Forward and inverse numerical modeling of fluid flow in a faulted reservoir: Inference of spatial distribution of the fault transmissibility

A finite element numerical model was used to analyze a quasi-steady-state, three-dimensional hydraulic head distribution measured in the vicinity of a fault partially displacing the Hickory aquifer system in central Texas. The spatial distribution of permeability of major stratigraphic units and fault rock was obtained utilizing kriging, forward modeling and geophysical inverse modeling. Core-scale permeability data, quasi-steady-state hydraulic head data and full-reservoir pump test data were used for analysis. The final permeability model provides a close match to the observed hydraulic head distribution with a correlation coefficient of 0.88.; The fault-rock permeability varies systematically with the spatial position along the fault from a maximum of 20 and to a minimum of 0.0001 md. The highest permeabilities of 10–20 and (a 50-fold reduction of the sandstone protolith permeability) occur in the lowest portion of the fault, where the fault displaces sandstone-dominant strata. Pump test data also clearly show fluid flow is focused through this region of the fault. The fault-rock permeability decreases progressively up dip along the fault in a fashion closely reflecting the increase of mudstone strata cut by the fault. Where the mudstone-rich Lower Middle Hickory is faulted against the sandstone-dominant Lower Hickory, permeabilities of 4 and are inferred. Where the mudstone-rich Lower Middle Hickory is faulted against itself, the permeability is 0.03 md.; The 10–20 and permeability inferred in the lower part of the fault is about a factor of 10 greater than that inferred from core-scale measurements of fault-rock samples as well as from earlier simple 1-D model estimates. This difference may reflect upscaling issues, but additional analysis is needed to more definitively reconcile the different estimates.; Multilevel monitoring systems provide a direct measure of effects of faults and stratigraphic heterogeneities upon fluid flow in an aquifer. Variations of drawdown histories in zones straddling a fault permit identification of delay times and changes in the functional form of the response curves associated with the fault. Analysis of vertical gradient variation with time allows one to separate hydraulic responses of the zones straddling low permeability faults, resolve geometry of the faulted region and obtain additional constraints for conceptual model and defining parameters.