A Method to Minimize the Cost of Pumping Fluids Containing Friction-Reducing Additives
Authors: Pruitt G.T. 
Published: December 2007

Abstract
This paper describes a method to predict friction loss of fluids which contain friction-reducing additives and to determine mathematically the additive concentration which will provide the minimum cost of performing a given fracturing operation. Equations are presented to predict friction pressure drops of both Newtonian and non-Newtonian fluids containing a water-soluble polymer. These equations were developed for oilfield tubular goods from 1 1/4 to 8 5/8 in. in diameter. These equations were derived from laboratory data in pipes up to 2 in. in diameter. The additive employed is capable of reducing horsepower requirements by a factor of five or six.
Introduction
The use of friction-reducing additives for fracturing operations is a routinely accepted practice. Until now, no analytical method has been available to select the correct amount of additive to provide the most horsepower delivered to the formation at a minimum cost. The purpose of this paper is to help remove this deficiency.
State of the Art
Recent evidence has shown that adding less than 0.01 per cent of some additives to water can reduce the usual turbulent frictional losses by as much as 83 per cent. This means that the horsepower requirements for a given flow rate can be reduced by a factor of six. Several attempts have been made in recent years to correlate these friction factors and predict the friction reduction. In each case the predicted friction is higher than is actually obtained. In addition, Bowen. Savins and others pointed out that the magnitude of the friction reduction is a function of the pipe diameter.
The details of the flow mechanisms that produce the friction reduction are not well understood for the non-Newtonian fluids involved.
Shaver and Merrill have classified these non-Newtonian fluids as pseudoplastics and defined them as "ones which have a viscosity that decreases reversibly with increasing shear rate". This means that as the shear rate is increased the apparent viscosity decreases.
Metzner and Reed, Shaver and Merrill, and Dodge and Metzner set forth equations which considered this decreasing viscosity by using the power law equation (which is given later) as a tool for predicting friction factors for pseudoplastic fluids.
Recent studies by Crawford, Metzner, Savins and others have revealed that the "power law" is inadequate for predicting friction losses. The friction reductions obtained are much greater than predicted by the present available correlations.
Many different types of additives are capable of reducing friction in water. The authors have investigated several dozen which give excellent reductions when added to water. Some linear and high-molecular-weight additives are able to reduce friction by as much as 40 per cent at 2 ppm and 60 per cent at 10 ppm. It is exciting and a little perplexing to contemplate a mechanism which will explain a phenomenon in which the addition of 1 to 2 ppm of a polymer to a solvent will produce a drag reduction of 20 to 40 parts/hundred, Yet if 1 cc of fluid is considered with a polymer concentration of 1 ppm, the aggregate length of polymer molecules in this 1 cc can be of the order of 100 million cm!
We propose that this network of molecules forms an elastic medium which is capable of absorbing and storing the turbulent mixing energy which would otherwise be dissipated.
Other additives which are comparatively short also give excellent friction reduction, but higher concentrations are needed. It has been the authors' experience that these low-concentration, high-molecular-weight additives are unable to sustain this excellent friction reduction at high rates of flow because of mechanical degradation.
JPT
P. 641ˆ