Method and device for simulating lithologic distribution of complex lithologic carbonate rocks

Abstract

The invention belongs to the technical field of fracturing, and particularly relates to a lithologic distribution simulation method and device for complex lithologic carbonate rocks. The method specifically comprises the following steps of: generating random numbers in a set grid by using sequential Gaussian simulation random pairs, sequencing all the random numbers to obtain a random number sequence in a set sequence, and dividing the random number sequence according to the required lithology type and the proportion of each lithology to obtain a corresponding interval; assigning the same numerical value to all random numbers in the same divided interval, forming a lithology random distribution space according to the assigned values, and generating a lithology distribution simulation image. According to the method, a controllable and random mineral distribution model with spatial relevance is established, and compared with a conventional simulation method, the acid fracturing simulation accuracy of the complex lithologic reservoir can be further improved, and the applicability of a mine field is enhanced.

Description

Technical Field

[0001] The invention belongs to the technical field of fracturing, and in particular relates to a method and a device for simulating the lithology distribution of carbonate rocks with complex lithology. Background Art

[0002] Carbonate reservoirs are rich in oil and gas resources and widely distributed around the world. The reserves of carbonate reservoirs account for 50.6% of the world's proven recoverable reserves of oil and gas. With the expansion of the exploration area, the lithological characteristics are becoming more and more complex. Generally, the mineral components of carbonate rocks are mainly calcium carbonate (CaCO3) and calcium magnesium carbonate (CaMg(CO3)2), but carbonate reservoirs are often accompanied by some authigenic minerals, such as gypsum, anhydrite, barite, etc. The disorder, anisotropy, and discontinuity of reservoir lithology distribution are ubiquitous. This absolute and unconditional reservoir heterogeneity is inevitably accompanied by the uncertainty and randomness of the value of any point in the reservoir attribute space. This is a major feature of the actual reservoir structure and physical property parameter distribution. Acidizing treatment is often performed to increase the permeability of the formation near the wellbore. For reservoirs with more complex lithology, different minerals have different reaction abilities with acid, and the content of mineral components is also an important influencing factor of acid-rock reaction. However, carbonate acid-rock reaction simulation usually uses a single mineral component as the simulation object, which is quite different from the actual reservoir lithology, and the lithology distribution on the fracture surface has large errors.

[0003] At present, the numerical simulation of acid fracturing is still dominated by single homogeneous minerals or simple Boolean distribution, which lacks consideration of the differences in acid fracturing reactions of multiple minerals and the spatial correlation of mineral distribution and porosity. The Chinese invention patent application with application publication number CN110797092A discloses an acid fracturing simulation method considering the dynamic process of variable viscosity acid, simulating the viscosity change of acid in the matrix system, combining the flow and reaction of variable viscosity acid on the fracture surface, calculating the pressure profile and filtration rate in the fracture system, and simulating the acid fracturing fracture morphology after considering the dynamic drop rate of variable viscosity acid. It is suitable for carbonate reservoirs with a single mean value. However, due to the different acid-rock reaction rates of acid and dolomite and limestone at different temperatures, the constitutive equations of temperature, calcium ion concentration, pH value and acid viscosity will change, so it is not applicable to actual reservoirs with heterogeneous distribution of multiple minerals.

[0004] The Chinese invention patent application with application publication number CN109882164A discloses a large-scale acidification simulation method for fractured carbonate reservoirs, which uses a dual-scale continuous model and a pseudo-fracture model to simulate the acidification process of fractured formations, divides the large-scale formation into several small-scale regions according to the initial flow field, sets a seepage resistance zone and boundary conditions in each region, and solves the problem of difficult calculation of large-scale and fractured formations in a step-by-step calculation manner. However, the mathematical model for establishing carbonate acidification does not take into account the differences in acid-rock reactions of multiple minerals, especially the differences in the acid-rock reaction order of limestone and dolomite, so it can only be applied to pure limestone or pure dolomite reservoirs, and cannot accurately simulate complex lithology reservoirs, which has certain limitations. Summary of the invention

[0005] The object of the present invention is to provide a method and device for simulating lithology distribution of carbonate rocks with complex lithology, so as to solve the problem of inaccurate lithology analysis under acid fracturing simulation of complex lithology.

[0006] In order to solve the above technical problems, the present invention provides a method for simulating lithology distribution of carbonate rocks with complex lithology, comprising the following steps:

[0007] 1) The image used to simulate the lithology distribution is gridded, and random numbers are randomly filled into each grid according to sequential Gaussian simulation;

[0008] 2) sorting the random numbers in all grids according to the set sorting method to obtain a random number sequence; dividing the random number sequence into intervals of corresponding numbers according to the number of lithology types required for simulation, and the proportion of the number of random numbers in each interval to the total number of random number sequences is the same as the distribution proportion of the corresponding lithology in the image;

[0009] 3) Assign the random numbers in the same interval to the same set value, one set value corresponds to one lithology, and a lithology random distribution space is formed according to the set value to generate a lithology distribution simulation image.

[0010] The beneficial effects are as follows: in order to solve the problem of inaccurate lithology analysis under acid fracturing simulation of complex lithology, the present invention uses sequential Gaussian simulation to randomly generate random numbers in a set grid, and sorts all random numbers to obtain a random number sequence of a set order, divides the random number sequence according to the required lithology type and the proportion of each lithology to obtain the corresponding interval, assigns the same value to all random numbers in the same divided interval, and forms a lithology random distribution space according to the assignment, and generates a lithology distribution simulation image. The method of the present invention establishes a controllable, random and spatially correlated mineral distribution model, which can further improve the accuracy of acid fracturing simulation of complex lithology reservoirs compared to conventional simulation methods, and enhances the applicability of mines.

[0011] Furthermore, in step 1), before the sequential Gaussian simulation, the correlation lengths in the horizontal and vertical directions are set to control the horizontal and vertical distributions.

[0012] The beneficial effects are as follows: the pore distribution is correlated in space, and the distribution of rock minerals is layered. The present invention combines the random distribution characteristics of rock minerals with the spatial correlation characteristics, and controls the spatial correlation strength through the characteristic parameter dimensionless correlation length, which can simulate the spatial distribution changes of actual reservoir lithology.

[0013] Furthermore, the specific steps of sequential Gaussian simulation include:

[0014] ① Determine the single variable conditional cumulative distribution function F of the original data {Z(x)|i=1,2,…,n} Z (Z);

[0015] ②Perform normal transformation to transform the data into y data with standard normal distribution;

[0016] ③ Randomly generate a simulation path and visit each node on the grid in turn;

[0017] ④ Calculate the distribution function of the first node and randomly extract a quantile from it, which is the estimated value of the node;

[0018] ⑤ Add the estimated value of the node to the data set to become the conditional data for simulating the next node, where the data set is composed of nodes whose estimated values ​​have been calculated;

[0019] ⑥ Repeat steps 1) to 5) until all the values ​​of the estimated points are simulated to obtain the first normal value y of the sequential Gaussian probability field simulation. (1) (u) Transform back to the simulated value Z of the original variable (1) (u);

[0020] ⑦ Generate simulation values ​​through random simulation of variance function and generate random variable distribution space.

[0021] The beneficial effect is: using the random numbers generated by sequential Gaussian simulation to represent the non-order, anisotropy and discontinuity of lithology distribution, to establish a non-uniform distribution model of various lithologies, and to achieve the simulation effect of actual mineral heterogeneity on site.

[0022] Furthermore, the specific steps of step ④ include:

[0023] a) Randomly select the i-th point in the space that has no simulation results;

[0024] b) Use simple Kriging interpolation to estimate the mean and variance of the Gaussian conditional probability distribution. The calculation formula is as follows:

[0025]

[0026]

[0027] Among them, Z * (x0) is the estimated value at a certain position x0; m0 is the average value of the estimated points at x0; λ i is the weight; Z(x i ) is a certain position x i The measured value at i For x i The measured value at the location and the average value of the measured values ​​of the surrounding j known quantities; j is the number of measured values ​​in the estimation process; C(x0-x j ) is the covariance between sampling points; C(x i -x j ) is the covariance between the estimation point and the sampling point;

[0028] c) Randomly draw a value from the local conditional probability distribution, and then calculate Z from the Gaussian distribution i , the calculation formula is as follows:

[0029]

[0030] Among them, P(Z i |Z1, Z2, ..., Z i-1 ) is Z i The probability distribution function of is the Gaussian distribution function, where is the value of e To the power of Z i Substitute into the Gaussian distribution function;

[0031] d) Add the newly simulated value to the data set, that is, when simulating the value Z of the i+1th grid point i+1 When , the simulation value of the i-th point is taken as the control point Zi to participate in the calculation.

[0032] Its beneficial effects are: it is conducive to the generation of random numbers by sequential Gaussian simulation, which is more in line with the distribution simulation of complex lithology, further improves the accuracy of acid fracturing simulation of complex lithology reservoirs, and enhances the applicability of mines.

[0033] Furthermore, the spatial correlation distribution function composed of the correlation lengths in the horizontal and vertical directions in step ⑦ is The control attributes are distributed in two-dimensional space, where (l x , l y ) are the dimensionless correlation lengths in the horizontal and vertical directions respectively. The dimensionless correlation length in the x direction is the correlation length divided by the actual size in the x direction. The formula is: l = L / 2r e .

[0034] The beneficial effect is that when the dimensionless correlation length l in the horizontal direction x When it is larger, the porosity value in the horizontal direction is more correlated. When the dimensionless correlation length l in the vertical direction is y When it is larger, the porosity values ​​in the vertical direction are more strongly correlated, which can be used to judge the random distribution characteristics and spatial correlation of rock minerals to establish a more accurate lithology distribution model.

[0035] Furthermore, the variance function refers to half of the variance of the increment of the second-order stable regional variation Z(x) at points x and x+h. With h as the horizontal coordinate and γ(h) as the vertical coordinate, the variance function diagram is constructed. The calculation formula is:

[0036]

[0037] Among them, x i is the coordinate of the i-th observation point; Z(x i ) and Z(x i +h) are x i and x i +h; h is the distance between the two observation points, which represents a data pair with a certain interval length. By changing the interval length, the semi-variable value under the corresponding interval is obtained, thereby generating some interval values ​​and semi-variable values; N(h) is the number of data pairs with a distance of h; γ(h) is the value of the variogram.

[0038] Its beneficial effects are: it is conducive to the generation of random numbers by sequential Gaussian simulation, which is more in line with the distribution simulation of complex lithology, further improves the accuracy of acid fracturing simulation of complex lithology reservoirs, and enhances the applicability of mines.

[0039] To solve the above technical problems, the present invention also provides a complex lithology carbonate rock lithology distribution simulation device, including a memory and a processor, the processor is used to execute computer program instructions stored in the memory to implement a complex lithology carbonate rock lithology distribution simulation method introduced above.

[0040] The beneficial effect is that the device ensures the effective and reliable execution of a method for simulating the lithology distribution of carbonate rocks with complex lithology. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flow chart of the method of the present invention;

[0042] Figure 2 The association length of the present invention is l x =20, l y =1, simulated image of dolomite and limestone distribution;

[0043] Figure 3 The association length of the present invention is lx =4,l y =1, simulated image of dolomite and limestone distribution;

[0044] Figure 4 The association length of the present invention is l x =20, l y =5, simulated image of dolomite and limestone distribution;

[0045] Figure 5 The association length of the present invention is l x =20, l y =1, the simulated images of the three lithology distributions of dolomite, limestone and gypsum;

[0046] Figure 6 The association length of the present invention is l x =4,l y =1, simulated images of the distribution of three types of lithology: dolomite, limestone and gypsum;

[0047] Figure 7 The association length of the present invention is l x =20, l y =5, the simulated images of the distribution of three types of lithology: dolomite, limestone and gypsum. DETAILED DESCRIPTION

[0048] The basic concept of the present invention is: input grid parameters in the sequential Gaussian simulation parameter file, set the x- and y-direction correlation lengths to simulate the values ​​of all points to be estimated; generate random simulation values ​​and random distribution space through the variogram; sort the generated simulation values ​​from small to large to select the values ​​in the simulation values ​​corresponding to the lithology ratio coefficient; set the lithology ratio to divide the corresponding values ​​into several intervals, and assign 0, 1, ..., n to the corresponding simulation value intervals, respectively representing n different lithology distributions; assign random numbers to form a lithology random distribution space, and then derive and generate a lithology distribution image. Based on this concept, a complex lithology carbonate rock lithology distribution simulation method and a complex lithology carbonate rock lithology distribution simulation device of the present invention can be realized.

[0049] The present invention will be described in detail below with reference to the accompanying drawings and method embodiments.

[0050] Method Example:

[0051] A method for simulating lithology distribution of carbonate rocks with complex lithology according to the present invention is shown in the flowchart as follows: Figure 1 As shown, the specific implementation steps include:

[0052] Step 1: Enter the grid parameters in the sequential Gaussian simulation parameter file and set the correlation lengths in the x and y directions to control the horizontal and vertical distributions. The specific simulation steps are as follows:

[0053] 1) Determine the single variable conditional cumulative distribution function F of the original data {Z(x)|i=1,2,…,n} Z (Z);

[0054] 2) Perform normal transformation to transform the data into y data with standard normal distribution;

[0055] 3) Randomly generate a simulation path and visit each node on the grid in turn;

[0056] 4) Calculate F of the first node Z (Z), randomly extract a quantile from it, which is the estimated value of the changed node. This process is performed by interpolation. The specific process is as follows:

[0057] ① Randomly select the i-th point in the space, which has no simulation results yet;

[0058] ② Use the simple Kriging interpolation method to estimate the mean and variance of the Gaussian conditional probability distribution. The calculation formula is as follows:

[0059]

[0060]

[0061] Among them, Z * (x0) is the estimated value at a certain position x0; m0 is the average value of the estimated points at x0; λ i is the weight; Z(x i ) is a certain position x i The measured value at i For x i The measured value at the location and the average value of the measured values ​​of the surrounding j known quantities; j is the number of measured values ​​in the estimation process; C(x0-x j ) is the covariance between sampling points; C(x i -x j ) is the covariance between the estimation point and the sampling point;

[0062] ③ Randomly extract a value from the local conditional probability distribution, and then calculate Z from the Gaussian distribution i , the calculation formula is as follows:

[0063]

[0064] Among them, P(Z i |Z1, Z2, ..., Z i-1 ) is Z i The probability distribution function of is the Gaussian distribution function, where is the value of e To the power of Z i Substitute into the Gaussian distribution function;

[0065] ④ Add the newly simulated value to the data set, that is, when simulating the value Z of the i+1th grid point i+1 When the simulation value of the i-th point is Z i The control points participate in the calculation.

[0066] 5) Add the new estimated value to the known data set to become the conditional data for simulating the next node;

[0067] 6) Repeat the above steps, and after simulating the values ​​of all the points to be estimated, the lNth normal value y of the sequential Gaussian probability field simulation is obtained. (1) (u) Transform back to the simulated value Z of the original variable (1) (u).

[0068] 7) Generate simulation values ​​by performing random simulation through the variance function to generate a random variable distribution space.

[0069] For the second-order stable regional variation Z(x), the variogram refers to half of the variance of the increment of Z(x) at points x and x+h, and its mathematical expression is:

[0070]

[0071] where x i is the coordinate of the i-th observation point, Z(x i ) and Z(x i +h) are x i and x i +h is the observation value at two points, where h is the distance between the two observation points, indicating a data pair with a certain interval length. By changing the interval length, the semi-variable value under the corresponding interval can be obtained, thereby generating some interval values ​​and semi-variable values;

[0072] N(h) is the number of data pairs with a distance of h; γ(h) is the value of the variogram, with h as the horizontal coordinate and γ(h) as the vertical coordinate, forming the variogram.

[0073] Step 2: Arrange the simulation values ​​from small to large to obtain a simulation value sequence; divide the simulation value sequence into a corresponding number of intervals according to the number of lithology types required for the simulation, and the proportion of each interval in the simulation value sequence is the same as the proportion of the corresponding lithology in all lithologies; assign the simulation values ​​in the same interval to the same set value, and assign the corresponding simulation value intervals to 0, 1, ..., n, respectively representing n different lithology distributions, and form a lithology random distribution space according to the set value to generate a lithology distribution simulation image.

[0074] The specific embodiments of the present invention are as follows:

[0075] Step 1: Enter the number of grids in the x direction as 500, the number of grids in the y direction as 50, the random number seed as 4785478, and set the correlation length l in the x and y directions. x =20, l y =1; Generate simulated values ​​by random simulation through variogram, and generate random variable distribution space, as shown below:

[0076]

[0077] is the average porosity, C v is the coefficient of variation, is the spatial correlation distribution function, (l x , l y ) are the dimensionless correlation lengths in the x and y directions respectively. The dimensionless correlation length in the x direction is the correlation length divided by the actual size l in the x direction. x =L / L x .

[0078] Step 2: sort the simulation values ​​from small to large to find the values ​​in the simulation values ​​corresponding to the lithology ratio coefficient.

[0079] The proportions of gypsum, dolomite and limestone are 20%, 40% and 40% respectively, and the corresponding values ​​of 20% and 60% in ascending order of simulation values ​​are -0.8463 and 0.2976;

[0080] Step 3: Select the corresponding values ​​of the ratio and divide them into several intervals.

[0081] It is divided into three numerical intervals, and the corresponding simulation value intervals are assigned 0, 1, and 2, which represent the distribution of three different lithologies. The interval <-0.8463 is assigned 0 to represent gypsum, the interval >0.2976 is assigned 2 to represent limestone, and the interval -0.8463 to 0.2976 is assigned 1 to represent dolomite.

[0082] Step 4: Assign random numbers to form a random distribution space of lithology, and then derive and generate a lithology distribution image, such as Figure 5 shown.

[0083] If you change l x =4,l y = 1, the simulated images of the three lithology distributions of dolomite, limestone and gypsum are as follows: Figure 6 shown.

[0084] If you change l x =20, l y = 5, the simulated images of the three lithology distributions of dolomite, limestone and gypsum are as follows: Figure 7 shown.

[0085] The present invention is x =20, ly = 1, the simulated images of dolomite and limestone distribution are as follows Figure 2 As shown. x =4,l y = 1, the simulated image of dolomite and limestone distribution is as follows: Figure 3 As shown. x =20, l y = 5, the simulated images of dolomite and limestone distribution are as follows: Figure 4 shown.

[0086] The present invention provides a method for simulating the lithology distribution of complex lithology carbonate rocks, which establishes a controllable, random and spatially correlated mineral distribution model. Compared with conventional simulation methods, it can further improve the accuracy of acid fracturing simulation of complex lithology reservoirs and enhance the applicability of mines.

[0087] Device Example:

[0088] A complex lithology carbonate rock lithology distribution simulation device of the present invention includes a memory and a processor, and the processor is used to execute computer program instructions stored in the memory to implement a complex lithology carbonate rock lithology distribution simulation method introduced in the method embodiment of the present invention. Among them, the processor can be a processing device such as a programmable logic device FPGA. The memory can be various memories that use electrical energy to store information, such as RAM, ROM, etc., and can also be other types of memories.

Claims

1. A method for simulating the lithology distribution of complex lithology carbonate rocks, characterized in that: The steps include: 1) The image used to simulate the lithology distribution is gridded, and random numbers are randomly filled into each grid according to sequential Gaussian simulation; 2) sorting the random numbers in all grids according to the set sorting method to obtain a random number sequence; dividing the random number sequence into intervals of corresponding numbers according to the number of lithology types required for simulation, and the proportion of the number of random numbers in each interval to the total number of random number sequences is the same as the distribution proportion of the corresponding lithology in the image; 3) Assign the random numbers in the same interval to the same set value, one set value corresponds to one lithology, and a lithology random distribution space is formed according to the set value to generate a lithology distribution simulation image.

2. The method for simulating lithology distribution of complex lithology carbonate rocks according to claim 1, characterized in that: In step 1), before the sequential Gaussian simulation, the correlation lengths in the horizontal and vertical directions must be set to control the horizontal and vertical distributions.

3. The method for simulating lithology distribution of complex lithology carbonate rocks according to claim 2, characterized in that: The specific steps of sequential Gaussian simulation include: ① Determine the single variable conditional cumulative distribution function F of the original data {Z(x)|i=1,2,…,n} Z (Z); ②Perform normal transformation to transform the data into y data with standard normal distribution; ③ Randomly generate a simulation path and visit each node on the grid in turn; ④ Calculate the distribution function of the first node and randomly extract a quantile from it, which is the estimated value of the node; ⑤ Add the estimated value of the node to the data set to become the conditional data for simulating the next node, where the data set is composed of nodes whose estimated values ​​have been calculated; ⑥ Repeat steps 1) to 5) until all the values ​​of the estimated points are simulated and the lth normal value y of the sequential Gaussian probability field simulation is obtained. (1) (u) Transform back to the simulated value Z of the original variable (1) (u); ⑦ Generate simulation values ​​through random simulation of variance function and generate random variable distribution space.

4. The method for simulating lithology distribution of complex lithology carbonate rocks according to claim 3, characterized in that: The specific steps of step ④ include: a) Randomly select the i-th point in the space that has no simulation results; b) Use simple Kriging interpolation to estimate the mean and variance of the Gaussian conditional probability distribution. The calculation formula is as follows: Among them, Z * (x0) is the estimated value at a certain position x0; m0 is the average value of the estimated points at x0; i is the weight; Z(x i ) is a certain position x i The measured value at m i For x i The measured value at the location and the average value of the measured values ​​of the surrounding j known quantities; j is the number of measured values ​​in the estimation process; C(x0-x j ) is the covariance between sampling points; C(x i -x j ) is the covariance between the estimation point and the sampling point; c) Randomly draw a value from the local conditional probability distribution, and then calculate Z from the Gaussian distribution i , the calculation formula is as follows: Among them, P(Z i |Z1,Z2,…,Z i-1 ) is Z i The probability distribution function of is the Gaussian distribution function, where is the value of e To the power of Z i Substitute into the Gaussian distribution function; d) Add the newly simulated value to the data set, that is, when simulating the value Z of the i+1th grid point i+1 When the simulation value of the i-th point is Z i The control points participate in the calculation.

5. The method for simulating lithology distribution of complex lithology carbonate rocks according to claim 3, characterized in that: The spatial correlation distribution function composed of the correlation lengths in the horizontal and vertical directions in step ⑦ The control attributes are distributed in two-dimensional space, where (l x ,l y ) are the dimensionless correlation lengths in the horizontal and vertical directions respectively. The dimensionless correlation length in the x direction is the correlation length divided by the actual size in the x direction. The formula is: l = l / 2r e .

6. The method for simulating lithology distribution of complex lithology carbonate rocks according to claim 5, characterized in that: The variance function refers to half of the variance of the increment of the second-order stable regional variation Z(x) at points x and x+h. With h as the horizontal coordinate and γ(h) as the vertical coordinate, the variance function diagram is constructed. The calculation formula is: Among them, x i is the coordinate of the i-th observation point; Z(x i ) and Z(x i +h) are x i and x i +h; h is the distance between the two observation points, which represents a data pair with a certain interval length. By changing the interval length, the semi-variable value under the corresponding interval is obtained, thereby generating some interval values ​​and semi-variable values; N(h) is the number of data pairs with a distance of h; γ(h) is the value of the variogram.

7. A complex lithology carbonate rock lithology distribution simulation device, characterized in that: The method comprises a memory and a processor, wherein the processor is used to execute computer program instructions stored in the memory to implement the method for simulating lithology distribution of complex lithology carbonate rocks as described in any one of claims 1 to 6.

Images