CN108444884B - Oil phase relative permeability curve characterization method based on Harris model - Google Patents
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Abstract
The invention provides an oil phase relative permeability curve characterization method based on a Harris model, which comprises the following steps: selecting typical oil-water relative permeability curve data capable of reflecting block or oil reservoir physical property characteristics; standardizing the relative permeability and the water saturation of the oil phase, and judging the relationship between the standardized relative permeability and the standardized water saturation of the oil phase; constructing a function expression of a relation curve of oil phase relative permeability and water saturation based on a Harris model; and solving and constructing coefficients in a function expression of the relation curve of the oil phase relative permeability and the water saturation by using a least square method. The oil phase relative permeability curve characterization method based on the Harris model performs mathematical characterization on the nonlinear law of oil phase relative permeability and water saturation, lays a foundation for oil reservoir engineering, a water flooding theory and derivation of an oil reservoir numerical simulation calculation method, and therefore accurately predicts the oil reservoir water flooding development effect and trend and guides oil field development and production practices.
Description
Technical Field
The invention relates to the technical field of oilfield development, in particular to a Harris model-based oil phase relative permeability curve characterization method.
Background
The percolation curve is the comprehensive reflection of the percolation characteristics of oil, water and two phases in rock gaps, and is the most basic law followed by the oil, water and two phases in the percolation process. The oil phase relative permeability curve is important data in oil reservoir engineering oil production prediction. The method effectively represents the relative permeability of the oil phase, and has important guiding significance for optimizing an oil field development scheme, increasing the oil field recovery ratio and improving the oil field development effect.
The existing method for characterizing the relative permeability of the oil phase mainly uses a power function characterization method, and the function characterization form is simple, but the precision is poor. Particularly in a low water saturation interval, a complex nonlinear relation between the relative permeability of the oil phase and the water saturation cannot be represented, so that the oil yield in the early development of the oil field cannot be accurately predicted, and the optimization of an oil field development scheme and the improvement of the ultimate recovery rate are influenced.
In order to accurately represent the nonlinear relation between the relative permeability of the oil phase and the water saturation, the selection of a reasonable mathematical model is particularly important. Therefore, a novel characterization method of the oil phase relative permeability curve based on the Harris model is invented, and the technical problems are solved.
Disclosure of Invention
The invention aims to provide an oil phase relative permeability curve characterization method which is constructed based on a Harris model and can accurately characterize the nonlinear relation between oil phase relative permeability and water saturation.
The object of the invention can be achieved by the following technical measures: the invention provides an oil phase relative permeability curve characterization method based on a Harris model, which comprises the following steps: step 1, selecting typical oil-water relative permeability curve data capable of reflecting block or oil reservoir physical property characteristics; step 2, standardizing the relative permeability and the water saturation of the oil phase, and judging the relationship between the standardized relative permeability and the standardized water saturation of the oil phase; step 3, constructing a function expression of a relation curve of oil phase relative permeability and water saturation based on a Harris model; and step 4, solving and constructing coefficients in a function expression of the relation curve of the oil phase relative permeability and the water saturation by using a least square method.
The object of the invention can also be achieved by the following technical measures:
in step 2, the relative oil permeability and water saturation are normalized, and the normalized relative oil permeability and water saturation are expressed as:
in the formula:
Kro-relative permeability of the oil phase, dimensionless;
Kromaxrelative permeability of the oil phase at irreducible water saturation, dimensionless;
Kron-normalized oil phase relative permeability, dimensionless;
Swwater saturation, dimensionless;
Swcirreducible water saturation, dimensionless;
Sor-residual oil saturation, dimensionless;
Swnnormalized water saturation, dimensionless.
In step 2, the relative permeability K of the oil phase is normalizedronWith the water saturation SwnThe normalized oil phase relative permeability K is judgedronWith the water saturation SwnThe relationship between them.
In step 2, the relative permeability K of the oil phase is normalizedronWith the water saturation SwnThe graph relationship between the two shows that the two are in a curve relationship of reverse S shape.
In step 3, the normalized oil phase relative permeability K established according to step 2ronWith waterSaturation SwnThe normalized oil phase relative permeability K can be known by the curve relation of 'reverse S' shape between the oil phase and the oil phaseronWater saturation S following normalizationwnIs increased and decreased.
In step 3, the water saturation S after normalizationwnApproaching 1, corresponding normalized relative oil phase permeability KronApproaching to 0; water saturation S after normalizationwnWhen approaching 0, the corresponding normalized relative permeability K of oil phaseronApproaching 1.
In step 3, the function expression of the relation curve of the oil phase relative permeability and the water saturation built based on the Harris model is as follows:
in the formula:
a. b-coefficient to be determined.
In step 4, formula (3) is converted to:
taking natural logarithm from both sides to obtain
Using the least square method, for
And lnSwnAnd linear fitting is carried out, so that the numerical values of the coefficients a and b can be determined.
According to the oil phase relative permeability curve characterization method based on the Harris model, a high-precision function expression of a nonlinear relation curve between the oil phase relative permeability and the water saturation is constructed by researching the mathematical relation between the oil phase relative permeability and the water saturation. And determining an optimal solving method to solve the coefficients in the expression, thereby realizing the mathematical representation of the oil phase relative permeability curve. The method is characterized in that an oil phase relative permeability curve is mathematically characterized based on a Harris model, and a foundation is laid for deducing an oil reservoir engineering, a water flooding theory and an oil reservoir numerical simulation calculation method, so that the oil reservoir water flooding development effect and trend are accurately predicted, and the oil field development and production practice is guided.
Drawings
FIG. 1 is a flow chart of an embodiment of a Harris model-based method for characterizing an oil phase relative permeability curve according to the present invention;
FIG. 2 shows ln (1/lnK) in an embodiment of the present inventionron-1) and lnSwnThe relationship is a graph.
Fig. 3 is a graph comparing a conventional exponential oil phase permeability characterization method with an oil phase relative permeability curve characterization method based on a Harris model in an embodiment of the present invention.
Detailed Description
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
As shown in fig. 1, fig. 1 is a flow chart of the characterization method of the oil phase relative permeability curve based on the Harris model according to the present invention.
In step 101, typical oil-water relative permeability curve data capable of reflecting block or reservoir physical characteristics is selected. In one embodiment, typical oil-water relative permeability curve data (table 1) of a certain block of a victory oil field is selected, and oil-water two-phase comprehensive seepage characteristics of an oil reservoir of the block can be accurately reflected.
TABLE 1 oil-water relative permeability data table for certain block of victory oil field
| Water saturation degree Sw | Relative permeability of oil phase Kro | Relative permeability of the aqueous phase Krw |
| 0.304 | 1.000 | 0.000 |
| 0.517 | 0.479 | 0.032 |
| 0.527 | 0.403 | 0.037 |
| 0.542 | 0.316 | 0.045 |
| 0.561 | 0.236 | 0.056 |
| 0.589 | 0.155 | 0.074 |
| 0.618 | 0.102 | 0.098 |
| 0.655 | 0.061 | 0.134 |
| 0.68 | 0.044 | 0.164 |
| 0.701 | 0.034 | 0.192 |
| 0.725 | 0.024 | 0.231 |
| 0.744 | 0.017 | 0.264 |
| 0.777 | 0.000 | 0.334 |
The flow proceeds to step 102.
At step 102, the oil phase relative permeability and water saturation are normalized, and the normalized oil phase relative permeability and water saturation are expressed as:
in the formula:
Kro-relative permeability of the oil phase, dimensionless;
Kromaxrelative permeability of the oil phase at irreducible water saturation, dimensionless;
Kron-normalized oil phase relative permeability, dimensionless;
Swwater saturation, dimensionless;
Swcirreducible water saturation, dimensionless;
Sor-residual oil saturation, dimensionless;
Swn-normalized water saturation, dimensionless;
as can be seen from Table 1, irreducible water saturation Swc0.304 residual oil saturation Sor1-0.777-0.223, the relative permeability K of the oil phase at irreducible water saturation is generally set by the laboratory according to industry standardsromaxNormalized to 1.000, the normalized relative oil phase permeability K can be obtained from the formulas (1) and (2)ronAnd normalized water saturation Swn(Table 2).
TABLE 2 oil phase relative permeability data table after standardization of certain block of victory oil field
Judging the relative permeability K of the oil phase after standardizationronWith the water saturation SwnThe shape of the curve in between.
The flow proceeds to step 103.
At step 103, the normalized oil phase relative permeability K established according to step 102ronWith the water saturation SwnThe normalized oil phase relative permeability K shows an inverse S-shaped curve relationronWater saturation S following normalizationwnIs reduced when normalized to the water saturation SwnApproaching 1, corresponding normalized relative oil phase permeability KronApproaching to 0; water saturation S after normalizationwnWhen approaching 0, the corresponding normalized relative permeability K of oil phaseronApproaching 1.
On the basis, a function expression of a relation curve of oil phase relative permeability and water saturation built based on a Harris model is established:
in the formula:
a. b-coefficient to be determined;
the flow proceeds to step 104.
In step 104, for equation (3), the transformation may be to
Taking natural logarithm from both sides to obtain
Using the least square method, for
And lnSwnBy performing a linear fit (FIG. 2), one obtains
Namely: lna-4.3318, b-5.2491,
the coefficient a is 76.0811 and b is 5.2491.
Finally, a function expression of a relation curve of oil phase relative permeability and water saturation constructed based on a Harris model is established:
according to the steps, fitting characterization of an oil phase relative permeability curve based on the Harris model is achieved.
According to the traditional oil phase relative permeability power function characterization method, the functional expression of the relation curve of the oil phase relative permeability and the water saturation is as follows:
Kron＝(1-Swn)1.7474R2＝0.9442 (8)
comparing the relation curve of the oil phase relative permeability and the water saturation calculated by the two methods with the actual experimental result (figure 3), the Harris model-based oil phase relative permeability curve characterization method can greatly improve the fitting precision of the oil phase relative permeability compared with the traditional oil phase relative permeability power function characterization method, can lay a foundation for the derivation of oil reservoir engineering, a water flooding theory and an oil reservoir numerical simulation calculation method, improves the prediction precision of the oil reservoir water flooding development effect and trend, and guides the high-efficiency development of oil fields.
Claims (7)
1. The characterization method of the oil phase relative permeability curve based on the Harris model is characterized by comprising the following steps of:
step 1, selecting typical oil-water relative permeability curve data capable of reflecting block or oil reservoir physical property characteristics;
step 2, standardizing the relative permeability and the water saturation of the oil phase, and judging the relationship between the standardized relative permeability and the standardized water saturation of the oil phase;
step 3, constructing a function expression of a relation curve of oil phase relative permeability and water saturation based on a Harris model, wherein the function expression comprises the following steps:
in the formula: a. b-coefficient of determinacy, Kron-normalized oil phase relative permeability, dimensionless; swn-normalized water saturation, dimensionless;
and 4, solving and constructing coefficients in a function expression of the relation curve of the oil phase relative permeability and the water saturation by using a least square method.
2. The Harris model-based oil phase relative permeability curve characterization method according to claim 1, wherein in step 2, the oil phase relative permeability and the water saturation are normalized, and the normalized oil phase relative permeability and water saturation are expressed as:
in the formula:
Kro-relative permeability of the oil phase, dimensionless;
Kromaxrelative permeability of the oil phase at irreducible water saturation, dimensionless;
Kron-normalized oil phase relative permeability, dimensionless;
Swwater saturation, dimensionless;
Swcirreducible water saturation, dimensionless;
Sor-residual oil saturation, dimensionless;
Swnnormalized water saturation, dimensionless.
3. The Harris model-based oil phase relative permeability curve characterization method according to claim 2, wherein in step 2, the normalized oil phase relative permeability K is used as a basisronWith the water saturation SwnThe normalized oil phase relative permeability K is judgedronWith the water saturation SwnThe relationship between them.
4. The Harris model-based oil phase relative permeability curve characterization method according to claim 3, wherein in step 2, the normalized oil phase relative permeability K is usedronWith the water saturation SwnThe graph relationship between the two shows that the two are in a curve relationship of reverse S shape.
5. The Harris model-based oil phase relative permeability curve characterization method according to claim 1, wherein in step 3, the normalization established according to step 2Relative permeability K of the oil phaseronWith the water saturation SwnThe normalized oil phase relative permeability K can be known by the curve relation of 'reverse S' shape between the oil phase and the oil phaseronWater saturation S following normalizationwnIs increased and decreased.
6. The Harris model-based oil phase relative permeability curve characterization method according to claim 5, wherein in step 3, the normalized water saturation SwnApproaching 1, corresponding normalized relative oil phase permeability KronApproaching to 0; water saturation S after normalizationwnWhen approaching 0, the corresponding normalized relative permeability K of oil phaseronApproaching 1.
7. The Harris model-based oil phase relative permeability curve characterization method according to claim 1, wherein in step 4, formula (3) is converted into:
taking natural logarithm from both sides to obtain
Using the least square method, for
And lnSwnAnd linear fitting is carried out, so that the numerical values of the coefficients a and b can be determined.
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| CN112883530B (en) * | 2019-11-29 | 2022-11-04 | 中国石油天然气股份有限公司 | Theoretical water flooding curve determination method and device |
| CN112081589B (en) * | 2020-10-26 | 2022-03-01 | 西南石油大学 | Method for acquiring relative permeability curve of chemical system by standardizing isoosmotic point variable |
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