Identification of aquifer transmissivities: The comparison model method

Abstract

A method for solving the inverse problem in hydrogeology is presented. This method is suitable for computing the interblock transmissivities (harmonic mean or others) referred to the sides of the network blocks of a nonhomogeneous, anisotropic aquifer in steady state flow. The interblock transmissivities computing procedure is based on the comparison between real gradients and the ones generated by a 'comparison model' whose initial transmissivity value is arbitrarily chosen and constant through out the surveyed area. Alternative solutions of interblock transmissivities, one for each constant initial transmissivity value utilized in the comparison model, are obtained. Generally, these solutions differ from each other, but all of them present the characteristics of being able to reproduce, with the precision of an arbitrarily small e, the real piezometric heads, respecting the geometry and the boundary conditions of the real aquifer. The selection of the value, or set of values, of the initial transmissivity to put into the comparison model in order to obtain one solution of computed interblock transmissivities close to the real ones, both as trends and as absolute values, is rather critical. The minimum head anomaly criterion and the bottleneck criterion enable one to select a value or a set of values of initial transmissivity. These criteria exploit only the data needed for the solution of the inverse problem (real piezometric heads, geometry, and boundary conditions), and they lead to a suitable initial transmissivity that, put into the comparison model, allow one to obtain a good and meaningful solution of computed interblock transmissivities. The comparison model method and the two aforementioned criteria have been applied to a numerical case study bearing good results. The method has been tested, in order to evaluate its effectiveness, even in the case of noisy piezometric heads (piezometric heads with random errors). Even in this case the method bore satisfactory and useful results. Finally, a promising approach to the inverse problem solution, when one has at his disposal at least four sets of data coming from as many hydraulic situations, has been briefly described. objective function composed of some measure of the difference between observed and computed heads. Among the authors who affronted the identification problem, we will mention Emsellem and DeMarsily [1971], Neuman [1973], Neuman et al. [1980], Frind and Pinder [1973], Hefez et al. [1975], Sagar et al. [1975], Neuman and Yakowitz [1979], and Irmay [1980]. Scarascia and Ponzini [1972] presented a method for the solution of the inverse problem that minimizes the anomalies between the measured piezometric heads and the computed ones. The present paper, which from some aspects is a continuation of the Scarascia and Ponzini [!972] paper, describes a method suitable for the identification of the transmissivities of a single-layer aquifer in steady state flow, in which the boundary conditions (piezometric heads at the boundaries or known flow rates, fl...

Discrete stability of the Differential System Method evaluated with geostatistical techniques

“…In some cases the noisy hydraulic gradient could be opposite to the reference gradient, so that the noisȳ ow direction is inverted with respect to the real one. Under these conditions, direct methods of inversion that rely on the discrete balance equation can identify values of the physical parameters that are absolutely unrealistic (Ponzini and Lozej, 1982), whereas in these cases the DSM can work better, since it is not based on the direct solution of the discrete balance equation. Furthermore in this paper we have applied the simplest version of the method, so that we do not prevent the computation of negative values of transmissivity (see, for instance, cases L, I and N); however these unphysical values can be avoided by modifying the criteria for the choice of the integration path in such a way to include constraints on the values of the identi®ed transmissivities.…”

“…In particular, correlated errors in the piezometric heads, for instance those introduced by interpolation, affect the discrete hydraulic gradients less than uncorrelated errors. Furthermore, recall that the ratio of r g with some representative hydraulic gradient is more signi®cant than the magnitude of r g itself (Ponzini and Lozej, 1982). In our case, for instance, the average hydraulic gradient is about 0.0045.…”

Modeling Groundwater Flow in Heterogeneous Porous Media with YAGMod

“…The CMM was proposed to identify T at every node of a discretization grid [18] and successively developed to directly compute internode transmissivities [19]. Further modifications were proposed by Ponzini and Crosta [20], Ponzini et al [26], Pasquier and Marcotte [27], Ponzini et al [28].…”

“…To ensure that the function defined in Equation (18) is continuous and continuously differentiable, the following relationship must be satisfied: (19) so that the user must specify only two parameters, f and ϑ r . The transmissivity, calculated with Equation (18) for every cell (i, j, k) of the domain, is used to calculate interblock transmissivity with harmonic average.…”

“…The calibration is performed for 2D flow conditions implementing the comparison model method (CMM). This method was originally proposed by Scarascia and Ponzini [18], successively developed by Ponzini and Lozej [19] and cast in a more formal mathematical framework by Ponzini and Crosta [20]. The CMM has been applied and implemented with success to study 2D hydraulic flow in regional aquifers [14,16,17,[21][22][23], and therefore, for the moment, its implementation within YAGMod covers these kinds of systems only.…”