Enhanced 2D Proppant-Transport Simulation: The Key To Understanding Proppant Flowback and Post-Frac Productivity

Abstract

Summary It has been assumed that along with fluid viscosity and pump rate, gravity dominates final proppant placement in hydraulic fractures. Results here, based on detailed multiphase-flow modeling, show that other factors such as slurry rheology (effect of adding proppant on slurry viscosity), fluid loss and layered fluid loss, and vertical fracture-width variations often are more important than gravity in controlling placement. 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 to predict this final proppant placement accurately. Most theoretical, modeling, and experimental efforts in this area have focused historically on understanding and predicting only gravity effects on proppant placement. However, for proppant-laden, viscous fluid or 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 fracture closure.A differential-fracture closure occurs when a fracture growing vertically penetrates zones with higher or lower closure stress. After shut-in, higher stress zones "close first." This forces any proppant-laden slurry covering these zones (at shut-in) to migrate to low stress zones where fracture width is greater, and can easily lead to "upward" proppant movement as fracture-closure stress generally decreases with depth.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) toward fluid-loss layers, often corresponding to "pay."As proppant is introduced to fluid, the resulting slurry has a higher density and tries to move downward. However, solids also act to increase viscosity, and more viscous slurry prefers the wide middle of a fracture. This serves to keep proppant near the middle of the fracture, often in the pay zone. This paper discusses the combined effect of these forces on proppant placement in a context of post-frac analysis of several field treatments. Analysis used a fracture model including "rigorous," numerical, 2D material transport, and the often-unexpected results are compared with 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, placing a proppant in the fracture creates this conductive path. The quality of proppant is designed to maintain lasting, high permeability under conditions of in-situ stress, temperature, etc. Because the only goal of field operations is to place this permeable proppant in the desired location, results from numerical design and analysis models must represent proppant transport in the fracture accurately. 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. Because the oil industry normally deals with near-vertical fractures, the influence of gravity on proppant placement and proppant settling is clearly a major concern. Kern et al.1 conducted laboratory experiments to determine a "critical" velocity where no additional sand dune formation would occur. This was followed by important work by Novotny,2 Clark and Quadir,3 and others. These works concentrated on single particle or "Stoke's law"-type proppant settling. Stoke's law can be stated asEquation 1 where the equation in this form must use consistent units. The actual phenomenon is more complex, of course, and final proppant placement is a function of pump rate and the effects of proppant concentration on slurry viscosity and thus on settling rates. In its simple form, however, this still shows settling as a combined function of gravity and viscosity. More recently, it was understood that proppant-laden slurry was denser than the "clean" fluid pad pumped to open a fracture. This heavier slurry tends to sink and tries to under-run the lighter pad fluid. This was probably first discussed (in terms of 3D fracture modeling) by Clifton and Wang.4 This behavior has been proposed as a major influence on proppant placement.5,6 Clark and Zhu7 proposed a dimensionless constant which uses consistent units, written asEquation 2 where values <1 would indicate a strong possibility for convection, while for values >1 lateral flow would dominate and convection-type settling would be minimal. If confirmed, this could prove a valuable tool for modeling, particularly for cases where a rigorous fluid-flow, proppant-transport solution is not used. While Nc is valuable as a screening tool, results and comparisons suggest the problem is more complex than suggested by this dimensionless constant. The additional complexity arises because of variations in fracture width over the fracture height, and effects of proppant on slurry rheology.

A Review of Hydraulic Fracturing Simulation

“…Their numerical results suggest a high leakoff restricts the spread of proppant along the direction of fracture propagation. Moreover, Smith et al [306] concluded that leakoff and the heterogeneity of formation can dramatically change the proppant distribution when the fracture shuts in. Another phenomenon resulting from leakoff is screen-out [334].…”

“…Another example of the P3D model is MFrac (Meyer Fracturing simulators), which has been developed since 1986 [204,205] and is widely used by the petroleum engineering industry. Some other examples and applications of the P3D model can be found in [9,127,306]. Comparisons between 2D models (the PKN model and the KGD model) and the P3D model were conducted by Rahim and Holditch [251] and Rahman and Rahman [255].…”

Fracturing-Fluid Flowback Simulation with Consideration of Proppant Transport in Hydraulically Fractured Shale Wells

“…Qi et al 23 developed a prediction model for proppant flowback, and this model coupled both the fracture shunt model and critical rate model. Smith et al 24 conducted numerical simulation, which considered fluid rheology, fluid loss, gravity, proppant concentration, viscosity, changes in fracture geometry, and in-site stress to model proppant flowback. Hu et al 25 proposed a mechanical model for proppant flowback before and after the fracture closure.…”

Phase-field modeling of proppant-filled fractures in a poroelastic medium

“…Mixing proppant with a Newtonian fluid has been investigated in [1,28,50,68], and with polymers in [64], [24], [69], [48] to name a few. These numerical studies have been performed using boundary element methods, discrete fracture networks or extended/generalized finite elements and have mainly treated 2D planar fractures.…”