Uncertainty of permeability and specific storage due to experimental error during data acquisition for pulse-transient technique

Transient fluid flow through rock is governed by two hydraulic properties: permeability (k) and the specific storage (S_s), which are often determined by the pulse-transient technique when k is extremely low (e.g. k < 10^-19 m²). The basic test system is composed of a pressure-confined rock sample connected to two closed reservoirs at its upstream and downstream ends. A pulse of pressure at the upstream boundary drives transient flow through the sample to the downstream end. The rock properties, k and S_s, can be determined by time-based recording of only one variable, the pressure change in each reservoir. Experimental error during data acquisition propagates through the data reduction process, leading to uncertainty in experimental results. In addition, unlike steady-state systems, the pressure-time curves are influenced by the compressive storage of the reservoirs and both the dimensions and properties of the sample. Thus, uncertainty in k and S_s may arise from errors in measurement of sample dimension, fluid pressure, or reservoir storages. In this study, the uncertainty in sample dimension is considered to be negligible, and reasonable error ranges in pressure and system storage measurements are considered. We first calculated pressure errors (P) induced by the difference between assumed, or experimentally measured values of k and S_s and their true values. Based on this result, the sensitivity coefficient (∂k/∂P and ∂S_s/∂P) is theoretically ~10 in percentage, i.e. 1% error of the pulse on average during a test cycle produces ~10% uncertainty in k and S_s. The sensitivity coefficient may become larger when the ratio of sample storage to upstream reservoir storage is extremely small. We also examined the sensitivity of experimental error in measuring the storage capacity of system reservoirs to uncertainty in resulting values of k and S_s. Because the reservoirs are typically small for tight rock samples and irregular in shape due to the combination of tubing, fittings, valves, and pressure transducers, the uncertainty should be much greater than that that of pressure. Our analysis reveals that 20% error in measurment of upstream storage causes ~5-15% uncertainty in permeability and ~30% uncertainty in specific storage, and varies linearly in this range. Our analytical model suggests that the pulse-transient method yields more accurate values of permeability than specific storage.