Sensitivity analysis of a pumping test on a well with wellbore storage andskin

This paper reviews the basic concepts of sensitivity analysis and points ou t their limitations. A case is then made for logarithmic sensitivity. The m agnitude of logarithmic sensitivity alone does not determine the accuracy o f an aquifer parameter estimate, especially when the relative measurement e rrors are not uniform throughout space and time. Deterministic parameter co rrelations and plausible relative errors in parameter estimates are introdu ced as imperfect measures of information content in measurements. A plausib le relative error in the parameter estimate combines the effect of logarith mic sensitivity with that of relative measurement error. Minimizing the pla usible relative errors rather than maximizing the corresponding sensitiviti es should serve as a guide to identifying the measurements most useful for parameter estimation or as candidate measurements for optimal sampling. Fur thermore, avoiding among them measurements with high parameter correlations as much as possible may help ensure that the sensitivity matrix X (or (XX) -X-T) is well-conditioned and, thus, that the parameter estimates are accur ate. The discussed concerts are then applied to a model of a pumping test conduc ted on a fully penetrating well situated in a confined aquifer. The model a ccounts for the wellbore storage and an infinitesimal skin. Tn contrast to the traditional and normalized sensitivities, the logarithmic sensitivities of the drawdown in the pumping well, the drawdown in an observation well, and the wellface flowrate to transmissivity, T, storativity, S, and the ski n factor, eta, depend on a small number of parameters. They can thus be rep resented by a single type curve or a family of a relatively few type curves . The plausible relative errors in T, S, and eta estimated from wellbore dr awdown rapidly decrease during the wellbore storage phase and reach a plate au or slowly decrease outside the wellbore storage phase. The plausible rel ative errors from the wellface flowrate rapidly decrease during the wellbor e storage phase before reaching a minimum (around the time when the wellfac e flowrate is equal to about half the pumping rate) and then rapidly increa se. This means that transient flowmeter test measurements of drawdown and w ellface flowrate should not be made during the early times of the wellbore storage phase. (C) 2001 Elsevier Science Ltd. All rights reserved.