CN108804750B - Three-dimensional vector permeability obtaining method suitable for numerical reservoir simulation - Google Patents
Three-dimensional vector permeability obtaining method suitable for numerical reservoir simulation Download PDFInfo
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Abstract
The invention provides a method for acquiring three-dimensional vector permeability suitable for numerical reservoir simulation, which comprises the following steps of: step 1, calculating the seepage area and the seepage length of adjacent node units, and determining the direction of a displacement pressure gradient; step 2, calculating cosine values of included angles between a normal vector of a seepage surface of an adjacent node unit and a horizontal X axis, a Y axis and a vertical Z axis; step 3, calculating a cosine value of an included angle between the seepage displacement direction and a seepage surface normal vector of an adjacent node unit; and 4, calculating the vector permeability value in the displacement pressure gradient direction between adjacent node units according to the horizontal permeability value, the vertical permeability value and the vector permeability model of the node units. The three-dimensional vector permeability acquisition method suitable for numerical reservoir simulation can quantitatively represent the permeability of different displacement pressure gradients and seepage paths in the numerical reservoir simulation, and lays a foundation for perfecting the numerical reservoir simulation technology.
Description
Technical Field
The invention relates to the technical field of oil reservoir development, in particular to a three-dimensional vector permeability obtaining method suitable for numerical reservoir simulation.
Background
Permeability is an important attribute parameter in numerical reservoir simulation techniques. The permeability has a vector characteristic, and the magnitude of the permeability has obvious directionality. The natural fractured reservoir develops fractures in different directions, so that the permeability of the reservoir has certain directionality, which is expressed as the directionality of the flow of fluid; in addition, the fracturing modification of the reservoir is an effective means for improving the development effect of the compact low-permeability reservoir, and the permeability of the modified reservoir is shown as a directional characteristic. In order to develop the oil reservoirs more efficiently, higher requirements are put forward on an oil reservoir numerical simulation technology, each crack is mainly represented accurately, and then the flow characteristics of reservoir fluid can be accurately described. The reservoir numerical simulation technology based on the unstructured grid technology is widely applied to fractured reservoir numerical simulation, and the used grid system is not limited to the traditional rectangular grid any more. Therefore, the acquisition of the spatial vector permeability is important. At present, no method for effectively obtaining the reservoir vector permeability in a three-dimensional space exists, and the flow among grid cells in reservoir numerical simulation is more accurately described. Therefore, the invention provides a three-dimensional vector permeability acquisition method suitable for numerical reservoir simulation, thereby solving the problems.
Disclosure of Invention
The invention aims to provide a three-dimensional vector permeability acquisition method which can quantitatively calculate spatial three-dimensional vector permeability and provides technical support for perfecting numerical reservoir simulation and is suitable for numerical reservoir simulation.
The object of the invention can be achieved by the following technical measures: the method for acquiring the three-dimensional vector permeability suitable for numerical reservoir simulation comprises the following steps: step 1, calculating the seepage area and the seepage length of adjacent node units, and determining the direction of a displacement pressure gradient; step 2, calculating cosine values of included angles between a normal vector of a seepage surface of an adjacent node unit and a horizontal X axis, a Y axis and a vertical Z axis; step 3, calculating a cosine value of an included angle between the seepage displacement direction and a seepage surface normal vector of an adjacent node unit; and 4, calculating the vector permeability value in the displacement pressure gradient direction between adjacent node units according to the horizontal permeability value, the vertical permeability value and the vector permeability model of the node units.
The object of the invention can also be achieved by the following technical measures:
the step 1 comprises the following steps:
a, node unit I and node unit J are two spatially adjacent node units, SABCDCalculating the body center coordinate I (xi, yi, zi) of the node unit I;
b, calculating the space coordinate O (x) of the center O of the ABCD surface of the seepage surfaceo,yo,zo);
c, calculating the seepage distance LIOAnd according to the seepage distance LIOCalculating the seepage distance LJO。
In step a, spatial point A, B, C, D, E, F, H, G is a spatial coordinate point constituting node element I whose body center coordinate xi is calculated by the formula
And calculating the values of the coordinate points yi and zi according to the calculation method of the coordinate point x.
In step b, the spatial coordinates O (x)o,yo,zo) The calculation method of (2) is the same as the calculation method of the body center coordinate xi of the node unit I.
In step c, the percolation distance L is calculatedIOThe calculation formula used is:
in step 1,. DELTA.PiIs the pressure, Δ P, of the node unit IjIs the pressure of the node unit J when Δ Pi>ΔPjWhen the displacement pressure gradient is in the direction from node unit I to node unit J, when Δ Pi<ΔPjIts displacement pressure gradient direction is from node unit J to node unit I.
In step 2, the normal vectors of the seepage surfaces of the node units I and J are calculated For the normal vectors of the seepage surface delta ABC of the adjacent node units I and J, the normal vectors are calculated by applying the cross multiplication of the vectorsIs calculated by the formulaNormal vector of seepage surface delta ABCHas a spatial coordinate of N (x)n,yn,zn)。
In step 2, a point coordinate X1(1,0,0) is taken on the coordinate axis X, and the normal vector of the seepage surface Δ ABC is calculatedCosine of an angle with the X axis:
taking a point coordinate Y1(0,1,0) on the coordinate axis Y, calculating the normal vector of the seepage surface delta ABCCosine of an angle with the Y axis:
taking a point coordinate X1(0,0,1) on the coordinate axis Z, calculating the normal vector of the seepage surface delta ABCCosine of an angle with the Z axis:
in step 3, vectorsThe vector of the node unit I along the seepage displacement gradient direction is in a specific formThe vector along the seepage displacement direction and the normal vector of the seepage surface delta ABCThe cosine value of the included angle between the two is calculated by the formula
In step 4, the permeability K of the node unit I in the X direction, the Y direction and the Z direction is obtainedxi、Kyi、Kzi(ii) a Obtaining permeability K of node unit J in X direction, Y direction and Z directionxj、Kyj、Kzj(ii) a And calculating the three-dimensional vector permeability of the node unit I and the adjacent node unit J in the displacement direction.
In step 4, when Δ Pi>ΔPjThe displacement pressure gradient direction is the three-dimensional vector permeability K from the node unit I to the adjacent node unit J along the displacement directionpiThe calculation formula is
Kpi=(Kxicos2α+K yicos2β+Kzicos2ψ)cosθ (8)
When Δ Pi<ΔPjThe three-dimensional vector permeability K in the direction of the displacement pressure gradient from node unit J to adjacent node unit IpjThe calculation formula is
Kpj=(Kxjcos2α+Kyjcos2β+Kzjcos2ψ)cosθ (9)
In the formula, Kpi,KpjPermeability, md, of two adjacent node units I and J in the direction of the displacement pressure gradient; kxi、KxjPermeability along the X axis in the horizontal direction, md, for node unit I and J, respectively; kyi、KyjPermeability of node units I and J in the horizontal direction Y axis, md, respectively; kzj、KzjRespectively the permeability of the node units I and J in the Z axis in the vertical direction, md; alpha, beta and psi are respectively included angles and radians between a normal vector of a common seepage surface of the node unit I and the adjacent node unit J and between a horizontal X axis, a Y axis and a vertical Z axis; theta is the included angle between the displacement pressure gradient direction and the normal vector of the seepage surface.
The method for obtaining the three-dimensional vector permeability suitable for numerical reservoir simulation is an important method for researching the seepage characteristics of underground fluids such as petroleum, natural gas and the like in a low-permeability porous medium and a numerical reservoir simulation technology. With the continuous deepening and deepening of the development research of the complex medium oil reservoir, the numerical simulation technology research and the application of the multiple medium oil reservoir are also greatly developed. Permeability is an important attribute parameter in numerical reservoir simulation techniques. The permeability has a vector characteristic, and the magnitude of the permeability has obvious directionality. In the numerical reservoir simulation, the directional difference of permeability directly affects the conductivity between adjacent nodes, and further affects the pressure propagation and saturation distribution under the model condition. Aiming at the problem of a vector permeability obtaining method in numerical reservoir simulation, the method calculates the permeability values on different seepage surfaces by applying a vector permeability calculation model on the basis of obtaining the horizontal and vertical permeability values of each node unit of the numerical reservoir simulation. The method establishes a method capable of quantitatively calculating the vector permeability in the numerical reservoir simulation, and lays a foundation for perfecting the numerical reservoir simulation technology.
Drawings
FIG. 1 is a flow chart of one embodiment of a method for obtaining three-dimensional vector permeability suitable for numerical reservoir simulation in accordance with the present invention;
FIG. 2 is a graph of adjacent mesh node unit flow path communication in accordance with an embodiment of the present invention;
FIG. 3 is a diagram illustrating a spatial relationship between a seepage surface and a seepage direction according to an embodiment of the present invention.
Detailed Description
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
As shown in fig. 1, fig. 1 is a flowchart of a method for obtaining three-dimensional vector permeability suitable for numerical reservoir simulation according to the present invention.
In step 101, the seepage area and the seepage length of the adjacent node unit are calculated, and the direction of the displacement pressure gradient is determined. The determination method of the seepage area, the seepage length and the direction of the displacement pressure gradient comprises the following steps: node element I and node element J are two spatially adjacent node elements, as shown in fig. 2.
SABCDThe seepage area is the total seepage area of the node unit I and the node unit J, the seepage area can be divided into a plurality of triangles according to the specific number of edges of the seepage surface, the area of each triangle is respectively calculated, the areas of all the triangles are accumulated to obtain the seepage surface, and the seepage surface ABCD shown in figure 2 is a quadrangle; the seepage surface ABCD can be divided into two triangles, and the areas of the two triangles are respectively calculated so as to obtain the area of the seepage surface ABCD;
LIO、LJOthe distances of node element I and node element J, respectively, to the face center O of the seepage face ABCD. At a percolation distance LIOThe calculation method is specifically described as an example: firstly, the body center coordinates I (xi, yi, zi) of the node unit I are calculated, the space point A, B, C, D, E, F, H, G is the space coordinate point forming the node unit I, and the calculation formula of the body center coordinates xi of the node unit I is as follows
Calculating values of the coordinate points yi and zi according to a calculation method of the coordinate point x; secondly, calculating the space coordinate O (x) of the center O of the ABCD surface of the seepage surfaceo,yo,zo) The calculation method is the same as that of the body center coordinate xi of the node unit I; finally, the seepage distance L is calculatedIOThe calculation formula used is as follows:
according to the seepage distance LIOCalculating the seepage distance LJO;
ΔPiIs the pressure, Δ P, of the node unit IjIs the pressure of the node unit J when Δ Pi>ΔPjWhen the displacement pressure gradient is in the direction from node unit I to node unit J, when Δ Pi<ΔPjIts displacement pressure gradient direction is from node unit J to node unit I.
In step 102, calculating cosine values of included angles between a normal vector of a seepage surface of an adjacent node unit and a horizontal X axis, a Y axis and a vertical Z axis;
firstly, calculating the normal vector of the seepage surface of the node units I and JAs shown in figure 3 of the drawings,for the normal vectors of the seepage surface delta ABC of the adjacent node units I and J, the normal vectors are calculated by applying the cross multiplication of the vectorsIs calculated by the formulaNormal vector of seepage surface delta ABCHas a spatial coordinate of N (x)n,yn,zn)。
Taking a point coordinate X1(1,0,0) on the coordinate axis X, calculating the normal vector of the seepage surface delta ABCCosine of an angle with the X axis:
taking a point coordinate Y1(0,1,0) on the coordinate axis Y, calculating the normal vector of the seepage surface delta ABCCosine of an angle with the Y axis:
taking a point coordinate X1(0,0,1) on the coordinate axis Z, calculating the normal vector of the seepage surface delta ABCCosine of an angle with the Z axis:
in step 103, calculating a cosine value of an included angle between the seepage displacement pressure gradient direction and the seepage surface normal vector of the adjacent node unit;
as shown in fig. 3, vectorsThe vector of the node unit I along the seepage displacement gradient direction is in a specific formThe vector along the seepage displacement direction and the normal vector of the seepage surface delta ABCThe cosine value of the included angle between the two is calculated by the formula
In step 104, the permeability K of the node unit I in the X direction, the Y direction and the Z direction is firstly obtainedxi、Kyi、Kzi(ii) a Obtaining permeability K of node unit J in X direction, Y direction and Z directionxj、Kyj、Kzj;
And calculating the three-dimensional vector permeability of the node unit I and the adjacent node unit J in the displacement direction. When Δ Pi>ΔPjThe displacement pressure gradient direction is the three-dimensional vector permeability K from the node unit I to the adjacent node unit J along the displacement directionpiThe calculation formula is
Kpi=(Kxicos2α+Kyicos2β+Kzicos2ψ)cosθ (8)
When Δ Pi<ΔPjFrom node unit J to phaseThree-dimensional vector permeability K of adjacent node unit I along displacement pressure gradient directionpjThe calculation formula is
Kpj=(Kxjcos2α+Kyjcos2β+Kzjcos2ψ)cosθ (9)
In the formula, Kpi,KpjPermeability, md, of two adjacent node units I and J in the direction of the displacement pressure gradient; kxi、KxjPermeability along the X axis in the horizontal direction, md, for node unit I and J, respectively; kyi、KyjPermeability of node units I and J in the horizontal direction Y axis, md, respectively; kzj、KzjRespectively the permeability of the node units I and J in the Z axis in the vertical direction, md; alpha, beta and psi are respectively included angles and radians between a normal vector of a common seepage surface of the node unit I and the adjacent node unit J and between a horizontal X axis, a Y axis and a vertical Z axis; theta is the included angle between the displacement pressure gradient direction and the normal vector of the seepage surface. The flow ends.
Claims (7)
1. The method for acquiring the three-dimensional vector permeability suitable for numerical reservoir simulation is characterized by comprising the following steps of:
step 1, calculating the seepage area and the seepage length of adjacent node units and determining the direction of a displacement pressure gradient;
step 2, calculating cosine values of included angles between a normal vector of a seepage surface of an adjacent node unit and a horizontal X axis, a Y axis and a vertical Z axis;
step 3, calculating a cosine value of an included angle between the seepage displacement direction and a seepage surface normal vector of an adjacent node unit;
step 4, calculating a vector permeability value in the displacement pressure gradient direction between adjacent node units according to the horizontal permeability value, the vertical permeability value and the vector permeability model of the node units;
the step 1 comprises the following steps:
a, node unit I and node unit J are two spatially adjacent node units, SABCDIs the common percolation area of node unit I and node unit J,calculating the body center coordinates I (xi, yi, zi) of the node unit I;
b, calculating the space coordinate O (x) of the center O of the ABCD surface of the seepage surfaceo,yo,zo);
c, calculating the seepage distance LIOAnd according to the seepage distance LIOCalculating the seepage distance LJO;
In step 1,. DELTA.PiIs the pressure, Δ P, of the node unit IjIs the pressure of the node unit J when Δ Pi>ΔPjWhen the displacement pressure gradient is in the direction from node unit I to node unit J, when Δ Pi<ΔPjWhen the displacement pressure gradient direction is from the node unit J to the node unit I;
in step 4, the permeability K of the node unit I in the X direction, the Y direction and the Z direction is obtainedxi、Kyi、Kzi(ii) a Obtaining permeability K of node unit J in X direction, Y direction and Z directionxj、Kyj、Kzj(ii) a Calculating three-dimensional vector permeability of the node unit I and the adjacent node unit J in the displacement direction;
when Δ Pi>ΔPjThe displacement pressure gradient direction is from the node unit I to the adjacent node unit J, and the three-dimensional vector permeability K along the displacement directionpiThe calculation formula is
Kpi=(Kxicos2α+Kyicos2β+Kzicos2ψ)cosθ (8)
When Δ Pi<ΔPjThe three-dimensional vector permeability K in the direction of the displacement pressure gradient from node unit J to adjacent node unit IpjThe calculation formula is
Kpj=(Kxjcos2α+Kyjcos2β+Kzjcos2ψ)cosθ (9)
In the formula, Kxi、KxjPermeability along the X axis in the horizontal direction, md, for node unit I and J, respectively; kyi、KyjPermeability of node units I and J in the horizontal direction Y axis, md, respectively; kzj、KzjRespectively the permeability of the node units I and J in the Z axis in the vertical direction, md; alpha, beta and psi are respectively included angles and radians between a normal vector of a common seepage surface of the node unit I and the adjacent node unit J and between a horizontal X axis, a Y axis and a vertical Z axis; theta is the included angle between the displacement pressure gradient direction and the normal vector of the seepage surface.
2. The method for obtaining three-dimensional vector permeability suitable for numerical reservoir simulation of claim 1, wherein in step a, the spatial point A, B, C, D, E, F, H, G is a spatial coordinate point constituting a node unit I, and the body center coordinate xi of the node unit I is calculated by the formula
And calculating values of the coordinate points yi and zi according to a calculation method of the body center coordinates xi of the node unit I.
3. The method for obtaining three-dimensional vector permeability suitable for numerical reservoir simulation of claim 1, wherein in step b, the spatial coordinate O (x) iso,yo,zo) The calculation method of (2) is the same as the calculation method of the body center coordinate xi of the node unit I.
5. the method for obtaining three-dimensional vector permeability suitable for numerical reservoir simulation of claim 1, wherein in step 2, the permeability of node units I and J is calculatedNormal vector of flow surfaceFor the normal vectors of the seepage surface delta ABC of the adjacent node units I and J, the normal vectors are calculated by applying the cross multiplication of the vectorsIs calculated by the formulaNormal vector of seepage surface delta ABCHas a spatial coordinate of N (x)n,yn,zn)。
6. The method for obtaining three-dimensional vector permeability suitable for numerical reservoir simulation of claim 5, wherein in step 2, a point coordinate X1(1,0,0) is taken on a coordinate axis X, and a normal vector of a seepage surface Δ ABC is calculatedCosine of an angle with the X axis:
taking a point coordinate Y1(0,1,0) on the coordinate axis Y, calculating the normal vector of the seepage surface delta ABCCosine of an angle with the Y axis:
7. the method for obtaining three-dimensional vector permeability suitable for numerical reservoir simulation of claim 6, wherein in step 3, the vector is obtainedThe vector of the node unit I along the seepage displacement gradient direction is in a specific formThe vector along the seepage displacement direction and the normal vector of the seepage surface delta ABCThe cosine value of the included angle between the two is calculated by the formula
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