CN104612660B - MRF-based oil and gas reservoir lithofacies stochastic simulation and achievement method - Google Patents

Abstract

The invention discloses an MRF-based stochastic simulation of oil and gas reservoir lithofacies and its realization method. Using the MRF conditional probability formula, the potential function is selected as a logarithmic transfer probability function to obtain the lithofacies occurrence probability at the target location. The known points and the simulated points, using the idea of combining sequential simulation and conditional simulation, calculate the occurrence probability of various lithofacies in the area to be simulated according to the transition probability function diagram, and use Monte Carlo stochastic simulation to obtain the grid Lithofacies simulation results. Using the API to integrate the method into the SGeMS platform in the form of an algorithm plug-in, the effect of rotating the target reservoir at any angle in the three-dimensional space and cutting the section at any position can be realized. Due to the existence of transfer probability directionality, the accuracy of MRF-based oil reservoir lithofacies prediction is significantly improved for describing the unidirectional distribution trend and anisotropy characteristics of lithofacies transfer.

Description

A stochastic simulation of oil and gas reservoir lithofacies based on MRF and its realization method

technical field

The invention relates to an MRF-based stochastic simulation of oil and gas reservoir lithofacies and its realization method.

Background technique

Petroleum reservoir visualization is a combination of reservoir model and visualization technology, which can intuitively display the distribution of reservoir properties through images. The relatively mature reservoir visualization software systems at home and abroad, such as GASOR, Petrel, and RMS, only provide the end-user operation interface, and it is difficult to integrate new reservoir modeling algorithms. For a large amount of geological survey data, although engineering computing software such as MATLAB has program scalability and visualization functions, it faces multiple challenges such as computing time and storage space, and its 3D simulation results often have inherent defects such as rough boundaries and difficult to characterize internal structures. . On the other hand, traditional reservoir modeling software is mostly based on the Kriging interpolation algorithm, and uses the Klicking variant simulation method. The Klicking algorithm has spatial symmetry, but the actual geological structure is often anisotropic and non-linear. homogeneity. Researching a set of portable algorithm plug-ins that can characterize complex reservoir structures based on a certain platform has become an urgent problem to be solved in petroleum exploration technology.

Contents of the invention

The present invention provides an MRF-based stochastic simulation of lithofacies of oil and gas reservoirs and its realization method. The purpose is to overcome the problems of rough boundaries and difficult characterization of internal structures in stochastic simulation of lithofacies of oil and gas reservoirs in the prior art.

An MRF-based stochastic simulation and realization method of oil and gas reservoir lithofacies, including the following steps:

Step 1: Obtain lithofacies attribute data of exploratory wells in oil and gas reservoirs in selected well sections in the area to be simulated;

Step 2: Carry out grid processing in the area to be simulated, and carry out digital marking of lithofacies;

According to the spatial size and lithofacies change law of the area to be simulated, the area to be simulated is gridded so that each grid has a lithofacies attribute, that is, each grid has a unique lithofacies digital mark;

Step 3: Calculate the transition probability between lithofacies at each position in the Cartesian direction for the grid of the simulated area, and obtain the transition probability function diagram of the Cartesian direction of the grid of the area to be simulated;

That is, the probability of transforming from existing lithofacies attributes to other lithofacies attributes at each position in the grid of the area to be simulated;

Step 4: According to the transition probability function diagram obtained in step 3, calculate the occurrence probability of each target position belonging to each lithofacies in the grid of the area to be simulated according to the following target conditional probability formula:

Described target conditional probability formula is to utilize the conditional probability formula of MRF, select potential function as logarithmic transition probability function and obtain;

MRF is an extension of Markov chain in space. It is characterized in that the conditional probability of the target position is only related to its neighbor system, and the probability expression of its joint distribution can be solved by Gibbs distribution;

Among them, s ₁ ,…,s _N are the neighbors of the target position s, and they are sequences arranged from near to far according to the distance from the target position; l ₁ ,…l _N ,k,f are lithofacies attribute numbers mark, the value range is {1,2,3,4,…,K}, corresponding to the lithofacies attribute of the study area obtained in step 1; h _i represents the distance between the target position and the neighbor points of the target position, It is called the hysteresis distance, and the values are taken in order according to the distance from near to far; Indicates the transition probability from the lithofacies attribute k at the target location to the lithofacies attribute l _i corresponding to the neighbors whose interval is h _i ; Indicates the transition probability that the lithofacies l ₁ corresponding to the drilling position s ₁ closest to the target position is transformed into the lithofacies k corresponding to the target position s, and the distance between the drilling position s ₁ and the target position s is h ₁ ; K Indicates the total number of all lithofacies types; N indicates the number of neighbors of the target position; x _s is the lithofacies attribute mark at the target position s, and x _r is the lithofacies attribute mark at position r.

In formula (1), by first selecting the sample point (drilling position) s ₁ closest to the target position, the lithofacies attribute l ₁ corresponding to the position s ₁ is converted into the lithofacies corresponding to the target position s away from h ₁ Transition probability of attribute k In this formula, the transition probability The direction of is just opposite to the direction of the transition probability of the remaining N-1 neighbor points of the target position. This method can effectively solve the problem of overestimation of large classes and overestimation of small classes in reservoir modeling;

Step 5: According to the occurrence probability of each location in the grid of the area to be simulated calculated in step 4 belonging to various lithofacies, use Monte Carlo random simulation to obtain a lithofacies distribution simulation map.

Reservoir simulation based on transition probability requires that the exploration data meet the Markov property, that is, short-range correlation; in order to make the lithofacies attribute data collected from exploration wells meet the requirements of Markov property, the collected lithofacies attribute data from exploration wells are used for reservoir simulation. Make the following judgments:

According to the set step size, for the lithofacies attribute data of the exploration well collected in step 1 in the vertical direction, the chi-square test is used to test the Markov property of the lithofacies attribute data of the exploratory well; The lithofacies attribute category of the area digitally marks the lithofacies attribute data, otherwise, if the lithofacies attribute data of the exploratory well does not have the Markov property, reselect the well section in the area to be simulated, and return to step 1 to obtain the lithofacies attribute data of the exploratory well .

The method described in the steps 1-step 5 is compiled to generate a dynamic link library, and at the same time, the simulation parameter input interface is written; the dynamic link library and the simulation parameter input interface are integrated into the plug-in directory of the SGeMS platform, and the debug and release Run the solution in the mode, get the MRF algorithm plug-in, and use the SGeMS platform integrated with the MRF algorithm plug-in to realize stochastic simulation of oil and gas reservoir lithofacies.

According to the occurrence probability of each position in the grid of the area to be simulated calculated in step 4 belonging to various lithofacies, Monte Carlo random simulation is used to assign the lithofacies attribute digital mark with the largest posterior probability in each position to the position, The lithofacies simulation results of the grid are obtained, and then the lithofacies distribution simulation map of the entire reservoir is obtained. By dragging with the mouse, the target reservoir can be rotated at any angle in three-dimensional space. Set the x, y, and z values of "VolumeExplorer" under the "Preferences" column of the SGeMS platform to obtain the cross-sectional cutting diagram of any position of the target body.

Beneficial effect

The present invention provides a stochastic simulation and realization method of lithofacies in oil and gas reservoirs based on MRF. The method utilizes the conditional probability formula of MRF and selects the potential function as a logarithmic transition probability function to obtain the occurrence probability of lithofacies at the target position. Considering The mathematical relationship between the group potential function and the transition probability function in the neighborhood uses the known points and simulated points in the neighborhood, adopts the idea of combining sequential simulation and conditional simulation, and calculates each area to be simulated according to the transition probability function graph. The occurrence probability of similar lithofacies is obtained by using Monte Carlo stochastic simulation to obtain the lithofacies simulation results of this grid. Using this simulation method to compile and integrate the MRF model into the SGeMS platform in the form of an algorithm plug-in through the application program interface, by setting the x, y, and z values of the "Volume Explorer" under the "Preferences" column of the platform, it can be realized in the SGeMS platform. The target reservoir in 3D space is rotated at any angle and the section is cut at any position. The MRF algorithm can well reflect the continuity of complex space and can more accurately describe the spatial distribution of geological bodies in application, while avoiding the calculation of complex equations that characterize reservoir morphology. Due to the existence of directionality in transfer probability, the simulation effect of the SGeMS software platform based on the MRF algorithm plug-in is better than that of the traditional reservoir visualization system based on the Klicking algorithm for describing the unidirectional distribution trend and anisotropy characteristics of lithofacies transfer. The accuracy of reservoir lithofacies prediction is significantly improved.

Description of drawings

Fig. 1 is a schematic diagram of the drilling position in the area to be simulated;

Figure 2 is the MRF algorithm data specifying interface;

Fig. 3 is the MRF algorithm condition input interface;

Fig. 4 is a schematic diagram of the simulation effect of applying the method of the present invention;

Fig. 5 is a section cut diagram of the target reservoir in 3D space.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

In this example, the simulation is carried out for the Sha 75 area of Tahe Oilfield. According to the drilling information of the S66 well, S92 well, S67 well and S75 well, and considering the characteristics of the reservoir in this area, the step length is 1 meter, and the S66 well, S92 well, S66 well, S92 well, Wells S67 and S75 carried out statistical analysis of lithofacies replacement in the vertical direction, and verified the Matensiority of lithofacies sequence with Chi-square test. There are four main types of lithofacies sequences observed, namely sandstone, conglomerate, mudstone, and limestone, represented by numbers 1, 2, 3, and 4 in turn.

An MRF-based stochastic simulation and realization method of oil and gas reservoir lithofacies, including the following steps:

Step 1: Obtain lithofacies attribute data of exploratory wells in oil and gas reservoirs in selected well sections in the area to be simulated;

Step 2: Carry out grid processing in the area to be simulated, and carry out digital marking of lithofacies;

According to the spatial size and lithofacies change law of the area to be simulated, the area to be simulated is gridded so that each grid has a lithofacies attribute, that is, each grid has a unique lithofacies digital mark;

According to the set step size, for the lithofacies attribute data of the exploration well collected in step 1 in the vertical direction, the chi-square test is used to test the Markov property of the lithofacies attribute data of the exploratory well; The lithofacies attribute category of the area digitally marks the lithofacies attribute data, otherwise, if the lithofacies attribute data of the exploratory well does not have the Markov property, reselect the well section in the area to be simulated, and return to step 1 to obtain the lithofacies attribute data of the exploratory well .

The Sha 75 area of Tahe Oilfield is 4000 meters long from north to south and 3000 meters long from east to west; 5200-5300 meters is selected as the interval depth of the simulated well section, which is the SQ2 lowstand system tract. The vertical interval is 1 meter and the lateral interval is 50 m, finally get the simulation space composed of grid system, as shown in Figure 1.

Step 3: Calculate the transition probability between lithofacies at each position in the Cartesian direction for the grid of the simulated area, and obtain the transition probability function diagram of the Cartesian direction of the grid of the area to be simulated;

That is, the probability of transforming from existing lithofacies attributes to other lithofacies attributes at each position in the grid of the area to be simulated;

Step 4: According to the transition probability function diagram obtained in step 3, calculate the occurrence probability of each target position belonging to each lithofacies in the grid of the area to be simulated according to the following target conditional probability formula:

Described target conditional probability formula is to utilize the conditional probability formula of MRF, select potential function as logarithmic transition probability function and obtain;

MRF is an extension of Markov chain in space. It is characterized in that the conditional probability of the target position is only related to its neighbor system, and the probability expression of its joint distribution can be solved by Gibbs distribution.

In formula (1), s ₁ ,…,s _N are the neighbors of the target position s, and they are sequences arranged from near to far according to the distance from the target position; l ₁ ,…l _N ,k,f are respectively Lithofacies attribute digital mark, the value range is {1,2,3,4,...,K _} , corresponding to the lithofacies attribute of the research area obtained in step 1; The distance between them is called the hysteresis distance, and the values are taken in order according to the distance from shortest to farthest. Indicates the transition probability from the lithofacies attribute k at the target location to the lithofacies attribute l _i corresponding to the neighbors whose interval is h _i ; Indicates the transition probability that the lithofacies l ₁ corresponding to the drilling position s ₁ closest to the target position is transformed into the lithofacies k corresponding to the target position s, and the distance between the drilling position s ₁ and the target position s is h ₁ ; K Indicates the total number of all lithofacies types; N indicates the number of neighbors of the target position; x _s is the lithofacies attribute mark at the target position s, and x _r is the lithofacies attribute mark at position r. The occurrence probability of lithofacies is the product of the normalized transition probabilities;

In formula (1), by first selecting the sample point (drilling position) s ₁ closest to the target position, the lithofacies attribute l ₁ corresponding to the position s ₁ is converted into the lithofacies corresponding to the target position s away from h ₁ Transition probability of attribute k In this formula, the transition probability The direction of is opposite to the transition probability of the neighbor points of the remaining N-1 target positions. This method can effectively solve the problem of overestimation of large classes and overestimation of small classes in reservoir modeling.

Step 5: Compile the method described in step 4 to generate a dynamic link library, and at the same time, write the simulation parameter input interface; integrate the dynamic link library and the simulation parameter input interface into the plug-in directory of the SGeMS platform, and run it in debug and release modes Solution, get the MRF algorithm plug-in. Described MRF algorithm plug-in mainly is made up of two parts: dynamic link library (DLL) and parameter input interface, plug-in interface as shown in Figure 2 and Figure 3; The concrete steps of design are as follows:

(1) Write the header file (MRF.h) named after MRF, and the main file (MRF.cpp) named after MRF. Give the definition of each function in the derived class, realize the acceptance and initialization of parameters through the initialization function initialize(), and store the received function in the data member. Defines the parameter interface. Add the algorithm tag at the top of the Ui file.

(2) Load the GEOSTAT_PLUGIN macro in the main file (MRF.cpp), and use the class name (MRF) as a parameter in the GEOSTAT_PLUGIN macro to call the function.

(3) Compile the C++ source file to obtain the dynamic link library (.dll), copy the dynamic link library (.dll) and the parameter input interface (.ui) to the plug-in directory, and run the solution in debug and release mode again to get MRF algorithm plugin.

In Figure 2, the "GRID" drop-down menu is used to select the grid of the area to be simulated, and the "New Property Name" is used to name the newly specified property. "Object" is used to select hard data (such as well data), and "Property Name" is used to select specific information in hard data (such as lithofacies attributes).

Figure 3 gives the search criteria. The "Min" and "Max" options under the "Condition data" column are used to specify the range of the number of neighbors within the search ellipse. "range" indicates the search radius, and you can set Max (maximum), Min (minimum) and Med (middle) values. "angles" refers to the search angle in the Cartesian direction, represented by "Azimuth" (azimuth, vertical z direction), "Dip" (apparent inclination, lateral x direction) and "Rake" (apparent inclination, lateral y direction) . "Transiogram" is used to import the existing transition probability model, "Number of category" gives the total number of types of the selected work area, and "Probability" requires the input of the marginal probability (i.e. prior probability) of various categories (such as lithofacies).

According to the occurrence probability of each position in the grid of the area to be simulated calculated in step 4 belonging to various lithofacies, Monte Carlo random simulation is used to assign the lithofacies attribute digital mark with the largest posterior probability in each position to the position, The lithofacies simulation results of this grid are obtained, and then the lithofacies distribution simulation map of the entire reservoir is obtained, as shown in Fig. 4. By dragging with the mouse, the target reservoir can be rotated at any angle in three-dimensional space. Set the x, y, and z values of the "Volume Explorer" under the "Preferences" column of the SGeMS platform to obtain the cross-sectional cutting diagram of any position of the target body, as shown in Figure 5.

Claims (3)

1. a kind of oil and gas reservoir stochastic simulation of lithofacies and implementation method based on MRF, it is characterised in that including following step Suddenly：

Step 1：Obtain the prospect pit petrofacies attribute data for waiting to simulate the oil and gas reservoir of well section selected by area；

Step 2：Treating simulation area carries out gridding process, and carries out petrofacies numeral mark；

According to waiting to simulate the space size and petrofacies Changing Pattern in area, treating simulation area carries out gridding process so that every There is individual grid a kind of petrofacies attribute, i.e. each grid to have unique petrofacies numeral mark；

Step 3：The regional grid of simulation is treated, the transition probability between petrofacies in each position in Descartes direction is calculated, acquisition is treated The transition function figure in the Descartes direction of the regional grid of simulation；

Step 4：The transition function figure obtained according to step 3, calculates according to goal of condition probability formula and waits to simulate In area grid, each target location belongs to the probability of happening of all kinds of petrofacies：

$P\{x_s=k|x_{s_1}=l_1,...,x_{s_N}=l_N\}=\frac{p_{l_{1}k}\left(h_1\right){\mathrm{\Π}}_{i=2}^k{p}_{{\mathrm{kl}}_i}\left(h_i\right)}{{\mathrm{\Σ}}_{f=1}^K\[p_{l_{1}f}\left(h_1\right){\mathrm{\Π}}_{i=2}^N{p}_{{\mathrm{fl}}_i}\left(h_i\right)\]}---\left(1\right)$

The goal condition new probability formula is the condition probability formula using MRF, chooses transition probability of the potential function for logarithmetics Function is obtained；

Wherein, s₁,…,s_NThe neighbours of target location s, and be according to the distance between target location from closely to remote arrangement Sequence；l₁,…l_N, k, f respectively petrofacies attribute numeral mark, span is { 1,2,3,4 ..., K }, corresponding in step 1 The petrofacies attribute of the survey region of acquisition；h_iThe distance between neighbours' point of target location and target location is represented, it is referred to as delayed Away from according to distance from closely to far value successively；Expression is changed at intervals of h by the petrofacies attribute k of target location_i's Petrofacies attribute l corresponding to neighbours_iTransition probability；Represent and the closest drilling well position s in target location₁Correspondence Petrofacies l₁It is converted into the transition probability of petrofacies k corresponding to the s of target location, the drilling well position s₁Between the s of target location away from From for h₁；K represents all of petrofacies species sum；N represents neighbours' number of target location；x_sIt is the petrofacies category at the s of target location Property mark, x_rIt is the petrofacies attribute mark at the r of position；

Step 5：According to the calculated probability of happening for treating that each position in simulated domain grid belongs to all kinds of petrofacies of step 4, profit Monte Carlo stochastic simulation is used, lithofacies distribution simulation drawing is obtained.

2. a kind of oil and gas reservoir stochastic simulation of lithofacies and implementation method based on MRF according to claim 1, its feature exist In, according to setting step-length, to step 1 collection prospect pit petrofacies attribute data in vertical direction, using X 2 test prospect pit rock The geneva of phase attribute data；

If prospect pit petrofacies attribute data has geneva, according to the petrofacies attribute classification for waiting to simulate area to petrofacies attribute data Numeral mark is carried out, otherwise, if the prospect pit petrofacies attribute data does not have geneva, the well for waiting to simulate area is chosen again Section, return to step 1 obtain prospect pit petrofacies attribute data.

3. a kind of oil and gas reservoir stochastic simulation of lithofacies and implementation method based on MRF according to claim 1 and 2, which is special Levy and be, dynamic link library is generated by program compiling to the method described in the step 1- step 5, meanwhile, write simulation ginseng Number inputting interface；Dynamic link library and analog parameter inputting interface are incorporated under the plug-in unit catalogue of SGeMS platforms, in debug With operational solution under release patterns, MRF algorithm groupwares are obtained, using the SGeMS platforms for having merged MRF algorithm groupwares Realize oil and gas reservoir stochastic simulation of lithofacies.