A Nonlinear Nonisothermal General Rate Model for Bimolecular Reactive Chromatography: A + B ⇌ C + D

Equilibrium-limited liquid-phase reactions can be intensified by coupling reaction and selective separation within a chromatographic bed, yet the interaction of reversible bimolecular kinetics with particle-scale mass and heat transport remains insufficiently resolved. For the reaction class A + B ⇌ C + D, we formulate a nonlinear nonisothermal general rate model coupling axial dispersion, external film transfer, intraparticle diffusion and conduction, competitive temperature-dependent Langmuir adsorption, and adsorbed-phase reversible kinetics whose equilibrium constant follows from the forward and reverse Arrhenius representation. Retaining the four species and temperature as coupled particle states yields a five-state accumulation system with an analytically derived 5 × 5 Jacobian, whose entries agree with central finite-difference approximations to below 1 × 10–6. Mesh refinement at two pore-diffusion levels gives observed orders of 2.2–2.4, and halving the time step changes no indicator by more than 6 × 10–5. For a representative acidic-resin parameter set, selective retention of the more strongly adsorbed product raises conversion to 91.7% against a 65.1% isothermal batch-equilibrium reference and generates temporally separated outlet excursions of +5.7 and – 1.7 K, because the thermal front travels with the weakly retained product and well ahead of the strongly retained one. A 90-case computational campaign resolves the transition from kinetic to separation-controlled behavior, which a Damköhler number locates near 102 for conversion: raising the forward rate constant gives diminishing returns once selective product removal becomes controlling, whereas stronger retained-product affinity adds approximately 24 percentage points of conversion. Adsorption selectivity, thermal feedback, intraparticle transport, and feed loading trace distinct trajectories in the purity–productivity plane, with purity becoming nonmonotonic under increasing load.