Comment on "Horizontal aquifer movement in a theis-theim confined system" by Donald C. Helm

In a recent paper, Helm [1994] presents an analysis of horizontal aquifer movement induced by groundwater withdrawal from a confined aquifer in which fluid and grains are incompressible. The analysis considers the aquifer in isolation (ignoring overlying and underlying strata) and assumes that the aquifer deforms purely in the horizontal direction (with no vertical movement). Helm's solution for grain displacement is obtained through introduction of a quantity known as bulk flux, q_b, defined as

q_b = nv_w + (1 - n)v_s

where n is porosity, v_w is velocity of water, and v_s is the velocity of the solid grains. On the basis of the bulk flux concept, Helm develops an explanation for the driving force on the bulk material.

It is our view that Helm's analysis is subject to four limitations. First, Helm's assumption of zero vertical displacement is not supported by field observations and could result in over- estimation of radial displacement. Second, in ignoring the role of overlying and underlying strata, Helm's solution does not yield reliable estimates of aquifer deformation. Third, Helm's solution method works only for problems that involve one spatial coordinate (for example, x or r) but does not generally work for problems involving three-dimensional flow and de- formation. Fourth, Helm's explanation of the driving force on the bulk material is faulty for general three-dimensional problems. The purpose of our comment is to discuss these four issues.