A simplified two-phase flow model using a quasi-equilibrium momentum balance

We propose a simple model of two-phase gas-liquid flow by imposing a quasi-equilibrium on the mixture momentum balance of the classical transient drift-flux model. This reduces the model to a single hyperbolic PDE, describing the void wave, coupled with two static relations giving the void wave velocity from the now static momentum balance. Exploiting this, the new model uses a single distributed state, the void fraction, and with a suggested approximation of the two remaining static relations, all closure relations are given explicitly in, or as quadrature of functions of, the void fraction and exogenous variables. This makes model implementation, simulation and analysis very fast, simple and robust. Consequently, the proposed model is well-suited for model-based control and estimation applications concerning two-phase gas-liquid flow.