An analytical model for pore volume compressibility of reservoir rock

The pore volume compressibility of reservoir rock is usually measured by volume method and the relation between compressibility and porosity follows the Hall plot. However, the volume method yields a high pore volume compressibility value and a negative correlation between compressibility and porosity. Both results illustrate that unconventional reservoirs with low porosity has higher elastic energy than conventional reservoirs with high porosity, which disagrees with the production practice. In this paper, volume method of pore volume compressibility is investigated and problems of Hall plot are analyzed. Then a novel analytical model on pore volume compressibility of reservoir rock is derived to resolve these problems. The reason on the improper results using volume method is discussed. The calculated results from our new model are validated by the experimental tests using mercury immersion method for pore volume compressibility measurement. The effects of compressibility on original oil in place and the flow radius are analyzed. The analytical model shows that pore volume compressibility of reservoir rock is related not only to porosity but also to elastic modulus and Poisson's ratio. There is a positive correlation between pore volume compressibility and porosity. The compressibility value of our model is much lower than that measured using volume method. The reason of the improper results from volume method is the micro interstice in core holder. Without the effects of micro interstice (mercury immersion method or loading and unloading stress treatment before the test), the measured pore volume compressibility shows a relatively low value and a positive correlation between pore compressibility and porosity, which validate the results of our analytical model. The pore volume compressibility calculated by volume method and Hall plot will overestimate the elastic energy of the reservoir and bring substantial errors in evaluation of original oil in place and the flow radius.