CN109858196B - Oil and gas reservoir parameter interpretation method and system - Google Patents
Oil and gas reservoir parameter interpretation method and system Download PDFInfo
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Abstract
The application discloses a method for explaining oil and gas reservoir parameters, which comprises the following steps: sampling parameters to be interpreted in a received numerical range to obtain a plurality of trial calculation examples; respectively calculating the trial calculation examples to obtain calculated pressure data corresponding to the trial calculation examples; triangulating the multi-dimensional parameter space to obtain a plurality of regions; based on a plurality of points contained in each area and the values of the points, respectively carrying out high-dimensional linear interpolation on each area so as to respectively construct a response surface function for each area; constructing an objective function aiming at the response surface function of each region respectively; respectively solving the optimal solution of each objective function and the parameter value of the parameter to be explained corresponding to each objective function by using an optimization algorithm; and determining an objective function with the minimum optimal solution in the plurality of objective functions, and determining the parameter value of the parameter to be explained corresponding to the objective function as an explanation result of the parameter to be explained. The method disclosed by the application can improve the interpretation precision of the oil and gas reservoir parameters.
Description
Technical Field
The application belongs to the technical field of oil exploitation, and particularly relates to an oil and gas reservoir parameter interpretation method and system.
Background
The basic purpose of reservoir research is to predict future dynamics of the reservoir and to find methods to increase ultimate recovery. Some engineering problems are encountered in the oil exploitation process, for example, how to build a reliable geological model, so that the problems of evaluating, managing and developing the oil and gas reservoir are solved based on the geological model, and the dynamic prediction of the oil and gas reservoir and the oil well is ensured. The formation parameters and wellbore parameters of the hydrocarbon reservoir need to be known for building the geological model.
Well testing is the most commonly used method for obtaining formation parameters and wellbore parameters of an oil and gas reservoir during its development. Generally, the well testing analysis is to analyze the data such as the measured pressure data and the yield, etc., and research various characteristic parameters of a testing well and a testing layer in the testing influence range, so as to accurately predict the formation parameters and the wellbore parameters of the oil and gas reservoir.
The numerical well testing is a new well testing interpretation technology developed in recent years, and is a numerical simulation technology for accurately describing physical processes through a large number of mathematical simulation operations. The oil and gas reservoir characteristics described by the numerical well test are more real, and the application range is wider. However, numerical well testing also faces a series of difficulties, and has many calculation parameters and long calculation time. In the numerical value well test interpretation process, well test interpreters need to manually adjust uncertain parameters to enable the calculated pressure to be as close as possible to the measured pressure. It is common that it may take weeks or even months to interpret a well or group of wells.
For those skilled in the art, how to improve the efficiency of numerical well testing interpretation and reduce the working strength of the well testing interpreter is an urgent problem to be solved.
Disclosure of Invention
In view of this, the present application aims to provide a method and a system for interpreting hydrocarbon reservoir parameters, so as to improve the efficiency and accuracy of numerical well testing interpretation and reduce the working strength of well testing interpreters.
In order to achieve the above purpose, the present application provides the following technical solutions:
the application provides a method for explaining oil and gas reservoir parameters, which comprises the following steps:
receiving input parameters to be interpreted and corresponding numerical value ranges, wherein the parameters to be interpreted comprise formation parameters and wellbore parameters;
sampling the parameters to be explained in the numerical range to obtain a plurality of trial calculation examples;
respectively calculating the trial calculation examples to obtain calculated pressure data corresponding to the trial calculation examples;
triangulating a multi-dimensional parameter space based on points corresponding to the trial calculation examples to obtain a plurality of regions, wherein the dimension of the multi-dimensional parameter space is the same as the number of parameters to be explained;
based on the values of a plurality of points and each point contained in each area, respectively carrying out high-dimensional linear interpolation on each area so as to respectively construct a response surface function for each area, wherein the value of the point corresponding to any trial calculation example is as follows: calculating pressure data corresponding to the trial calculation example;
constructing an objective function aiming at the response surface function of each area respectively, wherein the objective function indicates the deviation of the calculated pressure data and the measured pressure data;
respectively solving the optimal solution of each objective function and the parameter value of the parameter to be explained corresponding to each objective function by using an optimization algorithm;
and determining an objective function with the minimum optimal solution in the plurality of objective functions, and determining the parameter value of the parameter to be explained corresponding to the objective function with the minimum optimal solution as the explanation result of the parameter to be explained.
Optionally, in the above method, the triangulation is performed on the multidimensional parameter space based on the points corresponding to the multiple trial calculation examples to obtain multiple regions, specifically:
and performing Delaunay triangulation on the multi-dimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas.
Optionally, in the above method, the sampling the parameter to be interpreted within the numerical range to obtain a plurality of trial calculation examples, includes:
and sampling the parameters to be explained in the numerical range by utilizing a Latin hypercube sampling algorithm to obtain a plurality of trial calculation examples.
Optionally, in the above method, the constructing an objective function for the response surface function of each region respectively includes:
and respectively constructing an objective function aiming at the response surface function of each area based on the principle that the error of the calculated pressure data and the actually measured pressure data of the response surface function of each area under the trial calculation example is minimum.
Optionally, in the method, the respectively solving the optimal solution of each objective function and the parameter value of the parameter to be interpreted corresponding to each objective function by using an optimization algorithm includes:
and respectively optimizing each target function by using a feasible direction algorithm and a Latin hypercube sampling algorithm to obtain the optimal solution of each target function and the parameter value of the parameter to be explained corresponding to each target function.
The present application further provides a reservoir parameter interpretation system, comprising:
the data receiving unit is used for receiving input parameters to be interpreted and corresponding numerical value ranges, wherein the parameters to be interpreted comprise stratum parameters and wellbore parameters;
the sampling unit is used for sampling the parameters to be explained in the numerical range to obtain a plurality of trial calculation examples;
the trial calculation example calculation unit is used for calculating the trial calculation examples respectively to obtain calculation pressure data corresponding to the trial calculation examples;
the space subdivision unit is used for triangulating the multidimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas;
the response surface function constructing unit is used for respectively carrying out high-dimensional linear interpolation on each area based on a plurality of points and values of each point contained in each area so as to respectively construct a response surface function for each area, wherein the value of the point corresponding to any trial calculation example is as follows: calculating pressure data corresponding to the trial calculation example;
the target function constructing unit is used for constructing a target function aiming at the response surface function of each area respectively, and the target function indicates the deviation of the calculated pressure data and the measured pressure data;
the optimization unit is used for respectively solving the optimal solution of each objective function and the parameter value of the parameter to be explained corresponding to each objective function by utilizing an optimization algorithm;
and the parameter interpretation unit is used for determining an objective function with the minimum optimal solution in the objective functions and determining the parameter value of the parameter to be interpreted corresponding to the objective function with the minimum optimal solution as the interpretation result of the parameter to be interpreted.
Optionally, in the system, the space subdivision unit is specifically configured to: and performing Delaunay triangulation on the multi-dimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas.
Optionally, in the system, the sampling unit is specifically configured to: and sampling the parameters to be explained in the numerical range by utilizing a Latin hypercube sampling algorithm to obtain a plurality of trial calculation examples.
Optionally, in the system, the objective function constructing unit is specifically configured to: and respectively constructing a target function aiming at the response surface function of each area based on the principle that the error of the calculated pressure data and the actually measured pressure data of the response surface function of each area under the trial calculation example is minimum.
Optionally, in the above system, the optimization unit is specifically configured to: and respectively optimizing each target function by using a feasible direction algorithm and a Latin hypercube sampling algorithm to obtain the optimal solution of each target function and the parameter value of the parameter to be explained corresponding to each target function.
Therefore, the beneficial effects of the application are as follows:
the method comprises the steps of sampling parameters to be explained in a corresponding numerical range after receiving the parameters to be explained input by well testing interpreters and the numerical range of each parameter to be explained, obtaining a plurality of trial calculation examples, calculating the trial calculation examples respectively, obtaining corresponding calculated pressure data, triangulating a multidimensional parameter space based on points corresponding to the trial calculation examples to obtain a plurality of regions, performing high-dimensional linear interpolation on each region respectively based on a plurality of points and values of the points (namely calculated pressure data) included in each region so as to construct a response surface function for each region respectively, constructing a target function capable of indicating deviation between the calculated pressure data and the measured pressure data for each region respectively, solving an optimal solution of each target function and parameter values of the parameters to be explained corresponding to each target function, selecting the target function with the minimum solution from the optimal target functions, and taking the parameter values of the parameters to be explained corresponding to the target function as an explanation result of the parameters to be explained. Based on the oil and gas reservoir parameter interpretation method disclosed by the application, a well test interpreter only needs to input parameters to be interpreted and the numerical range of each parameter to be interpreted according to the type of the oil and gas reservoir, and the electronic equipment can automatically interpret formation parameters and wellbore parameters, so that the interpretation efficiency is greatly improved, and the working intensity of the well test interpreter is reduced; moreover, the response surface function is constructed by performing high-dimensional linear interpolation in each region, so that the response surface function is the quadratic function polynomial at most, the order of the response surface function is effectively low, the interpretation error can be reduced, and the interpretation precision of the hydrocarbon reservoir parameters is improved.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a reservoir parameter interpretation method disclosed herein;
FIG. 2-1 is a graph comparing a measured pressure curve to an estimated pressure curve;
FIG. 2-2 is a graph comparing a true pressure recovery curve, an estimated pressure recovery curve, a true pressure derivative curve, and an estimated pressure derivative curve;
FIG. 3 is a block diagram of a reservoir parameter interpretation system as disclosed herein.
Detailed Description
In the existing numerical value well test interpretation method, firstly, a well test interpreter sets parameter values of parameters to be interpreted (also called parameters to be obtained or uncertain parameters), solves calculation pressure according to the currently set parameter values of the parameters to be interpreted, compares the calculation pressure with actual measurement pressure, then, based on the comparison result, the well test interpreter manually adjusts the parameter values of one or more parameters in the parameters to be interpreted by means of own experience, solves calculation pressure according to the currently set parameter values of the parameters to be interpreted, compares the calculation pressure with the actual measurement pressure again, and enables the calculation pressure to be as close as possible to the actual measurement pressure by largely repeating the manual adjustment process. And when the difference between the calculated pressure and the measured pressure meets a preset condition, determining the parameter value of each parameter to be explained which is currently set as a final explanation result. It can be seen that the existing numerical well testing interpretation process consumes a lot of time, resulting in low efficiency of numerical well testing interpretation and high work intensity of well testing interpreters.
The application discloses an interpretation method and system of oil and gas reservoir parameters, which aim to improve the efficiency and precision of numerical well testing interpretation and reduce the working strength of well testing interpreters.
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort belong to the protection scope of the present application.
Referring to fig. 1, fig. 1 is a flowchart of a reservoir parameter interpretation method disclosed in the present application, and an execution subject of the automatic parameter finding method is an electronic device, such as a computer. The method includes steps S1 to S8.
Step S1: an input parameter to be interpreted and a corresponding numerical range are received. Wherein the parameters to be interpreted include formation parameters and wellbore parameters.
In the case of different reservoir types, the parameters to be interpreted will also differ.
The well test interpreter inputs parameters to be interpreted according to the type of the oil and gas reservoir, and in addition, the well test interpreter also needs to input the numerical range of each parameter to be interpreted, wherein the numerical range is an empirical value determined by the well test interpreter. The parameters to be interpreted include, among others, formation parameters and wellbore parameters.
Formation parameters typically include: a reservoir boundary of the reservoir; SRV of the reservoir (reservoir stimulated volume); permeability distribution, porosity distribution, and pressure distribution of the reservoir over the SRV range; permeability distribution, porosity distribution, and pressure distribution of the reservoir outside the SRV range and within the reservoir boundary; parameters of each primary fracture including the half-length and azimuth angle of the primary fracture.
Wellbore parameters typically include: skin and well storage coefficients.
Step S2: and sampling the parameters to be explained in a numerical range to obtain a plurality of trial calculation examples.
And after receiving the parameters to be explained and the numerical ranges of the parameters to be explained input by the well testing interpreter, the electronic equipment performs sampling processing to obtain a plurality of trial calculation examples. For example, the electronic device performs a sampling operation to obtain 1000 trial calculation examples.
Here, it should be noted that: each trial calculation example comprises a group of parameter values of a plurality of parameters to be explained, and the parameter value of at least one parameter to be explained in any two trial calculation examples is different.
And step S3: and respectively calculating the plurality of trial calculation examples to obtain the calculated pressure data corresponding to the plurality of trial calculation examples.
And respectively calculating according to each trial calculation example to obtain calculated pressure data. Here, in order to distinguish the measured pressure data, the pressure data calculated by the trial calculation example is referred to as calculated pressure data.
As an embodiment, calculating the pressure data includes: calculating pressure, calculating pressure change and calculating pressure derivative. Accordingly, the measured pressure data includes: measured pressure, measured pressure change and measured pressure derivative.
And step S4: and triangulating the multidimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas, wherein the dimensionality of the multidimensional parameter space is the same as the number of the parameters to be explained.
The dimensions of the multidimensional parameter space are the same as the number of parameters to be interpreted. Each trial calculation example comprises a set of parameter values of a plurality of parameters to be interpreted, the set of parameter values defining a point in the multidimensional parameter space, that is to say each trial calculation example corresponds to a point in the multidimensional parameter space. And triangulating the multi-dimensional parameter space according to points contained in the multi-dimensional parameter space to obtain a plurality of areas.
Step S5: and respectively carrying out high-dimensional linear interpolation on each area based on the plurality of points contained in each area and the values of the points so as to respectively construct a response surface function for each area.
Each region comprises a plurality of points, and the value of the point corresponding to any trial calculation example is as follows: the calculated pressure data corresponding to the trial calculation example.
The parameters to be explained are taken as a parameter A, a parameter B and a parameter C, and the number of trial calculation examples is 1000:
each trial calculation example comprises a group of parameter values of the parameter A, the parameter B and the parameter C, and the parameter value of at least one parameter to be explained in any two trial calculation examples is different. And (4) calculating according to each trial calculation example to obtain calculated pressure data. A group of parameter values contained in each trial calculation example define points in a three-dimensional parameter space, the values of the points are calculation pressure data corresponding to the trial calculation examples, and the total number of the points corresponding to 1000 trial calculation examples is 1000. And triangulating the three-dimensional parameter space according to 1000 points contained in the three-dimensional parameter space to obtain a plurality of areas, wherein each area contains a plurality of points. Any one area contains a plurality of points, the value of each point is known, and based on the plurality of points contained in the area and the value of each point, high-dimensional linear interpolation is carried out in the area, so that the response surface function of the area can be obtained.
It should be noted that a polynomial function is generally adopted as the response surface function. If the order (i.e., the number) of the response surface function is higher, on one hand, a larger interpretation error occurs, so that the interpretation precision of the reservoir parameters is lower, on the other hand, more undetermined coefficients are caused, and the required experiment design number is correspondingly increased. In addition, the higher order of the response surface function also leads to an increase in the number of objective functions, thereby leading to difficulty in optimization.
And constructing a response surface function by adopting a mode of carrying out high-dimensional linear interpolation in the region, so that the response surface function is a quadratic function polynomial at most, and the order of the response surface function is effectively lower. Accordingly, interpretation errors can be reduced, and interpretation precision of the hydrocarbon reservoir parameters can be improved.
Step S6: an objective function is constructed for the response surface function of each region, respectively, wherein the objective function indicates a deviation of the calculated pressure data from the measured pressure data.
The objective function OF is usually expressed in the form OF a simple sum OF squares, defined as follows:
OF therein k Is the objective function corresponding to the response surface function of the kth area,
in order to measure the pressure data of the pressure,
to calculate pressure data, ω j And representing the corresponding weight, wherein N is the number of points of the actually measured pressure data, and N is the total number of the areas obtained by triangulation. The goal of this inverse problem is to find an x such that the calculated pressure data is closest to the measured pressure data.
Note the book
X op Is a globally optimal parameter vector (i.e., the point in all regions where the actual observed data is closest to the simulation results).
Step S7: and respectively solving the optimal solution of each objective function and the value of the parameter to be explained corresponding to each objective function by using an optimization algorithm.
Step S8: and determining the objective function with the minimum optimal solution in the plurality of objective functions, and determining the value of the parameter to be explained corresponding to the objective function with the minimum optimal solution as the explanation result of the parameter to be explained.
The optimal solution for each objective function is a local optimal solution, and the minimum of these optimal solutions is a global optimal solution. Therefore, the optimal solutions of the plurality of objective functions are compared, the objective function with the minimum optimal solution is determined, and the parameter value of the parameter to be explained corresponding to the objective function is determined as the explanation result of the parameter to be explained.
The method comprises the steps of sampling parameters to be explained in a corresponding numerical range after receiving the parameters to be explained and the numerical range of each parameter to be explained input by a well testing interpreter, obtaining a plurality of trial calculation examples, calculating the trial calculation examples respectively to obtain corresponding calculated pressure data, triangulating a multi-dimensional parameter space based on points corresponding to the trial calculation examples to obtain a plurality of regions, performing high-dimensional linear interpolation on each region respectively based on values of a plurality of points and points (namely calculated pressure data) contained in each region to construct a response surface function respectively for each region, constructing target functions capable of indicating deviation between the calculated pressure data and measured pressure data respectively for each region, solving the optimal solution of each target function and the parameter values of the parameters to be explained corresponding to each target function, selecting the target function with the minimum solution from the optimal target functions, and taking the parameter values of the parameters to be explained corresponding to the target functions as the explanation results of the parameters to be explained.
Based on the oil and gas reservoir parameter interpretation method disclosed by the application, a well test interpreter only needs to input parameters to be interpreted and the numerical range of each parameter to be interpreted according to the type of the oil and gas reservoir, and the electronic equipment can automatically interpret formation parameters and wellbore parameters, so that the interpretation efficiency is greatly improved, and the working intensity of the well test interpreter is reduced; moreover, the response surface function is constructed by performing high-dimensional linear interpolation in the region, so that the response surface function is the quadratic function polynomial at most, the order of the response surface function is effectively low, the interpretation error can be reduced, and the interpretation precision of the hydrocarbon reservoir parameters is improved.
As an example, in the hydrocarbon reservoir parameter interpretation method disclosed in the above application, triangulation is performed on the multidimensional parameter space based on points corresponding to a plurality of trial calculation examples to obtain a plurality of regions, specifically: and performing Delaunay triangulation on the multi-dimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas.
Each region obtained by Delaunay triangulation of the multidimensional parameter space is a region enclosed by a hyperplane, for example: a triangle formed by line segments in a two-dimensional space and a tetrahedron formed by planes in a three-dimensional space.
And respectively giving constraint conditions for each area obtained by triangulation. Selecting hyperplane as example to construct constraint condition, and setting P 1 ,P 2 ,…,P i-1 ,P i+1 ,…P n+1 For linearly independent points on the hyperplane, note:
let P be any point on this plane,
is linearly independent, but
The correlation is linear. Namely:
using equation 1, we can obtain:
equation 2 above is a hyperplane equation.
From the arbitrariness of i, in n-dimensional space, each region can get n +1 hyperplane equations of the above form. Recording:
if f i (P i ) If < 0, the corresponding ith constraint inequality is:
f i (P)≤0，P∈Ω j
if f i (P i ) If > 0, the corresponding ith constraint inequality is:
f i (P)≥0，P∈Ω j
similar to the constraint conditions of other n hyperplanes, the constraint conditions of a plurality of hyperplanes form a constraint condition inequality set of the triangular region.
Note R = { i =1,2., n +1|f i (P i ) If > 0}, the constraint condition inequality of the triangular region is as follows:
assume one or more responses y and a plurality of variables x 1 ,x 2 ,…x n There is a relationship between them, which can be expressed as:
y＝f(x 1 ,x 2 ,…x n ) + epsilon type (4)
Where f is the unknown response surface function and epsilon represents the error term.
High-dimensional linear interpolation: in each region of the n-dimensional space, from n +1 linearly independent points, an interpolation function can be obtained as:
wherein the coefficient theta i (i =1,2, ·, n + 1) satisfies:
it should be noted that the interpolation function is a response surface function.
As an example, in the hydrocarbon reservoir parameter interpretation method disclosed in the above application, the parameter to be interpreted is sampled within a numerical range to obtain a plurality of trial calculation examples, specifically: and sampling the parameters to be explained in the numerical range by utilizing a Latin hypercube sampling algorithm to obtain a plurality of trial calculation examples.
Latin hypercube sampling is a sampling designed to accurately reconstruct the input distribution with a small number of iterations. The key to latin hypercube sampling is to stratify the input probability distribution. Layering divides the cumulative curve into equal intervals on a cumulative probability scale (0 to 1.0) and then randomly samples are drawn from each interval or "layer" of the input distribution. Latin hypercube sampling does not require more samples for more dimensions (variables), and this independence is a major advantage of this sampling scheme.
Briefly, assuming that m samples are to be extracted in an n-dimensional vector space, the Latin hypercube sampling step is:
step1: dividing each dimension into m intervals which do not overlap each other, so that each interval has the same probability (usually considering a uniform distribution, so that the intervals are the same length);
step2: randomly extracting a point in each interval in each dimension;
step3: and (3) randomly extracting the points selected in the step (2) from each dimension, and forming the points into vectors.
According to the oil and gas reservoir parameter interpretation method, the parameters to be interpreted are sampled for multiple times within a given numerical range by using the Latin hypercube sampling algorithm, so that the sampling data can cover the whole numerical range, and the accuracy of the interpretation result is improved.
In practice, the parameter to be interpreted may also be sampled within the value range using an equidistant sampling algorithm, a random sampling algorithm, a model carlo sampling algorithm, or a cluster sampling algorithm.
As an example, in the reservoir parameter interpretation method disclosed above in the present application, an objective function is constructed for the response surface function of each region, specifically: and respectively constructing a target function aiming at the response surface function of each area based on the principle that the error of the calculated pressure data and the actually measured pressure data of the response surface function of each area under the trial calculation example is minimum.
Based on the principle of minimum error, the objective function can be constructed quickly.
As an example, in the hydrocarbon reservoir parameter interpretation method disclosed above, the optimal solution of each objective function and the value of the parameter to be interpreted corresponding to each objective function are respectively solved by using an optimization algorithm, which specifically includes: and respectively optimizing each target function by using a feasible direction algorithm and a Latin hypercube sampling algorithm to obtain the optimal solution of each target function and the value of the parameter to be explained corresponding to each target function.
According to the objective function and the constraint conditions, the optimal solution of each objective function is solved to be a typical quadratic programming problem, the objective function can be optimized by using a feasible direction algorithm, the optimal solution of the objective function of each area is obtained, and therefore the parameter value of the parameter to be explained corresponding to each optimal solution is obtained.
In the oil and gas reservoir parameter interpretation method disclosed by the application, the objective function is optimized by using the feasible direction algorithm and the Latin hypercube sampling algorithm, and the optimal solution of the objective function can be quickly found, so that the interpretation efficiency of numerical well testing is further improved.
The implementation of the reservoir parameter interpretation method disclosed in the present application and the validity of the results will be described below with reference to an example.
A five-point well pattern model is used. The size of the oil-gas reservoir is 600m 400m, the thickness is 10m, the porosity is 0.2, the middle part is a production well, and the four corners are four injection wells. A composite area is arranged around the production well, the well opening time of the production well is 240 days, and the yield is 80m 3 And day, the shut-in time is 3 days. All four injection wells are injected for 240 days, and the wells are closed for 3 days. The injection flow rates of the injection wells 1,2, 3 and 4 were 20m 3 /day、30m 3 /day、10m 3 /day、20m 3 /day。
To verify the effectiveness of the reservoir parameter interpretation method disclosed herein, it is assumed that the oil and water viscosities are equal, the oil and water volume coefficients are equal, and the percolation curve is a straight line with a slope of 1, so the relative permeability at each saturation is 1. Thus, the two-phase flow here is equivalent to a single-phase flow.
The 4 parameters to be interpreted and their value ranges are selected as follows: a formation permeability K in the range of (100mD, 700mD); permeability K of composite zone 1 The numerical range is (100mD, 700mD); the production well bore stores C in the range of (0.1 m) 3 /MPa,1.0m 3 In MPa); and producing the well epidermal factor S, wherein the numerical range is (-3,3).
And fitting a bottom hole pressure recovery curve, a pressure change curve and a derivative curve of the pressure change curve of the production well on the premise of injection-production balance.
Firstly, 1000 trial calculation examples are determined by utilizing a Latin hypercube sampling algorithm.
And then, each trial calculation example is brought into a numerical well testing simulator for calculation to obtain corresponding calculated pressure data. And randomly selecting the calculation pressure data corresponding to 900 trial calculation examples from 1000 trial calculation examples as sample data, and triangulating the multidimensional parameter space based on the points corresponding to the 900 trial calculation examples to obtain a plurality of areas.
Then, based on the plurality OF points contained in each area and the values OF the points, high-dimensional linear interpolation is respectively carried out in each area, so that a response surface function is respectively constructed for each area, then a corresponding objective function OF is constructed for the response surface function OF each area, and the rest 100 groups are used as test data. And (3) obtaining the optimal solution of the target function of each area through optimization of a feasible direction algorithm, selecting the target function with the minimum optimal solution from a plurality of target functions, and taking the parameter value of the parameter to be explained corresponding to the target function as the estimated value (namely the explained result) of the parameter to be explained.
The comparison of the estimated value of the optimal parameter to be interpreted with the true value is shown in table 1.
TABLE 1
| Parameter name | K/mD | K 1 /mD | C/m 3 /MPa | S |
| True value | 130.588 | 167.810 | 0.8879 | 1.6012 |
| Estimated value | 130.578 | 169.356 | 0.8883 | 1.6989 |
| Error of the measurement | 0.010 | 1.546 | 0.0004 | 0.0977 |
And then, substituting the estimated value and the actual value of the parameter to be explained into a numerical well testing simulator to obtain an actual pressure curve and a calculated pressure curve, and also obtain an actual pressure recovery curve, an actual pressure derivative curve, a calculated pressure recovery curve and a calculated pressure derivative curve.
Referring to fig. 2-1, fig. 2-1 is a graph of a measured pressure curve versus an estimated pressure curve (i.e., a calculated pressure curve). Referring to fig. 2-2, fig. 2-2 is a graph comparing an actual pressure buildup curve (i.e., measured pressure buildup curve), an estimated pressure buildup curve (i.e., calculated pressure buildup curve), an actual pressure derivative curve (i.e., measured pressure derivative curve), and an estimated pressure derivative curve (i.e., calculated pressure derivative curve).
It can be seen that the reservoir parameter interpretation method based on the application can accurately interpret the formation parameters and the wellbore parameters, and cannot increase the multi-solution property.
The application discloses an oil and gas reservoir parameter interpretation method, and correspondingly, an oil and gas reservoir parameter interpretation system is further disclosed. The following description of the reservoir parameter interpretation system and the above description of the reservoir parameter interpretation method may be referred to one another.
Referring to fig. 3, fig. 3 is a structural diagram of a reservoir parameter interpretation system disclosed in the present application, and includes a data receiving unit 10, a sampling unit 20, a trial calculation example calculating unit 30, a space subdivision unit 40, a response surface function construction unit 50, an objective function construction unit 60, an optimization unit 70, and a parameter interpretation unit 80.
Wherein:
and the data receiving unit 10 is used for receiving the input parameters to be interpreted and the corresponding numerical value ranges. The parameters to be interpreted include, among other things, formation parameters and wellbore parameters.
And the sampling unit 20 is used for sampling the parameters to be interpreted within a numerical range to obtain a plurality of trial calculation examples.
The trial calculation example calculation unit 30 is configured to calculate a plurality of trial calculation examples, respectively, and obtain calculated pressure data corresponding to the plurality of trial calculation examples.
And the space subdivision unit 40 is configured to triangulate the multidimensional parameter space based on the points corresponding to the multiple trial calculation examples to obtain multiple regions.
And a response surface function constructing unit 50, configured to perform high-dimensional linear interpolation on each region respectively based on the plurality of points included in each region and the values of the points, so as to construct a response surface function for each region respectively. Wherein, the value of the point corresponding to any trial calculation example is as follows: and calculating pressure data corresponding to the trial calculation example.
An objective function constructing unit 60 for constructing an objective function for the response surface function of each region, respectively, the objective function indicating a deviation of the calculated pressure data from the measured pressure data.
And the optimizing unit 70 is configured to separately solve the optimal solution of each objective function and the parameter value of the parameter to be interpreted corresponding to each objective function by using an optimization algorithm.
The parameter interpretation unit 80 is configured to determine an objective function with the minimum optimal solution among the plurality of objective functions, and determine a parameter value of the parameter to be interpreted, which corresponds to the objective function with the minimum optimal solution, as an interpretation result of the parameter to be interpreted.
Based on the oil and gas reservoir parameter interpretation system disclosed by the application, a well test interpreter only needs to input parameters to be interpreted and the numerical range of each parameter to be interpreted according to the type of the oil and gas reservoir, and the electronic equipment can automatically interpret formation parameters and wellbore parameters, so that the interpretation efficiency is greatly improved, and the working intensity of the well test interpreter is reduced; moreover, the response surface function is constructed by performing high-dimensional linear interpolation in each region, so that the response surface function is the quadratic function polynomial at the highest, the order of the response surface function is effectively low, the interpretation error can be reduced, and the interpretation precision of the reservoir parameters is improved.
In another embodiment, the space-dividing unit 40 is specifically configured to: and performing Delaunay triangulation on the multi-dimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas.
In another embodiment, the sampling unit 20 is specifically configured to: and sampling the parameters to be explained in a numerical range by utilizing a Latin hypercube sampling algorithm to obtain a plurality of trial calculation examples.
In another embodiment, the objective function constructing unit 60 is specifically configured to: and respectively constructing a target function aiming at the response surface function of each area based on the principle that the error of the calculated pressure data and the actually measured pressure data of the response surface function of each area under the trial calculation example is minimum.
In another embodiment, the optimization unit 70 is specifically configured to: and respectively optimizing each target function by using a feasible direction algorithm and a Latin hypercube sampling algorithm to obtain the optimal solution of each target function and the parameter value of the parameter to be explained corresponding to each target function.
Finally, it should also be noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the description of the method part.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. A method for reservoir parameter interpretation, comprising:
receiving input parameters to be interpreted and corresponding numerical value ranges, wherein the parameters to be interpreted comprise formation parameters and wellbore parameters;
sampling the parameters to be explained in the numerical range to obtain a plurality of trial calculation examples;
respectively calculating the trial calculation examples to obtain calculated pressure data corresponding to the trial calculation examples;
triangulating a multi-dimensional parameter space based on points corresponding to the trial calculation examples to obtain a plurality of regions, wherein the dimension of the multi-dimensional parameter space is the same as the number of parameters to be explained;
based on the values of a plurality of points and each point contained in each area, respectively carrying out high-dimensional linear interpolation on each area so as to respectively construct a response surface function for each area, wherein the value of the point corresponding to any trial calculation example is as follows: calculating pressure data corresponding to the trial calculation example;
constructing an objective function aiming at the response surface function of each area respectively, wherein the objective function indicates the deviation of the calculated pressure data and the measured pressure data;
respectively solving the optimal solution of each objective function and the parameter value of the parameter to be explained corresponding to each objective function by using an optimization algorithm;
and determining an objective function with the minimum optimal solution in the plurality of objective functions, and determining the parameter value of the parameter to be explained corresponding to the objective function with the minimum optimal solution as the explanation result of the parameter to be explained.
2. The method according to claim 1, wherein the triangulation is performed on the multidimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of regions, specifically:
and performing Delaunay triangulation on the multi-dimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas.
3. The method according to claim 1 or 2, wherein said sampling said parameter to be interpreted within said range of values, resulting in a plurality of trial calculation examples, comprises:
and sampling the parameters to be explained in the numerical range by utilizing a Latin hypercube sampling algorithm to obtain a plurality of trial calculation examples.
4. The method of claim 1 or 2, wherein constructing the objective function separately for the response surface function of each region comprises:
and respectively constructing a target function aiming at the response surface function of each area based on the principle that the error of the calculated pressure data and the actually measured pressure data of the response surface function of each area under the trial calculation example is minimum.
5. The method according to claim 1 or 2, wherein the using an optimization algorithm to respectively solve the optimal solution of each objective function and the parameter value of the parameter to be interpreted corresponding to each objective function comprises:
and respectively optimizing each target function by using a feasible direction algorithm and a Latin hypercube sampling algorithm to obtain the optimal solution of each target function and the parameter value of the parameter to be explained corresponding to each target function.
6. A reservoir parameter interpretation system, comprising:
the data receiving unit is used for receiving input parameters to be interpreted and corresponding numerical value ranges, wherein the parameters to be interpreted comprise stratum parameters and wellbore parameters;
the sampling unit is used for sampling the parameters to be explained in the numerical range to obtain a plurality of trial calculation examples;
the trial calculation example calculation unit is used for calculating the trial calculation examples respectively to obtain calculation pressure data corresponding to the trial calculation examples;
the space subdivision unit is used for triangulating the multidimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas;
the response surface function constructing unit is used for respectively carrying out high-dimensional linear interpolation on each area based on a plurality of points and values of each point contained in each area so as to respectively construct a response surface function for each area, wherein the value of the point corresponding to any trial calculation example is as follows: calculating pressure data corresponding to the trial calculation example;
the target function constructing unit is used for constructing a target function aiming at the response surface function of each area respectively, and the target function indicates the deviation of the calculated pressure data and the measured pressure data;
the optimization unit is used for respectively solving the optimal solution of each objective function and the parameter value of the parameter to be explained corresponding to each objective function by utilizing an optimization algorithm;
and the parameter interpretation unit is used for determining an objective function with the minimum optimal solution in the objective functions and determining the parameter value of the parameter to be interpreted corresponding to the objective function with the minimum optimal solution as the interpretation result of the parameter to be interpreted.
7. The system of claim 6, wherein the spatial subdivision unit is specifically configured to: and performing Delaunay triangulation on the multi-dimensional parameter space based on the points corresponding to the plurality of trial calculation examples to obtain a plurality of areas.
8. The system according to claim 6 or 7, wherein the sampling unit is specifically configured to: and sampling the parameters to be explained in the numerical range by utilizing a Latin hypercube sampling algorithm to obtain a plurality of trial calculation examples.
9. The system according to claim 6 or 7, characterized in that the objective function construction unit is specifically configured to: and respectively constructing a target function aiming at the response surface function of each area based on the principle that the error of the calculated pressure data and the actually measured pressure data of the response surface function of each area under the trial calculation example is minimum.
10. The system according to claim 6 or 7, wherein the optimization unit is specifically configured to: and respectively optimizing each target function by using a feasible direction algorithm and a Latin hypercube sampling algorithm to obtain the optimal solution of each target function and the parameter value of the parameter to be explained corresponding to each target function.
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