Fishing Decisions Under Uncertainty
Authors: Harrison C. Glenn 
Published: December 2007

JPT Forum articles are limited to 1,500 words (including 250 per table or figure) or a maximum of two pages. Forum articles may present preliminary results or conclusions from continuing investigations or may impart general technical information that does not require publication as a full-length paper. Forum articles are subject to approval by an editorial committee. paper. Forum articles are subject to approval by an editorial committee. Letters to the editor are published as Dialog and may cover technical or nontechnical topics. SPE reserves the right to edit letters for style and content.

Summary
The drilling manager often is forced by an extended fishing operation to choose between the known costs incurred with abandonment of retrieval attempts and the unknown costs of continuing fishing operations. The successful manager makes the decision that costs the company the least money. Continuing fishing operations beyond some economic limit is failure, even if the fish is retrieved and that portion of the hole saved, because more money has been spent in the fishing attempt than would have been spent by not fishing. The strategy is to minimize losses. This analysis closely follows the theory of utility developed by von Neuman and Morgenstern.

Analysis
The decision tree (Fig. 1) shows the options available once a fish has been lost in the hole. The lower branch (I.B) leads to certain costs if fishing is not attempted. Those costs correspond to known costs C. The upper decision branch (I.A) leads to expected costs incurred if fishing is attempted. This cost is the expected cost C*, the sum of two expected costs: expected cost associated with a successful fishing operation (II.A) and expected cost associated with an unsuccessful fishing operation (II.C).
(1)
The drilling manager is faced with the following two alternatives.
Alternative I: Spend $B for certain, C.
Alternative II: Spend $A with probability p, C*,
and
Spend $C with probability 1-p,
C*
The only restriction is $A less than $B less than $C, in degrees of loss.
Let us denote U(B) as the utility function associated with Alternative I (not fishing) and let p U(A)+(1-p)U(C) be the utility function associated p U(A)+(1-p)U(C) be the utility function associated with Alternative II (expected cost of continuing fishing operations). Using the von Neuman-Morgenstern utility function nomenclature, the drilling manager is indifferent when
(2)
and ideally would want to continue fishing as long as
(3)
If the decision is made not to fish, the costs (B) that will be incurred will include the cost of the lost fish, the cost of cementing it in, the cost of sidetracking and redrilling back to the previous depth, plus rig time. Alternative I then should be fairly easily identifiable. (A) is the cost if the fish is recovered. For simplicity, let us assume this is only a function of fishing charges and fig time per day, although other factors may be considered if desired (e.g., hole reconditioning time after retrieval). Thus, a successful fishing job is the accruing cost of the daily operating expense for fig and personnel:
(4)
The worst case (C) occurs when the fishing operation is abandoned without retrieving the fish, thereby incurring fishing costs per day (A) and the cost associated with not fishing (B). (5)
This is consistent with the restriction A less than B less than C noted with Eq. 1.
JPT
P. 299