Connectivity effects on fluid age and residence time distributions in two- and three-dimensional pore networks

Shahram Asgari 

Pore-scale simulations are often run on a single plane cut from a three-dimensional image, because resolving the whole pore space is expensive. This study asks what that shortcut costs. What is at stake is the distribution of fluid ages, and above all its long tail, because that tail is what slow reactions respond to. We computed the distribution directly from the flow field, by labeling the fluid with its age and carrying one transport equation for every age. The first two moments of that equation give the mean age and the coefficient of variation (CV) of the age distribution. Solved numerically, they return the analytical mean age exactly and the analytical age variance to within 0.11 % for Pe ≥ 20. The same equations were then applied to two pore networks that are identical apart from the number of throats meeting at each pore, four in the flat network and six in the cubic one. With every throat open the two agree to 5 % in CV and 2.5 % in the upper tail, so dimension by itself changes little. Blocking throats at random changes this. At 45 % blocked, the flat network places the upper tail 3.8 times too high and leaves 5.4 times more pore volume without flow. Spanning probabilities measured on the same grids explain the difference. The flat grid loses its connected paths between 50 and 60 % blocked, while the cubic grid still spans at 70 %. In the blocked networks the resolved tail is a power law, with an exponent of -2.4 for the flat grid against -5.9 for the cubic one. What controls the old-water tail is therefore how well the pore space is connected, not how many dimensions are resolved. A flat section may be used where the pore space is comfortably connected, and should not be where it is not.