Revisiting approximate analytical solutions of estimating low permeability using the gas transient transmission test

The approximate analytical solution, which is a shortened version of the complete analytical solution, serves as a fast approach of calculating low permeability using the measured parameters during the gas transient transmission in pulse-decay experiments. However, there are several practical issues that need to be clarified for better implementations of the approximate analytical solution in routine pulse-decay experiments. These issues include whether the equilibrium pressure or the mean value of the initial upstream and downstream pressure should be applied in the formula of estimating permeability and how valid the analytical solutions is in estimating permeability when the upstream and downstream reservoir volumes are small, etc. In this work, we set up the numerical model as a benchmark to evaluate the accuracy of two widely used approximate analytical solutions. In terms of accuracy, we found that Dicker and Smits' solution is superior to the Brace et al.'s solution and quantified the difference for the first time. Our findings recommend the usage of equilibrium pressure after the pulse-decay experiment instead of the mean value between the initial upstream and initial downstream pressure in the final formula of calculating permeability. Otherwise, the percentage error increases as the pulse size increase. Dicker and Smits' analytical solution fails when the pore volume of the core is larger than the upstream reservoir volume and the downstream reservoir volume. We put forward a modified version of the analytical solution, which can be readily adopted by the readers in their measurements, to overcome this failure. The inapplicability of solution by Dicker and Smits when pore volume is large is resolved with our proposed analytical solution which significantly extends the capacity of the analytical approach and is validated numerically and experimentally.