Spatial analysis of aquifer response times for radial flow processes: Nondimensional analysis and laboratory-scale tests

A fundamental concept in groundwater hydrology is the notion of steady state, or equilibrium conditions. When a system at some initial steady state condition is perturbed by pumping, a transient cone of depression will develop and the system will approach a new steady state condition. Understanding the time scale required for the transient process to occur is of practical interest since it would help practitioners decide whether to use a steady state model or a more complicated transient model. Standard approaches to estimate the response time use simple scaling relationships which neglect spatial variations. Alternatively, others define the response time to be the amount of time taken for the difference between the transient and steady state solutions to fall below some arbitrary tolerance level. Here, we present a novel approach and use the concept of mean action time to predict aquifer response time scales in a two-dimensional radial geometry for pumping, injection and recovery processes. Our approach leads to relatively simple closed form expressions that explicitly show how the time scale depends on the hydraulic parameters and position. Furthermore, our dimensionless framework allows us to predict the response time scales for a range of applications including small scale laboratory problems and large scale field problems. Our analysis shows that the response time scales vary spatially, but are equivalent for pumping, injection and associated recovery processes. Furthermore, the time scale is independent of the pumping or injection flow rate. We test these predictions in a laboratory scale aquifer and find that our physical measurements corroborate the theoretical predictions