Summary
Development studies examine geologic, engineering, and economic factors to
formulate and optimize production plans. If there are many factors, these
studies are prohibitively expensive unless simulation runs are chosen
efficiently.
Experimental design and response models improve study efficiency and have
been widely applied in reservoir engineering. To approximate nonlinear oil and
gas reservoir responses, designs must consider factors at more than two
levels—not just high and low values. However, multilevel designs require many
simulations, especially if many factors are being considered. Partial factorial
and mixed designs are more efficient than full factorials, but multilevel
partial factorial designs are difficult to formulate. Alternatively, orthogonal
arrays (OAs) and nearly-orthogonal arrays (NOAs) provide the required design
properties and can handle many factors. These designs span the factor space
with fewer runs, can be manipulated easily, and are appropriate for computer
experiments.
The proposed methods were used to model a gas well with water coning. Eleven
geologic factors were varied while optimizing three engineering factors. An NOA
was specified with three levels for eight factors and four levels for the
remaining six factors. The proposed design required 36 simulations compared to
26,873,856 runs for a full factorial design. Kriged response surfaces are
compared to polynomial regression surfaces. Polynomial-response models are used
to optimize completion length, tubinghead pressure, and tubing diameter for a
partially penetrating well in a gas reservoir with uncertain properties.
OAs, Hammersley sequences (HSs), and response models offer a flexible,
efficient framework for reservoir simulation studies.
Complexity of Reservoir Studies
Reservoir studies require integration of geologic properties, drilling and
production strategies, and economic parameters. Integration is complex because
parameters such as permeability, gas price, and fluid saturations are
uncertain.
In exploration and production decisions, alternatives such as well
placement, artificial lift, and capital investment must be evaluated.
Development studies examine these alternatives, as well as geologic,
engineering, and economic factors to formulate and optimize production plans
(Narayanan et al. 2003). Reservoir studies may require many simulations to
evaluate the many factor effects on reservoir performance measures, such as net
present value (NPV) and breakthrough time.
Despite the exponential growth of computer memory and speed, computing
accurate sensitivities and optimizing production performance is still
expensive, to the point that it may not be feasible to consider all alternative
models. Thus, simulation runs should be chosen as efficiently as possible.
Experimental design addresses this problem statistically, and along with
response models, it has been applied in engineering science (White et al. 2001;
Peng and Gupta 2004; Peake et al. 2005; Sacks et al. 1989a) to
- Minimize computational costs by choosing a small but statistically
representative set of simulation runs for predicting responses (e.g.,
recovery)
- Decrease expected error compared with nonoptimal simulation designs (i.e.,
sets of sample points)
- Evaluate sensitivity of responses to varying factors
- Translate uncertainty in input factors to uncertainty in predicted
performance (i.e., uncertainty analysis)
- Estimate value of information to focus resources on reducing uncertainty in
factors that have the most significant effect on response uncertainty to help
optimize engineering factors.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
14 July 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
24 April 2007
- Manuscript approved:
4 May 2007
- Version of record:
20 December 2007
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