Message-ID: <1788604962.266.1586094508648.JavaMail.zibwiki@www03.zib.de> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_265_975706714.1586094508647" ------=_Part_265_975706714.1586094508647 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Optimum well placement

# Optimum well placement

### Mathematical models

Optimum well placement (determining optimum number, type and siting of w= ells) is a crucial step in field development

Automatic well placement optimization is an iterative procedure tha= t can be divided into following procedures:

1. Using engineering judgment, guess initial well(s) location
2. Use an optimization engine based on user-defined decision variable= s to suggest possible improved well location(s).
3. Apply a reservoir response model to report to the optimization eng= ine the performance of the proposed well locations.
4. Include the effect of uncertainty in reservoir properties, economi= c factors, etc, which can be an optional step.
5. Calculate the objective function (e.g. Net Present Value or NPV).=
6. Repeat steps 2 to 5 until stopping criteria (set by user) are met= .

The approaches to problems 1 to 5, may differ in the optimization a= lgorithm, reservoir response modeling technique, and available decisio= n variables and constraints. We now turn our focues to the modelling aspect= of the problem

### Model= ing and algorithmic considerations:

Concentrating our attention to the optimization problem after the i= nitial guess (problem n. 2), the well placement problem is translated into = optimization of an objective function (NPV or cumulative hydrocarbon produc= tion). Applying MILP models one can for instance, solves this problem throu= gh finding locations of a given number of wells (out of total possible well= locations) that minimizes the difference between the production and schedu= led demand. Hence, the drilling decision can only be made at particular loc= ations i which have to be identified beforehand (guess problem n. 1). The m= ost complex constraints come from the interaction between withdrawal rates = and pressures at all the wells, that must be defined by the nonlinear gas f= low equation. However this nonlinear constraint has a very good linearizati= on substitute, called influence equations. In these equations, the pressure= drop at well i is a linear function of withdrawal flow rates from all dril= led wells. This is defined by influence function matrices. After this prope= r linearization, the resulting problem is a mixed integer programming = problem, which can be solved by well known techniques.

Contributor:

Dr Fabrizio Lacalandra, QuanTek

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