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Durham University

Department of Engineering

Staff Profile

Publication details for Professor Simon Mathias

Mathias, S.A. & Roberts, A.W. (2013). A Lambert W function solution for estimating sustainable injection rates for storage of CO2 in brine aquifers. International Journal of Greenhouse Gas Control 17: 546-548.

Author(s) from Durham


It is often of interest to estimate the maximum possible CO2 injection rate for a given maximum pressure buildup and injection duration scenario. Analytical solutions exist to estimate pressure buildup due to constant rate injection for a specified duration. In this article, it is shown that such solutions can be rearranged for injection rate by virtue of the Lambert W function. It is also shown that the Lambert W function argument is sufficiently small such that a simple asymptotic approximation of the Lambert W function is sufficient in this context.