T his study presents an extension of the Tiab’s Direct Synthesis (TDS) technique to Multi-Fractured Horizontal Wells (MFHWs) in shale formations, using a five-region analytical model. The model accounts for pressure-dependent rock and f luid properties and incorporates multiple linear flow regimes to represent the complex interaction between the matrix and fractures. Using dimensionless analysis, a set of analytical expressions was derived to estimate key reservoir parameters such as half-fracture length, reservoir length, and effective permeability. The methodology also identifies critical flow regimes and transition points-early linear flow, intermediate pseudosteady-state, transitional linear flow, and late-time pseudosteady state-through characteristic slopes and curve intersections in pressure and reciprocal rate derivatives.

Although a wide range of permeability and geometric variations were evaluated, two synthetic examples are presented to validate the methodology. The estimated parameters closely matched the input values, with relative errors below 2%, confirming the accuracy of the proposed approach. Despite the robustness of the methodology, the dimensionless permeability modulus showed inconsistent unification across all cases, indicating an area for future refinement. Overall, the extended TDS technique offers a reliable, practical, and theoretically sound framework for interpreting transient tests in unconventional shale reservoirs with MFHWs. Also, equations are presented for the application of straight-line conventional analysis.