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Summary Conditional beta distributions are proposed with examples to evaluate the probability of intercepting specific proportions of target rocks in well planning. Geological facies or rock-type proportions are random variables pk(x) at each location, x. This paper recalls and further demonstrates that facies proportions can be modeled by local beta distributions. However, the highly variable shapes of the conditional probability-density functions (PDFs) for the random variables in the field lead to complex nonstationarity and nonlinearity issues. A practical and robust approach is to transform the proportion random variables to Gaussian variables, thus enabling the use of classical geostatistics. Although a direct relationship between Gaussian and beta random variables appears intractable, a suitable transformation that involves second-order expectations of proportions is proposed. The conditional parameters of the beta variables are recovered from kriging estimates after back transformation to proportions through Riemann sums.

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The present work integrates sonic logs, image logs, lab test, leak-off test (LOT), production, and injection data to build the basic geomechanical model in a mature field under peripheral water injection. In the modeling process, in-situ stresses (orientation and magnitude) were obtained and integrated form the available information. Additionally, rock mechanical properties derived from P and S-wave velocities, were calibrated with the static properties derived from lab tests (triaxial test). Statistical analysis of the dynamic rock properties allowed constructing the failure envelopes for reservoir intervals with different strengths using the Mohr-Coulomb failure criteria, giving extra information of the stiffness variation and anisotropy within the same reservoir rock. Moreover, the model was further validated by the stress polygon and the expected faulting regime was constraint, giving an insight of main fractures orientation. A wellbore stability analysis was also done to check on breakouts tendency and best trajectory for new sidetracks and horizontal wells to be drilled. For this particular field, the effects of many years of depletion without pressure support and the subsequent effect of peripheral water injection are better understood under the geomechanical point of view. Changes in the effective stresses during pore pressure drawdown show a stress path that could easily activate natural fractures and might had created bigger fracture channels favoring flow of reservoir fluids to the wellbore after the power water injection was initiated. By the same talking, water injection seemed to enhance the far field stress stability, but it might create tensile fractures at the injector's vicinity. In other words, knowledge of the in-situ stresses and its effects while depleting or increasing the pore pressure is of vital importance in reservoir management. Stability analysis suggests a formation stiff enough that can be drilled to any direction at any inclination angle; a condition that favors well spacing, but it should be handled with care in avoiding fracture corridors. The results of this work suggest that good reservoir management may require the geomechanics component to optimize well performance and reservoir development.