Constrained Least-Squares Multiwell Deconvolution

Abstract

In this paper, we reduce non-uniqueness and ensure physically feasible results in multiwell deconvolution by incorporating constraints and knowledge to the methodology of Cumming et al. (2014). The constraints discourage non-physical shapes for the deconvolved derivatives and improve solution quality. We also encode knowledge on the reservoir, for instance, if it is a closed system, we impose that all deconvolved derivatives should tend towards a common unit slope at some future time. Methods, Procedures, Process Single-well deconvolution (von Schroeter, Hollaender and Gringarten, 2001, 2004) transforms variable-rate pressure data from a well test, into a single constant-rate drawdown with the same duration as the pressure history. The resulting deconvolved derivative shows features not visible within the durations of any of the test build up or drawdown periods and therefore enhance analysis and interpretation. Single-well deconvolution, however, is applicable only to individual isolated wells. Multiwell deconvolution - introduced by Levitan (2006) and developed by Cumming et al. (2013) - generalises the solution methodology to the problem of multiple wells within the same connected system. Results, Observations, Conclusions Multiwell deconvolution yields not only the constant-rate deconvolved derivatives for every well in the system, but also the interference effects from any one well to any other. These interference effects provide valuable information concerning storativity and connectivity within the reservoir, which is not accessible otherwise. Multiwell deconvolution is, however, an overdetermined problem and may therefore yield non-unique solutions that can reproduce pressure histories to a similar degree of precision, but correspond to different, potentially conflicting, and possibly non-physical responses and interpretations. This non-uniqueness and the possibility of non-physical solutions need to be reduced for practical multiwell deconvolution of field data. Novel/Additive Information We demonstrate how a combination of constraints on the shapes of the deconvolved derivatives and knowledge of the reservoir results in an improved level of quality and consistency in multiwell deconvolution solutions. We illustrate this new constrained least-squares multiwell deconvolution approach with synthetic examples with known solutions involving up to nine wells.