Proppant Transport
Authors: Novotny E.J. 
Published: December 2007

Novotny, E.J., Member of SPE-AIME, Exxon Production Research Co.

Abstract
A method is presented for predicting:the transport of proppant in a vertical fracture during a hydraulic fracturing treatment,the settling of the proppant during closure of the fracture following the treatment, andfrom the final distribution of proppant, the increase in well productivity that results from the treatment.
The examples given illustrate that proppant settling during fracture closure can be important in the design of a hydraulic fracturing treatment. Field data illustrate the time required for fracture closure.
The computer program which models the fracturing process uses proppant settling velocities obtained from extensive laboratory data collected under simulated fracturing conditions. Proppant settling predictions include the effects of non-Newtonian fluids, concentrated slurries of proppant, fracture walls, and changes in fluid temperatures along the fracture. These substantially affect the settling velocity of the proppant and must be considered to obtain a realistic prediction of proppant transport.

Introduction
In hydraulic fracturing, fluid is injected into a well at a high enough rate and pressure to crack open the productive formation. when the fracture is estimated to be sufficiently wide and long, sand or some suitable propping material is injected along with additional fluid. The function of the proppant is to keep the fracture open after injection stops. The amount of production increase, or stimulation, from a hydraulic fracturing treatment depends on the conductivity and final distribution of proppant in the fracture.
While proppant is injected into the fracture, it travels along with the fluid away from the wellbore and settles downward at a rate that depends on the fluid properties and surrounding conditions. When the treatment is over, the fracture closes as fracturing fluid is lost through the permeable walls of the fracture. while this is happening, the proppant continues to settle until:the proppant forms a bank at the bottom of the fracture,the proppant concentration in the slurry becomes so high that it can no longer settle, orthe fracture closes on the slurry, trapping the proppant.
Pressure measurements following a treatment have indicated fracture closure in the field. Sometimes the rate of closure can determine the success or failure of the treatment. Until now, however, fracture closure has not been realistically considered in treatment design.
The prediction of proppant transport is intricate, because as the slurry travels from the wellbore, several things occur: The proppant and fluid are heated and the formation rock is cooled. Because fluid is continuously lost to the reservoir, the proppant concentration increases and the fluid velocity decreases. The width of the fracture decreases away from the wellbore, which alters the fluid velocity. These and other factors that affect the settling velocity of the proppant and its velocity along the fracture are too numerous and complex to model adequately unless numerical computational techniques are used.
Previous research that modeled the transport of proppant while fracturing did not model fracture closure. This paper presents a method that models the entire fracturing process, including closure. The equations for proppant settling are developed theoretically and verified experimentally. Most stimulation predictive methods assume a rectangular fracture, but in the method presented here the fracture permeability, width, and effective height can vary with fracture length. The following section discusses the importance of accurate proppant transport predictions for optimum treatment design, emphasizing fracture closure. Details of the computer model, theory, and experimental work will then be presented.

RESULTS AND DISCUSSION
Four computer-simulated example treatments are used to illustrate the importance of accurate proppant transport predictions, including the effect of fracture closure.