Fracture characteristics from well flowrate fluctuations: a statistical physics approach

Previous studies have indicated that fluctuations in flowrates from or into wells over the detailed production history of a mature oilfield are approximate proxies for geomechanical strain changes. Inter-well temporal correlations in the flowrate fluctuations were found to be statistically significant over long distances between wells, raising the possibility that field structure can be analysed with a process analogous to tomography. This paper expounds a theory for the extraction of fracture characteristics from the inter-well correlations of flowrate "noise". I use the maximum information entropy principle of Jaynes, with a constraint of fixed rate of energy input to the reservoir, balanced with either dissipation by Darcy flow or fluctuation in rock strain energy, to make the case for the reservoir system being in a state of maximum entropy production rate or flux. Fluctuating departures from this state allow a simple relationship between the covariances of flowrate fluctuations across all pairs of wells and a matrix of parameters including non-local stiffness tensors, from which estimates of local stress interactions are derived. Best fit fracture densities and orientations are then extracted at each well using the theoretical orientational distribution of the tensile stress field around a given extensional fracture. The novel method is seen as complementary to more conventional fracture characterisation exercises, providing information at low cost from the all-important inter-well regions. Its several assumptions imply that it can only be verified by comparison of its predictions with multiple sets of independent field data: early results are encouraging.