A new development of a multi-layered reservoir model is presented which considers the layers to be in communication only at the well. The importance of the presentation is the simplicity of the mathematical model and the use of the model to derive improved well test analysis techniques for both single and double porosity reservoirs. Analysis techniques based upon both pressure and flow rate data required to determine individual layer properties are presented.
Through the use of the Laplace Transformation, the behavior of a multi-layered reservoir system can be treated as an equivalent resistance network in which the total resistance to fluid flow can be obtained by adding the resistances to fluid flow in each layer using the elementary concept of resistances in parallel. The resistance functions for both single and double porosity layers with infinite, closed, or constant pressure outer boundaries are presented. The effects of wellbore storage are included.
Development of layered reservoir models where the layers are of different type (single or double porosity), with differing rock and fluid properties, and with differing outer boundaries is easily accomplished with the parallel resistance approach. Solutions for the wellbore pressure and the pressure in the reservoir for constant rate tests as well as solutions for the rate response during a constant pressure test are discussed.
A method to include wellbore storage into any reservoir model is presented as is a method for directly extending single porosity solutions to double porosity systems.