Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 13 8 2009 10.5194/hess-13-1399-2009 http://www.hydrol-earth-syst-sci.net/13/1399/2009/ http://www.hydrol-earth-syst-sci.net/13/1399/2009/hess-13-1399-2009.html http://www.hydrol-earth-syst-sci.net/13/1399/2009/hess-13-1399-2009.pdf 1399 1411 2009-08-05 A general real-time formulation for multi-rate mass transfer problems O. Silva orlando.silva@idaea.csic.es J. Carrera M. Dentz S. Kumar A. Alcolea M. Willmann Institute of Environmental Assessment and Water Research (IDǼA-CSIC), Barcelona, Spain Department of Geology and Geophysics, Texas A&M University, USA Hydrogeology Centre (CHYN), University of Neuchâtel, Neuchâtel, Switzerland Institute of Environmental Engineering, ETH Zurich, Switzerland Many flow and transport phenomena, ranging from delayed storage in pumping tests to tailing in river or aquifer tracer breakthrough curves or slow kinetics in reactive transport, display non-equilibrium (NE) behavior. These phenomena are usually modeled by non-local in time formulations, such as multi-porosity, multiple processes non equilibrium, continuous time random walk, memory functions, integro-differential equations, fractional derivatives or multi-rate mass transfer (MRMT), among others. We present a MRMT formulation that can be used to represent all these models of non equilibrium. The formulation can be extended to non-linear phenomena. 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