First principles models of complex industrial processes are often derived using finite element or finite difference methods. One of the advantages of these models is that the states in the model have a clear physical interpretation. Using such models we can attempt to monitor or control selected physical quantities, even though they may not be directly measurable. Unfortunately the CPU time associated with each model evaluation of these complex models is often far too large for use in modern online monitoring or control algorithms. This paper introduces a general purpose method to approximate the computationally expensive first principles models with a quasi-Linear Parameter Varying (qLPV) model structure. The CPU time associated with the resulting qLPV models is generally considerably less than the original first principles model. The identification algorithm is such that the physical interpretation of the state vector is retained in the identified model. In contrary to other qLPV identification algorithms, the proposed algorithm extensively utilizes the availability of the original first principles model.