An Original Contribution to Multiscale Fracture Propagation Theory for Hydraulic Fracturing in Laminated Shale-Carbonate Sequences of the Sokoto Basin, North West Nigeria

Hydraulic fracture propagation in laminated shale-carbonate sequences involves complex fracture geometry evolution governed by the interaction between hydraulic pressure, natural fracture networks, bedding plane interfaces, and the mechanical contrast between alternating rock layers. Existing fracture propagation theories based on planar fracture assumptions are inadequate for the multi-layer mechanical stratigraphy characteristic of the Sokoto Basin sequence. This study develops an original theoretical contribution to multiscale fracture propagation in laminated shale-carbonate sequences applicable to hydraulic fracturing operations in the Sokoto Basin, North West Nigeria. The theoretical development introduces a cohesive zone model for hydraulic fracture propagation that incorporates anisotropic fracture toughness, opening mode versus shear mode competition at bedding interfaces, and fluid-lag effects arising from the contrast between fluid flow and fracture front propagation rates. An original criterion for hydraulic fracture containment versus breakthrough at shale-carbonate interfaces is derived by analysing the energy balance at the fracture tip under the mixed-mode loading conditions arising from fluid pressure and far-field stress contrasts. Finite element implementation of the theoretical model is validated against physical experiments in synthetic layered specimens tested in a true-triaxial fracturing cell under simulated reservoir stress conditions. Parametric studies demonstrate that fracture containment within the carbonate interval requires a minimum horizontal stress contrast between shale and carbonate layers of 800 psi, below which fractures propagate into adjacent intervals and reduce stimulated reservoir contact. Keywords: hydraulic fracture propagation, laminated shale-carbonate, cohesive zone model, Sokoto Basin, fracture containment.