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Abstract
This paper presents a comprehensive set of experimental data for the membrane efficiency of four shales when interacting with different water-based and oil-based muds. Pressure transmission tests were used to measure the membrane efficiency using three different cations and two different anions at different concentrations (water activities).

It was found that the measured membrane efficiencies of shales when exposed to salt solutions were low, ranging from 0.18% to 4.23%. Useful correlations are presented between the membrane efficiency and other shale properties. Results suggest that the membrane efficiency of shales is directly proportional to the ratio of the cation exchange capacity and permeability of shales. Higher cation exchange capacities and lower permeabilities correlate very well with higher membrane efficiencies. Moreover, the ratio of the hydrated solute (ion) size to shale pore throat determines a shale's ability to restrict solutes from entering the pore space and controls its membrane efficiency. Cations and anions with large hydrated radii yielded higher membrane efficiencies, compared to ions with small hydrated diameters. Thus, the formulation of drilling fluids must take into account the types of cation and anion in the water-based fluid.

It was also found that the membrane efficiency of oil-based muds was high, however, these membrane efficiencies were not 100 % as postulated by many researchers.

Background and past work
Osmosis has long been recognized as a means to extract water out of a shale when the water activity of the shale is higher than that of the drilling fluid. In the absence of a hydraulic pressure gradient, the movement of mud filtrate into shale is mainly governed by the chemical potential difference between the pore fluid and the mud and this results in the osmotic transport of water, (Ewy and Stankovich 2000). However, it has been recently shown that the osmotic potential generated between shale and drilling fluid is greatly influenced by the flow of ions into or out of shale due to ionic concentration imbalances (Zhang et. al. 2004). Therefore, the actual osmotic effect is often less than the osmotic potential. This has spurred much interest to quantify the impact of ionic flow on the osmotic potential and that in turn has led to introducing the concept of shale membrane efficiency. The membrane efficiency describes the ability of a shale to hinder ion movement when interacting with drilling fluids. If the shale completely stops ionic flow, the shale is said to act as a perfect semi-permeable membrane with a membrane efficiency of unity. If the shale lets ions flow freely, the shale is said to act as a non-selective membrane with a membrane efficiency of zero.

Staverman (1952) was one of the first researchers to investigate the membrane efficiency of shale. He presented a model to estimate the reflection coefficient (i.e. the membrane efficiency) of shale membranes. He showed that the measured osmotic pressure obtained using a non-ideal membrane is different from the thermodynamically predicted value. Furthermore, this measured osmotic pressure is highly dependent on the permeability of the membrane to the solutes. Following Staverman, Low and Anderson (1958), Fritz and Marine (1983) and Ballard et al (1992), presented theories that suggested osmosis as a mechanism for swelling pressures generated by shales. These studies all showed that a shale could act as a leaky semi-permeable membrane since it did not completely stop the flux of ions.