A numerical simulation of an unsteady state gas permeameter has been developed which takes into account non-ideal gas and thermodynamic (non-isothermal) effects. It is shown that these effects have a profound influence on the pressure response of the apparatus. Although some Influences may be designed out, important effects associated with rock/gas interacting cannot be modified. These influences should be taken into account when analysing the data.
In a previous paper1, the performance of an unsteady state gas permeameter was modelled by means of a one dimensional numerical simulation. The model was used to analyse the influence of both slippage and inertial effects on the response of the instrument. The response of the instrument was then examined in the context of experimental errors and it was shown that, for certain permeability ranges, it is difficult, if not impossible, to measure Klinkenberg and/or Forchheimer coefficients. It was recommended that these parameters not be accepted as valid unless the Klinkenberg or Reynolds number respectively was greater than 0.1.
The model on which the previous paper was baaed contained these simplifying assumptions:
The gas is ideal
There are no thermodynamic effects associated with the decompression, that is, it is isothermal.
There are no heat transfer effects. (this Follows from 2)
The current paper presents the results obtained from an extended numerical model which removes these three assumptions. With these three assumptions negated, the approximate method proposed by Jones2 is no longer formally valid. However, this does not mean that the approximate method necessarily gives erroneous results. For this reason the approximate method' will be reconsidered in light of the new model.
In the past, many approximate analytical solutions besides that of Jones has been presented for this problem. One of these (Hsieh et a13) has often been referred to as an exact solution. It is not, however, exact since it solves a linearized version of the governing equation. For isothermal, Darcy flow, the equation solved in the approximate solutions, including that of Hsieh, is of the form:
Equations 1 (available in full paper) while the equation solved numerically in the present paper is of the form:
Equations 2 (available in full paper)
The parameters a and a are constants. To the authors' knowledge, no exact solution exists to Equation 2.
In the original numerical model, the pressure (P), temperature (T) and density (P) were assumed to be related by the ideal gas law: that is,
Equations 3 (available in full paper) where R is the ideal gas constant for the particular gas used. In the present, revised model, the gas is assumed to obey the Benedict-Webb-Rubin (BWR) equation:
Equations 4 (available in full paper)
Neglecting the influence of slippage and inertia, results for the pressure decline vary with the parameter tk (time multiplied by permeability), regardless of permeability (see reference 1).
