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Experimental studies have shown that osmosis could be one of the mechanisms of water transport in porous materials that act, to a certain extent, as semipermeable membranes. In this paper, an experimental apparatus and the corresponding model to measure and determine the osmotic efficiency, σ, of bulk porous materials are described. Both the apparatus and model to interpret water transport in samples are modifications of those of Sherwood and Craster. In addition to σ, the transport parameters of the model include Darcy permeability and water and salt diffusivity. These parameters are used to calculate the ratio of the individual components of the total molar flow. We used the apparatus to measure cylindrical samples made from an illitic clay with a diameter of 45 mm and thickness of 5 mm. The measured transport coefficients were then used to estimate the relative importance of the individual contributions to the total flow of water through the samples. Our results show that the contribution of the osmosis is 82–88%, while the diffusion contributes only 11–13% and the Darcy flow caused by the pressure difference contributes only 1–5%. Even after considering the uncertainties in the measurement of the transport coefficients, which are estimated to be up to 22%, the results show that osmosis makes an important contribution to the total water flow and should not be neglected in general.