A deterministic model is described which enables the stress conditions to be calculated based on the structural growth history. The method provides a framework for estimating natural fracture distribution and directions. The method is developed for two dimensional cross sections and can be extended to three dimensions.
A depth converted seismic profile is used for dividing the geological section into a finite number of time defined formations. The individual formations can be intersected by fault traces. The paleo-appearance of the cross section is constructed through steps in geological time by stripping off formations from the top. In each step the remaining section is decompacted under the decreased load based on the compaction trend of the individual formations. For structural restoration, unfolding and movement along fault traces are made. During this backstripping the displacements are recorded for the subsequent stress analysis.
Stresses are calculated by finite element modelling. An elastic/plastic strain hardening model is proposed. It includes a time dependent creep model making it possible to predict formation properties through geological time. An elastic/plastic finite element model has been designed to calculate stresses by use of these displacements.
The results of the stress analysis are predictions of the stress state being either elastic or plastic: compaction, compressible shear or tension fracture orientations is given too for each point in the reservoir at the steps in geologic time. The level of stress can be "history matched" with well data, well test analysis, fracture identification logs, in situ stress measurements etc..
Illustration of the method is presented for two oil bearing chalk reservoirs overlying salt diapirs in the North Sea. One example illustrates the stress state in a heavily fractured reservoir and the other, a less fractured reservoir.