Computational and physical consequences of interaction of closely located simultaneous hydraulic fractures

TL;DR

This paper investigates how closely spaced hydraulic fractures interact physically and computationally, revealing that their interaction affects propagation, and proposes methods to improve numerical simulation accuracy in shale fracturing.

Contribution

It introduces a computational approach to handle ill-conditioning in simulating closely spaced hydraulic fractures and demonstrates that replacing crack clusters with single cracks improves stability.

Findings

Closely spaced fractures cause numerical instability and physical reduction in crack opening.

Replacing crack clusters with single cracks improves computational stability.

Distant individual fractures are more likely to propagate than closely spaced ones.

Abstract

Strong interaction of closely located, nearly parallel hydraulic fractures and its influence on their propagation are studied. Both computational and physical aspects of the problem are considered. It is shown that from the computational point of view, when a distance between cracks is small as compared with their sizes, the system becomes ill-conditioned and numerical results deteriorate. The physical consequence of the interaction consists in decreasing of the crack opening and even greater decrease of conductivity. Then the resistance to fluid flow grows what results in the propagation of only those fractures, the distance between which is large enough. The research aims to suggests a means to overcome the computational difficulty and to improve numerical simulation of hydraulic fractures in shales. Numerical experiments are carried out for a 2D problem by using the complex variable hypersingular boundary element method of higher order accuracy. The condition number of the main matrix of a system, the opening of cracks, the stress intensity factors, effective conductivity and resistance of a cluster are calculated and analysed. The results imply that to avoid computational instability, it is possible to replace a cluster of cracks by a single properly located crack. The results also evidently confirm that the propagation of distant individual fractures rather than of an array of closely located cracks is to be expected in practice, what agrees with observations.