We have published already a three-layer p-3D fracture design optimization using the Unified Fracture Design (UFD) approach; fracture height, resulting from fracture geometry optimization and therefore net pressure, was matched against the value resulting from fracture height migration at the same pressure.
For a multi-layered formation a more robust and more general approach is suggested in this work. First a range of admissible reference treating pressures is prepared. For each pressure level we determine the up-down tip locations and hence we obtain the fracture height map. Thus, there is a relationship between induced height and net pressure and this relationship can be calculated from Linear Elastic Fracture mechanics before the actual design optimization is carried out.
According to the applicable fracture propagation model, for a given fracture half length, there exists a width and henceforth a net pressure. The ancillary height is a geometric byproduct. Matching the net pressure and height with the LEFM independently determined pair of height and net pressure results in a solution that satisfies both. The dimensionless productivity index, JD, is then calculated.
For the fracture half lengths, ranging from a minimum (corresponding to aspect ratio one with respect to the perforated thickness) to a laterally fully penetrating fracture, we repeat the above procedure to calculate JD and so forth, until a maximum JD is accomplished.