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The influence of unavoidable saturation averaging on the experimental measurement of dynamic capillary effects: A numerical simulation study

Hou, Lili, Sleep, Brent E., Kibbey, Tohren C.G.
Advances in water resources 2014 v.66 pp. 43-51
drainage, drainage systems, mathematical models, sand, surface tension, viscosity, water resources
Many studies over the past four decades have observed that capillary pressure–saturation (Pc–Sw) relationships are often different when measured dynamically under rapidly changing pressure inputs. This phenomenon has been referred to as a dynamic capillary effect, and its magnitude is often quantified by the dynamic capillary coefficient, τ. Experimentally-reported values of τ have varied by orders of magnitude, even for seemingly similar experimental systems. The purpose of the present work is to numerically explore the likely impact of fluid properties on the calculation of τ from experimental measurements. Specifically, the emphasis is on understanding how spatial averaging of the saturation profiles resulting from different fluid combinations contributes to the apparent magnitude of τ derived from experimental measurements.Simulations of dynamic drainage in a packed sand column were conducted using the CompSim multiphase flow simulator. Four nonwetting phase fluids with viscosities spanning four orders of magnitude were studied. Comparison between local and spatially-averaged rates of saturation change show significant differences, with the magnitude of the difference increasing with increasing viscosity to interfacial tension ratio and increasing drainage rate. Results show that at averaging scales likely to be experienced during experimental saturation measurements, this effect is likely to produce significant differences in the ultimate magnitude of the calculated τ values for different fluid systems and drainage rates. This result means that conventional flow phenomena may produce an inherent systematic bias in experimental measurements of τ, amplifying measured values for high viscosity or low interfacial tension systems and for experiments where higher drainage rates are used.