Derivation of Solute Transport Equation for the Skin of an Extraction Well without Equifinality
The governing equation of solute transport in the well skin produces multiple parameter estimates because of the equifinality of modeling radially convergent tracer tests.A new transport equation for the skin of an extraction well(i.e.,a new transient Robin boundary condition)is proposed.A new analytical model was developed to test a fully penetrating extraction well.The analytical solution of the model was obtained using the Laplace transform and finite Fourier cosine transform.A finite element solution was acquired for the test in a partially penetrating extraction well.Results suggest the skin governing equation produces the estimates of the skin width w and formation vertical dispersivity αz are arbitrary values chosen from the ranges of 0.5 m≤w≤1 m and 0.08 m≤αz≤0.1 m.These ranges exclude the default values.In contrast,the new Robin boundary condition accurately reflects the skin effect when the Peclet number,defined as the ratio of w to the longitudinal dispersivity of the skin,is less than 1.The present solution relying on this boundary condition predicts the single optimal estimates of w and αz.The estimates(w=0.31 m,αz=0.17 m)approach their default values.The present solution applies to field tests.
Radially convergent tracer testEquifinalityTransient Robin boundary conditionAnalytical solutionFinite element solution
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