The operation of lithium ion batteries in discharge and charge processes is addressed. A simple phenomenological model is developed to predict all variables values. A set of algebraic and differential equations is derived taking into account salt and lithium balances in electrodes, in the separator, and in particles. Balances are developed for finite volumes and appropriate average values of several variables such as concentrations, current densities, and electrochemical reaction rates are introduced. Definitions of current densities as volume fraction functions are critical issues in the computations. Experimental values taken from the literature for discharge processes are predicted very accurately. Constant salt concentration in the separator can be assumed and consequently, the model can be analytically solved. Charge and discharge times, initial cell capacity, lost capacity, and relaxation times are easily estimated from simple equations and cell parameters. The limiting processes taking place during cell discharge can be determined. Energy efficiency and capacity usage are quantified for cycles. (c) 2014 American Institute of Chemical Engineers AIChE J, 61: 90-102, 2015