Pseudotime application to hydraulically fractured vertical gas wells and heterogenous gasreservoirs using the TDS technique

Contrary to liquid flow, the viscosity and compressibility of gases change substantially as pressure varies. This phenomenon has to be carefully modeled, so the gas flow equation can be adequately linearized to allow the liquid diffusivity solution to satisfy gas behavior when analyzing gas transient test data. The first solution to this problem was the introduction of the pseudopressure function that responds for variations of viscosity, density and compressibility which are combined into a single “pseudopressure” variable. Since, the dimensionless time function is also sensitive to changes in both viscosity and compressibility of gases, then, the pseudotime function was incorporated to combine these simultaneous variations into a single variable. This makes more accurate the estimation of the reservoir parameters. A recent study using the TDS technique has found little differences in estimation of permeability, wellbore storage coefficient and skin factor using either pseudotime or real time. However, the estimation of the drainage area is better determined when using pseudotime. This paper has the objective of extending the TDS technique for hydraulically fractured gas wells and heterogeneous gas formations and conducting a comparative study in the estimation of both the half-length and conductivity of a vertical fracture and the naturally fractured reservoir parameters. The new relationships were successfully tested on synthetic and actual field data. It was found better results when using the pseudotime function.