An inverse system for incorporation of conditioning to pressure and streamline-based calibration

A streamline-based history matching technique is employed to perform fast and efficient permeability identification and to integrate tracer data into an inverse model. To incorporate tracer data into the inverse model, a given tracer breakthrough curve is interpreted as cumulative breakthrough along independent streamlines. Permeabilities are modified along each streamline to match the tracer breakthrough curve. In this way, there is no explicit computation of sensitivity coefficients, nor any matrix inversion. However, this approach is incomplete by itself. Since the modifications occur along the streamlines, the identified permeability distribution is often incompatible with the actual permeability distribution. Thus, streamlines should be positioned correctly before the streamline-based method is applied. To accomplish this, geostatistical methods such as kriging and sequential Gaussian simulation (SGS) are implemented to provide an appropriate disposition of streamlines at the beginning of the inverse process. Then, permeabilities are iteratively calibrated in a conventional grid system to satisfy pressure and permeability observation data, and simultaneously modified along streamlines to match tracer data. The two independent optimization processes assist mutually and lead to stable convergence to a minimum. By applying the proposed inverse system to synthetic reference fields, it is observed that identified fields satisfactorily reproduce the permeability distribution of the reference fields. In addition, the pressure distributions of the identified and the reference fields are fairly alike, and the identified tracer breakthrough curves are well fitted to those of the reference fields. With regard to spatial patterns of transport behaviors, the streamlines of the identified fields show similar trajectories to those of the reference fields, and the time of flight distributions of the inversed fields are also analogous to those of the reference fields. The proposed inverse system is capable of estimating the future performance of a two-dimensional aquifer from a constrained number of permeability and pressure observation data accompanied by tracer data.