Transient Gas Flow Through Finite Linear Porous Media
Authors: Dranchuk P. M. , Chwyl E. 
Published: March 2010

ABSTRACT
Five years of performance history are reviewed and compared with a newprediction that utilized a statistical zoning technique for layering thereservoir and a division of the pattern into octants to better simulate theareal variation of reservoir properties and withdrawals.
Some distortion of the flood front which has been observed to date is shownto be due to variations in reservoir properties and withdrawals. Theperformance also indicates a varying degree of communication between the highlypermeable conglomerate and the sand in which most of the wells are perforated.Predicted and actual break-through times generally do agree and the floodperformance is satisfactory following that predicted to date.

GENERAL
THE LOBSTICK CARDIUM UNIT is located along the northern (edge of the Pembina Cardium Field, roughly 80 miles west of Edmonton (Figure 1). The Cardiumformation in this portion of the Pembina Field is characterized by aconglomerate bar overlying the sand. The conglomerate exhibits permeabilitiesup to the range of 1 darcy or more, with the sand permeabilities averagingabout 100 times lower. The wells in this area exhibit high production rates dueto this high capacity. Upon unitization, two projects were formed within the Unit - a pattern waterflood which covered 12,560 acres and an interior miscibleflood covering 2,240 acres. The miscible flood is supported by one centralinjector and 36 offsetting producers, as shown in Figure 2. This patternwas selected because the high injection capacity permitted one injector replace voidage for theentire project and because the radial pattern would permit an efficient sweepby the miscible flood.
The solvent bank was formed by injecting alternate slugs of LPG (largelypropane) and a dry, lean-gas in a 1:1 mole ratio. The bank contains 44 per centmethane and 46 percent propane. The buffer gas is of normal sales gascomposition (89 percent methane).
the effects of molecular streamingarid inertial forces on the transient response were examined individually, theauthors are unaware of any previous attempt at considering both effectssimultaneously. It appears that, as in the steady-flow case, it has beenassumed that for all practical purposes these effects are mutually exclusive.That is, it was assumed that in the case of reservoir flow the mean pressurewas invariably large enough so that molecular streaming could be neglected andthat in the laboratory, flow was such that inertial effects were not important.Furthermore, the authors are unaware of any serious attempt at establishing thevalidity of either assumption. This is not to say that comparisons betweenpredicted and observed behavior have not been made; they have. However, discrepancies between the two were invariably attributed to poor experimentalequipment or technology, inhomogeniety, inability to accurately estimatereservoir properties or other similar reasons. On the basis of theseobservations and as part of a long-term research project regarding gas flowthrough porous media, it was decided to examine the transient response.
The plan consisted of initiating a number of small projects which wouldobserve transient flow in both linear and radial systems of known properties, predict transient response using mathematical models which accounted forviscous forces, inertial forces, molecular streaming and combinations thereof, and compare predicted and observed behavior in order to ascertain the range ofapplicability of the various models. The object of this paper is to present theresults of but one of these small projects; namely, the development of amathematical model capable of describing transient gas flow through porousmedia under conditions in which viscous, inertial and molecular streamingeffects are simultaneously operative.