Predicting and monitoring long-term compaction in unconsolidated reservoir sands using a dual power law model

Abstract

We propose a model for predicting the long-term creep compaction of unconsolidated sand reservoirs prior to significant depletion. The model is based upon linear viscoelasticity theory, whereby deformation is decoupled into instantaneous and time-dependent components. The instantaneous component of deformation is modeled using a power law function of effective pressure. Model parameters are solved by conducting a constant strain-rate laboratory experiment. The time-dependent deformation is modeled using a power law function of time. Associated model parameters are solved by conducting a creep-strain test at the anticipated in-situ effective pressure. In total, application of the model involves measurement of three model parameters obtained by conducting two different laboratory experiments. We illustrate the model utilizing samples from unconsolidated sand reservoirs in the Wilmington field in California and an offshore field in the Gulf of Mexico. We show that the stiffness change associated with the porosity reduction predicted by the model is large and could be monitored using P-wave velocity. This should make compaction observable with 4D seismic surveys of the example fields.