We modeled the relaxation dynamics of (lipid) vesicles upon osmotic upshift, taking into account volume variation, chemical reaction kinetics, and passive transport across the membrane. We focused on the relaxation kinetics upon addition of impermeable osmolytes such as KCl and membrane-permeable solutes such as weak acids. We studied the effect of the most relevant physical parameters on the dynamic behavior of the system, as well as on the relaxation rates. We observe that 1) the dynamic complexity of the relaxation kinetics depends on the number of permeable species; 2) the permeability coefficients (P) and the weak acid strength (pKa-values) determine the dynamic behavior of the system; 3) the vesicle size does not affect the dynamics, ...