Inversion for permeability distribution from time-lapse gravity data

Understanding reservoir properties plays a key role in managing a reservoir's resources and optimizing production. History matching is an important means for characterizing those properties. We developed a method to invert for the distribution of permeability directly from time-lapse gravity data. In this process, we used fluid flow in a porous medium coupled with forward modeling of the time-lapse gravity response as the forward operator, and then we solved a nonlinear inversion to reconstruct the permeability distribution in the reservoir. We were able to formulate the deterministic inversion as a Tikhonov regularization problem because of the relatively low computational cost of forward modeling time-lapse gravity data. The inversion can combine the information from time-lapse gravity and injection-production data sets to determine a static state of the reservoir described by the permeability. The resulting model satisfied all data sets simultaneously while obeying the mechanics of fluid flow through a porous medium. The inverse formulation also enabled the estimation of the uncertainty of the constructed permeability model with respect to the data, and our numerical simulations indicated that the information content in the two dynamic data sets appeared to be sufficiently high to constrain the recovery of permeability distribution.