A new analytical model of hydraulic fracturing under point-source conditions (LMN) has recently been proposed1 and later on corrected from a series of non critical mistakes.2 Its results for viscous fluids do agree with field evidences of an almost constant, however slightly increasing net pressure all along pad stages.
One severe limitation of the LMN model is its assumption of laminar flow, which had initially been made to ease up the mathematical treatment of the basic differential equation of the model, hence to rapidly come up with results directly applicable to the most common hydraulic fracturing jobs in highly deviated wells, i.e. those making use of crosslinked gels as proppant carriers.
The cases of Step Rate Tests pumped with water (or thin linear gels) and of the so-called riverfracs were deliberately disregarded during this first phase of the development of the LMN model. The present paper now addresses these cases by extending the latter to turbulent flow.
It is found that the resulting equation of the net pressure indicates an even weaker, however still positive, slope of the diagnostic (Nolte-Smith) plot than under laminar flow. In other words, the fracture width at the wellbore is about constant all along a fracturing treatment pumping a thin fluid at constant rate.