The introduction of the notion of pseudo-pressures allows rigorous, analytical solutions to a wide range of gas flow problems. However, in order to apply pseudo-pressure based solution techniques a number of cumbersome procedures are invoked to take reservoir pressures and convert them into pseudo-pressures. These include dimensionless cahier look up, numerical integration and regression analysis. To then convert the corresponding pseudo-pressures back to their analogous reservoir pressures, graphical and/or regression techniques need to be employed.
This paper, then, examines the use of a semi-analytical approach to real gas pseudo-pressure/pressure conversion and calculations and its application to well test analysis. The semi-analytical approach to real gas pseudo-pressures allows a simple, direct and exact solution for converting pseudo-pressure to pressure and vice versa, No numerical integration, graphical or regression techniques are needed and the approach is well-suited for desktop or minicomputers. It is applicable to a wide range of reservoir pressure up to 10,000 psia and reservoir temperatures up to 460 °C.
Well test analysis have then been carried out on a number of published buildup, drawdown and deliverability tests using the semi-analytical approach. Comparison have been test interpretation results using traditional pseudo-pressure calculations and analyses from the semi-analytical approach.
By combining mass and momentum balances the flow of a real gas in porous media can be modeled using the following fundamental non-linear, second-order partial differential equation:<Equation Available In Full Paper>
This particular form of the equation assume flow is isothermal, laminar and single-phase through a horizontal, homogeneous, porous media. Early on, only complex numerical solutions to equation 1 were possible gradients (V2p=0) is assumed to be constant.
A chance of variable, allowing more rigorous, analytical solutions to the gas flow equation without the limiting assumptions made above, was developed by Al-Hussain. In their 1996 paper they introduced the potion of real gas pseudo-pressure, a(p), when: Equation (Available in full paper)
This, in effect, allowed the variation of pressure dependent gas viscosity and super compressibility to be accommodated in analytical solutions of equation 1. That is, the assumption of constant gas viscosity or product, etc, were no longer needed for simple yet precise solution of pressure, time and space in real gas flow problems.
If reservoir permeability is assumed to be independent of pressure and the definition of real gas pseudo-pressure is introduced into equation 1, a partially linearized flow equation for real gases can be obtained as follows:
This equation has proven quite useful in providing closed form solutions for transience flow test and deliverability analysis. However, applications of equation for well test purposes require that pressure data be translated into real gas pseudo-pressure form.
To date, three techniques have been presented that convert reservoir pressure to real gas pseudo-pressure. These included:
(i) numerical integration,
(ii) cable look up and interpolation, and
(iii) curve fit approximations.
This paper will examine briefly these existing methods of determining m(p) as a function of pressure and introduces a semi-analytical approach to the m(p)-p relationship.