Sensitivity analysis of a no-crossflow model for the transient flowmeter test

Abstract

Logarithmic sensitivities and plausible relative errors are studied in a simple no-crossflow model of a transient flowmeter test (TFMT). This model is identical to the model of a constant-rate pumping test conducted on a fully penetrating well with wellbore storage, surrounded by a thick skin zone, and situated in a homogeneous confined aquifer. The sensitivities of wellbore drawdown and wellface flowrate to aquifer and skin parameters are independent of the pumping rate. However, the plausible relative errors in the aquifer and skin parameters estimated from drawdown and wellface flowrate data can be proportionally decreased by increasing the pumping rate. The plausible relative errors vary by many orders of magnitude from the beginning of the TFMT. The practically important flowrate and drawdown measurements in this test, for which the plausible relative errors vary by less than one order of magnitude from the minimum plausible relative errors, can begin approximately when the dimensionless wellface flowrate exceeds q D ¼ q=Q % 0:4. During most of this stage of the test, the plausible relative errors in aquifer hydraulic conductivity (K a ) are generally an order of magnitude smaller than those in aquifer specific storativity. The plausible relative errors in the skin hydraulic conductivity (K s ) are generally larger than the plausible relative errors in the aquifer specific storativity when the thick skin is normal (K s > K a ) and smaller when the thick skin is damaged (K s < K a ). The specific storativity of the skin zone would be so biased that one should not even attempt to estimate it from the TFMT.

The use of sensitivity analysis in on-line aquifer parameter estimation

“…Kabala (2001) proposed logarithmic sensitivity to analyze the pumping test on a well with wellbore storage and skin. In addition, Kabala et al (2002) also studied the logarithmic sensitivity, plausible relative errors, and deterministic parameter correlations in a simple semianalytic no-crossflow model of the transient flowmeter test (TFMT) that accounts for a thick skin around the wall. Vachaud and Chen (2002) analyzed a large-scale hydrologic model problem by sensitivity theory.…”