Download PDF by Toshiyuki Anraku: Discrimination Between Reservoir Models in Well Test

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34) where the integral is taken over all possible range of 6 ( m dimensions), and where Prob(y) is regarded as the expectation value of Prob(yl6) with respect to the probability distribution Prob(0). The quantity Prob(y) may be regarded as merely a C H A P T E R 3. CONFIDENCE INTERVALS 42 normalizing constant necessary to ensure that the posterior probability distribution Prob(B ly) integrates to one. Prob(8), which expresses what is known about 8 without knowledge of the data, is called the prior probability distribution of 8.

Discontinuity radius for a two-region reservoir ( R ) 4. Skin effect at the discontinuity (Sf) Ambastha (1988) presented the pressure derivative behavior of a well in a two+ region radial composite reservoir model at a constant flow rate. Ambastha (1988) also presented the pressure derivative behavior of a well in a three-region radial composite reservoir model at a constant flow rate. Extension from a composite reservoir model with two regions to that with more than two regions was straightforward by adding the corresponding parameters.

In the Gauss method, the second derivatives -are regarded as if they were zero. This is usually a good approximation at a minimum point, since the gradient of the objective function is zero. This modification makes the Hessian matrix positive definite and guarantees the convergence to a minimum point. The Marquardt method is useful when the Gauss-modified Hessian matrix is poorly conditioned. Adding a constant to the diagonal elements of the Hessian matrix improves the condition of the Hessian matrix and prevents the Hessian matrix from being numerically singular.

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Discrimination Between Reservoir Models in Well Test Analysis by Toshiyuki Anraku


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