Data processing: structural design – modeling – simulation – and em – Simulating nonelectrical device or system – Fluid
Reexamination Certificate
1999-09-21
2003-04-15
Frejd, Russell (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Simulating nonelectrical device or system
Fluid
C703S002000, C702S011000
Reexamination Certificate
active
06549879
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to methods for minimizing the costs of extracting petroleum from underground reservoirs. More specifically, the present invention relates to determining optimal well placement from a three-dimensional model of an underground reservoir.
2. Description of the Related Art
A critical function of reservoir management teams is the generation of a reservoir development plan with a selection of a set of well drilling sites and completion locations that maximizes productivity. Generation of the plan generally begins with a set of reservoir property maps and a set of infrastructure constraints. The team typically includes geologists, geophysicists, and engineers who choose well locations using reservoir models. The wells are located to optimize some desired property of the reservoir that is related to hydrocarbon productivity. In the early development of a field, these models might consist of porosity or lithology maps based primarily on seismic interpretations tied to a few appraisal wells. Once given the model, the team is often asked to quickly propose a set of locations that maximize production. Complicating this endeavor is the requirement that the selected sites obey a set of constraints, e.g. minimum interwell spacing, maximum well length, minimum distance from :fluid contacts or reservoir boundaries, and well configuration constraints. The combined problem is highly combinatorial, and therefore time consuming to solve. This is especially true for reservoirs that are heterogeneous with disconnected pay zones. Practical solutions to this problem typically involve evaluating a small subset of the possible well site combinations as case studies, and then selecting those with the highest value of the desired productivity metric, e.g. net pay or permeability-thickness (represented as “quality”).
As a reservoir is developed with production wells, a more comprehensive reservoir model is built with detailed maps of stratigraphy and pay zones. Pressure distribution maps or maps of fluid saturation from history matching may also become available. Then, proposing step-out or infill wells requires the additional consideration of constraints imposed by performance of the existing wells. Thus, the choice of selecting well locations throughout the development of a reservoir can become increasingly complicated. Again, this is especially true for reservoirs that are heterogeneous with disconnected pay zones. Finding solutions to the progressively-more complex well placement problem can be a tedious, iterative task.
There have been several reported studies that have attempted to use ad hoc rules and mathematical models to determine new well locations and/or well configurations in producing fields. The following publications are hereby incorporated herein by reference:
1. Seifert, D., Lewis, J. J. M., Hern, C. Y., and Steel, N. C. T., “Well Placement Optimisation and Risking using 3-D Stochastic Reservoir Modelling Techniques”, SPE 35520, presented at the NPF/SPE Europeanf Reservoir Modelling Conference, Stavanger, April 1996.
2. P. A. Gutteridge and D. E. Gawith, “Connected Volume Calibration for Well Path Ranking”, SPE 35503, European 3D Reservoir Modelling Conference, Stavanger, Apr. 16-17, 1996.
3. Rosenwald, G. W., and Green, D. W., “
A Method for Determining the Optimum Location of Wells in a Reservoir Using Mixed
-
Integer Programming
”, SPE J., (1973).
4. Lars Kjellesvik and Geir Johansen, “
Uncertainty Analysis of Well Production Potential, Based on Streamline Simulation of Multiple Reservoir Realisations
”, EAGE/SPE Petroleum Geostatistics Symposium, Toulouse, April 1999.
5. Beckner, B. L. and Song X., “
Field Development Planning Using Simulated Annealing—Optimal Economic Well Scheduling and Placement
”, SPE 30650, Annual SPE Technical Conference and Exhibition, Dallas, Oct. 22-25, 1995.
6. Vasantharajan S. and Cullick, A. S., “
Well Site Selection Using Integer Programming Optimization
”, IAMG Annual Meeting, Barcelona, September 1997.
7. Ierapetritou, M. G., Floudas, C. A., Vasantharajan, S., and Cullick, A. S., “A Decomposition Based Approach for Optimal Location of Vertical Wells”, AICHE Journal 45, April, 1999, p. 844-859.
8. K. B. Hird and O. Dubrule, “Quantification of reservoir Connectivity for Reservoir Description Applications”, SPE 30571, 1995 SPE Annual Technical Conference and Exhibition, Formation Evaluation and Reservoir Geology, Dallas, Tex.
9. C. V. Deutsch, “Fortran Programs for Calculating Connectivity of three-dimensional numerical models and for ranking multiple realizations,” Computers & Geosciences, 24(1), p. 69-76.
10. Shuck, D. L., and Chien, C. C., “
Method for optimal placement and orientation of wells for solution mining
”, U.S. Pat. No. 4,249,776, Feb. 10, 1981.
11. Lo, T. S., and Chu, J., “
Hydorcarbon reservoior connectivity tool using cells and pay indicators
”, U.S. Pat. No. 5,757,663, Mar. 26, 1998.
Seifert et al
1
presented a method using geostatistical reservoir models. They performed an exhaustive “pin cushioning” search for a large number of candidate trajectories from specified platform locations with a preset radius, inclination angle, well length, and azimuth. Each well trajectory was analyzed statistically with respect to intersected net pay or lithology. The location of candidate wells was not a variable; thus, the procedure finds a statistically local maximum and is not designed to meet multiple-well constraints.
Gutteridge and Gawith
2
used a connected volume concept to rank locations in 2D but did not describe the algorithm. They then manually iterated the location and design of wells in the 3D reservoir model. This is a “greedy” approach that does not accommodate the constraints on well locations, and the selection of well sites is done in 2D. Both this and the previous publication are ad hoc approaches to the problem.
Rosenwald and Green
3
presented an Integer Programming (IP) formulation to determine the optimum location of a small number of wells. He assumed that a specified production versus time relationship is known for the reservoir and that the potential locations for the new wells are predetermined. The algorithm then selected a specified number of wells from the candidate locations, and determined the proper sequence of rates from the wells.
Kjellesvik and Johansen
4
ranked wells' drainable volumes by use of streamlines for pre-selected sites. The streamlines provide a flow-based indicator of the drainage capability, and although streamline simulation is significantly faster than a full finite-difference simulation, the number of required operations in an optimization scheme, e.g. simulated annealing or genetic algorithm, is still O(N
2
), where N is the number of active grid cell locations in the model. The compute time is prohibitive when compared with using a static measure. Beckner and Song
5
also used flow simulation tied with a global optimization method, but they were only able to perform the optimization on very small data volumes.
Vasanthrajan and Cullick
6
presented a solution to the well site selection problem for two-dimensional (2D) reservoir maps as a computationally efficient linear, integer programming (IP) formulation, in which binary variables were used to model the potential well locations. This formulation is unsuitable for three-dimensional :data volumes. A decomposition approach was presented for larger data problems in three-dimensional (3D) maps by Ierapetritou et al
7
.
Hird and Dubrule
8
used flow simulation in 2D reservoir models to assess connectivity between two well locations. This was for relatively small models in 2D and only assesses connectivity between two specific points. C. V. Deutsch
9
presents a connectivity algorithm which approaches the problem with nested searches of growing “shells”. This algorithm is infeasibly slow.
Shuck and Chien
10
presented an ad hoc well-array placement method that selects the cell pattern of the well-array so that the cell area is customized and the major ax
Cullick Alvin S.
Dobin Mark W.
Vasantharajan Sriram
Frejd Russell
Mobil Oil Corporation
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