New calculation method for determining flow conductivity

Abstract

The present invention provides a new method for determining and calculating the flow conductivity, which comprises: step 1, calculating the initial porosity of the proppant and the contact force F between two proppant particles; step 2, calculating the porosity #imgabs0# and the permeability #imgabs1# of the proppant after being compressed in the crack; step 3, calculating the crack width #imgabs2#; step 4, calculating the flow conductivity Kw of the crack according to the above steps f ; Step 5, calculate the conductivity of the fracture after the proppant is embedded in the wall; Step 6, solve the conductivity of the fracture under the condition of proppant crushing; Step 7, calculate the conductivity of the fracture under the condition of proppant embedding in the wall and proppant crushing. This new calculation method for determining the conductivity avoids the uncertainty caused by empirical artificial prediction, thus providing more effective guidance for fracturing construction design.

Description

Technical Field

[0001] The invention relates to the technical field of fracturing technology research, and in particular to a new method for determining and calculating flow conductivity. Background Art

[0002] China is rich in tight oil and gas resources. In recent years, 60% to 80% of the proven oil reserves of PetroChina are low-permeability reservoirs. Now the development of low-permeability oil and gas fields has become the main body of oil and gas field development. For regional geological low-porosity, low-permeability, and high-pressure reservoirs, effective production capacity can only be obtained after reservoir transformation. Fracturing is a good transformation method. Hydraulic fracturing is a commonly used production increase measure for the development of low-permeability reservoirs. Hydraulic fracturing is to form high-conductivity cracks leading to the wellbore so that the fluid in the reservoir can flow into the wellbore better. At present, most of the studies on the conductivity of fractures are conducted through experiments, while there are few studies on its theoretical calculation model. For this reason, we have invented a new method for determining and calculating the conductivity, which solves the above technical problems. Summary of the invention

[0003] The purpose of the present invention is to provide a new method for determining and calculating the conductivity, which can predict the approximate range of the conductivity according to the local geological parameters of the construction site and deduce the trend of the conductivity changing with the closing pressure.

[0004] The object of the present invention can be achieved by the following technical measures: a new method for determining the conductivity, the new method for determining the conductivity comprising: step 1, calculating the initial porosity of the proppant and the contact force F between two proppant particles; step 2, calculating the porosity of the proppant after being compressed in the fracture and permeability K; Step 3, calculate the crack width w f ; Step 4, calculate the conductivity Kw of the crack according to the above steps f ; Step 5, calculate the conductivity of the fracture after the proppant is embedded in the wall; Step 6, solve the conductivity of the fracture under the condition of proppant crushing; Step 7, calculate the conductivity of the fracture under the condition of proppant embedded in the wall and proppant crushing.

[0005] The purpose of the present invention can also be achieved by the following technical measures:

[0006] The new method for determining and calculating fracture conductivity also includes, before step 1, establishing assumptions of a proppant model.

[0007] Prior to step 1, the following assumptions were made about the proppant distribution:

[0008] 1) Assume that the proppant is arranged in a hexagonal closest-packed arrangement;

[0009] 2) The proppant is spherical;

[0010] 3) After the proppant is compressed, only the contact area is deformed, and the rest of the area remains unchanged;

[0011] 4) The proppant and wall materials conform to the elastic mechanics assumptions.

[0012] Step 1 includes:

[0013] 1a, according to the arrangement of proppants in the fracture, assuming that the proppants are distributed in a hexagonal closest arrangement, the eight closely adjacent balls are taken as hexahedral units; according to the arrangement of the balls, the volume occupied by a ball in a hexahedron is the volume of the entire ball, and its volume is

[0014]

[0015] Where: r is the radius of the proppant, in m;

[0016] 1b. Find the volume V of the proppant sphere in the unit after the proppant is arranged in the densest manner. 球 and the total volume of the hexahedron V 六 ;

[0017]

[0018] Where: S is the bottom area of ​​the hexahedron, in m 2 ; h is the height of the hexahedron, in meters;

[0019] 1c, calculate the porosity after proppant arrangement

[0020]

[0021] 1d, according to the arrangement of the proppant in a diamond shape, the number of balls per unit area is

[0022]

[0023] 1e, when the closing pressure is P, the average force applied to a single ball is

[0024]

[0025] Where: P is the closing pressure, unit is Pa.

[0026] Step 2 includes:

[0027] 2a, when the proppants are in contact with each other, the distance between the two sphere centers will be reduced due to pressure. Let the reduced distance between the two sphere centers be a. According to elastic mechanics, the value of the reduced distance a is,

[0028]

[0029] Where: E is the elastic modulus of the proppant, in Pa; μ is the Poisson's ratio of the proppant; r is the radius of the proppant, in m; F is the contact force between the two proppants;

[0030] 2b, when the proppant is compressed, the volume V of the hexahedral unit will decrease, which is

[0031]

[0032] 2c, in the hexagonal closest packing, each proppant is connected to the 12 adjacent proppant, and the volume of the ball in the unit body is the volume of the whole ball minus the volume of the 12 spherical gaps.

[0033]

[0034] Therefore, the porosity will change after compression.

[0035]

[0036] The pore radius in the crack of the proppant is determined by the smallest hole, which is determined by the gap between the three tangent balls. The pore radius is the radius R of the largest sphere passing through the middle gap. The size after compression is

[0037] The permeability K is

[0038]

[0039] Where: τ is the tortuosity.

[0040] Step 3 includes:

[0041] 3a, set the sand concentration to C, the proppant density to ρ, and assume that the volume of a single proppant is V 单 , the number of balls per unit area is

[0042]

[0043] The number of paving layers is

[0044]

[0045] Where:

[0046] C is the concentration of sand, in kg / m

[0047] ρ is the density of the proppant, in kg / m 3

[0048] V 单 is the volume of a single proppant, in m 3

[0049] r is the radius of the proppant, in m;

[0050] 3b, after the sphere is compressed, the number of layers remains unchanged, the distance between the two layers will decrease, and the height h between each layer will decrease to

[0051]

[0052] a is the distance between the two sphere centers;

[0053] 3c, according to steps 3a and 3b, the slit width is

[0054]

[0055] In step 4, the conductivity of the fracture Kw f The calculation formula is:

[0056]

[0057] Where:

[0058] Step 5 includes:

[0059] 5a, considering the case where the proppant is embedded in the wall, the distance h1 of the proppant embedded in the wall is obtained according to elastic mechanics:

[0060]

[0061] Where:

[0062] E1 is the elastic modulus of the wall, in Pa;

[0063] μ1 is the Poisson’s ratio of the wall;

[0064] 5b, after the proppant is embedded in the wall, it only affects the crack width, so the crack width becomes w f for

[0065]

[0066] 5c, calculate the distance that the proppant is embedded in the wall after being compressed, and then combine it with the conductivity formula in step 4 to obtain the conductivity after the proppant is embedded in the wall:

[0067]

[0068] Step 6 includes:

[0069] 6a, assuming that the proppant breakage rate is B t According to the experimental data of crushing rate, the curve B of crushing rate and closing pressure is fitted. t=f(P); Assuming that the proppant is broken and filled in the void, it will affect the crack width and porosity, and the porosity will affect the permeability; the volume occupied by the spheres in the unit after the proppant is broken becomes

[0070]

[0071] 6b, the porosity change is calculated as:

[0072]

[0073] 6c, the calculated slit width becomes

[0074]

[0075] 6d, the conductivity is obtained when only the proppant breakage is considered.

[0076]

[0077] In step 7, the conductivity considering the embedding of proppant in the wall and the breaking of proppant is

[0078]

[0079] The new calculation method for determining the flow conductivity in the present invention can predict the approximate range of the flow conductivity according to the local geological parameters of the construction, and can deduce the trend of the flow conductivity changing with the closure pressure, thereby avoiding the uncertainty caused by empirical artificial prediction, and providing more effective guidance for fracturing construction design. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 The flowchart is a specific embodiment of the method for determining and calculating the new flow conductivity of the present invention. DETAILED DESCRIPTION

[0081] In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings.

[0082] like Figure 1 As shown, Figure 1 The present invention is a flowchart of a new method for determining and calculating flow conductivity.

[0083] Step 101: Proppant Model Assumptions

[0084] The following assumptions are made about the proppant distribution:

[0085] 1) Assume that the proppant is arranged in a hexagonal closest-packed arrangement;

[0086] 2) The proppant is spherical;

[0087] 3) After the proppant is compressed, only the contact area is deformed, and the rest of the area remains unchanged;

[0088] 4) The proppant and wall materials conform to the elastic mechanics assumptions.

[0089] Step 102: Calculate the initial porosity of the proppant and the contact force F between two proppants;

[0090] (1) According to the arrangement of proppants in the fracture, assuming that the proppants are distributed in a hexagonal closest arrangement, the eight closely adjacent balls are taken as hexahedral units. According to the arrangement of the balls, the volume occupied by the balls in a hexahedron is the volume of the entire ball, and its volume is

[0091]

[0092] Where: r is the radius of the proppant, in m

[0093] (2) Calculate the volume V of the proppant sphere in the unit after the proppant is arranged in the densest manner 球 and the total volume of the hexahedron V 六 ;

[0094]

[0095] (3) Calculate the porosity after proppant arrangement

[0096]

[0097] (4) According to the arrangement of the proppant in a diamond shape, the number of balls per unit area is

[0098]

[0099] (5) When the closing pressure is P, the average force applied to a single ball is

[0100]

[0101] Where: P is the closing pressure, unit is Pa

[0102] Step 103: Calculate the porosity of the proppant after it is compressed in the fracture and permeability K

[0103] (1) When the proppants are in contact with each other, the distance between the two sphere centers will decrease due to pressure. Let a be the distance between the two sphere centers. The value of the reduced distance a can be calculated based on elastic mechanics as

[0104]

[0105] Where: E is the elastic modulus of the proppant, in Pa; μ is the Poisson's ratio of the proppant;

[0106] (2) When the proppant is compressed, the volume of the hexahedral unit will decrease.

[0107]

[0108] (3) In the hexagonal closest packing, each proppant is connected to the 12 adjacent proppant, and the volume of the sphere in the unit body is the volume of the entire sphere minus the volume of the 12 sphere gaps.

[0109]

[0110] Therefore, the porosity will change after compression.

[0111]

[0112] The pore radius in the crack of the proppant is determined by the smallest hole, which is determined by the gap between the three tangent balls. The pore radius is the radius R of the largest sphere passing through the middle gap. The size after compression is

[0113] The permeability K is

[0114]

[0115] Where: τ is the tortuosity

[0116] Step 104: Calculate the crack width w f

[0117] (1) Set the sand concentration to C, the proppant density to ρ, and assume that the volume of a single proppant is V 单 , the number of balls per unit area is

[0118]

[0119] The number of paving layers is

[0120]

[0121] Where:

[0122] C is the concentration of sand, in kg / m

[0123] ρ is the density of the proppant, in kg / m 3

[0124] V 单 is the volume of a single proppant, in m 3

[0125] (2) After the sphere is compressed, the number of layers remains unchanged, the distance between the two layers decreases, and the height between each layer decreases to

[0126]

[0127] (3) According to (1) and (2), the slit width can be obtained as

[0128]

[0129] Step 105: According to the above steps, the conductivity Kw of the crack can be obtained. f for

[0130]

[0131] Where:

[0132] Step 106: Calculate the conductivity of the fracture after the proppant is embedded in the wall

[0133] (1) Considering the case where the proppant is embedded in the wall, the distance h1 of the proppant embedded in the wall is obtained according to elastic mechanics:

[0134]

[0135] Where:

[0136] E1 is the elastic modulus of the wall, in Pa;

[0137] μ1 is the Poisson’s ratio of the wall;

[0138] (2) After the proppant is embedded in the wall, it only affects the crack width, so the crack width becomes w f for

[0139]

[0140] (3) Calculate the distance that the proppant is embedded in the wall after being compressed, and then combine it with the conductivity formula in step 105 to obtain the conductivity of the fracture after the proppant is embedded in the wall:

[0141]

[0142] Step 107: Solve for the fracture conductivity considering proppant breakage

[0143] (1) Assume that the proppant breakage rate is B t According to the experimental data of crushing rate, the curve B of crushing rate and closing pressure is fitted. t =f(P). Assuming that the proppant is broken and filled in the voids, it will affect the crack width and porosity, and the porosity will affect the permeability. After the proppant is broken, the volume occupied by the sphere in the unit body becomes

[0144]

[0145] (2) Calculate the porosity change as:

[0146]

[0147] (3) Calculate the slit width to

[0148]

[0149] (4) The fracture conductivity when only considering proppant breakage is

[0150]

[0151] Step 108: Considering the proppant embedded in the wall and the proppant broken, the conductivity of the fracture is

[0152]

Claims

1. A new method for determining flow conductivity, characterized in that: The new calculation method for determining the flow conductivity includes: Step 1, calculating the initial porosity of the proppant and the contact force F between two proppant particles; Step 2: Calculate the porosity of the proppant after it is compressed in the fracture and permeability K; Step 3, calculate the crack width w f ; Step 4: Calculate the conductivity Kw of the crack according to the above steps f ; Step 5, calculating the conductivity of the fracture after the proppant is embedded in the wall; Step 6, solving the fracture conductivity considering proppant breakage; Step 7, calculating the fracture conductivity considering the embedding of proppant into the wall and the breaking of proppant; Step 5 includes: 5a, considering the case where the proppant is embedded in the wall, the distance h1 of the proppant embedded in the wall is obtained according to elastic mechanics: Where: E1 is the elastic modulus of the wall, in Pa; μ1 is the Poisson’s ratio of the wall; r is the radius of the proppant, in m; E is the elastic modulus of the proppant, in Pa; μ is the Poisson’s ratio of the proppant; F is the contact force between two proppants; 5b, after the proppant is embedded in the wall, it only affects the crack width, so the crack width becomes w f for Where: h is the height of the hexahedron, in meters; a is the distance between the two sphere centers, in meters; C is the concentration of topsand, in kg / m; ρ is the density of the proppant, in kg / m 3 ; V 单 is the volume of a single proppant, in m 3 ; 5c, calculate the distance that the proppant is embedded in the wall after being compressed, and then combine it with the conductivity formula in step 4 to obtain the conductivity after the proppant is embedded in the wall: Where: τ is the tortuosity; Step 6 includes: 6a, assuming that the proppant breakage rate is B t According to the experimental data of crushing rate, the curve B of crushing rate and closing pressure is fitted. t =f(P); Assuming that the proppant is broken and filled in the void, it will affect the crack width and porosity, and the porosity will affect the permeability; the volume occupied by the spheres in the unit after the proppant is broken becomes 6b, the porosity change is calculated as: Where: V is the volume of the hexahedral unit, in m 3 ; 6c, the calculated slit width becomes 6d, the conductivity is obtained when only the proppant breakage is considered. In step 7, the conductivity considering the embedding of proppant in the wall and the breaking of proppant is 2. The new method for determining and calculating flow conductivity according to claim 1 is characterized in that: The new calculation method for determining the conductivity further includes, before step 1, establishing assumptions of a proppant model.

3. The new method for determining and calculating flow conductivity according to claim 2 is characterized in that: Prior to step 1, the following assumptions were made about the proppant distribution: 1) Assume that the proppant is arranged in a hexagonal closest-packed arrangement; 2) The proppant is spherical; 3) After the proppant is compressed, only the contact area is deformed, and the rest of the area remains unchanged; 4) The proppant and wall materials conform to the elastic mechanics assumptions.

4. The new method for determining and calculating flow conductivity according to claim 1, characterized in that: Step 1 includes: 1a, according to the arrangement of proppants in the fracture, assuming that the proppants are distributed in a hexagonal closest arrangement, the eight closely adjacent balls are taken as hexahedral units; according to the arrangement of the balls, the volume occupied by a ball in a hexahedron is the volume of the entire ball, and its volume is 1b. Find the volume V of the proppant sphere in the unit after the proppant is arranged in the densest manner. 球 and the total volume of the hexahedron V 六 ; Where: S is the bottom area of ​​the hexahedron, in m 2 ; 1c, calculate the porosity after proppant arrangement 1d, according to the arrangement of the proppant in a diamond shape, the number of balls per unit area is 1e, when the closing pressure is P, the average force applied to a single ball is Where: P is the closing pressure, unit is Pa.

5. The new method for determining and calculating flow conductivity according to claim 4 is characterized in that: Step 2 includes: 2a, when the proppants are in contact with each other, the distance between the two sphere centers will be reduced due to pressure. Let the reduced distance between the two sphere centers be a. According to elastic mechanics, the value of the reduced distance a is, 2b, when the proppant is compressed, the volume V of the hexahedral unit will decrease, which is 2c, in the hexagonal closest packing, each proppant is connected to the 12 adjacent proppant, and the volume of the ball in the unit body is the volume of the whole ball minus the volume of the 12 spherical gaps. Therefore, the porosity will change after compression. The pore radius in the crack of the proppant is determined by the smallest hole, which is determined by the gap between the three tangent balls. The pore radius is the radius R of the largest sphere passing through the middle gap. The size after compression is The permeability K is Where: τ is the tortuosity.

6. The new method for determining and calculating flow conductivity according to claim 5, characterized in that: Step 3 includes: 3a, set the sand concentration to C, the proppant density to ρ, and assume that the volume of a single proppant is V 单 , the number of balls per unit area is The number of layers is 3b, after the sphere is compressed, the number of layers remains unchanged, the distance between the two layers will decrease, and the height h between each layer will decrease to a is the distance between the two sphere centers; 3c, according to steps 3a and 3b, the slit width is 7. The new method for determining and calculating flow conductivity according to claim 6, characterized in that: In step 4, the conductivity of the fracture Kw f The calculation formula is: Where:

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