We present a fully implicit mixed hybrid finite-element (FE) formulation for general-purpose compositional reservoir simulation. The formulation is locally conservative, and the momentum and mass balance equations are solved simultaneously; including Lagrange multipliers on element interfaces. The method utilizes automatic differentiation for the Jacobian construction. This hybrid FE approach accommodates unstructured grids, and we present black-oil and compositional test cases with permeability tensors. We also discuss the accuracy and computational efficiency for the new formulation. For all tests, we compare the performance and accuracy of the proposed approach with the Multi-Point Flux Approximation (MPFA-O) method.

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