CN110909466A - Method for improving calculation precision of differential pore sorting reservoir average capillary pressure curve - Google Patents
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Abstract
The invention provides a regression method for effectively improving the calculation accuracy of an average capillary pressure curve of a differential pore sorting reservoir, which comprises the following steps: selecting a plurality of core samples on the same reservoir stratum to carry out capillary pressure experiments, recording corresponding numerical values of capillary pressure and wetting phase saturation, carrying out J function dimensionless treatment on all capillary pressure curves, recording corresponding numerical values of J values and wetting phase saturation, and respectively carrying out multiple nonlinear regression on data by using fractal J function regression formulas 1 and 2 to obtain two sets of regression parameters and a determination coefficient R2Selecting the regression result to be within the data point range, and determining the coefficient R2The formula closer to 1 is used as a basic formula of the average capillary pressure curve of the reservoir, and the average capillary pressure and the saturation of the wetting phase are calculated according to the J function definition formula by utilizing the regression parameters, the interfacial tension, the wetting angle, the average porosity and the average absolute permeability of the reservoirI.e. the mean capillary pressure curve.
Description
Technical Field
The invention relates to the field of oilfield development, and discloses an application method for effectively improving the calculation accuracy of an average capillary pressure curve of a differential pore sorting reservoir.
Background
The method mainly comprises a J function method for calculating an average capillary pressure curve representing the averaging property of pore structures of the same type of reservoirs in the field of oil field development at present, wherein the method introduces a capillary pressure curve for testing a single core sample of a reservoir into the capillary pressure curve
And performing dimensionless operation, performing power function regression on the J function values and the water saturation of a plurality of cores of the reservoir, and obtaining an average capillary pressure curve of the reservoir together with the porosity and the absolute permeability averaged by the reservoir. In theoretical and practical application, the method mainly has the following two problems: (1) measured pore sorting differenceThe J function curve of the reservoir is not in an empirical power function form, namely the regression precision of an empirical formula is low, and the applicability is limited; (2) the empirical formula of the J function lacks a theoretical basis, and regression parameters have no physical significance.
The average capillary pressure curve of the reservoir has important significance in representing the averaging property of complex pore structures containing microcracks, karst caves and the like, is used as a middle parameter for calculating the initial water saturation of an oil reservoir to influence the reserve calculation result and also used as a direct input parameter for predicting numerical simulation development indexes to influence the yield prediction result, and for the reservoir with poor pore sorting, the regression precision of the current empirical power function on the dimensionless capillary pressure curve is low, so that research needs to be carried out aiming at the core of the technology, namely the dimensionless J function regression method, so as to improve the regression precision of the reservoir and provide theoretical explanation.
Disclosure of Invention
In view of the above problems, the present invention provides a regression analysis formula for effectively improving the regression accuracy of the J function of the poor reservoir.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method of calculating an average capillary pressure curve for a reservoir, comprising the steps of:
1) selecting a plurality of core samples on the same reservoir, performing a group of capillary pressure experiments on each core sample, and recording capillary pressure and wetting phase saturation data;
2) for each core sample, using the data recorded in step 1, respectively using the formula
Carrying out dimensionless J function processing, and establishing a numerical value corresponding relation between the J function and the water saturation;
3) respectively using the data recorded in the step 2 to respectively use the formula for all core samples of the same reservoir
Performing regression solution, wherein the parameter variation range limits A2＞0,C2＞0,B2Is greater than 0, and regression parameter A is obtained2、B2、C2And a first determination coefficient
Respectively using the data recorded in the step 2 to respectively use the formula for all core samples of the same reservoir
Performing regression solution, wherein the parameter variation range limits A4＞0,C4＞0,0＜B4< 1, obtaining a regression parameter A4、B4、C4And a second determination coefficient
4) And (3) plotting the regression result and the data recorded in the step 2, selecting a formula with the regression result positioned in the range of the water saturation and the J function in the step 2, determining a formula with a coefficient closer to 1 as a basic formula of the average capillary pressure curve, and taking the regression parameters of all core samples of the same type of reservoir in the step 3) corresponding to the basic formula as the regression parameters corresponding to the average capillary pressure curve of the reservoir.
Wherein, the unit conversion coefficient a is different when processing because the capillary pressure units obtained by different testing methods are different.
Wherein the first and second determining coefficients are of the same type, i.e., the first and second determining coefficients are both of the same type
Wherein SSR (regression sum of squares) is regression sum of squares, SSE (error sum of squares) is residual sum of squares, and SST (total sum of squares) is total sum of squares.
The selection method for selecting the optimal formula comprises the following steps:
3-1) taking the J function and water saturation relation data points of a plurality of dimensionless core samples of the same reservoir as true values, calculating the J function regression value corresponding to the water saturation by using the formula (2) and the parameters obtained by regression of the true values and the formula (2) as regression values 1, and recording the determination coefficient 1 as the regression value 1
Calculating a J function regression value corresponding to the water saturation by using the formula (3) and a parameter obtained by the regression of the true value as the formula (3), taking the J function regression value as a regression value 2, and recording a determination coefficient 2 as
Selecting a corresponding formula with a regression value within the range of the true value as an optimal formula;
3-2) for the case that all 2 formulas are within the range of true values, the magnitude of the coefficient is determined by comparison:
if it is
Is greater than or equal to
The basic formula of the average capillary pressure curve of the reservoir to be detected is a formula (2);
if it is
Is greater than or equal to
The basic formula of the average capillary pressure curve of the reservoir to be detected is formula (3).
In the step 3-2), when the basic formula of the average capillary pressure curve of the reservoir to be tested is the formula (2), the average capillary pressure curve of the reservoir to be tested is
Wherein A is2＞0,C2＞0,B2＞0；
When the basic formula of the average capillary pressure curve of the reservoir to be tested is formula (3), the average capillary pressure curve of the reservoir to be tested is
Wherein A is4＞0,C4＞0,0＜B4＜1。
Wherein the number of the cores subjected to the capillary pressure experiment in the step 3-1) is more than or equal to 1.
Wherein, each core sample is subjected to 1 group of capillary pressure experiments; and recording the corresponding relation between the water saturation and the capillary pressure value, the wetting angle, the two-phase interfacial tension, and the porosity and the absolute permeability of the rock core in the capillary pressure experiment.
Wherein the regression parameter A4、A2、B4、B2Related to fractal dimension, inlet pressure, maximum capillary pressure, C4And C2Related to the fractal dimension.
Wherein, A is2、B2、C2Can be represented by formula
Wherein A is2＞0，C2＞0，B2Is greater than 0; or
Wherein A is2＞0，C2＞0，B2More than 1, obtained by multivariate nonlinear regression, saturation of wetting phase SwNon-wetting phase saturation SnwHas a relationship of Sw+Snw＝1；
A is described4、B4、C4Can be represented by formula
Wherein A is4＞0，C4＞0，0＜B4< 1 or
Wherein A is4＞0，C4＞0，B4Greater than 0, obtained by multivariate nonlinear regression, wet phase saturation SwNon-wetting phase saturation SnwHas a relationship of Sw+Snw＝1。
The invention deduces the fractal expression of J function regression formula based on fractal geometry theory
(applicable conditions D < 3 and rmin→0)、J＝A(Sw+B)C(applicable conditions D < 3 and rmin→ epsilon > 0) and J ═ A (1-BS)w)C(applicable conditions 3 < D < 5 and rminGreater than 0), establishing the relation between the regression parameter of the original empirical power-law formula and the fractal dimension theoretically, and indicating that the formula is better for separating pores, the fractal dimension D is less than 3, and the minimum pore radius rmin→ 0, on the other hand, the function form of the original regression equation is generalized, the separation of pores is poor, the fractal dimension D is less than 3, rmin→ epsilon > 0 and 3 < D < 5, rminFor reservoirs larger than 0, two wide-fit fractal regression methods J ═ A (S) are providedw+B)CAnd J ═ A [1-BS ]w]CThrough the verification of actual oil field data, the two methods can effectively improve the J function regression precision (determining coefficient R) of the reservoir2Closer to 1), the initial water saturation obtained by the method is closer to the interpretation result of the saturation logging curve, thereby indirectly proving that the average capillary pressure curve of the reservoir obtained by the method has higher precision and is closer to the underground practical situation, and laterally proving the more universal applicability of the invention.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. the method is characterized in that a relation is established between regression parameters and fractal dimension, maximum capillary pressure and minimum capillary pressure based on mathematical derivation of a fractal theory, the physical significance is clear, a solid theoretical basis is achieved, and a theoretical basis is provided for a general empirical formula (power function) at present; 2. the saturation does not need to be normalized, so that the data processing link is simplified; 3. the method has the advantages that the J function regression precision, the initial water saturation calculation precision and the capillary pressure curve calculation precision of the reservoir with poor pore sorting are effectively improved, and the application range is wider.
Drawings
FIG. 1 is a graph of regression of J-function for a particular actual limestone reservoir type as compared to the current method in example 1;
FIG. 2 is a graph of the regression of the J function of the present invention versus the current method for a practical limestone reservoir type II reservoir in example 1;
FIG. 3 is a graph of regression of J function for a practical limestone reservoir of example 1 in accordance with the present invention and the present method;
FIG. 4 is a graph of regression of J function for the present invention versus the current method for four types of reservoirs of an actual limestone reservoir in example 1;
FIG. 5 is a comparison of the average capillary pressure curve calculation results of a practical limestone reservoir of example 1, compared with the average capillary pressure curve calculation results of the prior art;
FIG. 6 is a comparison of the average capillary pressure curve calculation results of a practical limestone reservoir of example 1 in accordance with the present invention and the prior art;
FIG. 7 is a comparison of the average capillary pressure curve calculation results of a practical limestone reservoir of example 1 in accordance with the present invention and the prior art;
FIG. 8 is a comparison of the average capillary pressure curve calculation results of the present invention compared to the prior art for four types of actual limestone reservoirs in example 1;
FIG. 9 is the initial water saturation field for one to four reservoir types of an actual limestone reservoir determined using the present method in example 1;
FIG. 10 is the initial water saturation field for one to four reservoir types of an actual limestone reservoir determined using the method of the present invention in example 1;
FIG. 11 is a histogram statistics of the initial water saturation field of one to four reservoir types of an actual limestone reservoir determined using the present method in example 1;
FIG. 12 is a histogram statistics of the initial water saturation field of one to four types of reservoir of an actual limestone reservoir determined using the method of the present invention in example 1;
FIG. 13 is a comparison of the single well initial water saturation and logging interpretation saturation for four reservoir types of actual limestone reservoir, as determined by the present invention and the present method; from left to right, the five figures are respectively: BU-28 well, BU-29 well, BU-30 well, BU-31 well and BU-41 well, wherein the black line is a water saturation logging curve, the green line is a saturation curve calculated by the existing method, and the red line is a saturation curve calculated by the method.
Detailed Description
The invention is described in detail below with reference to the following formula derivations, the figures and the examples.
The expression of the dimensionless J function of the capillary pressure is
Its existing regression formula
Broad-fit fractal regression formula 1:
and broad-fit fractal regression formula 2:
and the applicable conditions of each formula, and the derivation process of the parameter variation range is as follows.
According to the fractal geometry theory, if the pore size distribution of the reservoir pores conforms to the fractal structure, the fractal structure can be filled with a certain self-similar basic unit body, and according to a non-equal-diameter equal-length straight capillary bundle seepage model, the unit body can be a straight capillary with the radius and the length of r. In the mercury pressing process, in a certain mercury saturation increasing interval, the power function relationship exists between the number N (> r) of capillaries filled with mercury and the radius r of the cluster of capillaries just filled with mercury in the interval:
in the formula (I), the compound is shown in the specification,rmaxthe maximum capillary radius, P (r) is the pore size distribution density function, D is the fractal dimension, and a is the proportionality constant.
The expression of the pore size distribution density function P (r) can be obtained by deriving r according to the formula (1):
P(r)＝-Da·r-D-1formula (2)
Substituting the formula (2) into the integral of the formula to obtain the accumulated pore volume of the interval with the capillary radius less than r and without being filled with mercury
In the formula (I), the compound is shown in the specification,
and obtaining a total pore volume expression of the core in the same way:
wherein V (< r) represents the pore volume occupied by the wetting phase and V (r) represents the total pore volume.
The wetting phase air saturation in the interval is easy to obtain:
the relationship between capillary pressure and pore radius is:
where σ is the mercury-air interfacial tension, typically 480mN/m, and θ is the mercury-air wetting angle, typically 140 °.
Formula (6) is substituted for formula (5) to give:
if using SHg＝1-SAirReplacement ofWhen the mercury saturation is satisfied, the formula (7) becomes the formula (8):
in the formulae (7) and (8), PmaxMaximum capillary pressure, P, corresponding to minimum capillary radiuseThe displacement pressure is the minimum capillary pressure corresponding to the maximum capillary radius.
The fractal dimension D of the medium and high porosity permeability reservoir stratum with the separated pores is less than 3, rmin＜＜rmaxThe pore radius is mainly concentrated above rminIf r is in the range of mercury intrusion to residual air saturationmin→ 0, known by the nature of power functions
Corresponds to Pmax→+∞，
The formulas (7) and (8) can be simplified into the formulas (9) and (10):
the fractal function of the mercury intrusion into the heredity ancestor (9) or (10) is not normalized in saturation compared with the Brooks-Corey function, and because the fractal dimension D is less than 3, the point with the normalized saturation of 0 exceeds the definition domain when the power exponent of the power function is negative, the fractal function of the mercury intrusion into the heredity ancestor (9 or 10) is more reasonable.
Poor pore sorting reservoir with large fractal dimension, rmin＜rmaxThe concentration of the small pore radius becomes high, rminNot to be ignored, two ranges of fractal dimensions are discussed:
(1) d < 3, poor separation, mercury intrusion to residual air saturation, ① if rmin→ 0 for Pmax→ infinity, also by power function nature
Still obtain the formula (9), the formula (10); ② if rmin→ ε > 0 corresponds to PmaxThe maximum value, but not infinity, is derived from equation (7):
from formula (8):
(2) d is more than 3 and less than 5, sorting is extremely poor, the concentration degree of small pore radius is further increased, and the pore radius r corresponding to the saturation degree of residual airmin> 0, by power function properties
Corresponds to Pmax＞0，
From formula (7):
from formula (8):
the formula (11) or the formula (12) is a mercury intrusion fractal function regression formula with D < 3, rminThe form in the case of → epsilon > 0, the form in which the formula (13) or the formula (14) is a fractal function regression of mercury intrusion in the case of 3 < D < 5, pore sorting is extremely poor, and the saturation is likewise not normalized as compared with the Li function.
And simplifying the seepage model with equal-diameter capillary bundles into rock pore space in a seepage state. From the law of panicum pratense, pressure differenceUnder the action of delta p, mercury with viscosity of mu flows through the radius of riThe flow of a single bundle of bristles of length L is:
volume of single capillary
Substituting formula (15) to obtain:
n (r) root capillary flow rate is added to obtain the total flow rate of the porous medium:
the single capillary volume is expressed in terms of mercury saturation as:
in the formula (18), A is the core sectional area, L is the core length, and SHgiIs the mercury saturation of a single capillary tube. Substituting formula (18) for formula (17) yields:
alli darcy's law:
obtaining an expression for absolute permeability, and considering the continuous distribution of pores, yields:
the J function is defined as dimensionless capillary force and eliminates the effects of porosity and permeability:
for a conventional medium and high porosity and pore-sorted reservoir, formula (6), formula (10) and formula (21) are substituted into formula (22), and the formula can be obtained:
in practical applications, the equation (23) is simplified in form as follows, without being tied to the intrinsic correlation of each parameter:
the formula (24) is a J function power form empirical regression formula widely applied at present, and the application conditions of the formula (24) are revealed to be that the fractal dimension D is less than 3 and r is under the residual air saturation through derivation based on the fractal theorymin→ 0, the formula relates empirical parameter A0、B0Has a relationship with fractal dimension, wherein A0＞0，B0＞0。
When formula (6), formula (12) or formula (21) is substituted for formula (22), it is possible to obtain:
if formula (11) is substituted instead of formula (12), then:
equation 25 (equation 26) is a generalization of the empirical regression equation for the power-law type of J function, formally simplified as:
the method is applicable under the conditions that the fractal dimension D is less than 3 and r is under the saturation of residual airmin→ ε > 0, if rmin→ 0, corresponding to Pmax→+∞，
In formula 25
In formula 26
The two equations are returned to the power law equation 24. Regression parameter A1、A2、B1、B2Related to fractal dimension, inlet pressure, maximum capillary pressure, C1、C2Only related to the fractal dimension. In the derivation process of the formula, r caused by the concentration of the pore diameter of a poor sorting reservoir in the direction of the small pore is mainly consideredminGreater than 0, but because the fractal dimension D is less than 3, the rock pore sorting cannot be too poor, rmin→ ε, so the application conditions of this formula are D < 3 and r at residual air saturationmin→ epsilon > 0, wherein A1＞0，A2＞0，C1＞0，C2＞0，B1＞1，B2＞0。
For the worse low-porosity and low-permeability reservoir, formula (6), formula (14) and formula (21) are substituted into formula (22):
if formula (11) is substituted instead of formula (12), then:
equations (29) and (30) may be simplified in form to:
formula (31) or formula (32), i.e., J-function fractal regression, at 3 < D < 5 and residual air saturation rminFunctional form in the case > 0, corresponding to the physical case where the worse-sorted reservoir pore size is further concentrated towards the small pore direction, resulting in rminAnd the fractal dimension 3 < D < 5 is the applicable condition of the formula. Regression parameter A3、A4、B3、B4Related to fractal dimension, inlet pressure, maximum capillary pressure, C3、C4Only related to the fractal dimension. Wherein A is3＞0，A4＞0，C3＞0，C4＞0，B3＞0，0＜B4＜1。
It should be noted that the wetting angle and interfacial tension related to the fluid properties are eliminated in the derivation process, i.e., J-function fractal regression equations (27), (28), equations (31) and (32) are not only applicable to mercury intrusion process, but also applicable to any two-phase fluid displacement process, i.e., SAirCorresponding to the saturation of the wetting phase Sw,SHgCorresponding to the non-wetting phase saturation SnwThe relationship between the two is Sw+Snw＝1。
In summary, the following steps: in order to improve the calculation precision of the average capillary pressure curve of the differentially selected reservoir, a formula (28)
And type (32)
Respectively in J function wide-fit fractal expression form, and the applicable conditions are D < 3 and rmin> 0 and 3 < D < 5, rmin＞0。
1) First use formula (22)
The method comprises the steps of performing J function dimensionless processing on actually measured capillary pressure curves (function relation between capillary pressure and water saturation) of a plurality of cores of the same reservoir, establishing numerical value corresponding relation between the J function and the water saturation, and paying attention to that unit conversion coefficients a are different during processing due to different capillary pressure units obtained by different testing methods, and the detailed table is shown in a table 1, and common interfacial tension and wetting angle data are shown in a table 2.
TABLE 1 tubing pressure curve J function dimensionless unit conversion coefficient table obtained by different testing methods
TABLE 2 data sheet for interfacial tension and wetting angle in general
2) By means of existing regression models
Regression of J function and water saturation data of the same type of reservoir to obtain regression result and determination coefficient R2(ii) a Using a wide-fitting fractal function 1
And a broad fractal function 2
Regression is carried out on J functions of the same type of reservoir, the regression result is selected to be located in the J function and water saturation data point range of the reservoir, and a coefficient R is determined2The fractal function closer to 1 serves as an optimal regression method.
3) The parameter result can be obtained by solving a multivariate nonlinear regression program, namely a wide-fit fractal function 1
Has a parameter variation range of A2＞0,C2＞0,B2Is greater than 0; wide-fit fractal function 2
Has a parameter variation range of A4＞0,C4＞0,0＜B4＜1。
4) According to the average porosity and absolute permeability of the same type of reservoir, according to S in the 4 th stepwAnd PcThe average capillary pressure curve of the reservoir from initial to terminal states is solved for subsequent simulation of the development scheme.
In order to prove that the average capillary pressure curve of the reservoir obtained by the regression method of the invention is more consistent with the underground actual condition, the initial water saturation curve of the reservoir and the water saturation curve of the single well logging obtained by calculation under the control of the regression method of the invention and the existing method can be compared.
5) Analytical relationship between capillary pressure and J function in equation (22)
Establishing an analytical relational expression of capillary pressure and water saturation, and for the same type of reservoir:
① if the original regression function is used, that is
Then
② if fractal function 1 is used
Then
③ if fractal function 2 is used
Then
Since the calculator function in the mainstream modeling digital-analog integration software Petrel (version 2018.2) does not have a function with a power exponent of any power, three equations can be equivalently rewritten with an exponent and a logarithmic function with a base 10 as:
6) and establishing the attribute h (m) of each grid distance free water interface height difference in the model. According to the relation P of the initial capillary pressure and the height differencecAnd (4) solving the initial capillary pressure value of each grid of the model as delta rho gh.
7) According to S established in the step 4wAnd PcSubstituting the parameter value regressed in the step into the same type of reservoir:
① if the original regression function is used, that is
Then substitute for A0、B0；
② if a fractal function 1 is used, i.e.
Then substitute for A2、B2、C2；
③ if fractal function 2 is used, i.e.
Then substitute for A4、B4、C4. Substituting the porosity and permeability of each grid to obtain the initial water saturation field S of the modelwiIt can be demonstrated by way of example that the single well water saturation curve obtained by the present invention will be closer to the single well logging saturation curve than that obtained by the prior art method, i.e. that the regression accuracy (determination coefficient R) is higher by using the present invention2The J function fractal regression equation which is closer to 1) is adopted, the solved average capillary pressure curve is more in line with the actual pore structure of the underground reservoir, and the oil field production dynamics and the recovery ratio simulated by the average capillary pressure curve are more in line with the underground reality.
Example 1
Taking a limestone reservoir of a middle east B oil field as an example, calculating the average capillary pressure curve of the reservoir according to the method
1. The B field reservoirs were classified into four categories, one category, two category, three category and four category according to the method for reservoir classification in "description of carbonate rock reservoir based on rock type" (pit school, liberty, authored by zhang jun, china oil university press, eastern 2016, 6 months, 1 st edition). The method comprises the following steps that a first type reservoir comprises 4 core samples, a second type reservoir comprises 19 core samples, a third type reservoir comprises 16 core samples, a fourth type reservoir comprises 4 core samples and 43 core samples, a group of capillary pressure experiments are carried out on each core sample, and capillary pressure and wetting phase saturation data are recorded;
2. for 43 capillary pressure curves corresponding to 43 rock samples respectively, using the formula (22)
Dimensionless J function processing is carried out, the numerical value corresponding relation between the J function and the water saturation is established, and relevant parameters are shown in tables 1 and 2. And respectively aggregating the J function and the Sw data according to 4 types of reservoirs to obtain 4 groups of J function and Sw data point sets to be regressed, wherein the data points are shown in the data scatter points of the figures 1-4.
3. By means of existing regression models
Sequentially regressing the relation of J functions Sw of the same type of reservoir, and determining the coefficient R2The reservoir type 0.9482, the reservoir type 0.7551, the reservoir type 0.7101 and the reservoir type 0.7693 are respectively two fractal regression forms by using multivariate nonlinear regression software, wherein the fractal regression forms are shown in a formula (28)
And type (32)
Regression solution, in which the parameter variation limits A2＞0,C2＞0,0＜B2＜+∞，A4＞0,C4＞0,0＜B4< 1, obtaining a regression parameter A2、B2、C2、A4、B4、C4And determining the coefficients
4. The regression curve is projected on the data scatter points of the graphs 1 to 4, the regression result of the formula (32) is obviously not in the range of data points for one type of reservoir, the regression results of the formula (28) and the formula (32) for the second, third and fourth types of reservoirs are in the range of data points, and coefficients are determined by comparison
And
last-class reservoirThe fractal form (28) is selected for the three-type reservoir and the four-type reservoir, the fractal form (32) is selected for the two-type reservoir, and after the fractal regression formula is adopted, the regression results (solid lines in figures 1-4) are all located in the range of actually measured data points, the regression precision is improved compared with the existing regression formula, and the coefficient R is determined2In aspects, one type of reservoir was raised to 0.9978, two type of reservoir was raised to 0.9714, three type of reservoir was raised to 0.9978, and four type of reservoir was raised to 0.8129, as detailed in table 3.
TABLE 3 comparison of regression results for two fractal J-functions
5. According to the average porosity and absolute permeability of various reservoirs (see table 4 in detail), substituting the analytical relationship between capillary pressure and J function in formula (22)
The average capillary pressure curve (the relation between capillary pressure and water saturation) in the whole process of oil field development can be solved and directly input parameters as a model for numerical simulation development index prediction, wherein four types of reservoirs respectively correspond to the parameters in the table 3, and the comparison result of the method with the prior method is shown in the graph 5-8. The results of the oil quantity, the water quantity, the pressure and the like of the single well obtained by inputting the calculation result of the improved formula into a numerical model for simulation are more consistent with the underground actual conditions. To demonstrate this conclusion, the following is a comparison of the single well water saturation calculation under regression control of the J-function of the present invention with the single well water saturation curve.
TABLE 4 mean porosity and Absolute Permeability of middle east B oilfield reservoir
| Reservoir classification | Porosity, decimal fraction | Absolute permeability, mD |
| Reservoir stratum | 0.141 | 228.0 |
| Reservoir of the second kind | 0.159 | 12.5 |
| Three types of reservoirs | 0.165 | 3.3 |
| Four types of reservoirs | 0.161 | 1.1 |
6. Based on the original regression formula
The established relationship between capillary pressure and water saturation is as follows:
one type of reservoir:
two types of reservoirs:
three types of reservoirs:
four types of reservoirs:
the relationship between capillary pressure and water saturation established based on the improved fractal regression formula is as follows:
one type of reservoir:
two types of reservoirs:
three types of reservoirs:
four types of reservoirs:
7. establishing the attribute h (m) of the height difference of each grid distance free water interface in a geological model, and according to the relation P between the initial capillary pressure and the height differencecThe initial capillary pressure of each grid is worked out as delta rho gh, the initial water saturation fields of the four types of reservoirs are worked out by four improved formulas in the last step, the initial water saturation fields are compared with the initial saturation fields worked out by the original formulas and are shown in figures 9-10, the statistical histograms are shown in figures 11-12, and as is obvious from figures 11-12, the water saturation peak calculated by the original method is all 0.2, while the method is about 0.35. This shows that the original water saturation field found by the present invention directly affects the model reserve calculation.
8. The comparison of the initial saturation curve of the single well and the saturation of the logging calculated by the improved formula and the original formula is shown in fig. 13, and it can be seen from the trend that compared with the calculation result of the existing method (solid line and hollow square in fig. 13), the water saturation (solid line and solid circle in fig. 13) under the control of the improved formula of the invention is obviously closer to the interpreted saturation curve of the single well actual logging (solid line in fig. 13), and has more obvious effect on poor second-class reservoirs, third-class reservoirs and fourth-class reservoirs (I, II marked by Facies is corresponding to the first-class reservoirs, III and IV are corresponding to the second-class reservoirs, V is corresponding to the third-class reservoirs, and VI is corresponding to the fourth-class reservoirs). The improved regression method improves the regression accuracy, and means that the calculation result of the original geological reserve model between wells controlled by the method is closer to the single-well logging result than the existing method, namely better accords with the actual underground condition.
The above examples are only used to illustrate the present invention, wherein the capillary pressure testing method, the rock core lithology, the porosity, the permeability, etc. may be varied, and all equivalent changes and modifications based on the technical solution of the present invention should not be excluded from the protection scope of the present invention.
Claims (8)
1. A method of calculating an average capillary pressure curve for a reservoir, comprising the steps of:
1) selecting a plurality of core samples on the same type of reservoir, performing a group of capillary pressure experiments on each core sample, and recording capillary pressure and wetting phase saturation data;
2) for each core sample, using the data recorded in step 1) with the formula respectively
Carrying out dimensionless J function processing, and establishing a numerical value corresponding relation between the J function and the water saturation;
3) respectively using the data recorded in the step 2) to respectively use the formula for all core samples of the same reservoir
Performing regression solution, wherein the parameter variation range limits A2＞0,C2＞0,B2Is greater than 0, and regression parameter A is obtained2、B2、C2And a first determination coefficient
Respectively using the data recorded in the step 2) to respectively use the formula for all core samples of the same reservoir
Performing regression solution, wherein the parameter variation range limits A4＞0,C4＞0,0<B4<1, obtaining a regression parameter A4、B4、C4And a second determination coefficient
4) And (3) plotting the regression result and the data recorded in the step 2), selecting a formula with the regression result positioned in the range of the water saturation and the J function in the step 2), determining a formula with a coefficient closer to 1 as a basic formula of the average capillary pressure curve, and taking the regression parameters of all core samples of the same type of reservoir in the step 3) corresponding to the basic formula as the regression parameters corresponding to the average capillary pressure curve of the reservoir.
2. A method of calculating a reservoir average capillary pressure curve as claimed in claim 1, wherein said first and second determining coefficients are of the same type, i.e. both said first and second determining coefficients are of the same type
Wherein SSR is regression sum of squares, SSE is residual sum of squares, SST is total sum of squares.
3. The method of calculating a reservoir average capillary pressure curve of claim 1, wherein the optimal formula is selected by:
3-1) taking the J function and water saturation relation data points of a plurality of dimensionless core samples of the same reservoir as true values, calculating the J function regression value corresponding to the water saturation by using the formula (2) and the parameters obtained by regression of the true values and the formula (2) as regression values 1, and recording the determination coefficient 1 as the regression value 1
The formula (3) and the true valueThe regression value of the J function corresponding to the water saturation is calculated as a regression value 2 by using the regression formula (3) as the regression parameter obtained by regression, and the determination coefficient 2 is recorded as
Selecting a corresponding formula with a regression value within the range of the true value as an optimal formula;
3-2) for the case that all 2 formulas are within the range of true values, the magnitude of the coefficient is determined by comparison:
if it is
Is greater than or equal to
The basic formula of the average capillary pressure curve of the reservoir to be detected is a formula (2);
if it is
Is greater than or equal to
The basic formula of the average capillary pressure curve of the reservoir to be detected is formula (3).
4. The method for calculating an average capillary pressure curve of a reservoir according to claim 3, wherein in the step 2), when the basic formula of the average capillary pressure curve of the reservoir to be calculated is formula (2), the average capillary pressure curve of the reservoir to be calculated is
Wherein A is2＞０,C2＞０,B2＞0；
When the basic formula of the average capillary pressure curve of the reservoir to be calculated is formula (3), the average capillary pressure curve of the reservoir to be calculated is
Wherein A is4＞0,C4＞0,0<B4<1。
5. A method for calculating an average capillary pressure curve of a reservoir according to any one of claims 1 to 4, wherein the number of cores subjected to a capillary pressure experiment in the step 1) is more than or equal to 1.
6. A method of calculating an average capillary pressure curve for a reservoir according to any one of claims 1 to 4, wherein 1 set of capillary pressure experiments is performed on each core sample; and recording the water saturation, capillary pressure, wetting angle and two-phase interfacial tension in the capillary pressure experiment.
7. A method of calculating a reservoir average capillary pressure curve as claimed in any one of claims 1 to 6, wherein said regression parameter A4、A2、B4、B2Related to fractal dimension, inlet pressure, maximum capillary pressure, C4And C2Related to the fractal dimension.
8. The method of calculating a reservoir average capillary pressure curve of claim 7, wherein A is2、B2、C2Can be represented by formula
Wherein A is2＞0，C2＞0，B2Is greater than 0; or
Wherein A is2＞0，C2＞0，B2More than 1, obtained by multivariate nonlinear regression; a is described4、B4、C4Can be represented by formula
Wherein A is4＞0，C4＞0，0<B4<1 or
Wherein A is4＞0，C4＞0，B4Greater than 0, obtained by multivariate nonlinear regression, wet phase saturation SwNon-wetting phase saturation SnwHas a relationship of Sw+Snw＝1。
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