Deliverablity of Natural Gas.

It has been known for some time that, using concepts of pseudo-pressure and pseudo-time, the partial differential equation describing the flow of natural gas in a Darcy regime becomes nearly linear and susceptible to analytical solution. Current practice in gas well deliverability analysis involves using the laminar solution for constant terminal rate, along with a skin factor and rate proportional turbulence term added to the pseudo-pressure drop at the wellbore. In this study, starting from Forchheimer's representation of turbulence in porous media, a simulator was developed for numerical analysis of unsteady state turbulent gas flow. A series of numerical simulations permitted a critical evaluation of present methods for predicting gas well performance including wellbore storage, skin, and turbulence effects as well as gas property variations due to pressure drop. Dimensional considerations of flow of real gas through porous media indicated that the deliverability problem could be completely described in terms of several dimensionless groups. These included dimensionless pseudo-pressure drop m(,D) as the dependent variable, a function of dimensionless radius r(,D) and dimensionless pseudo-time t(,aD) for specific values of the other dimensionless numbers. The other dimensionless groups include turbulence intensity number N(,T), dimensionless flowrate Q(,D), viscosity ratio (gamma), and pseudo-time ratio (alpha). When wellbore storage unloading effects are considered two more dimensionless numbers are shown to affect early time well deliverability. These are the wellbore storage constant C(,D) and the wellbore decay factor W(,D). Numerical calculations simulating a large number of real gas flow situations, show that the potential drop at high level turbulence intensity cannot be accurately predicted by a mere addition of a wellbore turbulence term through a constant D times Q(,sc), the terminal rate. Furthermore, this research has shown that the present methods of calculating gas well drawdown by mere addition of skin and turbulence potential drops at the wellbore will not satisfy material balance requirements throughout the drainage area. Accordingly, a new approach is suggested by modifying the turbulence factor D through a variable yet predictable correlating coefficient. Several practical applications of the new gas well performance evaluation are proposed and discussed. These include the newly defined concepts of Inverse Productivity Index and AOF plots for interpretation of gas well test data.Ph.D.Chemical engineeringEnergyUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161126/1/8621324.pd