研究院 | Method for determination of sandstone oil reservoir oil-water relative permeability under different temperature gradients |
| CN108226010A (en) * | 2018-03-07 | 2018-06-29 | 中国矿业大学 | A kind of assay method of fluid permeance property in porous media |
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