MULTI-CAPILLARY FORCE CURVE AVERAGING METHOD BASED ON MULTI-SAMPLE OVERALL VIRTUAL MEASUREMENT

Abstract

The present invention relates to a multi-capillary force curve averaging method based on the overall virtual measurement of a plurality of samples. The method includes the following steps: 1, taking m types of rock samples, obtaining a capillary force-saturation curve, an apparent volume and a porosity of each sample; 2, inspecting the quality of the capillary force-saturation curve of each sample and preprocessing the end points of each curve; 3, calculating an averaged wet phase saturation corresponding to different capillary force values of the plurality of samples under the overall virtual measurement of a plurality of samples; and 4, denoting data points on a graph by using the wet phase saturation as the abscissa and capillary force as the ordinate, and finally connecting all data points smoothly to obtain the averaged capillary force curve. This method of the present invention is reliable in principle and easy to operate, can be directly operated on the capillary force curves, is also suitable for various types of samples with different physical properties in consideration of the influence of the numbers of reservoirs represented by samples, has a wide range of applications, and accurate and convenient calculation results, and is more consistent with actual working conditions.

Claims

1. A multi-capillary force curve averaging method based on the overall virtual measurement of a plurality of samples, sequentially comprising the following steps: 1, taking m types of rock samples, obtaining a capillary force-saturation curve , an apparent volume V.sub.b and a porosity ϕ of each sample, and marking the capillary force-saturation curve of a j.sup.th sample as , the apparent volume as and the porosity as ϕ.sup.j; 2, inspecting the quality of the capillary force-saturation curve of each sample and preprocessing the end points of each curve, wherein the specific process is as follows: (1) ensuring that the change in the capillary force P.sup.j.sub.c of each capillary force-saturation curve over the saturation S.sub.w satisfies a monotonic function feature; (2) ensuring that a maximum value of capillary force-saturation curves is greater than a maximum capillary force value P.sub.c max required by the averaged capillary force-saturation curve; (3) extrapolating a gentle section of the capillary force-saturation curve to the wet phase saturation S.sub.w=1, wherein the corresponding capillary pressure is a displacement pressure; taking the minimum displacement pressure in all samples as P.sub.c min, and replacing the original curve section of the same saturation interval with the curve section obtained by extrapolation; and (4) naming the processed capillary force-saturation curve as 3, taking a series of enough values at equal intervals or unequal intervals from a real number interval [P.sub.c min, P.sub.c max], and denoting them as , wherein the subscript i represents an i.sup.th data point, and ; calculating an averaged wet phase saturation corresponding to different capillary force values P.sub.ci under the overall virtual measurement of a plurality of samples, wherein the specific process is as follows: (1) when the capillary force-saturation curve is expressed by an analytical function: $p_c=\text{?}\leftarrow (j\in (1,2,.Math.,m\})$ $\text{?}\text{indicates text missing or illegible when filed}$ since the change in the capillary force with saturation satisfies monotonicity, the capillary force-saturation function has an inverse function: $S_w=\mathrm{anti}\text{?}$ $\text{?}\text{indicates text missing or illegible when filed}$ calculating the averaged wet phase saturation of a plurality of samples by using the following formula: $\stackrel{\_}{S_{\mathrm{wi}}}=\text{?}$ $\text{?}\text{indicates text missing or illegible when filed}$ (2) when the capillary force-saturation curve is represented by a graphical curve, finding the corresponding wet phase saturation , from the capillary force-saturation curve of each sample for each capillary force value P.sub.ci, in the sequence , and then calculating the averaged wet phase saturation S.sub.wi of the plurality of samples according to the following formula:) $\text{?}\left(i\in \left\{0,1,.Math.,N\right\}\right)$ $\text{?}\text{indicates text missing or illegible when filed}$ (3) when the capillary force-saturation curve described with a data table, two processing methods may be adopted: according to a function relationship represents a total number of data points in the capillary force data table of the j.sup.th sample) determined based on the data sheet, determining a P.sub.ci, value on the capillary force-saturation curve of the j.sup.th sample by using internal interpolation manner; and calculating an averaged wet phase saturation of the plurality of samples according to the following formula: $\text{?}\left(i\in \left\{0,1,.Math.,N\right\}\right)$ $\text{?}\text{indicates text missing or illegible when filed}$ 4, denoting data points on the graph by using the wet phase saturation as the abscissa and capillary force P.sub.ci as the ordinate, and finally connecting all data points smoothly to obtain the averaged capillary force curve.

2. The multi-capillary force curve averaging method based on the overall virtual measurement of a plurality of samples according to claim 1, wherein in the step 2, ensuring that a maximum value of all capillary force-saturation curves is greater than a maximum capillary force value P.sub.c max required by the averaged capillary force-saturation curve means to extending an end point curve of the capillary force-saturation curve that does not meet the requirements by an extrapolation method until the maximum capillary force value of the capillary force-saturation curves exceeds P.sub.c max.

3. The multi-capillary force curve averaging method based on the overall virtual measurement of a plurality of samples according to claim 1, wherein in the step 3, when the capillary force-saturation curve is represented with a graphic curve or described with a data table, if P.sub.ci, is less than the minimum capillary force value on the capillary force-saturation curve of the j.sup.th sample, is taken.

4. The multi-capillary force curve averaging method based on the overall virtual measurement of a plurality of samples according to claim 1, wherein in the step 3, when the capillary force-saturation curve is described with a data table, a graph of capillary force-saturation curve is drawn according to these data points, and converted to a case (2) for processing.

5. The multi-capillary force curve averaging method based on the overall virtual measurement of a plurality of samples according to claim 1, wherein in the step 3, when the capillary force-saturation curve is expressed in a mixed way of function, graph and data table description, the averaged wet phase saturation is obtained respectively according to the cases (1) to (3) in the step.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG. 1 is a schematic diagram of a multi-capillary force curve averaging method based on multi-sample overall measurement.

[0028] a is capillary force curves respectively measured for a sample a and a sample (3; b is capillary force curves obtained by taking the sample a and the sample 13 into an instrument together for overall measurement; and c is a capillary force curve obtained by taking different numbers of sample a and sample 13 into the instrument for overall measurement.

[0029] FIG. 2 is a schematic diagram of preprocessing of end points of a capillary force curve.

[0030] a is an original capillary force curve; b is a curve after the capillary force curve is extended at the end points.

[0031] FIG. 3 shows a corresponding wet phase saturation for different capillary forces (P.sub.ci) by different capillary force curves z,999 .

[0032] a is a schematic diagram of two types of sample curves; and b is a schematic diagram of m type of samples.

DETAILED DESCRIPTION

[0033] To facilitate those skilled in the art to understand the present invention, the present invention will be further described below according to the accompanying drawings. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes fall within the spirit and scope of the present invention defined and determined by the appended claims, they are all protected.

[0034] In the present invention, the subscript w represents a wet phase fluid; the subscript n represents a non-wet phase fluid; P.sub.c represents a capillary force; S represents a saturation; S.sub.w represents a wet phase saturation; V.sub.b represents an apparent volume of a rock sample; and ϕ represents a porosity of a sample. A variable m represents the number of samples; the superscript j represents a j.sup.th sample.

[0035] Referring to FIG. 1, taking an oil-water two-phase capillary force as an example, if there are two samples α and β, capillary force curves measured respectively by) experiments are: the averaged capillary force is equivalent to putting the two samples into the instruction at the same time for measurement. In FIG. 1, a is capillary force curves respectively measured for the sample α and the sample β; b is capillary force curves Fe .sup.Ss.sup.. obtained by taking the sample α and the sample β into an instrument together for overall measurement; and c is a capillary force curve obtained by taking different numbers of sample α and sample β into the instrument for overall measurement.

[0036] The multi-capillary force curve averaging method based on the overall virtual measurement of a plurality of samples sequentially comprises the following steps:

[0037] 1, taking m types of rock samples, obtaining a capillary force-saturation curve , an apparent volume V.sub.b and a porosity ϕ of each sample, and marking the capillary force-saturation curve of the j.sup.th sample as the apparent volume as and the porosity as ϕ.sup.J ;

[0038] 2, inspecting the quality of the capillary force-saturation curve of each rock sample and preprocessing the end points of each capillary force-saturation curve (as shown in FIG. 2), and the specific process is as follows: [0039] (1) ensuring that the change in the capillary force P.sup.J.sub.c of each capillary force-saturation curve over the saturation S.sub.w satisfies a monotonic function feature; otherwise indicating that the quality of the capillary force-saturation curve is unqualified and needs to be corrected; [0040] (2) ensuring that a maximum value of all capillary force-saturation curves is greater than a maximum capillary force value Pc max required by the averaged capillary force-saturation curve; otherwise, extending an end point curve of the capillary force-saturation curve that does not meet the requirements by an extrapolation method until the maximum capillary force value of the capillary force-saturation curves exceeds P.sub.c max; [0041] (3) extrapolating a gentle section of the capillary force-saturation curve to the wet phase saturation S.sub.w=1, wherein the corresponding capillary pressure is a displacement pressure; taking the minimum displacement pressure in all samples as P.sub.c min, and replacing the original curve section of the same saturation interval with the curve section obtained by extrapolation; and [0042] (4) naming the processed capillary force-saturation curve as (corresponding to the capillary force-saturation curve before processing);

[0043] 3, taking a series of enough values at equal intervals or unequal intervals from a real number interval [P.sub.c min, P.sub.c max], and denoting them as , wherein the subscript i represents an i.sup.th data point, and ; calculating an averaged wet phase saturation corresponding to different capillary force values P.sub.ci, under the overall virtual measurement of a plurality of samples (this saturation can be understood as a type of weighted average saturation), and denoting it as , wherein the specific process is as follows:

[0044] considering that there are four ways to express the capillary force-saturation curves in practice, that is, a. analytical formula method; b. graphic method; c. data table; d. hybrid method, the present invention is also divided into four methods for processing;

[0045] (1) when the capillary force-saturation curve is expressed by an analytical function:

[00006]$\begin{array}{cc}{p}_c=\text{?}\leftarrow (j\in (1,2,.Math.,m\})& \left(1\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0046] since the change in the capillary force with saturation satisfies monotonicity, the capillary force-saturation has an inverse function, denoted as:

[00007]$\begin{array}{cc}{S}_w=\mathrm{anti}\text{?}& \left(2\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0047] calculating the averaged wet phase saturation of a plurality of samples by using the following formula:

[00008]$\begin{array}{cc}\stackrel{\_}{S_{\mathrm{wi}}}=\text{?}& \left(3\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0048] substituting all P.sub.ci, into Formula (3) sequentially, to calculate the corresponding averaged wet phase saturation S.sub.wi;

[0049] (2) when the capillary force-saturation curve is represented by a graphical curve, finding the corresponding wet phase saturation from the capillary force-saturation curve of each sample for each capillary force value P.sub.ci, in the sequence , and denoting it as S.sup.j.sub.wi, and then calculating the averaged wet phase saturation S.sub.wi, of the plurality of samples according to the following formula:

[00009]$\begin{array}{cc}\text{?}\left(i\in \left\{0,1,.Math.,N\right\}\right)& \left(4\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0050] if certain P is less than a minimum capillary force value on the capillary force-saturation curve of the .sup.th sample, taking S.sup.j.sub.wi=1 (as shown in FIG. 3);

[0051] (3) when the capillary force-saturation curve is described with a data table, two processing methods may be adopted:

[0052] 1) drawing a graph of capillary force-saturation curve according to these data points, and converting it to a case (2) for processing; 2) according to a function relationship (represents a total number of data points in the capillary force data table of the j.sup.th sample) determined based on the data sheet of each sample, determining a P.sub.ci, value on the capillary force-saturation curve of the j.sup.th sample by using internal interpolation manner, and denoting said value as ; and calculating an averaged wet phase saturation of the plurality of samples according to Formula (4), wherein

[0053] if certain P is less than the minimum capillary force value on the capillary force-saturation curve of the J.sup.th sample, taking directly (as shown in FIGS. 3); and

[0054] (4) when the capillary force-saturation curve is expressed in a mixed way of function, graph and data table description, obtaining the averaged wet phase saturation of the plurality of samples respectively according to the cases (.sub.1) to (.sub.3) in this step; and

[0055] 4, denoting data points on the graph by using the wet phase saturation as the abscissa and capillary force P.sub.ci, as the ordinate, and finally connecting all data points smoothly to obtain the averaged capillary force curve.