Numerical modeling of a long-term in situ chemical osmosis experiment in the Pierre Shale,South Dakota

We have numerically modeled evolving fluid pressures and concentrations from a nine-year in situ osmosis experiment in the Pierre Shale, South Dakota. These data were obtained and recently interpreted by one of us (C.E.N.) as indicating a potentially significant role for chemical osmosis in media like the Pierre Shale. That analysis considered only the final pressure differentials among boreholes that were assumed to represent osmotic equilibrium. For this study, the system evolution was modeled using a recently developed transient model for membrane transport. The model simulates hydraulically and chemically driven fluid and solute transport. The results yield an estimate of the thickness of the water film between the clay platelets b of 40 Å, which corresponds to an osmotic efficiency σ of 0.21 for the ambient pore water salinity of 3.5 g/l TDS. These values largely confirm the results of the earlier equilibrium analysis. However, the new model analysis provides additional constraints suggesting that intrinsic permeability k = 1.4 × 10⁻¹⁹ m², specific storage S_s = 1.7 × 10⁻⁵ m⁻¹, and diffusion coefficient D* = 6 × 10⁻¹¹ m²/s. The k value is larger than certain independent estimates which range from 10⁻²¹ to 10⁻²⁰; it may indicate opening of microcracks during the experiments. The fact that the complex transient pressure and concentration behavior for the individual wells could be reproduced quite accurately, and the inferred parameter values appear to be realistic for the Pierre Shale, suggests that the new model is a useful tool for modeling transient coupled flows in groundwater systems.