The majority of planar hydraulic fracture models use two distinct approaches. The first one, referred to as the planar 3D model, is more accurate but also very CPU intensive. The second one is referred to pseudo-3D (P3D) model, and separately considers the vertical growth and horizontal propagation of the fractures. This approach is less CPU intensive, but requires the fracture being initiated in the lower stress layer. In practice, this assumption is not always verified, and the fracture height growth can become unstable. This paper presents a new model as an enhancement of the P3D, which consists of multiple rows of elements vertically stacked and connected. For each row of elements, the assumption of the fracture front being in the lower stress layer is satisfied locally. The width profile and stress intensity factor at the top and bottom of the fracture depend on the stress profile and the pressure profile along the stack of elements. This model predicts the fracture height more accurately than the P3D model, and gives results close to the ones from the full planar 3D model.
The rapid development of shale resources in the past decade has brought a focus on the process of hydraulic fracturing. Shale reservoirs tend to be characterized by a complex 3D stress field and vertically heterogeneous mechanical properties, which have always been challenging for hydraulic fracturing modeling and particularly for properly predicting the shape of an induced fracture . Most state-of-the-art planar fracture simulators use two distinct approaches. In the first one, referred to as the planar 3D model (PL3D), the fracture is assumed to be a plane and its entire footprint is discretized into elements. The equations governing fluid flow, elasticity, and mass balance are solved numerically, coupled with the fracture propagation rules. This approach is very accurate but also very CPU intensive . This type of model is mostly used when a large portion of the fracture propagates outside of the zone where the fracture was initiated and significant amount of vertical flow is expected. The second approach is based on the cell-based pseudo-3D (P3D) model , which separately considers the vertical growth and horizontal propagation of the fractures. In this approach, the width profile and fracture height are calculated based solely on the local pressure and local vertical stress profile. This approach is less CPU intensive, but relies on several assumptions including the fracture being initiated and its leading front propagating in the lower stress layer compared to the neighboring layers above and below. If this is not the case, the fracture height growth can become unstable, since it is not directly correlated to the global fracture mass balance as in the PL3D model, and this can lead to significant inaccuracy in the predicted fracture height growth.