  We analyze a semi-explicit time discretization scheme of first order for
poroelasticity with nonlinear permeability provided that the elasticity model
and the flow equation are only weakly coupled. The approach leads to a
decoupling of the equations and, at the same time, linearizes the nonlinearity
without the need of further inner iteration steps. Hence, the computational
speed-up is twofold without a loss in the convergence rate. We prove optimal
first-order error estimates by considering a related delay system and
investigate the method numerically for different examples with various types of
nonlinear displacement-permeability relations.
