Drilling and Production-Equipment, Methods and Materials - Relative Productivity of Perforated Casing-II.

The effect of depth of formation penetration by casing perforations has been studied by means of an electrolytic model. It is found that the relative productivity of perforated casing is profoundly affected by the depth to which the formation is penetrated. The first in. of penetration i: of especial importance. A scaling equation which was shown to agree with experimental results at zero penetration is used to calculate the relative productivity of a waled down casing with scaled down perforations. INTRODUCTION In an earlier piper' the authors showed that the point sink representation of casing perforations is inade- quate. It was Pointed out at that time that while the electrolytic model results were a marked improvement over point-sink calculations, they still left a great deal to be desired in that the electrolytic model represented a case not realizable in practice, namely, a clean hole through the casing but undisturbed formation on the other side of the casing. Obviously, to be effective, the perforation must penetrate a finite distance into the producing formation. It was the purpose of the present investigation to find how the relative productivity of perforated casing varies with depth of penetration. The term "depth of penetration" as used in this paper refers to the distance which the perforation penetrates the producing formation. The amount of casing and cement penetrated is not taken into account, a fact which is discussed more fully later. The "casing radius," therefore, is to be interpreted as the radius of the boundary between cement and formation wall. in cases where the casing is not in contact with the formation wall. APPARATUS The electrolytic model experimental setup was identical with that described in the previous paper' except that the platinum electrodes were now allowed to project from the lucite cylinder by varying amounts. When fewer than eight electrodes were used, the unused ones were covered with a coat of insulating material to minimize disturbances to the current flow-lines. Comparison runs made with the unused electrodes uninsulated, however, showed that the values of Q/Q0 so obtained did not vary by more than the experimental error from the values obtained with the unused electrodes insulated RESULTS The variation of relative productivity* with perforation density is shown for various penetration depths from 0 to 4.03 in. in Fig. 1. It will be seen that even one in. of penetration into the formation results in a huge increase in the relative productivity. Moreover, as-the depth of penetration increases, it becomes less and less advantageous to use large perforation densities, 80 pel. cent of open hole productivity being obtained with only three 0.5-in. diameter holes per foot when the penetration is 4.03 in.