This contribution investigates hydraulic fracturing in fluid-saturated porous media using a second-order computational homogenization approach [1, 2]. The method models a heterogeneous porous medium by distinguishing two spatial scales, referred to as the micro- and macroscales [3, 4]. At the microscale, the topological heterogeneity of the structure and material nonlinearities are explicitly resolved, whereas the macroscale describes the porous medium in an averaged sense. Compared to first-order homogenization, the adopted second-order approach relaxes the requirement of strict scale separation and incorporates intrinsic length-scale effects originating from the microscale [5]. At the microscale, Biot's theory of poroelasticity is considered, combined with Darcy-type fluid flow in the porous matrix and Poiseuille-type flow within fractures [2]. The resulting macroscopic model is a gradient-enhanced poromechanics formulation governed by a variational principle of minimization type [1]. The presentation outlines the modeling framework and its numerical implementation, and concludes with numerical examples demonstrating fluid-driven fracture initiation and propagation in elastic porous media. References [1] E. Polukhov and M.-A. Keip. Second-Order Computational Homogenization of Nonlinear Fluid Flow through Porous Media. International Journal for Numerical Methods in Engineering, 127:e70100, (2026). [2] Miehe, Christian, Steffen Mauthe and Stephan Teichtmeister. Minimization principles for the coupled problem of Darcy-Biot-type fluid transport in porous media linked to phase field modeling of fracture. Journal of the Mechanics and Physics of Solids, 82, 186–217 (2015). [3] V.G. Kouznetsova, M.G.D. Geers and W.A.M. Brekelmans. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Computer methods in Applied Mechanics and Engineering, 193, 5525–5550 (2020). [4] I. A. Rodrigues Lopez and F. M. Andrade Pires. Unlocking the potential of second-order computational homogenisation: An overview of distinct formulations and a guide for their implementation. Archives of Computational Methods in Engineering, 1–55 (2021). [5] E. Polukhov and M.-A. Keip. Computational homogenization of transient chemo-mechanical processes based on a variational minimization principle. Advanced Modeling and Simulation in Engineering Sciences, 7, 1–26 (2020).