A method for predicting conductivity of proppant-supported fractures in deep formations

Abstract

A method for predicting the conductivity of a deep formation proppant-supported fracture, relating to the technical field of oil and gas development, comprises the following steps: collecting rock mechanical parameters, proppant particle geometry and mechanical parameters, and formation parameters in the area where the fracture to be tested is located, selecting the fracture to be tested whose uniformity meets the requirements, and selecting any one of them as a test point, calculating the number of proppant layers, embedding depth, and effective pore radius at the test point, and considering the situations where proppant particles are embedded in the fracture and not embedded in the fracture, respectively calculating the porosity and conductivity of the proppant layer at the test point; the method solves the problems of low efficiency and high labor cost in predicting fracture conductivity by obtaining a semi-empirical formula by fitting a large amount of experimental data, and at the same time considers the influence of proppant embedding, fracture width and height changes on the conductivity of the proppant fracture, and the prediction result combining multiple factors is more accurate than the prior art.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas development, and in particular to a method for predicting the conductivity of a proppant-supported fracture in a deep formation. Background Art

[0002] At present, deep formation oil and gas exploitation mostly adopts reservoir transformation measures such as hydraulic fracturing to improve reservoir seepage capacity and increase oil and gas recovery rate. Hydraulic fracturing technology will inject proppants while pressing the formation to keep the cracks open. In the actual production process, the proppant will be embedded under the action of the formation pressure, resulting in a decrease in the width of the hydraulic fracture. The reduction in the width of the fracture leads to a decrease in the porosity of the supporting layer, resulting in a decrease in the conductivity of the supporting layer fracture. For the prediction of the conductivity of fracturing fractures, most existing technologies use semi-empirical formulas. This method takes into account the factors of proppant embedding, fracture width and height changes, so the data may not be accurate. Therefore, it is necessary to take into account the factors of proppant embedding, fracture width and height changes, and combine rock mechanics and particle mechanics to derive a method for predicting the conductivity of deep formation proppant-supported fractures. Summary of the invention

[0003] In view of this, an object of the present invention is to provide a method for predicting the conductivity of proppant-supported fractures in deep formations, which can accurately predict the conductivity of proppant-supported fractures by comprehensively considering various influencing factors.

[0004] In order to solve at least one of the above technical problems, the technical solution provided by the present invention is:

[0005] A method for predicting the conductivity of proppant-supported fractures in deep formations is provided, which mainly comprises the following steps:

[0006] Step S1: Collect rock mechanical parameters, proppant particle geometry and mechanical parameters, and formation parameters of the area where the fracture to be tested is located, wherein the rock mechanical parameters include rock elastic modulus E1 and rock Poisson's ratio v1; proppant particle geometry and mechanical parameters include particle size mean R, proppant Poisson's ratio v2, and proppant elastic modulus E2; formation parameters include bottom hole pressure P w , formation fluid parameter P0;

[0007] Step S2: Select the fracture to be tested, and judge whether the uniformity of the fracture to be tested meets the requirements according to the difference in the number of proppant laying layers of the fracture width, and adjust the range of the fracture to be tested that does not meet the requirements until it meets the requirements;

[0008] Step S3: Select a point in the fracture to be tested that meets the uniformity requirements as a test point, and calculate the number of proppant layers N, the embedding depth h, and the effective pore radius r at the test point;

[0009] Step S4: considering the cases where proppant particles are embedded in the fractures and not embedded in the fractures, respectively calculating the porosity of the proppant layer at the test point;

[0010] Step S5: Based on the porosity result of the proppant layer at the test point in the fracture to be tested, the conductivity of the test point considering the proppant particles embedded in the fracture and not embedded in the fracture is calculated respectively, and the conductivity of the test point is output as the conductivity result of the fracture to be tested.

[0011] The technical effects of the present invention are:

[0012] The present invention directly calculates the conductivity of any section of a fracture in a three-dimensional state based on the actual parameters obtained, thereby solving the problems of inefficient and high labor cost in predicting fracture conductivity by obtaining a semi-empirical formula by fitting a large amount of experimental data. Meanwhile, the influence of proppant embedding, fracture width and height changes on the conductivity of propped fractures is considered, and the prediction result based on comprehensive multiple factors is more accurate than that of the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0014] Figure 1 It is a model diagram of wellbore fracture length in the present invention;

[0015] Figure 2 is a graph showing the relationship between the number of proppant layers and the seam width in the present invention;

[0016] Figure 3 is a proppant layer distribution diagram when the proppant particles are not embedded in the gaps in the present invention;

[0017] Figure 4 It is a diagram of effective pores and particle embedding of the proppant layer in the present invention. DETAILED DESCRIPTION

[0018] The present invention will be further described in detail below in conjunction with the embodiments and drawings.

[0019] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention.

[0020] A method for predicting the conductivity of a proppant-supported fracture in a deep formation comprises the following steps:

[0021] Step S1: Collect rock mechanical parameters, proppant particle geometry and mechanical parameters, and formation parameters of the area where the fracture to be tested is located, wherein the rock mechanical parameters include rock elastic modulus E1 and rock Poisson's ratio v1; proppant particle geometry and mechanical parameters include particle size mean R, proppant Poisson's ratio v2, and proppant elastic modulus E2; formation parameters include bottom hole pressure P w , formation fluid parameter P0, and the calculation method of the mean value of proppant particle size R can refer to the calculation method of the prior art, as shown in formula (14):

[0022]

[0023] In formula (16), R1, R2, R n is the particle size, The particle size is R1, R2...R n The particle size ratio.

[0024] Step S2: Select the fracture to be tested, and judge whether the uniformity of the fracture to be tested meets the requirements according to the difference in the number of proppant laying layers of the fracture width, and adjust the range of the fracture to be tested that does not meet the requirements until it meets the requirements;

[0025] See also Figure 1 The method for selecting the fracture to be tested is as follows: in any long fracture with a length of L, take the wellbore as the origin and intercept the fracture with a distance of L from the origin. i The point is the starting point and the distance to the origin is L i+1 The point is the end point of a crack. It can be seen that when the length of the crack to be measured is equal to the long crack, L i+1 With L i The difference is equal to L, and then the maximum width W of the crack to be measured is obtained max , minimum slit width W min , Maximum seam height H max , minimum seam height H min, crack tortuosity τ.

[0026] See also Figure 2 Based on the distribution of proppant particles in the fracture, the relationship between the number of proppant layers N and the fracture width W should be as shown in equations (15) and (16):

[0027]

[0028] In formulas (15) and (16), R is the mean particle size.

[0029] The maximum slit width W max , minimum slit width W min Substitute them into formula (18) to obtain the maximum width W of the crack to be measured. max and the corresponding maximum number of proppant layers N max and minimum slit width W min The corresponding minimum number of proppant layers N min , the calculation formulas are shown in formula (1) and formula (2) respectively:

[0030]

[0031] Then, the maximum number of proppant layers N is calculated using formula (3): max and the minimum number of proppant layers N min The difference in the number of layers N0:

[0032] N0=N max -N min (3)

[0033] According to the stacking model, the difference in the number of layers N0 is set within the range of 0 to 0.5 based on the particle radius, ensuring close stacking between particles in the same layer, and the error. Therefore, when N0∈[0,0.5], it is considered that the uniformity of the crack to be measured meets the requirements, and the difference in the crack width change is small, which can be used for subsequent calculations.

[0034] When the width W of the selected cracks to be tested is too different to be used for subsequent calculations, it is necessary to gradually shorten the length of the cracks to be tested delineated in the long cracks according to the specific situation, and recalculate the difference in the number of delineated layers N0 until it meets the uniformity requirements. In the subsequent calculations, the conductivity of the cracks to be tested that meet the uniformity requirements is calculated.

[0035] Step S3: Select a point in the fracture to be tested that meets the uniformity requirements as a test point, and calculate the number of proppant layers N, the embedding depth h, and the effective pore radius r at the test point;

[0036] The calculation formula of the number of layers N at the test point and the maximum number of proppant layers N max and the minimum number of proppant layers Nmin The number of layers is the same, so formula (4) is used for calculation:

[0037]

[0038] In formula (4), W is the average width of the crack to be measured;

[0039] The calculation formula of the average crack width W to be measured is shown in formula (5):

[0040]

[0041] According to the Hertz theory, the proppant embedding depth h is calculated, where E0 is the generalized elastic modulus, E1 is the rock elastic modulus, ν1 is the rock Poisson's ratio, E2 is the proppant elastic modulus, and ν2 is the proppant Poisson's ratio. The relevant calculation formulas are shown in equations (17) and (18):

[0042]

[0043] Among them, the inter-particle contact stress σ1 is approximately equal to the difference between the crack closure stress P1 and the fluid pressure P2 in the support layer. P1 can be obtained by the crack width W and the crack length L x Get, L i ≤L x ≤L i+1 . P2 can be composed of P0 and P w We get: P0 is the formation fluid pressure, P w is the bottom hole pressure. Therefore, the inter-particle contact stress σ1 can also be expressed as formula (19):

[0044]

[0045] Substituting equation (21) into equation (19), we can obtain the calculation formula for the proppant embedment depth h as shown in equation (6):

[0046]

[0047] In formula (6), L x is the distance from the test point to the origin, and L x ∈[L i , L i+1 ], L is the total length of the arbitrarily long crack.

[0048] As for the proppant placement inside the fracture, if N layers are placed, there are 2N effective flow pores in one unit length fracture, of which 2 are in contact with the fracture and (2N-2) are not. The calculation formula for the effective pore radius r of the proppant layer can be obtained as shown in formula (7):

[0049]

[0050] In formula (7), r1 is the effective flow radius of the pores not in contact with the crack wall, and r2 is the effective flow radius of the pores in contact with the crack wall;

[0051] Considering the pore radius within a unit length fracture, the equivalent effective flow pore radius is calculated, and then we have equations (8) and (9):

[0052] The calculation formula of the effective flow radius r1 of the pores not in contact with the crack wall is shown in formula (8):

[0053]

[0054] The calculation formula of the effective flow radius r2 of the pore in contact with the crack wall is shown in formula (9):

[0055]

[0056] Step S4: considering the cases where proppant particles are embedded in the fractures and not embedded in the fractures, respectively calculating the porosity of the proppant layer at the test point;

[0057] See also Figure 3 , considering that the particles are not embedded, in (L i ,L i+1 The calculation formula of the porosity φ1 of the fracture segment proppant layer in the interval is shown in formula (20):

[0058]

[0059] Among them, L x is chosen as a multiple of the radius R, and n is an integer.

[0060] See also Figure 4 , considering the embedding of proppant, L is calculated using formula (21) x (L i ≤L x ≤L i+1 ) at the proppant layer porosity φ2:

[0061]

[0062] Step S5: Based on the porosity result of the proppant layer at the test point in the fracture to be tested, the conductivity of the test point considering the proppant particles embedded in the fracture and not embedded in the fracture is calculated respectively, and the conductivity of the test point is output as the conductivity result of the fracture to be tested.

[0063] When proppant embedding is not considered, h = 0, the three-dimensional state can be calculated, and the permeability K1 and conductivity A1 of a proppant-supported fracture can be obtained. τ is the fracture tortuosity, as shown in Equations (22) and (23):

[0064]

[0065] In the above formula, considering that the pores in the supporting layer are occupied by other fluids and do not participate in the effective flow, the permeability correction coefficient ψ is introduced to represent the influence of liquid residue and proppant breakage on the permeability. The calculation method of the permeability correction coefficient ψ is shown in formula (24):

[0066]

[0067] In formula (24), A 实 is the conductivity of the fracture to be tested obtained from the actual experiment. According to the embedding situation of the proppant, the porosity φ1 before embedding and the porosity φ2 after embedding can be selected and brought into the calculation. That is, the value of ψ is obtained by comparing the theoretically calculated conductivity with the actual proppant-supported fracture conductivity.

[0068] When proppant embedding is considered, the three-dimensional state, fracture permeability K2 and conductivity A2 under proppant embedding can be calculated, as shown in Equations (25) and (26):

[0069]

[0070] Example:

[0071] Step 1: Obtain the required parameters, carry out indoor fracture core permeability test experiments, lay a single layer of proppant, calculate the fracture conductivity at the outlet, and obtain the relevant parameters as shown in Table 1:

[0072] Table 1 Core conductivity test related parameters

[0073]

[0074]

[0075] In Table 1, there is no liquid residue in the proppant layer, that is, the liquid does not occupy the proppant space, and the proppant breakage is not considered, so the permeability correction coefficient ψ is taken as 1.

[0076] Step 2: Calculate crack width and height.

[0077] For core cracking and single-layer paving, after adding confining pressure, the crack width W = 0.03cm; the crack height H = 2.50cm

[0078] Step 3: Calculate the mean proppant radius.

[0079] Screen the proppant with a sieve to obtain a proppant radius of R = 0.02 cm

[0080] Step 4: Proppant single layer laying, N = 1

[0081] Step 5: According to the calculation, the porosity of the proppant layer is φ1≈0.3019 when the particles are not embedded, as shown in formula (27):

[0082]

[0083] Step 6: Calculate the equivalent effective flow pore radius r 2 =r2 2 ≈12131.4576μm 2 , as shown in formulas (28)-(30):

[0084]

[0085] h≈0.0000001899≈0(29)

[0086]

[0087] Step 7: Calculate the porosity of the support layer φ2≈0.3019 when the proppant is embedded, as shown in formula (31):

[0088]

[0089] Step 8: Calculate the permeability K2≈457.8109μm at the exit of the proppant fracture when the proppant is embedded. 2 And the flow capacity at the outlet A2=13.7343μm 2 cm, as shown in formula (32) and (33):

[0090]

[0091] A2=K2W=13.7343μm 2 cm (33)

[0092] The experimental data show that the fracture permeability at the exit of the proppant embedding condition is about 457.8 μm. 2 , the conductivity is calculated to be about 13.7μm 2 ·cm.

[0093] In the description of the present invention, it should be pointed out that the terms "upper", "lower", "front", "back", "left", "right", "top", "bottom", "inside" and "outside" etc. indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and should not be understood as a limitation on the present invention.

[0094] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for predicting the conductivity of proppant-supported fractures in deep formations, characterized in that: The following steps are involved: Step S1: Collect rock mechanical parameters, proppant particle geometry and mechanical parameters, and formation parameters of the area where the fracture to be tested is located, wherein the rock mechanical parameters include rock elastic modulus E1 and rock Poisson's ratio v1; proppant particle geometry and mechanical parameters include particle size mean R, proppant Poisson's ratio v2, and proppant elastic modulus E2; formation parameters include bottom hole pressure P w , formation fluid parameter P0; Step S2: Select the fracture to be tested, and judge whether the uniformity of the fracture to be tested meets the requirements according to the difference in the number of proppant layers of the fracture width, and adjust the range of the fracture to be tested that does not meet the requirements until it meets the requirements. The method for selecting the fracture to be tested is: in any long fracture, take the wellbore as the origin, and intercept the fracture with a distance L from the origin. i The point is the starting point and the distance to the origin is L i+1 The crack with the point as the end point is the crack to be tested, and the maximum crack width W of the crack to be tested is obtained. max , minimum slit width W min , Maximum seam height H max , minimum seam height H min , crack tortuosity τ; The method for judging the uniformity of the crack to be tested based on the difference in the number of proppant layers of the crack width is as follows: calculate the maximum crack width W of the crack to be tested respectively. max and the corresponding maximum number of proppant layers N max and minimum slit width W min The corresponding minimum number of proppant layers N min , the calculation formulas are shown in formula (1) and formula (2) respectively: Then, the maximum number of proppant layers N is calculated using formula (3): max and the minimum number of proppant layers N min The difference in the number of layers N0: N0=N max -A min (3) When N0∈[0,0.5], it is considered that the uniformity of the crack to be measured meets the requirements; Step S3: A point in the fracture to be tested whose uniformity meets the requirements is selected as a test point, and the number of proppant layers N, the embedding depth h, and the effective pore radius r at the test point are calculated. The calculation formula for the number of proppant layers N at the test point is as shown in formula (4): In formula (4), W is the average width of the crack to be measured; The calculation formula of the average crack width W to be measured is shown in formula (5): The calculation formula of embedding depth h is shown in formula (6): In formula (6), L x is the distance from the test point to the origin, and L x ∈[L i , L i+1 ], L is the total length of the arbitrarily long crack; The calculation formula of the effective pore radius r is shown in formula (7): In formula (7), r1 is the effective flow radius of the pores not in contact with the crack wall, and r2 is the effective flow radius of the pores in contact with the crack wall; The calculation formula of the effective flow radius r1 of the pores not in contact with the crack wall is shown in formula (8): The calculation formula of the effective flow radius r2 of the pore in contact with the crack wall is shown in formula (9): Step S4: Considering the cases where proppant particles are embedded in the cracks and not embedded in the cracks, the porosity of the proppant layer at the test point is calculated respectively. Considering the case where the proppant particles are not embedded in the cracks, the calculation formula of the porosity φ1 of the proppant layer at the test point is as shown in formula (10): When the proppant particles are embedded in the fracture, the calculation formula of the porosity φ2 of the proppant layer at the test point is shown in formula (11): Step S5: Based on the porosity result of the proppant layer at the test point in the fracture to be tested, the conductivity of the test point under the conditions of proppant particles being embedded in the fracture and not being embedded in the fracture is calculated respectively, and the conductivity of the test point is output as the conductivity result of the fracture to be tested, wherein the calculation formula of the conductivity A1 under the condition of proppant particles not being embedded in the fracture is shown in formula (12): The calculation formula of the conductivity A2 considering the embedding of proppant particles into the fracture is shown in formula (13): In formulas (12) and (13), Ψ is the permeability correction coefficient.

2. A method for predicting conductivity of proppant-supported fractures in deep formations according to claim 1, characterized in that: The method for adjusting the range of the cracks to be tested that do not meet the requirements until they meet the requirements is: shortening the length of the cracks to be tested, recalculating the difference N0 of the number of layers, and repeating the process until it meets the uniformity requirements.

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