Well Design Using a Computer Model
- Mohamed Wael Helmy (Texas A&M U.) | Fouad Khalaf (Cairo U.) | T.A. Darwish (Cairo U.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- March 1998
- Document Type
- Journal Paper
- 42 - 46
- 1998. Society of Petroleum Engineers
- 1.11.2 Drilling Fluid Selection and Formulation (Chemistry, Properties), 4.6 Natural Gas, 2.4.3 Sand/Solids Control, 1.2.2 Drilling Optimisation, 4.1.5 Processing Equipment, 1.6.6 Directional Drilling, 1.6 Drilling Operations, 1.10 Drilling Equipment, 4.1.2 Separation and Treating, 1.6.3 Drilling Optimisation
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In this study, the theory of nonlinear optimization is used to develop a well-design computer model to determine the optimum directional parameters to minimize drilling depth and reduce drilling costs. The model uses the sequential unconstrained minimization technique (SUMT) to minimize drilling-depth objective function. Also, the model is used to calculate well surveys, simulate bit walk, and determine optimum lead angle to kick a well off. The minimum drilling depth is achieved at the minimum values for kickoff point, inclination, and angle-buildup and -dropoff rates. These minimum parameters reduce the dogleg severity, which, in turn, reduces the chances for operational problems like high torque and drag. The computer model has been validated by comparing a conventional design and an optimized design for a well drilled in the Gulf of Suez. The optimization model produced less drilling depth and lower inclination and dogleg severity.
For years, directional well design has been based mainly on the following conventional trial-and-error approach (for a semi-S well, as an example).1.
Assume kickoff and dropoff depths.2.
Assume angle-buildup and -dropoff rates.3.
Assume inclination (after buildup and after dropoff).4.
Check to see if well trajectory is feasible.5.
If trajectory is not feasible, adjust assumptions.6.
Repeat until a satisfactory design is achieved.
Well designs based on this approach are subject to the engineer's experience, judgment, and intuition. Although the method is still considered effective, the selected well design may not be the best one technically and/or economically. (Selection criteria may be lower dogleg or lower angle to reduce operational problems, or less drilling depth to reduce cost.) In this conventional approach, there might be a design that has not been considered that would better satisfy the selection criteria and further reduce drilling costs. The whole process is time consuming and inefficient because many alternatives must be formulated and studied with no assurance that the final design is the best (optimum) one.
The optimization theory provides a more efficient approach for making decisions among different designs. In this approach, an intelligent search is conducted among feasible designs to reach the best, most practical design that satisfies the selection criteria within the design constraints.1-3
This study involves the application of the optimization theory to the directional-well-design problem. The objective is to develop a computational method to optimize the directional well-design parameters (kickoff depth, angle-buildup and -dropoff rates, and inclination) to minimize the drilling depth, thereby reducing drilling cost (with all other drilling parameters constant, e.g., mud properties, hydraulics, etc.).
The problem is mathematically formulated with an objective function describing the well trajectory in terms of the design parameters and constraints that are placed to satisfy specific design requirements (casing-setting depths, maximum inclination, etc).
A computer program is developed (incorporating the SUMT algorithm) to determine the optimum well-design parameters. The optimization process can assure a solution as close to the optimum as is practically possible. The method is less time consuming and more efficient when compared to the conventional trial-and-error approach.
Generally, applications of the optimization theory in the different aspects of oilwell drilling have been limited4 because most of the drilling parameters (e.g., influence of mud or solids content) cannot be easily quantified and formulated into mathematical optimization models describing the drilling process.
So far, drilling optimization has been achieved through on-line control; a number of input data are derived from wells drilled in the vicinity of the new well to be optimized, then the derived data are analyzed and the apparent optimum parameters are used for the new well. To the best of the authors' knowledge, none of the previous research work has rigorously addressed the mathematical optimization of directional-well design.
However, applications of the optimization theory in other areas of the oil industry have been significant. Applications in production and reservoir engineering, and field development, have been published.
The directional-well-design optimization problem is stated as follows (refer to Fig. 1). Given the coordinates of the surface and target locations of a well, determine the following optimum directional well parameters so as to minimize the total drilling depth within practical operational constraints.
Kick-off depth, Dk, ft
Rate of building angle, qbr,°/100 ft
First hold angle, q1°
Rate of dropping angle, qd,°/100 ft
Second hold angle, q2°
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