One‐dimensional fluid diffusion induced by constant‐rate flow injection: Theoretical analysis and application to the determination of fluid permeability and specific storage of a cored rock sample

Abstract

[1] We describe the conceptual design and first application of a new method for simultaneously measuring the fluid permeability and specific storage of a rock sample. In our laboratory tests, a constant flow rate single-stroke piston pump injects fluid into a cored rock specimen placed between two reservoirs in which fluid pressure is recorded. For this geometry we have derived a new analytic solution of the governing diffusion equation describing the one-dimensional fluid flow. This new analytic solution in the time domain consists of two parts: an asymptotic linear function of time, and a transient part which decays to zero as time increases. The model predicts that the fluid pressures of the upstream and downstream reservoirs both increase linearly with time after the initial transient vanishes. The slope of the linear pressure variation depends on the specific storage of the rock sample for a given test condition, and the differential pressure between the two reservoirs is related to the permeability. If the downstream pressure is not recorded, the permeability can be calculated from the zero intercept of the linear upstream fluid pressure variation. This calculation is quite straightforward and no tedious history curve matching is required. We applied our new method to measure fluid permeability and specific storage of Westerly granite. The measured values of the permeability are consistent with those published in the literature. The main advantages of our method are the reliability of the testing method, its economy of time, and the flexibility in adapting the system parameters to tests at different conditions.

Effect of Water Infiltration, Injection Rate and Anisotropy on Hydraulic Fracturing Behavior of Granite

“…Confining pressure, shear stresses as well as other factors such as temperature will influence permeability of granite samples (Morrow et al 1986;Song et al 2004;Alam et al 2015). As a result, water infiltration varies at different in situ conditions.…”

“…This could result in dilation of granite specimen and permeability increase from an early stage of injection. Song et al (2004) found that the permeability of Westerly granite increases with decreasing effective pressure hence increasing pore pressure. The pores in the two sandstones are much less compressible and show negligible deformation at the early pressure stage.…”

Measurement of specific storage of rock for supercritical carbon dioxide using constant flow pump and constant head permeability techniques

“…Later, Esaki et al [5] enhances the accuracy and efficiency of the mathematical model by considering the effect of storage capacity of the pump system. Song et al [17] introduced more straightforward mathematical model of the technique with less tedious numerical simulation to solve the model.…”

Theoretical Analysis of One-Dimensional Pressure Diffusion from a Constant Upstream Pressure to a Constant Downstream Storage

“…A sudden change in geologic pore pressure can result in catastrophic hazards (TALWANI and ACREE 1984;REID 1994;IVERSON et al 2000;PAROTIDIS et al 2003;SHAPIRO et al 2003). Pore pressure prediction is essential for modeling various geologic processes, evaluating seismic sensitivity and landslide triggering, the safe design of deep drilling, the production of fluid resources, and the storage of hazardous wastes in geologic formations (SONG et al 2004).…”

“…Flooding of a cylindrical rock sample in a triaxial system is the most commonly used technique to obtain the hydraulic parameters k x and S s in the xdirection (BRACE et al 1968;TRIMMER et al 1980;TRIMMER 1981TRIMMER , 1982OLSEN et al 1985;SONG et al 2004;RENNER 2006, 2007). If j x is constant, and assuming one-dimensional laminar flow through a homogeneous medium in the x-direction, then Eq.…”