Semi-analytical solution to pumping test data with barrier, wellbore storage, and partial penetration effects

There exist some difficulties in determining aquifer parameters based on pumping test data within a partially penetrated retaining walls using traditional Cooper-Jacob method. Many other site-specific factors, such as the effect of partially penetrating well and the large diameter of the wells, cannot easily be accommodated in theoretical well formulae. The semi-log drawdown-time curves affected by the effects of barrier, wellbore storage, and partial penetration well can be characterised by four distinct stages of drawdown: i) Stage I, drawdown is unaffected by the barrier, ii) Stage II, drawdown is significantly influenced by the barrier, iii) Stage III, the drawdown-time curve runs parallel to that deduced from greenfield conditions, and iv) Stage IV, the drawdown becomes a constant value. To handle the four distinct stages of drawdown, a semi-analytical method using the slope of the late-time drawdown asymptote of Stage III for determining the transmissivity is proposed. The horizontal intercept, resulting from an extension of the late-time drawdown asymptote from Stage II, is used for determining the storage coefficient. Pumping test data from a case history are analysed using the proposed semi-analytical method, and the results obtained are compared with those deduced from the numerical simulation. The comparison between the analytical results and those obtained from the numerical simulation appeared satisfactory.