Transient fluid flow in and around a fault

We present the results of simple numerical experiments in which we study the evolution with time of fluid flow around and within a permeable fault embedded in a less permeable porous medium. Fluid movement is driven by an imposed vertical pressure gradient. The results show that fluid flow is controlled by two timescales: τ_f = Sl²/κ_F and τ_F = Sl²/κ_M, where S is the specific storage of the porous material, l the length of the fault, and κ_M and κ_F are the hydraulic conductivities of the porous material and the fault, respectively. Fluid flow and the associated fluid pressure field evolve through three temporal stages: an early phase [t < τ_f] during which the initial fluid pressure gradient within the fault is relaxed; a second transient stage [τ_f < t < τ_F] when fluid is rapidly expelled at one end of the fault and extracted from the surrounding rocks at the other end leading to a reduction in the pressure gradient in the intact rock; a third phase [t < τ_F] characterized by a steady‐state flow. From the numerical experiments we derive an expression for the steady‐state maximum fluid velocity in the fault and the values of the two timescales, τ_f and τ_F. A comparison indicates excellent agreement of our results with existing asymptotic solutions. For km‐scale faults, the model results suggest that steady‐state is unlikely to be reached over geological timescales. Thus, the current use of parameters such as the focusing ratio defined under the assumption of steady‐state conditions should be reconsidered.