Idealised Discrete Pore-Scale Model of Poro-Elasticity via Closed-Form Analytical Expressions

This paper describes a simple (idealized) lattice-type model of porous materials, and uses that model to derive analytical expressions that determine interactions between the pore fluid and the material framework. The examples included here address the change in horizontal stress associated with fluid depletion, and also the way that fracture apertures are changed due to alterations of fluid pressure. The predictions agree in magnitude with observations and large-scale inferences. Analysis of the model’s behavior leads to questions concerning the validity, or not, of the scale-independence of stress, along with posing questions about the use of continuum ideas for porous materials. The notion of effective stress is considered within the framework of the model, which reveals that the so-called poro-elastic coefficient is not a material property.