GENERALIZED FORM OF INFLOW EQUATION UNDER SEMI-STEADY STATE CONDITIONS

The semi-steady state inflow equation developed in sec. 6.2 appears to be restrictive in that it only applies for a well producing from the centre of a circular shaped drainage area. When a reservoir is producing under semi-steady state conditions each well will assume its own fixed drainage boundary, as shown in fig. 5.3, and the shapes of these may be far from circular. The inflow equation will therefore require some modification to account for this lack of symmetry. Equation (6.12) can be expressed in a generalized form by introducing the so-called Dietz shape factors3 denoted by CA, which are presented for a variety of different geometrical configurations in fig. 6.4. Precisely how these shape factors were generated, in the first place, will be explained in the appropriate place, Chapter 7, sec. 6. For the moment the reader is asked to accept the following tenuous argument for the generalization of the inflow equation. Excluding the mechanical skin factor, equ. (6.12) can be expressed as

For a reservoir which is producing under semi-steady state conditions, then as already noted, the volume drained by each well is directly proportional to the well's production rate. Therefore, it is a fairly straightforward matter to estimate the volume being drained by each well and, using the average thickness in the vicinity of the well, the area. If structural contour maps are available for the reservoir, then the areas so determined can be roughly matched to the reservoir geometry to obtain a reasonable estimate of the shape of the drainage area. Fig. 6.4 should then be consulted to determine the shape factor CA which can be seen to be dependent not only on the drainage shape but also upon the position of the well with respect to the boundary. For irregular shapes, interpolation between the geometrical configurations presented by Dietz may be necessary. Naturally it is never possible to obtain the exact shape of the drainage volume but a reasonable estimate can usually be made which, when interpreted in terms of a shape factor and used in equ. (6.22), can considerably improve the accuracy of calculations made using the inflow equation. Also listed in fig. 6.4 is the dimensionless time group tDA = kt/φµcA, in which t is the time for which the well has been producing at a reasonably steady rate of production. Unless the calculated value of tDA exceeds the figure quoted for each geometrical configuration then the well is not producing under semi-steady state conditions and the Dietz shape factors cannot be used.