Simultaneous Interpretation of Pressure, Temperature and Flowrate Data for Improved Model Identification and Reservoir Parameter Estimation

Abstract

Abstract Permanent downhole gauges (PDGs) provide a continuous source of downhole pressure, temperature, and sometimes flowrate data. Until recently, the measured temperature data have been largely ignored. However, a fine scale observation of the temperature measurements reveals that the temperature signal is not constant but changes with changing flow conditions. This observation inspired the study of the temperature distribution in the reservoir as a possible source of additional reservoir information beyond that conventionally obtained in pressure transient analysis. As a first step to this problem, a physical model was developed for the temperature profile in flowing and shut-in reservoirs as a function of formation parameters, fluid properties, and flow conditions in space and time. A semianalytical solution scheme, Operator Splitting and Time Stepping (OSAT), was applied to the model and this gave an approximate solution in the form of a convolution integral between a convective temperature term, which depends strongly on flowrate, and a diffusive temperature term. This convolution is also quasilinear between temperature and flowrate measured at the well. The solution matched both field and synthetic data. In the second step, Bayesian inverse modeling was applied to the problem for the assimilation of pressure and temperature data. This stochastic inverse technique treats parameters as jointly distributed random fields, and yields confidence intervals in addition to best estimates of the parameters. When applied to this assimilation problem, the method allowed for the deconvolution of the pressure and temperature signals, yielding discrete forms of their kernel, which are useful in reservoir parameter estimation and flowrate reconstruction. A useful outcome of the temperature function deconvolution is the ability to generate approximate estimates of the flowrate using temperature signals only. This is a useful in the common situations where downhole flowrate information is unavailable. The Bayesian inverse method was also applied to data denoising in cases where the temperature, pressure and flowrate signals are corrupted with noise. When applied iteratively, the method yielded estimates of the signals that were very close to the true reservoir response. The Bayesian inversion framework also allows also the computation of large number of conditional realizations which are equiprobable solutions given the data and these in turn help give better understanding of the unknown function.