Controlled fracture geometry is one of the most important criteria that measure the success of a hydraulic fracturing treatment. Typical stress conditions often lead to generation of a planar vertical fracture. Even for this simple geometry, fracture growth in a multilayered rock depends on many factors, such as stress, toughness and modulus contrasts across layers, fracturing fluid viscosity and injection rate. In the present work, a new cell-based pseudo-3D (P3D) model, which uses plane strain deformation in each vertical cross-section and simplified 2D flow assumptions, is described, with an aim to extend the classical P3D model to consider the effect of multiple elastic layers. To capture the effect of viscous fluid flow on height growth, the flow direction at a point along a cell is taken either lateral or vertical, depending on the local pressure level. The lateral flow region is divided into a so called central part that is subject to the maximum fluid pressure in a cell and the vertical flow region which is called the filling segment or part of the cell. The vertical and lateral fracture growth is controlled by the toughness criterion, and, the lateral stress intensity factor is used to convert a filling segment into the central part so as to accelerate lateral fracture growth by changing the local pressure level to the maximum of the cell. The governing equations associated with the problem are provided. A comparison is made between numerical results and the fully 3D (F3D) simulations for a vertically planar fracture propagating in a homogeneous rock subject to stress contrast. The numerical results appear reasonably acceptable. Some solution features associated with the proposed model are delineated. In addition, a special example for hydraulic fracture propagation in a layered rock is examined and the fracture height is found to increase much slower than the fracture length.

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