One of the most crucial decisions in any new oil field development project is to decide how many wells to drill. The optimal number of wells, of course, is a matter of economics. In this blog we are going to look at a quick method, based on analytical exponential theory, to answer that question by maximizing the net present value (NPV). Although the method is simple, it is surprisingly accurate, practical and useful. It has proven to provide excellent starting points in many actual studies and projects. Try it out yourself, retrospectively, on any existing oil field developments - you will likely find the answers remarkably precise. In the video at the bottom of this blog we will present the method in much more detail, and provide a graphical method to estimate the optimal number of wells. Use the chart near the bottom to estimate the optimal number of wells. All you have to do is to calculate two terms, A and B, and read the well count directly from a chart at the point specified by (A,B). Just make sure that if the NPV discount rate, r, is the yearly discount rate, then the flow rates should also be yearly flow rates (i.e. multiply daily flow rates by 365.25). Where: the ultimate volumetric recovery. The ultimate recovery is governed by the drive mechanisms, not by the number of wells. The reservoir is assumed to be connected, not compartmentalized, so a single well could in principle produce the UR. Many wells would not produce more than a single well, just faster.UR = NPV discount rate. It typically ranges from 0.05 to 0.15 and is normally set by management.r =the plateau rate.qp = the price of one volume unit (stb or Sm³) oil.Oilprice = the cost of drilling and completing one well.Costwell = The annual operating costs of one well.Opexwell = To find the optimal number of wells, calculate A and B from the formulas above (also shown in the axis titles on the chart itself). Mark the point (A, B) in the chart below and identify the number of wells by selecting the representative colored curve. Alternatively, you can find the exact number of wells by iteration, as explained in the text-box in the chart itself.The following video explains the method in greater detail. Enjoy! You can find this video and many more at our YouTube channel.
14 Comments
Mark Burgoyne
3/31/2017 04:45:55
There is an analytical solution to the number of wells;
Reply
Michael Hovdan
3/31/2017 07:41:32
Mark, you are absolutely right! :)
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Mark Burgoyne
4/3/2017 01:03:49
Hi Mike,
Michael Hovdan
4/3/2017 07:02:53
Mark, to my knowledge this is 'original' stuff. My earliest notes (without opex) date back to 2005.
Mark Burgoyne
4/5/2017 01:26:50
Hi Mike,
Mark Burgoyne
4/5/2017 02:46:31
Unless I'm mistaken, the discounted sumnation of OPEX costs for wells that came online during plateau is also missing for the period from plateau end to tabandon.
Michael Hovdan
4/5/2017 08:13:20
Mark, you are right again. The method described is just a simple approximation - which quickly gets incredibly complicated once you start adding things! - and is intended only as a starting point for more a elaborate optimization effort.
Mark Burgoyne
5/3/2017 07:24:04
One thing that you will have to watch out for is for 'optimal' solutions of well count, where nw x qi < qp. That is to say, if the plateau rate is unachievable, then the asnwer may be misleading as it assumes that the plateau rate IS achievable. I've just got a simple check on the solution to establish whether nw x qi > qp, and if not a solving macro to iteratively reduce the qp to a level where it equals the optimal nw x qi......
Mark BUrgoyne
5/3/2017 08:56:02
..In fact for those cases with no plateau, where in effect qp = qi * nw, you can reformulate the equation to be
Mark Burgoyne
5/3/2017 13:02:52
Update: My previous math was incorrect. Went back to the original NPV and redid the integrals & derivatives (substituting qp = nw * qi, and removing plateau related groups), I think the following is now correct for cases where no plateau exists;
Michael Hovdan
5/7/2017 19:04:27
Mark, you are right again. If there is no plateau restriction, then you should use the quadratic equation (nw+A)²=A²B where A is unchanged but where the occurrence of qp in B is replaced by qi. Just as you said.
Abderahmane DADA
4/2/2017 15:49:47
Hi folks. Does anyone have an idea on how to determine the number of wells for a : (*) Multi-layer reservoir (**) Fractured reservoir (conductive /non-conductive fractures)
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Michael Hovdan
4/2/2017 19:29:43
Have you tried the method described here?
Reply
Abderahmane DADA
4/3/2017 08:05:12
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