Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters
✍ Scribed by M.P. Dainton; M.H. Goldwater; N.K. Nichols
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 522 KB
- Volume
- 130
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
similar to that of [10,2] and is an extension of techniques that we have previously developed for the stochastic A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the timesteady-state reservoir flow problem and for a transient dependent, one phase, two-or three-dimensional equations of flow mass-balance model with uncertain parameters [3][4][5]. Prethrough a porous medium. The uncertainty in the solution is modliminary results obtained by this procedure have been pubelled as a probability distribution function and is computed from lished in [6,7].
given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about
The procedure generates an expansion of the mean solua deterministic solution to the system equations using a perturbation about a deterministic solution to the system equations tion to the mean of the input parameters. Hierarchical equations using a perturbation to the mean of the input parameters.
that define approximations to the mean solution at each point and A set of hierarchical equations is obtained for the terms to the field covariance of the pressure are developed and solved in the expansion of the mean at each point and for the field numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a covariance of the solution. Apart from the deterministic given development scenario. This method involves only one (albeit equation, the hierarchical equations are all linear and can complicated) solution of the equations and contrasts with the more be solved sequentially (or, to a large extent, in parallel).
usual Monte-Carlo approach where many such solutions are re-This allows a simple, efficient, numerically stable technique quired. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with to be developed for computing approximations to the mean uncertain data. ᮊ 1997 Academic Press to any order required. The method can be applied easily to other physical systems governed by linear or nonlinear partial differential equations with stochastic data.
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