Analytical solutions characterizing coupled water flow and salt solution transport were presented. The paper focused on comparing four mud/shale interaction testing results with the analytical solutions to determine the optimal field parameters such as effective mud salt concentration under the specified well pressure and shale formation conditions. The parametric sensitivity study using analytical approaches was performed on the four testing cases to delineate the dominant trends, practical ranges and individual impacts of the key factors in the flow-transport process. The paper highlights the approach to distinguish the hydraulic potential and chemical potential from the total pressure that may lead to the effective treatments for minimizing the detrimental impact of mud/shale interactions.
Pressure transmission (PT) tests have been considered as primary experiments for testing shale stability.[1, 2, 3, 4, 5, 6] The PT tests involve created pressure differences and chemical concentration differences between upstream and downstream with reference to the position of tested shale, which are the driving forces for water flow and ion exchange between invading mud (upstream) and shale sample (downstream) during the tests. In the past, the results of PT tests were analyzed using a certain phenomenological model that relates the water activities of mud and shale to the specified osmotic pressure under the known shale membrane efficiency, testing temperature and designated fluid volume. This model is usually expressed as:
where posm is the osmotic pressure difference (i.e., with reference to the initial pressure), am is the membrane efficiency, R is the universal gas constant, T is the absolute temperature, V is the molar volume of water, awm is the mud water activity, and aws is the shale water activity. Even though it is simple, the phenomenological model cannot reveal the time-dependency of mud/shale interactions, which can be critical to the wellbore stability during the drilling operation since transient effects of shale swelling may affect wellbore stability significantly within certain time frames. The mud with effective solute concentration and adequate mud weight to support the wellbore must be imposed in a timely fashion to prevent time-dependent wellbore failure. As a remedy to resolving this issue, Chen et al. employed the analytical solutions to examine the transient behavior of mud/shale interactions and to calibrate the experimental PT tests. Inducing ion/water exchange between drilling mud and formation shales may effectively dehydrate the pore fluid in shales to prevent shale swelling. This coupled chemo-hydraulic process seems to be dictated by three factors: a) shale permeability, b) shale membrane efficiency, and c) ion diffusivity. The verification of the pressure transmission tests can be accomplished by invoking partially coupled analytical solutions, as performed by Chen et al. This paper focuses on evaluating the results from four mud/shale testing cases and attempts to identify the impacts of critical factors with the aid of the developed analytical solutions.