CONDITIONING OF MARKED POINT-PROCESSES WITHIN A BAYESIAN FRAMEWORK

Shale units with low permeability create barriers to fluid flow in a s andstone reservoir. A spatial stochastic model for the location of sha le units in a reservoir is defined, The model is based on a marked poi nt process formulation, where the marks are parameterized by random fu nctions for the shape of a shale unit. This extends the traditional fo rmulation in the sense that conditioning on the actual observations of the shale units is allowed in an arbitrary number of wells penetratin g the reservoir, The marked point process for the shale units includes spatial interaction of units and allows a random number of units to b e present, The model is defined in a Bayesian setting with prior pdfs assigned to size-shape parameters of shale units, The observations of shales in wells are associated with a likelihood function. The posteri or pdf of the marked point process can only partially be developed ana lytically; the final solution must be determined by sampling using the Metropolis-Hastings algorithm. An example is presented, demonstrating the consequences of increasing the number of wells in which observati ons are made.