Abstract The objective of Experimental Design (ED) is to develop one or more proxy equations to represent a reservoir simulator model and then use that equation for Monte Carlo (MC) simulation. A proxy equation is generally a quadratic (1) Y = a 0 + a 1 X 1 + a 2 X 2 + … + a n X n + b 1 X 1 2 + b 2 X 2 2 + … + b n X n 2 + c 1 X 1 X 2 + c 2 X 1 X 3 + … which sometimes reduces to linear with no Xi2 or XiXj terms. Here Y represents a reservoir simulator output of major interest such as expected ultimate recovery (EUR) oil or gas. The Xis are initialization parameters for the simulator. These variables are inherently uncertain, such as gas-water contact, pore volume or its components, permeabilities, or trapped gas saturation. The ultimate deliverables of ED are a probability distribution for Y and a sensitivity chart ranking the Xis. The obvious advantage of a proxy equation is that it can be executed in microseconds while the simulator requires hours or even days. The shortcoming is that a proxy equation cannot completely represent the complexities of the simulator. We propose to contrast and compare three recent Colombian ED studies, ranging from an exploration project to a mature field; from two parameters to 10; from 13 years of production history to a single well test; both linear and quadratic proxy equations, and a variety of choices for Y. Each project offered new challenges and required some departure from a traditional workflow. These mini case studies illustrate the breadth of ED and some pitfalls we encountered. Aside from the simulator and Excel, the only software packages used were generic Monte Carlo and statistical packages. Any ED project begins by identifying uncertain initialization parameters and ends with a proxy equation and its Monte Carlo simulation. What happens in between, however, depends on the particular situation. The nature of the key output(s), the number of variables, the complexity of the reservoir simulator, the challenge of any history match, and the quality of the results can vary considerably from one project to another. With a methodology relatively new to our industry, sharing the strengths and weaknesses of the process can be valuable.
Tópico:
Reservoir Engineering and Simulation Methods
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4
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FuenteLatin American and Caribbean Petroleum Engineering Conference