121 DESCRIPTION OF THE UNIVERSITY OF SEVILLE (USEV) 3-D MODEL (PACIFIC OCEAN APPLICATION) X-1. GENERAL DESCRIPTION This model is based on the same dispersion equations described in Annex V: USEV 2-D model applied to the Baltic Sea), but written in a 3-D form. Thus, only a brief summary is given. Water circulation has been obtained from the JCOPE2 hydrodynamic model. There has been evidence to suggest that uptake takes place in two stages: fast surface adsorption followed by slow migration of ions to pores and interlattice spacings [X-1–3]. Consequently, two USEV kinetic models have been tested in the Pacific Ocean application. The one-step model considers that exchanges of radionuclides between water and sediments are governed by a first-order reversible reaction, being k1 and k2 the forward and backward rates respectively, as described in the 2-D case. The two-step model considers that exchanges are governed by two consecutive reversible reactions, i.e. surface adsorption is followed by another process that may be a slow di?usion of ions into pores and interlattice spacings, inner complex formation or a transformation such as an oxidation. k3 and k4 are forward and backward rates for this second reaction (see Figure X-1). Thus, sediments are divided in two phases, i.e. a reversible and a slowly reversible fraction. It has been shown that the two-step model reproduces both the adsorption and release kinetics of 137Cs in the Irish Sea, where it is released from Sellafield nuclear fuel reprocessing plant [X-4]. Equations are presented below, for the sake of simplicity, in the case of a one-step kinetic model. The extension to the two-step kinetic model may be seen, for instance, in Ref. [X-4]. In a similar way to the depth averaged model shown in Annex V above, the kinetic coe?cient k1 is written as: ?? = ?(?? + ????) = ??? + ??? (X-1) where Sm and Ss are the exchange surfaces for suspended matter and bottom sediments, respectively (dimensions [L]?1) and ? is a parameter with the dimensions of a velocity denoted as the exchange velocity (see Annex V above). The delta function is introduced to take into account that only the deepest water layer interacts with the bed sediment. Thus, ?b = 1 for the deepest layer and ?b = 0 elsewhere. The equation that gives the time evolution of the radionuclide concentration in the dissolved phase, Cd, is: ??? ?? + ?(???) ?? + ?(???) ?? + ?(???) ?? = ??? ??? ??? + ? ??? ??? ? + ? ?? ?? ??? ?? ? ? ???? + ????? + ???? ??????? ? (X-2) where Cs and As are, respectively, the concentrations of radionuclides in suspended matter and bottom sediments. u, v and w are water velocities along the x, y and z axis and A and K are, respectively, the horizontal and vertical di?usion coe?cients. m is the suspended matter concentration, ?s the sediment bulk density, f the fraction of fine sediments and is the thickness of the deepest water layer in contact with the seabed. Finally, ? is a correction factor that takes into account that part of the sediment particle surface may be hidden by other sediment particles.