Abstract Background gas has been observed in oil based drilling fluids in contact with gas bearing formations. It has been postulated that such background gas is caused by diffusion. The objective of this study was to quantify the transport of gas by diffusion. The effect of filtrate flow into the formation (against the gas transport) has been evaluated. The diffusion coefficients of the filter cakes were determined in the laboratory at various temperatures and pressures. The significance of diffusion was mostly decided by the rate of filtration. The flux of gas by diffusion drops sharply at some threshold value of pressure differential in the wellbore, irrespective of the temperature.
Introduction Background gas has been observed in drilling fluids, even when the mud weight is sufficient to prevent gas flow by convection into the wellbore. It has been postulated that such background gas is caused by diffusion, wherein natural gas in contact with the filter cake diffuses through the cake into the wellbore. This diffusion is greater in oil based drilling fluids than in water based fluids due to solubility effects.
The presence of gas in the drilling fluid often alarms the drilling crew. Knowledge of diffusion rates can be useful in distinguishing the sources of gas in the wellbore. It may also have implications in determining the cost of maintaining the drilling fluids.
The diffusion of gas into wellbore is countered by the flow of filtrate into formation. This convective infiltration is caused by the higher hydrostatic pressure in the wellbore. The diffusion process is controlled by the diffusion coefficient of the filter cake while filtration is governed by the permeability of the cake. This study evaluates relative importance of diffusion in the presence of counter current convection of filtrate. Diffusion coefficients of filter cakes were measured in the laboratory at various temperatures and pressures. These values along with the measured permeabilities were used in a model to predict flux of gas into a wellbore. Even though the diffusion of gases into liquids is a well established phenomenon, there are no reported data for the diffusion of gas in a multi-component solvent such as diesel oil (C9 to C24). The diffusion in porous media has been mostly studied with catalysis in which diffusion is accompanied by a chemical reaction. These studies and other empirical works have limited use in estimating the diffusion coefficients of filter cakes under wellbore conditions. Reid et al., Hayduk and Cheng, and Hayduk and Buckley have reported diffusion coefficients for methane, ethane, and propane into single-component heavier hydrocarbons. Their results were used for comparison with the results obtained in this study.
Transport of Gas in a Wellbore Consider the mass transfer of formation gas through a filter cake as shown in Fig. 1. When both, the diffusion of gas and the convection of filtrate take place at the same time the net transfer is the resultant of a diffusion component and an opposing convection component:
(1)
where, F is the net flux at any radius r, D is the effective diffusion coefficient of the filter cake, C is the concentration of gas, k is the permeability of the filter cake, is the filtrate viscosity, and is the pressure differential across the filter cake. The first term in Eq. 1 is the diffusion component of the net flux given by Fick's theory: (2)
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