Superposition in Bounded or Partially Bounded Reservoirs

Although Eq. (8.39) applies to infinite reservoirs, it may be used in conjunction with the superposition principle to simulate boundaries of closed or partially closed reservoirs. The effect of boundaries is always to cause greater pressure drops than those calculated for the infinite reservoirs. The method of images is useful in handling the effect of boundaries. For example, the pressure drop at point x (Fig. 8.19), owing to production in a well located a distance d from a sealing fault, will be the sum of the effects of the producing well and an image well that is superimposed at a distance d behind the fault. In this case, the total pressure drop is given by Eq. (8.54), where the individual pressure drops are again given by Eq. (8.39), or for the case shown in Fig. 8.19,

Figure 8.19 Method of images used in the solution of boundary problems.