Numerical modeling of crack reorientation and link-up

Advances in Engineering Software 33 (2002) 577–587 www.elsevier.com/locate/advengsoft

Numerical modeling of crack reorientation and link-up
C.Y. Dong*, C.J. de Pater
Department of Applied Earth Sciences, Delft University of Technology, Delft, The Netherlands Received 17 October 2000; accepted 1 July 2002

Abstract The FRANC3D/BES software system has been used to simulate the reorientationand link-up of hydraulic fractures in three-dimensional (3D) problems. The adopted technique only needs to discretize the body surface and the crack surface. The crack propagation direction is determined using the minimum strain energy criterion. Crack propagation amount is calculated using the mode I stress intensity factor. In hydraulic fracturing, the number of multiple cracks for a givennumber of perforations depends on the resulting interaction of the cracks. The interaction may be expressed by the fracture stiffness which has been obtained for 3D problems in this paper. q 2002 Civil-Comp Ltd and Elsevier Science Ltd. All rights reserved.
Keywords: Multiple cracks; FRANC3D/BES; Crack propagation

1. Introduction Many researchers are working in the field of hydraulic fracturingwhich plays an important role in improving production from oil and gas wells drilled in relatively impermeable formation. Reviews of hydraulic fracturing can be found in Refs. [4,12,13,17]. The technique of hydraulic fracturing uses the pressure of fluid from the wellbore to produce a fracturing path through which hydrocarbon flows into the well from low permeability formation [8]. Hydraulic fracturinginitiation occurs at the location of high stress concentration such as perforations, natural cracks and so on. We consider fracture initiation from a cased wellbore, with a number of perforations that allow for fluid communication between the steel casing and the formation. The perforations are shot with explosives that create holes of some 0.02 m diameter and a length of about 0.5 m. Fig. 1 showsthe geometry of a typical perforated wellbore [7]. Crack reorientation and multiple cracks near the wellbore hinder the flow of fluid from hydrocarbon reservoirs. The crack passage depends on the in situ stresses, the orientation of the well and the pressure in the wellbore [19]. Though there is crack
* Corresponding author. Present address: Department of Civil Engineering, The University of HongKong, Pokfulam Road, Hong Kong, People’s Republic of China. E-mail address: cdong@hkucc.hku.hk (C.Y. Dong).

tortuosity near wellbore, the crack path far from the wellbore approaches the direction in which the crack propagation is perpendicular to the minimum in situ horizontal stress. To maintain good communication between wellbore and crack, the crack path should gradually reorient to thepreferred crack plane. A near-wellbore region exists with multiple cracks [11, 16,19,20] which may cause proppant entry problems [14]. In order to reduce the number of multiple cracks, very small perforated intervals should be adopted. But this might also reduce the fluid flow to the well, since the hydrocarbon flow would converge to a very small interval. For a given number of perforations, the number ofmultiple cracks depends on the resulting interaction of the cracks. This kind of interaction can be determined by an effective fracture stiffness which may be considered as a relation between the net pressure and the average width of the multiple crack system. The effective stiffness has been computed for a twodimensional (2D) crack system [20], but the fracture stiffness is unknown for athree-dimensional (3D) case. Therefore, we decided to study the crack interaction in 3D case, starting with idealized systems of a few parallel cracks. In this paper, we use FRANC3D/BES software system, which has been developed by the Structural Engineering Department of Cornell University, to simulate the crack reorientation and link-up in 3D problems [19]. The basic

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