Physics-based models in a closed-loop feedback control of a premixed charge compression ignition (PCCI) engine can improve the combustion efficiency and potentially reduce harmful NOx and soot emissions. A stand-alone multi-zone combustion model has been proposed in the literature using a physics-based mixing approach. The scalar dissipation rate emerged as the determining parameter in the model for mixing among different zones in the mixture fraction space. However, the calculation of the scalar dissipation rate depends on three approaches: three-dimensional computational fluid dynamics (3-D CFD) combustion simulations based on representative interactive flamelet (RIF) model, tabulation, or an empirical algebraic model of the scalar dissipation rate fitted for the given operating conditions of the engine. While the 3-D CFD approach provides accurate results, it is computationally too expensive to use the multi-zone model in closed-loop control. Tabulation or empirical models are computationally cheap but are not physical, and hence, they limit the usability of the model to preset operating conditions. In this work, an integral model for the scalar dissipation rate based on the one-dimensional cross-sectionally averaged multi-phase spray equations is proposed as a first step towards model-based control. Due to the 1-D character of the resulting equations, time to solution is significantly reduced compared to full 3-D CFD models. The model provides distribution of fuel in the liquid and vapor phase as well as the scalar dissipation rate in physical space and time. The integral model coupled to a flamelet solver constitutes the integral combustion model, which can capture unsteady non-premixed combustion behavior. The model is able to reasonably predict ignition delay times for the Spray A case compared to 3-D CFD as well as measurements. The model can capture trends of the ignition delay time with respect to oxygen concentration as well as temperature. While the model is still not sufficiently fast for feedback control, as a physics-based stand-alone model based on the solution of partial differential equations, it will serve as a very good basis for further model reductions. The new method can also be used to generate data to train artificial neural networks that can then be used in model-based feedback control.