The traditional approach to reconciling geologic models to production data involves an "amplitude matching," that is, matching the production history directly. These include water-cut, tracer concentration, and pressure history at the wells. It is well known that such amplitude matching results in a highly nonlinear inverse problem and difficulties in convergence, often leading to an inadequate history match. The nonlinearity can also aggravate the problem of nonuniqueness and instability of the solution. Recently, production data integration by "travel-time matching" has shown great promise for practical field applications. In this approach, the observed data and model predictions are lined up at some reference time such as the breakthrough or "first arrival" time. Further extensions have included amplitude information by a "generalized travel-time" inversion. Although the benefits of travel-time inversion are well documented in the context of seismic inversion, no systematic study has been done to examine its merits for field-scale history matching.
In this paper, we quantitatively investigate the nonlinearities in the inverse problems related to travel time, generalized travel time, and amplitude matching during production data integration and their impact on the solution and its convergence. In our previous works, we speculated on the quasilinear nature of the travel-time inversion without quantifying it. Our results here show, for the first time, that the commonly used amplitude inversion can be orders of magnitude more nonlinear compared to the travel-time inversion. We also examine the resulting implications in field-scale history matching. The travel-time inversion is shown to be more robust and exhibits superior convergence characteristics. The travel-time sensitivities are more uniform between the wells compared to the amplitude sensitivities that tend to be localized near the wells. This prevents overcorrection near the wells.
We have demonstrated our results using a field application involving a multiwell, multitracer interwell tracer injection study in the McCleskey sandstone of the Ranger field, Texas. Starting with a prior geologic model, the traditional amplitude matching could not reproduce the field tracer response, which was characterized by multiple peaks. Both travel time and generalized travel time exhibited better convergence properties and could match the tracer response at the wells with realistic changes to the geologic model.