A Three-Dimensional Model to Compute Land Subsidence

An attempt is made to improve the existing analytical three-dimensional models to predict land subsidence due to the extraction of fluids from natural reservoirs. The elastic model proposed by McCann and Wilts (1951) and the poro-elastic one introduced by Geertsma (1957, 1966) are presented first. The general equations of recent poro-elastic theory are mentioned. Then follows a new, more generalized, three-dimensional approach from which the previous models can be derived as particular cases. The contribution to the land subsidence of the depressurized oil or water bearing strata is separated from that of the surrounding strata. It is possible in this way to take into account the different physical properties of the reservoir and of the remaining medium. It is finally shown that the elastic model can be considered as a limit poro-elastic one and therefore its application appears more strictly correlated with the real condition of the sub-soil. In particular, the model by McCann and Wilts (1951) proves to be advantageous only when the depressurized reservoir is much more liable to deformation than the surrounding medium.