CALCULATION OF FIRST-ORDER RATE COEFFICIENTS FROM SINGLE-WELL PUSH-PULL TEST DATA

A method for obtaining first-order rate coefficients from push-pull tests is derived. It is more general than previous methods that assume instantaneous injection or use the average concentration in the aquifer at the end of the injection stage. Both the injection and extraction phases are directly incorporated into the solution. A rest phase can be included if there is no significant advection of the slug during the rest stage. The effect of wellbore storage is included by assuming immiscible displacement of the water in the well by the injected or recovered fluid. The decay coefficient within well bore can differ from the decay coefficient in the aquifer. The effects of dispersion are reasonably included by plotting ln[Cd/Cd,0]-ln[Ctr/Ctr,0] versus the time since initiation of extraction where Cd and Cd,0 are the time dependent concentration and the injected concentration of the decaying solute and Ctr and Ctr,0 are the time dependent concentration and the injected concentration of the conservative tracer. There is good agreement between the approximate solution and numerical simulations.