Transition to Pseudosteady State from Infinite Acting Behavior

Earlougher (1977) indicated that the time, t_pss, at which pseudosteady state begins is given by

where A is the drainage area and t_DA has a characteristic value that depends on the drainage shape. For a regular shape such as a circle or a square, the dimensionless time at the onset of pseudosteady state, t_DApss, is equal to 0.1. For a well in a 1 × 2 rectangle, t_DApss is equal to 0.3; and for a 1 × 4 rectangle, it is equal to 0.8. Off-centered wells in irregular patterns have even larger values of t_DApss, implying that the well will “feel” the farther-off boundaries after a significantly longer time.

If the drainage area can be approximated by a circle with an equivalent drainage radius r_e, then Equation (2-41) (with t_DApss = 0.1) yields

at the onset of pseudosteady state. The time t_pss is in hours, and all other variables are in the customary oilfield units.