On the determination of the skin factor and the turbulence term coefficient through a single constant gas pressure test

The best correlation for evaluating the turbulence term coefficient, D(μ), for transient flow in gas wells under constant flow rate conditions is currently that of Lee et al. [Lee, R.L., Logan, R.W., Tek, M.R., 1987. Effect of turbulence on transient flow of real gas through porous media. SPE Form. Eval. (March), 108–120]. Several authors have used this correlation to calculate the production decline for wells that produce under constant bottomhole pressure conditions, but it is not clear if this is correct. When exploiting any gas reservoir, the flow rate and the average reservoir pressure decrease with time. This process makes D(μ) increase, whereas D(μ)qsc decreases with time; in contrast, when a well is produced under constant flow rate conditions, D(μ)qsc increases with time. Due to this fact, it can be of considerable practical interest to analyze the behavior of the high velocity pseudoskin factor, D(μ)qsc, for gas wells that produce under constant bottomhole pressure conditions. This paper presents the results of a study aimed at obtaining a correlation of both the mechanical skin factor, s, and the turbulence term coefficient, D(μ), for constant bottomhole pressure conditions through the analysis of a single test. Results obtained through a radial real gas flow simulator, carefully validated for pseudosteady state conditions were used as a database for the development of the new correlations. The skin effect considered varies from 0 to 10. Two different gases are considered. Other variables studied are the constant pressure, the reservoir size re/rw and formation permeability. The correlation is presented by means of straight-line fits of st/[s(1−rw/rd)] in the vertical axis and D(μi)qsc in the horizontal axis. The correlation coefficient was 0.9976. The error obtained when one evaluates the skin factor, s, using the correlation presented in this work is less than 10%. The error is substantially less when production rates are low. These rates strictly correspond to the case of low permeability reservoirs, where the constant pressure boundary condition considered is this study closely apply.