THE STABILIZED INFLOW EQUATIONS

The solution of the diffusivity equation under semi-steady state flow conditions has been described in detail in section 6.2 since the mathematical approach is quite general and can be applied to more complex radial flow problems. Consider, for instance, the case of a well which has been stimulated by steam soaking, refer Chapter 4, sec. 7. In this type of stimulation several thousand tons of steam are injected into the well and, upon re-opening, the well will produce at a greatly increased rate. As a first approximation it will be assumed that, due to the steam injection, the temperature distribution can be described by a temperature step function1 so that, for rw < r < rh, the temperature Ts is uniform and initially equal to the condensing steam temperature at the sandface. During production, Ts will decrease due to heat losses by conduction and convection. For r > rh, the temperature is the original reservoir temperature Tr. The situation at any time during the production cycle is shown in fig. 6.2,

This PI improvement is probably pessimistic since it has been assumed that steady state conditions prevail from the start of production. In fact, transient flow is more likely during the initial stage which will give an early boost to production, in excess of that calculated from steady state considerations.