Multipole moment decomposition for imaging hydraulic fractures from remote elastostatic data

B Lecampion, A Peirce
2007 Inverse Problems  
Hydraulic fracturing involves the propagation of a fracture in brittle rock by the intrusion of a high pressure viscous fluid. There is considerable interest in identifying characteristics of these evolving underground fractures via the passive monitoring of remote elastostatic deformations. In this paper, we present a far-field multipole expansion procedure to identify the harmonic moments of the fracture. The harmonic moments are related to fundamental quantities such as fracture volume and
more » ... acture asymmetries. We illustrate the efficacy of the multipole moment expansion technique by inverting synthetic displacement data from a hydraulic fracture simulator in order to identify the harmonic moments up to second order. These results are compared to those obtained by identifying the parameters of a dislocation model with a prescribed geometry-a procedure which is commonly used for such problems. The multipole moment expansion technique has the following features: it provides significantly more accurate fracture volume information; it provides accurate estimates of first-order moments that can be used to identify asymmetric fractures; it is possible to adapt the truncation process to optimize the information content of a given set of measurements; it can, in some cases, provide estimates of the higher order moments which can be used to determine geometric attributes of the fracture. Given this last feature, we explore the possibility of using up to second-order harmonic moments to identify the dimensions of a simple polygonal model of the fracture footprint. This procedure is tested by attempting to identify fracture footprints from synthesized hydraulic fracture data.
doi:10.1088/0266-5611/23/4/016 fatcat:77vncmvnszczph5dxngkg45ssq