This paper describes a new method based on the analysis of non-steady state wellbore temperature distributions impacted by geothermal temperature profile, Joule-Thomson and adiabatic effects in reservoir flow to describe near wellbore parameters such as permeability distribution and to estimate flow rate distribution between producing layers.
The solution of the inverse problem with respect to parameters of near wellbore zone is based on the quantitative analysis of the transient baro-thermal effects resulting from the single-phase fluid flow from the reservoir into the wellbore. In the steady state case the reservoir thermal effect is the same as the throttling (Joule-Thomson) one. It is reduced to the adiabatic effect while the fluid is stagnant. In the general case for non-steady state flow the change of reservoir fluid temperature is a combination of frictional heating and cooling resulting from the expansion of the fluid. Non-isothermal well testing (NIT) relies on the analysis of these fluid temperature changes. The method discussed in this paper allows evaluating parameters of near wellbore region (permeability and radius of damaged zone) and could be complimentary to the conventional well testing practices for a single-layer reservoir and to estimate flow rate distribution among the pay zones in a multi-layer case (zonal allocation). The paper develops mathematical models and presents the results of numerical simulation for transient processes after the start of the production phase and during well test operations including multi-rate testing.
Limited to the particular cases of unsteady processes after specific wellbore operations (changes of production regimes and shut-ins), the transient analytical solutions assume that the fluid may be considered incompressible and that no conductive heat transfer occurs. In order to take into account compressibility and thermal conductivity, detailed numerical modeling has been performed. The paper compares the numerical results to experimental data and shows that the fluid heat capacity in wellbore perforated zone must be considered for appropriate interpretation of initial bottomhole temperature change versus time, in particular for small rates. Based on the analysis of the simulation results, an inverse model solution for the estimation of the near wellbore zone parameters from reservoir fluid temperature and wellbore pressure transients is proposed. The method comprises first-order estimation from analytical solution and their further numerical refinements by non-linear regression for the system "reservoir-wellbore". Example of interpretation of non-isothermal well testing field data is presented demonstrating the usefulness of this new methodology.