We discuss a nonlinear domain-decomposition preconditioning method for fully implicit simulations of multicomponent porous media flow based on the additive Schwarz preconditioned exact Newton method (ASPEN). The method efficiently accelerates nonlinear convergence by resolving unbalanced nonlinearities in a local stage and long-range interactions in a global stage. ASPEN can improve robustness and significantly reduce the number of global iterations compared with standard Newton, but extra work introduced in the local steps makes each global iteration more expensive. We discuss implementation aspects for the local and global stages. We show how the global-stage Jacobian can be transformed to the same form as the fully implicit system, so that one can use standard linear preconditioners and solvers. We compare the computational performance of ASPEN to standard Newton on a series of test cases, ranging from conceptual cases with simplified geometry or flow physics to cases representative of real assets. Our overall conclusion is that ASPEN is outperformed by Newton when this method works well and converges in a few iterations. On the other hand, ASPEN avoids time-step cuts and has significantly lower runtimes in time steps where Newton struggles. A good approach to computational speedup is therefore to adaptively switch between Newton and ASPEN throughout a simulation. A few examples of switching strategies are outlined.