Summary
Current downhole measuring technologies have provided a means of acquiring downhole measurements of pressure, temperature, and sometimes flow-rate data. Jointly interpreting all three measurements provides a way to overcome data limitations that are associated with interpreting only two measurements—pressure and flow-rate data—as is currently done in pressure-transient analysis. This work shows how temperature measurements can be used to improve estimations in situations where lack of sufficient pressure or flow-rate data makes parameter estimation difficult or impossible.
The model that describes the temperature distribution in the reservoir lends itself to quasilinear approximations. This makes the model a candidate for Bayesian inversion. The model that describes the pressure distribution for a multirate flow system is also linear and a candidate for Bayesian inversion. These two conditions were exploited in this work to present a way to cointerpret pressure and temperature signals from a reservoir.
Specifically, the Bayesian methods were applied to the deconvolution of both pressure and temperature measurements. The deconvolution of the temperature measurements yielded a vector that is linearly related to the average flow-rate from the reservoir and, hence, could be used for flow-rate estimation, especially in situations in which flow-rate measurements are unavailable or unreliable. This flow rate was shown to be sufficient for a first estimation of the pressure kernel in the pressure-deconvolution problem.
When the appropriate regularization parameters are chosen, the Bayesian methods can be used to suppress fluctuations and noise in measurements while maintaining sufficient resolution of the estimates. This is the point of the application of the method to data denoising. In addition, because Bayesian statistics represent a state of knowledge, it is easier to incorporate certain information, such as breakpoints, that may help improve the structure of the estimates. The methods also lend themselves to formulations that make possible the estimation of initial properties, such as initial pressures.
Deconvolution problem of deeply virtual Compton scattering