A multisolid-wax adiabatic flash formulation based on a nested isothermal equilibrium kernel

• A multisolid-wax isothermal flash is extended to adiabatic operation • The adiabatic model preserves the original multisolid equilibrium kernel • The extension requires only an outer enthalpy balance on temperature • Simultaneous vaporization and wax precipitation are predicted consistently • A synthetic-mixture benchmark illustrates the proposed PR-EOS framework A multisolid-wax adiabatic flash formulation is presented for systems in which vaporization, liquid-phase redistribution, and wax precipitation may occur simultaneously under pressure-enthalpy constraints. The formulation extends a previously developed multisolid-wax isothermal flash without altering its equilibrium structure. The original isothermal kernel, based on the Peng-Robinson equation of state, a multisolid representation of wax precipitation, a liquid-multisolid subproblem, and a modified Rachford-Rice equation written in terms of effective separation factors, is retained as the inner equilibrium solver. The adiabatic extension is achieved by adding an outer temperature-correction loop driven by the enthalpy residual, so that the equilibrium temperature is determined together with the phase split. The resulting formulation preserves the computational simplicity of the isothermal method while enabling pressure-enthalpy calculations relevant to adiabatic expansion, throttling, and flashing of wax-prone mixtures. A synthetic 9-component benchmark mixture is used to illustrate the method. For the benchmark outlet state at 40 bar and 260 K, the formulation predicts vapor-liquid-multisolid equilibrium with a vapor fraction on a feed basis of V / F = 0.4718378 , a liquid fraction on a feed basis of L / F = 0.4306230 , and a total solid fraction on a feed basis of S / F = 0.0975386 , with PC-2 and PC-3 as the precipitating species. Under the generalized caloric closure adopted for reproducibility, the corresponding adiabatic inlet condition is obtained at 400 bar and 297.67 K. The proposed formulation provides a practical bridge between multisolid wax thermodynamics and modern adiabatic flash methodology. Its original contribution is not the introduction of a new wax thermodynamic model or a new general PH-flash framework, but the extension of a previously published multisolid-wax isothermal flash to pressure-enthalpy conditions by embedding the original equilibrium kernel within an outer enthalpy-balance loop. In this way, the work connects multisolid-wax thermodynamics with modern PH-flash methodology while preserving the original isothermal kernel. The method is therefore suitable as a transparent and implementation-friendly framework for future applications in petroleum and chemical engineering problems involving coupled phase behavior and energy effects. The benchmark used here is synthetic and is intended to demonstrate the formulation rather than to provide a fully transferable predictive model for real crude oils.