Overdamped slug test in monitoring wells: review of interpretation methods with mathematical, physical, and numerical analysis of storativity influence

Abstract

Several methods are available to interpret slug tests; however, when applied to the same test data, they usually yield very different results. The methods are classified into three categories depending on their assumptions about the solid matrix deformability during the test. This paper deals with overdamped tests for elastic solids that deform instantaneously. It provides a unified interpretation of transmissivity T and storativity S based on the velocity graph for variable-head tests in monitoring wells or cased boreholes. If S has little influence, the velocity graph is a straight line. If S has some influence, the graph should give a smooth curve. However, smooth curves are exceptions in practice, thereby leading to a reexamination of the influence of S during a slug test. Three independent approaches are used. (1) A mathematical review shows that the overdamped solution, as adapted from a heat conduction problem, did not correctly treat storativity terms and the type of problem: it corresponds to a special pulse test, not a slug test. (2) A physical investigation of deformability shows that the influence of S does not exceed 1% of the initial slug for most compressible materials. Thus, it is almost impossible to detect its influence in test results. (3) Numerical analyses confirm that S has a negligible influence: test results provide straight lines, not curves. The numerical analysis of the special pulse test provides exactly the classical solution, and the correct values of T and S after eliminating the confusion about storativity terms. It is concluded that (1) S has a negligible influence in slug tests, (2) the existing classical solution giving T and S must be abandoned, and (3) the velocity-graph equation and its integral equation (Hvorslev or Bouwer and Rice) which correctly describe the process must be used.Key words: slug test, hydraulic conductivity, storativity, numerical modeling.