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# Lumped rate model without pores (LRM)¶

The lumped rate model without pores [3, 4] deviates from the lumped rate model with pores (see Section Lumped rate model with pores (LRMP)) by neglecting pores completely. The particle phase \(c^p\) is removed and the porosity \(\varepsilon_t\) is taken as total porosity

The phase ratio is denoted by \(\beta_t = \varepsilon_t / (1 - \varepsilon_t)\) accordingly. The model equations are given by

where \(\beta_t = \varepsilon_t / (1 - \varepsilon_t)\) denotes the (total) phase ratio. The equations are complemented by Danckwerts boundary conditions [8]

Both quasi-stationary and dynamic binding models are supported:

By default, the following initial conditions are applied for all \(z \in [0,L]\):

Note that by setting \(\varepsilon_t = 1\), removing all bound states by setting \(N_{\text{bnd},i} = 0\) for all components \(i\), and applying no binding model, a dispersive plug flow reactor (DPFR) is obtained. For the specification of flow rate and direction, the same holds as for the general rate model (see Section Specification of flow rate / velocity and direction).

For information on model parameters see Lumped Rate Model Without Pores.