Joint Inversion of Temperature and Pressure Measurements for Estimation of Permeability and Porosity Fields

Abstract

ABSTRACT The acquisition of temperature measurements from wells using downhole devices such as Distributed Temperature Sensors (DTS) and Permanent Downhole Gauges (PDG) is becoming a common practice in the industry. Temperature data acquired continuously at the perforation sandface show transients that may contain information about the characteristics of the producing formation, presenting an opportunity for the combination of flow and heat transport models in reservoir characterization. The physical model for temperature distribution in a reservoir during production shows a strong dependence of temperature on the porosity distribution. The dependence of this model on permeability is weakly linked to flow through convection. On the other hand, the model for flow is more strongly dependent on permeability than on porosity. These models are coupled through the dependence of the heat model on flow velocity, and the dependence of the flow model parameters on temperature. In this work, the heat and flow models were inverted jointly to obtain an estimate of the permeability and porosity fields in a synthetic reservoir, using combined quasilinear Bayesian inversion methods and Ensemble Kalman Filter (EnKF) for data assimilation. A first posterior mean and covariance of the log-permeability and porosity fields were found using the first set of data and the quasilinear inversion approach (similar to the maximum a-posteriori probability MAP estimate). The ensembles in EnKF were then obtained as conditional realizations using these statistics. The production data (bottomhole pressure and production rates) and temperature measurements were then jointly assimilated with each advancement in time, to obtain log-permeability fields that compared favorably with the true permeability fields, and porosity fields that also compared favorably with the true porosity field. Also, it was found that the inclusion of temperature measurements improved the resolution of the estimates of both porosity and log-permeability in the test cases, compared to using only production data. Particularly, the porosity fields showed marked improvement with the addition of temperature measurements. The results demonstrate that temperature measurements that are now routinely obtained in producing fields are a potential source of relevant data for constraining characterization of heterogeneous reservoirs.