Relationship between porosity and permeability with stress using pore volume compressibility characteristic of reservoir rocks

Effective stress is one of the most important parameters which strongly affects pore volume compressibility curve, which is used in assessing the reservoir rock properties. It causes change in porosity as well as permeability of the reservoir rocks. In the present study, pore volume compressibility characteristics of the reservoir rocks at different effective stresses were used to derive the relationship of porosity and permeability with the effective stress. To this end, analytical processes for deriving the porosity-stress and permeability-stress relationships are discussed in relation to the reservoir rocks. As a result, a porosity-stress formulation is proposed which is in good agreement with the experimental data. Also, two formulas are proposed for permeability-stress relationship; one on the base of Kozeny-Carman permeability-porosity model and the other one is based on a differential form of permeability-porosity relationship. After calibrating the required coefficients for one sandstone and three limestones, it was concluded that the first permeability-stress model is the upper bound correlation while the latter is the lower bound. Furthermore, it is shown that the latter has better agreement to the real experimental data of the sansdstone samples, while the first one is close to the experimental observations from limestone samples. Also, it is concluded that structure of pores is a key factor on permeability-stress relationship, so that there is a significant difference between the experimental data and the proposed relationship for a limestone sample with vuggy pore spaces.