Pseudo-3D (P3D) fracture models have been extensively researched. However most of these models are either very simple or too complex. This study proposes a workflow, based on equilibrium height concept (EHC) and layered reservoir data, to calculate fracture height along length axis and optimally size frac treatments.
The main calculation is based on Linear Elastic Fracture Mechanics. It estimates the fracture height by equating stress intensity factor at tip & bottom of frac to fracture toughness of that layer. The original model was designed for a 3-layer system, which inadequately captured formation heterogeneity especially when fracking interbedded reservoirs. To overcome the limitation, this workflow extrapolates the EHC using reservoir layer table where rock properties are defined with respect to depth. Initially a fracture height is assumed to calculate treatment pressure, which is then compared with pressure from 2D models. If the difference is greater than error limit, higher height is assumed to rerun the model. For each height, fracture top & bottom depths are calculated using frac geometric description. These depths are correlated with reservoir table to obtain rock parameters for those layers. This algorithm is run iteratively until a solution is achieved within error limit. As rock parameters are correlated for each run, any layer above and below the target zone can act as bounding layer therefore no grouping of layers is required. Further, the frac is divided in number of units along the length axis and optimum width & net pressure is calculated for each unit to estimate its height. Final output is a schematic of fracture height all along the length axis that is calculated from reservoir description. Number of units in which frac is divided along length axis to calculate height should be a compromise between resolution and computational time. As height is calculated from P3D module for all units, this is analogous to 3D models that work on mesh-grids, hence workflow is named Quasi-3D (Q3D) model. Finally, the calculated height can be used in Unified Fracture Design module to optimally size the frac treatment honoring height constraints.
Q3D model results are compared with original model to evaluate differences and quantify its superiority over previous algorithms. The use of multilayer model allows the understanding of height growth therefore penetration into unwanted layers can be avoided. As height is also calculated away from wellbore, dipping of fracture or unwanted zone penetration away from the wellbore can also be observed and avoided by adjusting treatment size. Lastly, couple of worked examples are discussed to demonstrate the working of this model. Q3D model allows estimation of frac height in asymmetric multilayer lithology without grouping layers. Further, complete cross-section of height is constructed along the length axis emulating working of 3D models.