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A composite reservoir is one with multiple lateral compartments; each having distinct rock and fluid properties separated by geologic discontinuities. Using transform methods, a general three dimensional point source semi-analytical solution for the drawdown response in composite clastic and naturally fractured systems separated by a leaky fault is developed. This solution is converted to line source for horizontal and vertical wells and plane source for hydraulically fractured wells, while treating the fault as a thin finite conductivity fracture. For the first time, it is documented that the intersection time between the long-time approximation of both observer pressure drawdown and observer pressure derivative is unique. Commercial simulator and field data from the Niger Delta was used to validate this model and direct synthesis of reservoir parameters from the resulting equations for various wells under different boundary conditions are examined. The result of this work is attractive where formation juxtapositions separated by leaky faults in the reservoir are suspected to allow flow from adjacent fields and where vertical permeability plays a major role in depletion.