(Xi 'an Petroleum Institute Computer Science Department, Xi 'an 7 10065)
Zhangtuanfeng
(Basic Science Department of Xi 'an Petroleum Institute, Xi 'an 7 10065)
Huangcangdian
(Xi 'an Petroleum Institute Computer Science Department, Xi 'an 7 10065)
In this paper, the random walk model is used to simulate the two-dimensional distribution of branched rivers with frequent connections and branches. Two-dimensional grid data PP(i, J), as a linear combination of permeability, porosity and shale content, can be used to distinguish the types of grid nodes: river channel, mudstone or sandstone between river channel and mudstone. Fractal Brownian motion is used to simulate the two-dimensional distribution of these three parameters in oil wells. Define the center line of the river first, and then consider the boundary of the river. Finally, the paper introduces the research example of Shen 84 area 100 wells in Liaohe Oilfield.
Keywords random walk simulation, realize braided channel
1 Introduction
The study area is located in the sub-region between the delta front fan and the delta plain. The sediment comes from the northeast and consists of braided channel and sandstone between channel and mudstone. Due to the weak hydrodynamic conditions of delta fan deposition, there is less sandstone between river channel and point dam, and braided river channel is the main skeleton of the study area.
In the reservoir, the single channel sand body has two forms: shoelace shape and lentil shape. All braided rivers are distributed from northeast to southwest. Because of the small width of the river channel, the river channel frequently branches during the deposition process, so these braided rivers often branch, detour, connect and cross each other.
The physical parameters of reservoirs vary greatly. For example, in the same layer, the vertical and horizontal permeability can be different by 10 ~ 100 times.
Simulation of physical parameter conditions of reservoir 2
Due to the strong heterogeneity of reservoirs, the distribution of geophysical parameters can be simulated by fractal Brownian motion. You can use a two-dimensional random field {z (x); X∈D) establishes a geophysical parameter model, and assumes that the increment of random field satisfies a Gaussian process far from a trend. In the study, the trend surface is used. The expected value EZ(x) is selected as follows:
fT(x)β=β 1+β2x 1+β3 x2
Where: β t = (β 1, β2, β3).
Consider the random process of filtering out this trend surface:
Y(x)=Z(x)-fT(x)β
Where: Y(x) is a stationary Gaussian process with EY(x)=0. Let DL be a grid system with the size of (2n+ 1)×(2n+ 1) in the study area, where n0 = (2n+1) × (2n+1)-1,and d0 represents the size of DL after the position I moves out of DL. Therefore, the distribution of this conditional probability is Gaussian distribution:
Mathematical geology and geological information
Where:; γ is the variation function of the model, γi is a vector with the size of 1×(N0+ 1), and its j-th component is -γ | i-j |. When j∈D0, the (N0+ 1) th component of the vector is 1. Is a matrix with the size of (N0+ 1)×(N0+ 1), and its elements are -γ | k-l |, k, l ∈ d0, except (n0+1)× (n0+6544. Z * is a vector with the size of 1×(N0+ 1) and the component of ZJ; J∈D0, and the final component value is 0.
Sequential window hierarchy algorithm can get the realization of permeability, porosity and shale content, which can be used as input to simulate braided channel. The actual process is as follows.
Simulation of 3-branch channel conditions
According to the reservoir characteristics in the study area, the position of braided river is determined by using the first three geophysical parameters. With the increase of depth, geophysical parameters will become smaller, so in order to determine the river course, these values are calibrated by depth.
Let Per, Por, Sh and h represent permeability, porosity, shale content and formation depth respectively. The difference value PP can be used to determine whether a two-dimensional point belongs to a river:
Mathematical geology and geological information
Where: α 1, α2 and a3 are non-original coefficients, which are determined by geological experience and depend on the depth h; if PP≥Q, the location belongs to the river; If PP < q, this position belongs to sandstone between river channel and mudstone; If Per=0, this position belongs to mudstone. Here, the value q is a value determined by geological experience and also depends on the depth h.
Based on the formula (1), grid data {PP (I, j)} can be obtained from the grid data of POR, PER and SH. j= 1，…，Ny； I= 1, …, Nx).Nx is the number of grid nodes in x direction, and Ny is the number of grid nodes in y direction. The PP value can be used as the input to simulate the river position, and will be considered again when determining the river width.
Next, the process of simulating the location of the bifurcated channel is discussed. First, simulate the center line of each river; Secondly, the boundary of the river is obtained by widening the center line of the river. This process can ensure that the simulation channel intersects with the observation channel in the well with a probability of 1. The connection and branching of rivers follow geological experience.
3. 1 braided channel position simulation
The core technology is the simulation of the location of the bifurcated river. Firstly, the starting point of each river in the research area is searched, and then the center line of the river is found by using the random walk model. The result is a series of grid nodes, where the starting point is the first node.
The main factors to be considered here are: ① the location of the well; ② Phase distribution expressed by well data (channel, mudstone and sandstone between channel and mudstone); ③PP value. Based on these, all possible rivers can be determined, and the connections and branches of braided rivers are also considered.
Firstly, the relevant phase information of each well is assigned to the grid node closest to the well position. The integer KG(i, j) may have the following possible values:
Mathematical geology and geological information
3.2 Starting position of river course
Let DL be a grid system in the study area (figure 1), and δ x and δ y contain several grid spacings (five in this example), which are the widths corresponding to the two narrow bands. Starting from (i, j), I searched from 1 to Nx, and J searched from Ⅳ j to Ny in a narrow band along the east-west direction. If the first position (i 1, j 1) is found on a grid node with kg (I 1) equal to 3, and the next position (i2, j2) is found on a grid node with KG(i2, j2) equal to 2 or 1, then I can be considered as I/.
Similarly, starting from point (I, j), in another narrow band along the north-south direction, I searches from n to NX, and J searches from 1 to Ny. If the first position (i3, j3) is found, where KG(i3, j3) is equal to 3, j3-Nj can be marked as the y coordinate of the starting position of the river.
Figure 1 Finding the initial position of the river course
Figure 2 Transfer of Grid Nodes
In the study area, the starting points of all possible rivers can be found in turn according to the previous process.
The two-dimensional random walking model can be used to determine whether grid nodes move in one of directions A, B and C (see Figure 2).
3.3 Conditional Simulation of Flow and Bifurcation Position of the First Channel
Let the current position be Q(i, J), and the determination of the next point depends on one of the three directions: A, B and C.
(1) direction a
Find the nearest observation position (ia, j) from position Q(i, j) along direction a, where ia represents the corresponding nearest position. Let λ mean "find a position (I, j+ 1) that satisfies KG(i, j+ 1)=3". If p [q (i, j) → q (i+ 1, j) represents the transition probability, then there is
Mathematical geology and geological information
Where: da = | ia-I |× dx
; dx =(Nx- 1)×dx； Dx represents the distance between two adjacent grid nodes in the X direction; MaxPP is the maximum value of PP in grid system; α 1, α2, α3, α4 are non-negative values determined by geological experience, 0 < α I < 1, I = 1, 2, 3, 4.
If the next point is found along the direction A, let kg (I+ 1, j) = 3, otherwise consider the direction B.
(2) direction b
Direction b is to the lower left, and the migration probability is p [q (i, j) → q (i+ 1, j+ 1)]:
Mathematical geology and geological information
Where:; Dx represents the distance between two adjacent grid nodes in the X direction. dy-(Ny- 1)×dy； Dy represents the distance between two adjacent grid nodes in the y direction. β 1, β2, β3, β4 are non-negative values determined by geological experience, 0 < β I < 1, I = 1, 2,3,4.
If the realization of channel A moves to direction B, that is, Q(i, j)→Q(i+ 1, j+ 1), then let KG(i+ 1, j+ 1)=3, otherwise, consider direction C.
(3) direction c
If the transfer direction is neither A nor B, it must be C, and its path is from Q(i, j) to Q(i, j+ 1). Let KG(i, j+ 1)=3.
Repeat the previous process until kg (i, j) = 1, thus simulating the position of the first river.
3.4 Simulation of all other possible river courses
In order to simulate the location of other rivers, the value of KG(i, j) will be changed as follows:
Mathematical geology and geological information
In the following chapters, the connection and branching of rivers will be considered.
(1) direction a
Move the position Q(i, j) to the direction A until the position of the first river channel is (ia, j), where a = "Find a position (i, j+ 1) from the position (i, j+ 1) to the direction A, and satisfy the requirement of kg (i, j+/kloc). P [q (I, j) → q (I+ 1, j) represents the transition probability, so there is
P〔Q(i，j)→Q(i+ 1，j)〕=
Mathematical geology and geological information
In which: DA=|ia-i|×Dx, dx and dx have the same meanings as before; MaxPP is the maximum value of PP in grid system; γ 1, γ2, γ3, γ4, γ5, γ3. are non-negative values determined by geological experience, and