METHOD FOR PREDICTING FRACTURE HEIGHT DURING FRACTURING STIMULATION IN MULTI-LAYER FORMATION

Abstract

The present invention discloses a method for predicting fracture height during fracturing stimulation in multi-layer formation, comprising specific steps of: (1) acquiring basic parameters; (2) calculating a displacement discontinuity quantity of an artificial fracture; (3) calculating induced stress generated by the fracture; (4) calculating stress intensity factors at a fracture tip without considering a fracture tip plasticity; (5) calculating sizes of a plastic zone; (6) calculating stress intensity factors at the fracture tip considering the plastic zone; and (7) judging a relationship between the stress intensity factors and a fracture toughness. The present invention is suitable for multiple stratums, and the influences of parameters of tip plasticity, induced stress, crustal stress, and rock mechanics are considered so that a calculation result is more accurate and calculation efficiency is higher.

Claims

1. A method for predicting fracture height during fracturing stimulation in multi-layer formation, comprising the following steps: S1: acquiring parameters of geology, rock mechanics, and artificial fracture; S2: calculating displacement discontinuity quantities D of n artificial fractures based on a displacement discontinuity method; S3: calculating induced stress Δσ generated by then artificial fractures on an n+1.sup.th fracture; S4: calculating stress intensity factors K.sub.I+ and K.sub.I− at fracture tips of the n+1.sup.th fracture without considering the fracture tip plasticity based on an equilibrium height theory; S5: calculating sizes S.sub.u and S.sub.l of a plastic zone at the fracture tip of the n+1.sup.th fracture; S6: calculating stress intensity factors K′.sub.I+ and K′.sub.I− at fracture tips of the n+1.sup.th fracture considering the plastic zone; S7: judging whether the stress intensity factors K′.sub.I+ and K′.sub.I− are greater than a fracture toughness at the fracture tip; when the stress intensity factors K′.sub.I+ and K′.sub.I− are greater than the fracture toughness, getting back to the step S4; and when the stress intensity factors K′.sub.I+ and K′.sub.I− are not greater than the fracture toughness, ending the operation to output the n+1.sup.th fracture height.

2. The method for predicting fracture height during fracturing stimulation in multi-layer formation according to claim 1, wherein in the step S6, the stress intensity factors K′.sub.I+ and K′.sub.I− at an upper tip and a lower tip of the n+1.sup.th fracture are that: $\{\begin{array}{c}{K}_{I-}^{\prime }=\sqrt{\frac{1}{\pi \frac{2c+S_u+S_l}{2}}}\underset{-\frac{2c+S_u+S_l}{2}}{\overset{\frac{2c+S_u+S_l}{2}}{\int }}\left[-\rho {\mathrm{gy}}_r+p_{\mathrm{ref}}+\rho g\left(d_{\mathrm{mid}}-d_{\mathrm{ref}}\right)-\left({\sigma }_h^r+{\mathrm{\Delta \sigma }}_{\mathrm{NN}}^r\right)\right]\sqrt{\frac{\frac{2c+S_u+S_l}{2}-y}{\frac{2c+S_u+S_l}{2}+y}}\mathrm{dy}\\ K_{I+}^{\prime }=\sqrt{\frac{1}{\pi \frac{2c+S_u+S_l}{2}}}\underset{-\frac{2c+S_u+S_l}{2}}{\overset{\frac{2c+S_u+S_l}{2}}{\int }}\left[-\rho {\mathrm{gy}}_r+p_{\mathrm{ref}}+\rho g\left(d_{\mathrm{mid}}-d_{\mathrm{ref}}\right)-\left({\sigma }_h^r+{\mathrm{\Delta \sigma }}_{\mathrm{NN}}^r\right)\right]\sqrt{\frac{\frac{2c+S_u+S_l}{2}+y}{\frac{2c+S_u+S_l}{2}-y}}\mathrm{dy}\end{array}$ where ρ is a fluid density (kg/m.sup.3); g is an acceleration of gravity (m/s.sup.2); p.sub.ref is a pressure at a depth of a middle portion of a perforation (Pa); d.sub.mid is a depth of a middle portion of the fracture (m); d.sub.ref is the depth of the middle portion of the perforation (m); ρ.sup.r.sub.h is a minimum horizontal principal stress of an r.sup.th stratum (Pa); c is a half height of the fracture (m); and y.sub.r is a depth (m).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] FIG. 1 is a flow chart of predicting fracture height during fracturing stimulation in multi-layer formation.

[0024] FIG. 2 is a cross-section view of fracture height during fracturing stimulation in multi-layer formation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] The preferred embodiments of the present invention are described hereinafter with reference to the drawings. It should be understood that the preferred embodiments described herein are only used for describing and explaining the present invention and are not intended to limit the present invention.

[0026] After fracturing a dense sandstone gas reservoir, basic parameters are measured as shown in Table 1.

TABLE-US-00001 TABLE 1 Basic parameter table Minimum horizontal Fracture Shear Layer Top depth Thickness principal toughness modulus Poisson's number (m) (m) stress (MPa) (MPa .Math. m.sup.1/2) (GPa) ratio #1 2680 100 44 5 50 0.35 #2 2780 20 38 2 20 0.17 #3 2800 40 44 5 30 0.25 #4 2840 20 38 2 20 0.17 #5 2860 40 44 5 30 0.25 #6 2900 20 48 7 40 0.3 #7 2920 100 53 9 50 0.35 Perforation Depth of middle portion of perforation (m) 2850 Fluid Density (kg/m.sup.3) 1100

[0027] Allowing that n=1, a distance between an n.sup.th fracture and an n+1.sup.th fracture is 25 m, a height of the n.sup.th fracture is 25 m, a pressure at the depth of the middle portion of the perforation is 42.6 MPa, and a step size of the pressure is set to be 0.01 MPa. Based on the data in Table 1, steps S1 to S7 are executed in sequence, and a formula is a numerical solution. The final calculation results are shown in FIG. 2.

[0028] The above is only the preferred embodiments of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed by the preferred embodiments, the preferred embodiments are not intended to limit the present invention. Those skilled in the art can make some changes or modifications as equivalent embodiments with equivalent changes by using the technical contents disclosed above without departing from the scope of the technical solutions of the present invention. However, for the contents not departing from the scope of the technical solutions of the present invention, any simple modifications, equivalent changes, and modifications made to the above embodiments according to the technical essence of the present invention are still included in the scope of the technical solutions of the present invention.