Optimized design method for temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells

Abstract

The present invention discloses an optimized design method for a temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells, which comprises the following steps: calculating a particle size and a volume range of a candidate temporary blocking agent in an applicable target area; establishing a hydraulic fracture expansion calculation model with complete fluid-solid coupling; calculating an optimal average particle size required for effective temporary blocking; determining the particle size distribution of the temporarily blocked particles according to the optimal average particle size; calculating the particle volume of the temporary blocking agent required for effective temporary blocking; and predicting and evaluating a fracturing effect after the preferred temporary blocking design is adopted in the target area. The optimized design method for the temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells is used for improving the uniformity of fracture development of staged multi-cluster fracturing in horizontal wells, and has practicability and accuracy.

Claims

1. An optimized design method for a temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells, comprising the following steps: Step S10, collecting reservoir geological and engineering parameters of a target area, and calculating a particle size range and calculating a particle volume range of a candidate temporary blocking agent in an applicable target area; Step S20, establishing a hydraulic fracture expansion calculation model with complete fluid-solid coupling; Step S30, calculating an optimal average particle size required for effective temporary blocking based on the hydraulic fracture expansion calculation model; Step S40, determining a particle size distribution of the candidate temporary blocking agent according to the optimal average particle size; Step S50, calculating a particle volume of the candidate temporary blocking agent required for effective temporary blocking based on the hydraulic fracture expansion calculation model; and Step S60, predicting and evaluating a fracturing effect after a preferred temporary blocking agent is adopted in the target area; and pumping the preferred temporary blocking agent for synchronous expression of multiple fractures during hydraulic fracturing in the horizontal wells; wherein the hydraulic fracture expansion calculation model in the step S20 is as follows: $w=\Delta t\left[Q_{s}A\left(D,w\right)p\right]+\Delta t\left(Q_{V,n}/h\right)\delta +w_{t-1}$ $Q_s={\left(1-\varphi \right)}^2,\varphi =\frac{C}{C_{m\mathrm{ax}}}$ $\{\begin{array}{c}{p}_{in}^1+p_p^1=p_{in}^2+p_p^2=\mathrm{.Math.}=p_{in}^n+p_p^n\\ Q=\underset{n=1}{\overset{N}{.Math.}}{Q}_{V,n}\end{array}\tan \left(\theta /2\right)=-\frac{2\kappa }{1+\sqrt{1+8{\kappa }^2}},\kappa =\underset{r->0}{\lim }\frac{u}{w}w\varphi -w_{t-1}{\varphi }_{t-1}=\Delta t\nabla \left({\mathrm{BQ}}_s{Q}_p\frac{w^3}{12\mu }\nabla p-B\frac{a^{2}w}{48\mu }\mathrm{\Delta \rho }{G}_p\right)+\Delta t\left(Q_v/h\right)\Phi \delta Q_p=1.2{\varphi \left(1-\varphi \right)}^{0.1}{G}_p=2.3{\varphi \left(1-\varphi \right)}^{2}B=\{\begin{array}{cc}1& w>4a\\ \frac{w-3a}{4a-3a}& 4a\ge w\ge 3a\\ 0& w<3a\end{array}$ where: w is the width of a hydraulic fracture, m; w.sub.t−1 is a fracture width of the previous time unit, m; D is a fracture spacing, m; p is a fluid pressure within the fracture, Mpa; A(D, w) is a fluid-solid coupling coefficient matrix, m.Math.Mpa.sup.−1; Δt is a time unit, s; h is a reservoir thickness, m; δ is a Dirac δ function, representing a fracturing fluid injection point source, m.sup.−1; Q.sub.s is a fluid flow behavior correction function, no dimension; C is a particle volume concentration, no dimension; C.sub.max is an extreme particle volume concentration, the value is 0.585, no dimension; φ is a dimensionless particle volume concentration of the temporary blocking agent, no dimension; Q.sub.y,n is a fracturing fluid pumping flow rate of the n.sup.th fracture, m.sup.3/s; N is the number of hydraulic fractures in the fracturing section, no dimension; p.sub.in is a fracture inlet pressure of the n.sup.th fracture, Mpa; p.sub.p is the perforation hole friction of the n.sup.th fracture, Mpa; θ is a steering angle of the hydraulic fracture, no dimension; κ is a ratio of a type II stress intensity factor to a type I stress intensity factor, no dimension; φ.sub.t−1 is a dimensionless particle volume concentration of the previous time unit, no dimension; u is the fracture surface shear amount, m; r is a distance between any point and a fracture tip of the hydraulic fracture, m; Φ is a dimensionless particle volume concentration of pumped fluid, no dimension; μ is pure fracturing fluid viscosity, Mpa.Math.s; Q.sub.p is a temporary blocking agent particle migration behavior correction function, no dimension; G.sub.p is a temporary blocking agent particle settlement behavior correction function, no dimension; B is a temporary blocking agent particle blockage behavior correction function, no dimension; Δp is a density difference between the temporary blocking agent and a fracturing fluid, kg/m.sup.3; a is the average particle size of the temporary blocking agent, m.

2. The optimized design method for the temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells according to claim 1, wherein a specific process of the Step S10 comprises: Step S101: collecting geological and engineering parameters of the target area; and Step S102, calculating a particle size range of the candidate temporary blocking agent according to the geological and engineering parameters of the target area, wherein an equation for calculating the particle size of the candidate temporary blocking agent is as follows: $a={{\lambda }_1^{-1}\left[\frac{12\mu Q^3{t}_s^2\left(1-v^2\right)}{h^{3}E}\right]}^{\frac{1}{6}}$ where: a is the average particle size of the candidate temporary blocking agent, m; E is the Young's modulus of a reservoir rock, Mpa; v is the Poisson's ratio of the reservoir rock, no dimension; μ is the viscosity of pure fracturing fluid, MPa.Math.s; h is a reservoir thickness, m; t.sub.s is a pumping time before a temporary blocking operation, s; Q is a total pumping flow of fracturing fluid, m.sup.3/s; λ.sub.1 is a constant coefficient, no dimension; the values of λ.sub.1 are 4, 5, 6, 7, and 8, and an average particle size value of first five sets of different candidate temporary blocking agents is calculated; Step S103, calculating the particle volume range of an applicable candidate temporary blocking agent by using the following equation; $V_p={\frac{C_{\mathrm{ma}x}\xi }{{\lambda }_2}\left[\frac{12Q^3{h}^3\left(1-v^2\right)\mu t_s^2}{E}\right]}^{\frac{1}{6}}$ where: E is the Young's modulus of the reservoir rock, MPa; v is the Poisson's ratio of the reservoir rock, no dimension; μ is the viscosity of the pure fracturing fluid, Mpa.Math.s; h is the reservoir thickness, m; t.sub.s is the pumping time before temporary blocking operation, s; Q is the total pumping flow rate of fracturing fluid, m.sup.3/s; λ.sub.2 is a constant coefficient, no dimension; V.sub.p is the particle volume of the applicable temporary blocking agent, m; C.sub.max is an extreme particle volume concentration, the value is 0.585, no dimension; ξ is a stable temporary blocking layer thickness of temporary blocking agent particles, m, wherein the values of λ.sub.2 are 0.15, 0.2, 0.25, 0.3, and 0.35, and the particle volumes of second five sets of different candidate temporary blocking agents are calculated.

3. The optimized design method for the temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells according to claim 1, wherein a specific process of the Step S30 comprises: Step S301, based on the hydraulic fracture expansion calculation model for establishing complete fluid-solid coupling, substituting the geological and engineering parameters of the target area, taking the particle volume of the candidate temporary blocking agent calculated when λ.sub.2 is 0.25, respectively taking the average particle size of the first five sets of different candidate temporary blocking agents and performing analog calculation to obtain five sets of different hydraulic fracturing results; Step S302, then calculating a coefficient of variation C.sub.v of each hydraulic fracture length after five sets of different hydraulic fracturing respectively by the following equation; $C_v=\frac{{\sigma }_1}{\left(\underset{n}{\overset{N}{.Math.}}{l}_n\right)/N}$ where: C.sub.v is the coefficient of variation of each hydraulic fracture length, no dimension; σ.sub.1 is a standard deviation of each hydraulic fracture length, m; l.sub.n is a fracture length of the n.sup.th fracture, m; N is the number of hydraulic fractures in the fracturing section, no dimension; Step S303, based on the five sets of different hydraulic fracturing calculation results, selecting the average particle size of the candidate temporary blocking agent particles corresponding to the lowest C.sub.v value as the optimal average particle size a.sub.r.

4. The optimized design method for the temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells according to claim 3, wherein a specific process of the Step S40 comprises: Step S401, according to the optimal average particle size a.sub.r and a correspondence table between common particle sizes and mesh numbers, selecting two kinds of particles of larger and smaller particles for use in combination, wherein the particle size a.sub.b of the larger particle is larger than the optimal average particle size a.sub.r, and the particle size a.sub.s of the smaller particle is less than the optimal average particle size a.sub.r; Step S402, calculating the volume percentage x of the larger particles and the particle size distribution of the larger and smaller particles according to the following equation;
a.sub.bx+a.sub.s(1−x)=a.sub.r where: a.sub.b and a.sub.s are the particle sizes of larger and smaller particles, m; a.sub.r is the optimal average particle size, m; x is the volume percentage of larger particles, no dimension; Step S403, determining the volume percentage x of the larger particles obtained by the above calculation; and when x is less than 0.7, selecting smaller particles of a smaller order according to the correspondence table between common particle sizes and mesh numbers, and then repeating steps S401-S403 until x is greater than or equal to 0.7.

5. The optimized design method for the temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells according to claim 4, wherein a specific process of the Step S50 comprises: Step S501, based on the established hydraulic fracture expansion model, substituting the geological and engineering parameters of the target area, and performing analog calculation on particle volumes of the second five sets of different candidate temporary blocking agents respectively by using the optimal average particle size a.sub.r and the particle size distribution obtained in step S40, to obtain five sets of different hydraulic fracturing results; Step S502, calculating the coefficient of variation of each hydraulic fracture length after five sets of different hydraulic fracturing by using the following equation: $C_v=\frac{{\sigma }_1}{\left(\underset{n}{\overset{N}{.Math.}}{l}_n\right)/N}$ where: C.sub.v is the coefficient of variation of each hydraulic fracture length, no dimension; σ.sub.1 is a standard deviation of each hydraulic fracture length, m; l.sub.n is a fracture length of the n.sup.th fracture, m; N is the number of hydraulic fractures in the fracturing section, no dimension; and Step S503, based on the five sets of different hydraulic fracturing calculation results, selecting the particle volume of the candidate temporary blocking agent corresponding to the lowest value of C.sub.v as the particle volume of the temporary blocking agent required for effective temporary blocking.

6. The optimized design method for the temporary blocking agent to promote uniform expansion of fractures produced by fracturing in horizontal wells according to claim 5, wherein a specific process of the Step S60 comprises: Step S601, according to the calculated optimal average particle size a.sub.r, the particle size distribution and the particle volume of the temporary blocking agent required for effective temporary blocking, carrying out analog calculation on a fracturing operation process by using the established hydraulic fracture expansion model, predicting a fracture shape after fracturing, and calculating the coefficient of variation C.sub.v of each hydraulic fracture length; when C.sub.v<0.25, it is considered that a temporary blockage optimization design is reasonable; otherwise, returning to step S10, expanding the range of λ.sub.2 by ±0.5 and performing the optimized design method again.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flow chart for calculating a hydraulic fracture expansion calculation model established in Step 2.

(2) FIG. 2 is a schematic diagram of a model of a first section of a shale gas well SY (three clusters of perforations in the section).

(3) FIG. 3 is a fracture size pattern obtained by numerical simulation based on preferred parameters (the length of the gray horizontal line in the figure is 1000 times the scale width of the fracture enlarged).

DETAILED DESCRIPTION

(4) The present invention will be further described below in conjunction with the embodiments and the accompanying drawings.

(5) Taking a first section of a shale gas well SY in a block of Longmaxi Formation in southern Sichuan in China as an example, the specific reservoir geological and engineering parameters are shown in Table 2.

(6) TABLE-US-00002 TABLE 2 key geological and engineering parameters of the first section of the shale gas well SY. Young Modulus, MPa 28000 Pumping time t.sub.s before 600 temporary blocking, S Poisson's ratio ν 0.2 Fracture interval D, m 10 Fracturing fluid 2 × 10.sup.−8 Number N of hydraulic 3 viscosity μ, MPa .Math. s fractures in fracturing section Total pumping flow 0.033 Pumped dimensionless 0.2 Q of fracturing particle volume fluid, m.sup.3/s concentration Φ Reservoir 30 Thickness density Δρ 2000 thickness h, m between particles and fracturing fluid, kg/m.sup.3

(7) In Step 1, based on equation (1), five sets of candidate values of the average particle sizes of the applicable temporary blocking agents are calculated: a.sub.1=1.09 mm, a.sub.2=0.87 mm, a.sub.3=0.73 mm, a.sub.4=0.62 mm, and a.sub.5=0.55 mm.

(8) Based on equation (2), five sets of candidate values of particle sizes of the applicable temporary blocking agents are calculated, and the temporary blocking experiment result ξ=2 m, which are V.sub.1=0.396 m.sup.3, V.sub.2=0.297 m.sup.3, V.sub.3=0.237 m.sup.3, V.sub.4=0.198 m.sup.3 and V.sub.5=0.170 m.sup.3 respectively.

(9) In Step 2, based on the geological and engineering conditions of the first section of the shale gas well SY (Table 2), a hydraulic fracture expansion calculation model (FIG. 2) with complete fluid-solid coupling is established, and is solved according to the flow sequence of FIG. 1. The particle volume of the temporary blocking agent is set to V.sub.3=0.237 m.sup.3, and the average particle sizes of five sets of different candidate temporary blocking agents are a.sub.1=1.09 mm, a.sub.2=0.87 mm, a.sub.3=0.73 mm, a.sub.4=0.62 mm and a.sub.5=0.55, and are subjected to analog calculation (the pumping time is 1200 s) to obtain five sets of different hydraulic fracturing results. As shown in Table 3, the fracture length variation coefficient C.sub.v is determined by the equation (11) for the five sets of calculation results, and the average particle size a.sub.r=0.55 mm of the temporary blocking agent corresponding to the lowest value of 0.204 is taken as the preferred result.

(10) TABLE-US-00003 TABLE 3 the coefficient of variation C.sub.v of the fracture length calculated under the conditions of particle size a.sub.1 to a.sub.5. Average particle size a.sub.r 1.09 mm 0.87 mm 0.73 mm 0.62 mm 0.55 mm Coefficient 0.205 0.206 0.206 0.205 0.204 of variation C.sub.v

(11) In Step 3, according to the preferred average particle size a.sub.r=0.55 mm of the temporary blocking agent, two particles of 30 meshes and 35 meshes are selected for use in combination according to Table 1. According to equation (12), particles of 30 meshes account for 53%, and particles of 35 meshes account for 47%, which do not meet the requirement of 70% or more of large particles. Therefore, the temporary blocking agent particles of 30 meshes and 40 meshes are selected for use in combination, and the particle size distribution of particles of 30 meshes accounting for 77% and particles of 40 meshes accounting for 23% is calculated.

(12) In Step 4, according to the average particle size and particle size distribution of the preferred temporary blocking agent, the particle volumes of five sets of different candidate temporary blocking agents are taken as V.sub.1=0.396 m.sup.3, V.sub.2=0.297 m.sup.3, V.sub.3=0.237 m.sup.3, V.sub.4=0.198 m.sup.3 and V.sub.5=0.170 m.sup.3 and subjected to analog calculation (the pumping time is 1200 s), to obtain five sets of different hydraulic fracturing results. As shown in Table 4, the fracture length variation coefficient C.sub.v is determined by the equation (11) for the five sets of calculation results, and the particle volume V.sub.r=0.237 m.sup.3 of the temporary blocking agent corresponding to the lowest value of 0.204 is taken as the preferred result.

(13) TABLE-US-00004 TABLE 4 Fracture length variation coefficient C.sub.v calculated under the conditions of volume V.sub.1 to V.sub.5 Volume V 0.396 m.sup.3 0.297 m.sup.3 0.237 m.sup.3 0.198 m.sup.3 0.170 m.sup.3 Coefficient 0.499 0.239 0.204 0.282 0.720 of variation C.sub.v

(14) In step 5, the numerical calculation of the fracturing operation is carried out by adopting the numerical model established in step 2 based on the preferred temporary blocking operation parameters, and the fracture morphology simulation result is shown in FIG. 3. Based on the equation (11), C.sub.v<0.25 is satisfied, and the optimized design scheme is considered reasonable. According to the preferred temporary blocking agent parameters, the temporary blocking operation of the first section of the shale gas well SY is implemented. According to the roughly estimated length under the field micro-seismic data, C.sub.v=0.223 is measured preliminarily, and the temporary blocking optimization design scheme is considered effective.

(15) The above is not intended to limit the present invention in any form. The present invention has been disclosed by the above embodiments, but is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications by using the technical content disclosed above to obtain equivalent embodiments in equivalent changes without departing from the scope of the technical solutions of the present invention. Any simple changes, or equivalent changes and modifications may be made for the above embodiments in accordance with the technical spirit of the present invention without departing from the contents of the technical solutions of the present invention, and are still within the scope of the technical solutions of the present invention.