Semi-analytic modeling of transient multi-layer flow with TTim
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semi-analytic approach has been developed for the modeling of transient flow in multi-layer systems (Hemker and Maas 1987; Bakker and Kuhlman 2011; Bakker 2013). As the approach is analytic, no grid, time-stepping, or closed model boundary are needed. The approach is based on the Laplace-transform analytic element method (Furman and Neuman 2003; Kuhlman and Neuman 2009) Received: 25 July 2012 / Accepted: 6 March 2013 Published online: 25 April 2013 * Springer-Verlag Berlin Heidelberg 2013 M. Bakker ()) Water Resources Section, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands e-mail: [email protected]
Hydrogeology Journal (2013) 21: 935–943
and is implemented in the free and open-source computer code TTim (pronounced: tee-tim) (Bakker 2012). Analytic element models have been used for the simulation of steady flow at a variety of scales, from screening models to large regional models, and for a variety of problems from wellhead protection to groundwater/surface-water interaction (Strack 2003; Hunt 2006). The objective of this note is to discuss the current capabilities of the analytic element code TTim for modeling transient multi-layer flow (version 0.2). This note consists of three parts. First, the main approximations and the main features of the TTim code are presented. Second, TTim is benchmarked against both a semi-analytic solution and a numerical solution; and third, a practical application is presented to demonstrate how TTim may be used to analyze a pumping test near a river with a leaky bed. A few alternative codes are available for the semianalytic simulation of transient head variations in multilayer systems; the large number of numerical codes that apply, for example, the finite difference or finite element method are not reviewed here. PhreFlow is a free program for the simulation of transient three-dimensional (3D) flow in an unconfined aquifer including partially penetrating wells and ellipsoidal inhomogeneities; elastic storage is neglected in PhreFlow (Janković and Barnes 2001). MLU is a commercial code for the simulation of transient multilayer flow to wells. It applies the same theory as used in TTim with a few different choices in implementation. MLU has a nice Windows interface and includes automatic parameter estimation and a free two-layer version is available (Hemker and Post 2011; Carlson and Randall 2012). Cihan et al. (2011) developed a free code with a subset of the capabilities of MLU (no skin effect, no well bore storage, no user interface, and no parameter estimation) but with abandoned wells; the FORTRAN code may be obtained from the authors. AnAqSim is a commercial code for transient multi-layer modeling that includes wells, line-sinks, and inhomogeneities. AnAqSim is less analytic than TTim and MLU as the spatial distribution of the leakage between aquifers and the release from storage is approximated by radial basis functions and transient flow is approximated with time stepping. However, AnAqSim may be used to simulate variable tra
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