We have established the concept of Unified Fracture Design (UFD) to maximize the dimensionless productivity index (JD) following a hydraulic fracture treatment. For a given mass of proppant there is a specific dimensionless fracture conductivity, which we called the optimum, at which the JD becomes maximum. The Proppant Number is a seminal quantity unifying the propped fracture and the drainage volumes and the two permeabilities, those of the proppant pack and the reservoir.
For each injected proppant mass there is a corresponding Proppant Number and, at the optimum conductivity, the dimensionless PI can be readily determined. Increasing the proppant mass or the proppant-pack permeability would result in an increase in the JD, which has a maximum limit of approximately 1.9. In a recent publication we have shown how to push the limits in hydraulic fracturing by injecting very large volumes of proppant of very large retained permeability.
There are physical constraints to our approach, one of which is an upper limit of the net pressure resulting from both the physical limitations of injection equipment and tubulars but also from the need to prevent undesirable fracture height migration. However, the use of much larger proppant pack permeability leads to a correspondingly smaller width for the same fracture conductivity. The smaller width requirement allows the injection of far larger proppant masses before the net pressure constraints are met. This is a departure from current industry practices, which are aimed to "save" injection costs for a specific rate. Our approach, in medium to high permeability formations is to maximize the rate within the injection constraints. Rudimentary economics suggest that such treatments pay for themselves in just a few days of incremental production.
We present here field case studies and results showing the application and success of our design approach.
Valkó and Economides1,2 introduced a physical optimization technique to maximize the productivity index.
They introduced the concept of the dimensionless Proppant Number, Nprop, given by:
where Ix is the penetration ratio and CfD is the dimesnionless fracture conductivity, Vr is the reservoir drainage volume, and Vp is the volume of the proppant in the pay. It is equal to the total volume injected times the ratio of the net height to the fracture height.
They also presented convenient algorithms to calculate JD and they found that for a given value of Nprop there is an optimal dimensionless fracture conductivity at which the productivity index is maximized.
At "low" proppant numbers, the optimal conductivity, CfD=1.6. The absolute maximum for JD is 6/p=1.909 (this value is the productivity index for a perfect linear flow in a square reservoir). When the propped volume increases or the reservoir permeability decreases, the optimum dimensionless fracture conductivity increases somewhat.
Under the assumption of the pseudosteady-state flow regime Valkó and Economides1,2 presented correlations for the maximum achievable dimensionless productivity index as a function of the proppant number.
Similarly correlations have been presented for the optimal dimensionless