Enhanced 2D Proppant Transport Simulation: The Key To Understanding Proppant Flowback and Post-Frac Productivity
Authors: Smith M.B. , Bale A. , Britt L.K. , Hainey B.W. , Klein H.K. 
Published: December 2007

Smith, M.B., SPE, NSI Technologies, Bale, A., SPE, STATOIL Britt, L.K., SPE, Amoco Production Co., Hainey, B.W., SPE, ARCO Exploration & Production Technology, Klein, H.K., SPE, JAYCOR Copyright 1997, Society of Petroleum Engineers, Inc.

Abstract
The goal of a hydraulic fracture treatment is to create a large flow area exposed to the formation, and connected to the wellbore along a conductive path. The only goal of hydraulic fracture models is accurately predicting this final proppant placement! This goal is well understood. However, most of the theoretical, modeling, and experimental effort in this area has historically focused on understanding and predicting only gravity effects on proppant placement. However, for proppant laden, viscous fluid, slurry flowing along a fracture, other forces are always more important than gravity, and can easily cause proppant to move upwards, both during pumping and during fracture closure. Among others, these forces include:Differential Fracture Closure - A fracture growing vertically generally penetrates zones with higher/lower closure stress. After shut-in, higher stress zones "close first," squeezing out proppant laden slurry there, often upwards, to lower stress zones.Fluid Loss - After shut-in of a propped fracture treatment, all fluid must leak-off into permeable formations penetrated by the fracture. Until closure, viscous fluid continues to transport proppant (possibly upward) towards fluid loss layers, often corresponding to "pay".Slurry Rheology - As proppant is introduced to the fluid, the resulting slurry has a higher density and tries to move downward. However the solids also act to increase viscosity, and the more viscous slurry prefers the wide, middle, of a fracture. This serves to keep proppant near the middle of the fracture, which is often right in the pay zone.
This paper will discuss combined effects of these forces on proppant placement. This discussion is placed in a context of post-frac analysis of several field treatments. The analysis used a fracture model including "rigorous", numerical, 2-D material transport, and the often unexpected results are compared to supporting evidence from post-frac well performance. In many instances, the combined effect of proppant placement forces is beneficial, with more proppant placed across the "pay" than suggested by simple models. In other cases, post-shut-in proppant redistribution can (and did) cause catastrophic job failure.

Introduction
The goals of a hydraulic fracture treatment are to increase the flow area exposed to the formation, and then to connect that flow area to the wellbore via a high permeability path. For propped fracture treatments, this conductive path is created by placing a proppant in the fracture. The quality of the proppant is designed to maintain lasting, high, permeability under conditions of in situ stress, temperature, etc. Since the only goal of field operations is to place this permeable proppant in the desired location, the results from numerical design and analysis models must accurately represent proppant transport in the fracture.
The importance of this, has long been recognized, and proppant transport has received its share of attention along with the required analysis/design steps of understanding and predicting fracture geometry and fluid loss. This led immediately to studying effects of gravity on proppant placement.
As anyone falling off a ladder can attest, gravity is a major natural force. Since the oil industry is normally dealing with near vertical fractures, the influence of gravity on proppant placement, and proppant settling, is clearly a major concern, and the study of this began early. Probably the first attention to this aspect of fracturing was by Kerns and Perkin who conducted laboratory experiments to determine a "critical" velocity where no additional sand dune formation would occur. P. 447^