Oil saturation calculation method based on oil-water relative permeability ratio

Abstract

The invention relates to the technical field of oil-gas field development, in particular to an oil saturation calculation method based on an oil-water relative permeability ratio. The method comprises the following steps: obtaining an oil-water relative permeability ratio and a water saturation general formula according to an oil-phase relative permeability general formula and a water-phase relative permeability general formula; taking a natural logarithm from the general formula, and adopting ln (1 + x) series expansion to obtain a cubic polynomial form which can realize whole-course fitting of the oil-water relative permeability ratio and contains constant parameters c1, d1, e1 and f1; establishing an oil-water relative permeability ratio and water content relational expression according to oil phase and water phase plane radial flow yield formulas in combination with water content definition; establishing a water saturation and water content relational expression by taking an oil-water relative permeability ratio as a link; and solving the water saturation and the oil saturation of the given underwater by applying the relational expression. The calculation method provided by the invention is simple in calculation, convenient to operate, rapid and accurate.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field development, and in particular to a method for calculating oil saturation based on an oil-water relative permeability ratio. Background Art

[0002] Oil saturation is an important parameter in the calculation of proven reserves and an important basis for the potential of remaining oil. Currently, many methods for calculating oil saturation are based on the original oil saturation, and there are three main methods: first, the direct core measurement method, which uses a closed coring well to directly measure the original oil saturation, is the most direct method, but it is expensive; second, the geophysical logging method, which uses the Archie formula as the theoretical basis to establish the relationship between formation water, reservoir resistivity and original oil saturation; third, the capillary pressure curve method, which uses the capillary pressure curve measured by the mercury injection method to determine the original oil saturation, mainly including the J function method and the Wall method.

[0003] The publicly released patents "An Archie model method for determining the original oil saturation of oil layers", "A method for calculating the original oil saturation of water-flooded layers in core wells during the extremely high water-cut period", and "A method for calculating reservoir oil saturation using MDT cable formation testing data" are all methods established for the original oil saturation, and are mainly used to calculate the original geological reserves.

[0004] The above methods all calculate the original oil saturation from a static perspective, while the oil saturation changes dynamically after the reservoir is put into development, showing a continuous decline. At this time, the static method for calculating the original oil saturation is no longer applicable. There are two main applicable methods: one is the reservoir numerical simulation method. History fitting is the key to reservoir numerical simulation. The fitting time is long, and different people will get different fitting results. The uncertainty of the fitting results is very large; the second is the reservoir engineering method. At present, there is only one document "A method for obtaining reservoir oil saturation using production data". There are three defects in this method: first, the coefficients of the empirical formula are difficult to obtain, and the accuracy is difficult to guarantee, which affects its application effect; second, it can only be applied after the type A water drive characteristic curve has a straight line segment; third, it is impossible to obtain the current oil saturation of a single well or a single layer.

[0005] In summary, there is currently no method that can quickly and easily calculate the oil saturation of blocks, single wells, and single layers at different water-cut stages during the development process to support development adjustment work. Therefore, a method for calculating oil saturation based on the oil-water relative permeability ratio is proposed. Summary of the invention

[0006] 1. Technical issues to be resolved

[0007] The present invention provides a method for calculating oil saturation based on the oil-water relative permeability ratio. Based on the oil-water two-phase permeability theory, a general formula for the oil-water relative permeability ratio is proposed, and then a method for calculating oil saturation under different water-containing stages is derived.

[0008] (II) Technical solution

[0009] In order to solve the above problems, the present invention provides a method for calculating oil saturation based on the oil-water relative permeability ratio, comprising:

[0010] Step S1: Obtaining a general formula of oil-water relative permeability ratio and water saturation according to a general formula of oil phase relative permeability and a general formula of water phase relative permeability;

[0011] Step S2: taking the natural logarithm of the general formula of the oil-water relative permeability ratio of step S1, and expanding it by ln(1+x) series to obtain a cubic polynomial form that can achieve full fitting of the oil-water relative permeability ratio and contains constant parameters c1, d1, e1 and f1;

[0012] Step S3: According to the radial flow production formula of the oil phase and water phase plane, combined with the definition of water content, a relationship between the oil-water relative permeability ratio and the water content is established;

[0013] Step S4: establishing a water saturation-water content relationship equation based on the cubic polynomial form of the oil-water relative permeability ratio and water saturation in step S2 and the relationship between the oil-water relative permeability ratio and water content in step S3;

[0014] Step S5: using the relationship between water saturation and water content obtained in step S4, solving the water saturation under a given water content;

[0015] Step S6: Calculate the oil saturation of the block, oil well, and single layer according to the calculation result of the water saturation obtained in step S5.

[0016] Preferably, in step S1, the general formula of the oil-water relative permeability ratio is:

[0017]

[0018] Among them, a o 、a w 、b o 、b w —Formula parameters; K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; n o —Oil phase index, f; n w —Water phase index, f; S w —Water saturation, f.

[0019] Preferably, the calculation formula of the oil phase relative permeability formula and the water phase relative permeability formula are respectively:

[0020]

[0021]

[0022] Among them, a o 、b o 、a w 、b w —Formula parameters; K ro —Oil phase relative permeability, f; n o —Oil phase index, f; K rw — relative permeability of water phase, f; n w —Water phase index, f; S w —Water saturation, f.

[0023] Preferably, in step S2, the cubic polynomial of the oil-water relative permeability ratio and water saturation is:

[0024]

[0025] Among them, K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; c1, d1, e1, f1— formula parameters, f; S w —Water saturation, f.

[0026] Preferably, the calculation formulas for c1, d1, e1 and f1 in the cubic polynomial form of the oil-water relative permeability ratio full-process fitting are respectively:

[0027]

[0028]

[0029]

[0030]

[0031] Where: a o 、a w 、b o 、b w , c1, d1, e1, f1—formula parameters, f; n o —Oil phase index, f; n w —Water phase index, f.

[0032] Preferably, in step S3, the relationship between the oil-water relative permeability ratio and the water content is:

[0033]

[0034] Among them, K ro —Oil phase relative permeability, f; n o —Oil phase index, f; K rw — relative permeability of water phase, f; μ r —Water-oil viscosity ratio, f; f w —Containing water, f.

[0035] Preferably, the water-oil viscosity ratio formula is:

[0036]

[0037] Where: μ r —Water-oil viscosity ratio, f; μ o —Oil phase viscosity, mPa·s; μ w —Viscosity of water phase, mPa·s; f w —Containing water, f.

[0038] Preferably, in step S4, the relationship between water saturation and water content is:

[0039]

[0040] Among them, c1, d1, e1, f1 are formula parameters, f; S w —water saturation, f; μ r —Water-oil viscosity ratio, f; f w —Containing water, f.

[0041] Preferably, in step S5, the method for solving the water saturation is a cubic equation solution method or a single variable solution method in Excel software.

[0042] Preferably, in step S6, the calculation formula for the oil saturation of the block, oil well, and single layer is:

[0043] S o =1―S w (12)

[0044] Where: S o —Oil saturation, f; S w —Water saturation, f.

[0045] (III) Beneficial effects

[0046] The oil saturation calculation method based on the oil-water relative permeability ratio provided by the present invention can quickly and accurately calculate the oil saturation at different water-containing stages. Compared with the traditional method, it fills the gap in the prior art and provides a new calculation method for oil and gas field development. The method can not only be implemented on a single well and a single layer, but also has simple calculation and convenient operation. The calculation results can be used to guide the development and adjustment work such as infill well deployment, fine water injection, side drilling horizontal well layer optimization, polymer drive layer optimization, oil well repeated fracturing layer selection, etc., and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a method for calculating oil saturation based on the oil-water relative permeability ratio according to an embodiment of the present invention;

[0048] Figure 2 The average phase permeability curve of the permeability 1-10mD of the embodiment of the present invention;

[0049] Figure 3 The average phase permeability curve of the embodiment of the present invention with a permeability of 10-50mD;

[0050] Figure 4 This is an average phase permeability curve diagram of the embodiment of the present invention with a permeability of more than 50mD;

[0051] Figure 5 is the ln(K of the permeability 1-10mD in the embodiment of the present invention ro / K rw )Fitting result graph;

[0052] Figure 6 is the ln(K of the permeability 10-50mD in the embodiment of the present invention ro / K rw )Fitting result graph;

[0053] Figure 7 The permeability of the embodiment of the present invention is ln(K ro / K rw )Fitting result graph. DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] Figure 1 FIG. 1 is a flow chart of a method for calculating oil saturation based on the oil-water relative permeability ratio according to an embodiment of the present invention. Figure 1 As shown, the present invention provides a method for calculating oil saturation based on the oil-water relative permeability ratio, comprising:

[0056] Step S1: Obtain the general formula of oil-water relative permeability ratio and water saturation according to the general formula of oil phase relative permeability and the general formula of water phase relative permeability.

[0057] In practical applications, the general formula for the oil-water relative permeability ratio is:

[0058]

[0059] Among them, a o 、a w 、b o 、b w —Formula parameters; K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; n o —Oil phase index, f; n w —Water phase index, f; S w —Water saturation, f.

[0060] It should be noted that the general formula of oil-water relative permeability ratio and water saturation includes the general formula of oil phase relative permeability and the general formula of water phase relative permeability.

[0061] Therefore, the general formula of oil phase relative permeability is:

[0062]

[0063] Among them, a o 、b o —Formula parameters; K ro —Oil phase relative permeability, f; n o —Oil phase index, f; S w —Water saturation, f.

[0064] In addition, the general formula of water phase relative permeability is:

[0065]

[0066] Among them, a w 、b w —Formula parameters; K rw — relative permeability of water phase, f; n w —Water phase index, f; S w —Water saturation, f.

[0067] Step S2: Take the natural logarithm of the general formula of the oil-water relative permeability ratio in step S1, and expand it using the ln(1+x) series to obtain a cubic polynomial form that can achieve full fitting of the oil-water relative permeability ratio and contains constant parameters c1, d1, e1 and f1.

[0068] In this calculation method, the cubic polynomial for the oil-water relative permeability ratio is:

[0069]

[0070] Where: c1, d1, e1, f1—formula parameters, f; K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; S w —Water saturation, f.

[0071] Among them, the calculation formulas for c1, d1, e1 and f1 in the cubic polynomial form of the whole process fitting of the oil-water relative permeability ratio are:

[0072]

[0073]

[0074]

[0075]

[0076] Where: a o 、a w 、b o 、b w , c1, d1, e1, f1—formula parameters, f; K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; n o —Oil phase index, f; n w —Water phase index, f; S w —Water saturation, f.

[0077] Step S3: According to the radial flow production formula of the oil phase and water phase, combined with the definition of water content, a relationship between the oil-water relative permeability ratio and the water content is established.

[0078] In this calculation method, the relationship between the oil-water relative permeability ratio and water content is:

[0079]

[0080] Where: K ro —Oil phase relative permeability, f; K rw— relative permeability of water phase, f; μ r —Water-oil viscosity ratio, f; f w —Containing water, f.

[0081] Among them, in practical applications, the water-oil viscosity ratio calculation formula is:

[0082]

[0083] Where: μ r —Water-oil viscosity ratio, f; μ o —Oil phase viscosity, mPa·s; μ w —Viscosity of water phase, mPa·s; f w —Containing water, f.

[0084] Step S4: According to the oil-water relative permeability ratio and water saturation relationship formula of step S2, combined with the oil-water relative permeability ratio and water content relationship formula of step S3, a water saturation and water content relationship formula is established.

[0085] In this calculation method, the relationship between water saturation and water content is:

[0086]

[0087] In the formula: c1, d1, e1, f1—formula parameters, f; S w —water saturation, f; f w —Containing water, f.

[0088] Step S5: using the relationship between the water saturation and water content obtained in step S4, the water saturation at a given water content is solved.

[0089] In practical applications, the solution to water saturation is the cubic equation solution method or the single variable solution method in Excel software.

[0090] Step S6: Calculate the oil saturation of the block, oil well, and single layer according to the calculation result of the water saturation obtained in step S5.

[0091] In practical applications, the calculation formula for oil saturation of blocks, oil wells, and single layers is:

[0092] S o =1―S w (12)

[0093] Where: S o —Oil saturation, f; S w —Water saturation, f.

[0094] It is important to note that the sum of water saturation and oil saturation is 1.

[0095] In this method, the general formula of oil-water relative permeability ratio and water saturation is derived based on the general formula of relative permeability of oil phase and water phase. Through ln(1+x) series expansion, a cubic polynomial form that can realize the full fitting of oil-water relative permeability ratio is obtained, which overcomes the problem that the previous linear form can only fit the middle section. According to the plane radial flow formula of seepage mechanics, the relationship between oil-water relative permeability ratio and water content is established. With the oil-water relative permeability ratio as the link, the functional relationship between water saturation and water content is established; using this relationship, the water saturation at different development stages can be calculated, and then the oil saturation can be obtained.

[0096] The following is a detailed description of the implementation process of this oil saturation calculation method based on the oil-water relative permeability ratio:

[0097] Step 1: Collect the oil-water relative permeability data corresponding to different permeability levels of an oil field or block, and then obtain the average oil-water relative permeability curves at different permeability levels to prepare for subsequent steps.

[0098] It should be noted that the levels of permeability include 1-10mD, 10-50mD and above 50mD.

[0099] In this embodiment, Figure 2 The average phase permeability curve of the permeability 1-10mD of the embodiment of the present invention is shown in FIG. Figure 3 This is the average phase permeability curve of the permeability 10-50mD of the embodiment of the present invention, Figure 4 The average phase permeability curve of the embodiment of the present invention with a permeability of more than 50mD is shown in FIG. Figures 2 to 4 As shown, by obtaining the average oil-water relative permeability curves at three permeability levels, the corresponding data can be obtained respectively to prepare for the subsequent steps.

[0100] Step 2: Construct a trinomial form of the oil-water relative permeability ratio and water saturation, and obtain the fitting coefficients c1, d1, e1, and f1 corresponding to different permeability levels through regression analysis of the fitting formula coefficients.

[0101] In this embodiment, Figure 5 is the ln(K of the permeability 1-10mD in the embodiment of the present invention ro / K rw )Fitting result graph, Figure 6 is the ln(K of the permeability 10-50mD in the embodiment of the present invention ro / K rw )Fitting result graph, Figure 7 The permeability of the embodiment of the present invention is ln(K ro / K rw ) The fitting result graph is as follows: Figures 5 to 7 shown.

[0102] Table 1 shows the different permeability levels ln(K ro / K rw )The fitting coefficients c1, d1, e1, and f1 are shown in Table 1.

[0103] Table 1 Different permeability levels ln(K ro / K rw )Fitting coefficient

[0104]

[0105] Step 3: Based on the plane radial flow formula, establish the relationship between the oil-water relative permeability ratio and water content.

[0106] In this embodiment, the relationship between the oil-water relative permeability ratio and the water content is:

[0107]

[0108] Where K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; μ r —Water-oil viscosity ratio, f; f w —Containing water, f.

[0109] Step 4: Construct a functional relationship between water saturation and water content. According to different permeability levels, select corresponding fitting coefficients c1, d1, e1, f1, and use the cubic equation method or the single variable solution method in Excel software to calculate the water saturation of blocks, oil wells, and single layers at different development stages.

[0110] In this embodiment, the relationship between water saturation and water content is:

[0111]

[0112] In the formula: c1, d1, e1, f1—formula parameters, f; S w —water saturation, f; f w —Containing water, f.

[0113] It should be noted that at different permeability levels, different fitting coefficients c1, d1, e1, and f1 are selected to solve their specific water saturation.

[0114] Step 5: After finding the water saturation, calculate the oil saturation.

[0115] In this embodiment, the calculation formula for the oil saturation of a block, an oil well, and a single layer is:

[0116] S o =1―Sw (12)

[0117] Where: S o —Oil saturation, f; S w —Water saturation, f.

[0118] It should be noted that since the sum of oil saturation and water saturation is 1, the water saturation must be obtained first before the oil saturation can be obtained.

[0119] The oil saturation calculation method based on the oil-water relative permeability ratio provided by the present invention can quickly and accurately calculate the oil saturation at different water-containing stages. Compared with the traditional method, it fills the gap in the prior art and provides a new calculation method for oil and gas field development. The method can not only be implemented on a single well and a single layer, but also has simple calculation and convenient operation. The calculation results can be used to guide the development and adjustment work such as infill well deployment, fine water injection, side drilling horizontal well layer optimization, polymer drive layer optimization, oil well repeated fracturing layer selection, etc., and has good application prospects.

[0120] The above implementation modes are only used to illustrate the present invention, but not to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The patent protection scope of the present invention should be defined by the claims.

Claims

1. A method for calculating oil saturation based on oil-water relative permeability ratio, characterized in that: include: Step S1: Obtaining a general formula of oil-water relative permeability ratio and water saturation according to a general formula of oil phase relative permeability and a general formula of water phase relative permeability; Step S2: taking the natural logarithm of the general formula of the oil-water relative permeability ratio of step S1, and expanding it by ln(1+x) series to obtain a cubic polynomial form that can achieve full fitting of the oil-water relative permeability ratio and contains constant parameters c1, d1, e1 and f1; Step S3: According to the radial flow production formula of the oil phase and water phase plane, combined with the definition of water content, a relationship between the oil-water relative permeability ratio and the water content is established; Step S4: establishing a water saturation and water content relationship equation based on the cubic polynomial form of the oil-water relative permeability ratio and water saturation in step S2 and the oil-water relative permeability ratio and water content relationship equation in step S3; Step S5: using the water saturation and water content relationship equation obtained in step S4, solving the water saturation under a given water content; Step S6: Calculate the oil saturation of the block, oil well, and single layer according to the calculation result of the water saturation obtained in step S5.

2. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 1, characterized in that: In step S1, the general formula of the oil-water relative permeability ratio is: Among them, a o 、a w , b o , b w —Formula parameters; K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; n o —Oil phase index, f; n w —Water phase index, f; S w —Water saturation, f.

3. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 2, characterized in that: The general formulas for the relative permeability of the oil phase and the relative permeability of the water phase are respectively: Among them, a o 、b o 、a w 、b w —Formula parameters; K ro —Oil phase relative permeability, f; n o —Oil phase index, f; K rw — relative permeability of water phase, f; n w —Water phase index, f; S w —Water saturation, f.

4. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 1, characterized in that: In step S2, the cubic polynomial of the oil-water relative permeability ratio and water saturation is: Among them, K ro —Oil phase relative permeability, f; K rw — relative permeability of water phase, f; c1, d1, e1, f1— formula parameters, f; S w —Water saturation, f.

5. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 4, characterized in that: The calculation formulas for c1, d1, e1 and f1 in the cubic polynomial form of the oil-water relative permeability ratio full-process fitting are: Where: a o 、a w , b o , b w , c1, d1, e1, f1—formula parameters, f; n o —Oil phase index, f; n w —Water phase index, f.

6. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 1, characterized in that: In step S3, the relationship between the oil-water relative permeability ratio and the water content is: Among them, K ro —Oil phase relative permeability, f; n o —Oil phase index, f; K rw — relative permeability of water phase, f; μ r —Water-oil viscosity ratio, f; f w —Containing water, f.

7. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 6, characterized in that: The water-to-oil viscosity ratio formula is: Where: μ r —Water-oil viscosity ratio, f; μ o —Oil phase viscosity, mPa·s; μ w —Viscosity of water phase, mPa·s; f w —Containing water, f.

8. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 1, characterized in that: In step S4, the relationship between water saturation and water content is: Among them, c1, d1, e1, f1 are formula parameters, f; S w —water saturation, f; μ r —Water-oil viscosity ratio, f; f w —Containing water, f.

9. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 1, characterized in that: In step S5, the water saturation is solved by a cubic equation or a single variable solution method in Excel software.

10. The method for calculating oil saturation based on oil-water relative permeability ratio according to claim 1, characterized in that: In step S6, the calculation formula for the oil saturation of the block, oil well, and single layer is: S o =1―S w (12) Where: S o —Oil saturation, f; S w —Water saturation, f.

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