By Toshiyuki Anraku
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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.
Discrimination Between Reservoir Models in Well Test Analysis by Toshiyuki Anraku