Sensitivity analysis of Gassmann's fluid substitution equations: Some implications in feasibility studies of time-lapse seismic reservoir monitoring

Abstract

Here, we discuss the sensitivity of the seismic response to uncertainties in the physical parameters of the reservoir rock. For this purpose, a probabilistic sensitivity analysis of Gassmann's fluid substitution equations using a Monte Carlo approach was carried out. We represented uncertainties related to each parameter as probability density functions to evaluate the contribution of each parameter uncertainty to the variance of the seismic response ( V p), calculated by means of the Monte Carlo approach. We show that uncertainties related to grain density ( ρ gr), dry shear modulus ( G d) and dry bulk modulus ( K d) contribute more significantly on the variance of V p, if all parameters are uncorrelated. This outcome changes, when physical dependencies are represented as correlations in the Monte Carlo sampling of some of the parameters. In this sense, correlations distribute more evenly the contributions to uncertainty in V p. On the other hand, we also evaluated scenarios of fluid substitution, in which fluid 1 is replaced by fluid 2, with the corresponding variations in seismic response. In this case, V p2 is the P-wave velocity of rock saturated with a fluid 2. If V p2 were forecasted from an initial set of parameters of the rock saturated with fluid 1 ( V p1, V s1, etc.) the uncertainties related to V p1, V s1 and K gr would contribute more significantly to the variance of V p2. From these three initial parameters, the most important contributions come form V p1 and V s1. Concomitantly, we evaluated the contribution of possible variations in fluid phase density and bulk modulus and of a pore pressure perturbation (4MPa) for several scenarios of connate and injection fluids on the variance of V p. We did this for several values of initial differential pressure. Results indicate that the contribution of the elastic piezosensitivity and possible changes in the fluid phase properties depend not only on the initial differential pressure, but also on the type of fluids involved in substitution process. We conclude that sensitivity information, limited in this case to Gassman's equations, can be used as a tool to improve feasibility studies in time-lapse seismic reservoir monitoring and as a priori qualitative knowledge. The latter can guide the inversion process or help to diminish the uncertainties due to poorly constrained inversion schemes.