In recent years, an increasing effort has been put into the study of enhanced oil recovery (EOR) processes, especially miscible gas injection. A key parameter in the design of a miscible gas injection process is the minimum miscibility pressure (MMP), the minimum pressure at which the local displacement efficiency approaches 100%. For n_c components, it is well known that the compositional path of the process, i.e. path in the compositional space representing the total composition, consists of n_c - 1 key tie lines and n_c - 2 non tie lines. The multi-contact miscibility of this process is controlled by a sequence of n_c - 1 key tie lines: the initial tie line, the injection tie line, and n_c – 3 crossover tie lines. The MMP is therefore the lowest pressure at which any of the key tie lines is a critical tie line. There are many criteria that can be used to determine the MMP. In our recent work, we demonstrate that zero key tie-line length is a robust criterion for determining the MMP. Upon increasing pressure, the pressure at which the tie-line length of one of the n_c - 1 key tie lines reaches zero is the MMP. Therefore, the problem reduces to how to identify key tie lines. Currently, the only method proposed to identify key tie lines is the tie-line intersection approach, which states that any two adjacent key tie lines must intersect. By solving 2n_c (n_c-1) equations, all n_c - 1 key tie lines can be found. The main problems for this approach are the determination of initial guesses and the non-uniqueness of the solution. In this work, a new approach based on our multiple-mixing-cell model is proposed to identify the key tie lines, and therefore to calculate the MMP. A multiple-mixing-cell model is a discrete model of a continuous gas injection process in the slim tube experiment. A packed slim tube is discretized into a series of constant volume cells and the continuous gas injection is discretized into a series of constant batch volumes. In this approach, for n_c components, we find that there are n_c+1 constant-composition zones and n_c-1 key tie lines. Upon increasing the batch number of the injected gas, these key tie lines appear in a reverse order, i.e., the initial tie line appears first and the injection tie line appears last. This finding leads to a new approach to identifying the key tie lines. This approach provides a unique solution to find all the key tie lines and is therefore particularly suitable for gas injection studies. Predicted results from the proposed approach are shown to be in excellent agreement with slim tube data and other slim tube simulators presented in the literature.