Computer Simulations of Proppant Transport in a Hydraulic Fracture
- A.T. Mobbs (Schlumberger Cambridge Research) | P.S. Hammond (Schlumberger Cambridge Research)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Facilities
- Publication Date
- May 2001
- Document Type
- Journal Paper
- 112 - 121
- 2001. Society of Petroleum Engineers
- 1.6.9 Coring, Fishing, 2.5.2 Fracturing Materials (Fluids, Proppant), 5.3.2 Multiphase Flow, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 4.3.4 Scale, 5.1.1 Exploration, Development, Structural Geology
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Equations of motion of a slurry in a narrow slot, such as a hydraulic fracture, are presented and solved numerically to obtain an estimate of the amount of gravity-driven vertical motion of proppant that can occur within a fracture during placement.
Two types of gravity-driven motion are studied: settling of heavy-proppant particles; and convective proppant transport, which refers to the motion driven by large-scale density differences between regions of different proppant concentration.
Computer simulations are performed using realistic parameter values. In particular, the vertical motion of proppant in a slurry in which proppant particles are uniformly distributed across the fracture width (referred to as homogeneous flow) is compared with that in a slurry in which some unspecified, but rapid, process has caused all proppant to migrate across the fracture width into a close-packed sheet at the fracture center (referred to as sheet flow).
In addition to considering a constant channel width, we also investigate the effects of an elliptic-fracture cross section on proppant placement. This fracture shape is predicted by idealized fracture propagation models such as the Perkins-Kerns-Nordgren (PKN) model.
Main conclusions are that during placement:
Proppant settling and convection can occur under practical conditions;
Convection rates are slightly greater in sheet flow than in homogeneous flow, and settling is greatly enhanced in sheet flow. Overall, settling in sheet flow gives the worst vertical motion of proppant. Settling and convection in homogeneous flow cause no problems under conditions considered in this paper;
In elliptic fractures, heavy, proppant-laden slurry can override earlier-pumped lighter pad (zero solids) under most fracturing conditions.
Hydraulic fracturing is commonly used to enhance oil and gas recovery. It involves using a non-Newtonian fluid to pressurize a wellbore until a fracture develops in the rock formation. Fluid flows into the fracture, extending it farther into the reservoir. Particles, known as proppant, are added to the fluid to prevent the fracture from closing completely at the end of the process.
Strong gravity-driven motions can cause uniformity of proppant over the total fracture height to be lost or proppant to be placed over only part of the fracture height. This would be particularly important if there was a shale layer imbedded in the pay zone. If proppant did not extend vertically through the layer and into the above section of the pay zone, production could be reduced dramatically from the upper section. Two types of gravity-driven motions are studied here: proppant settling and convective proppant transport, which refers to the motion driven by large-scale density differences between regions of different proppant concentration.
Almost all fracturing gels used in hydraulic fracturing are viscoelastic with high normal stresses. Nolte1 discusses the general occurrence of migrating proppant particles across fluid streamlines in non-Newtonian and viscoelastic fluids in a pipe or channel and the consequences of such migration. Tehrani et al.2 studied particle migration in laminar flow of non-Newtonian and viscoelastic suspensions in vertical pipe. They observed that the direction in which particles migrate depends strongly on the rheological properties of the suspending fluid. By choosing mean-flow velocities comparable to fracturing conditions, Tehrani et al.2 generated shear-rate gradients in pipe flow similar to those within a fracture. Visual observation showed that migration of particles to the pipe axis is strongest in highly elastic fracturing fluids and occurs within a 3-ft length of pipe, which is considerably shorter than a conventional fracture length of several hundred feet.
The aim of this paper is to investigate the effects of such migration on settling and convection. To simplify the problem and clarify these effects, some processes are ignored. In particular, processes causing migration are not addressed here. Fluid-mechanical mechanisms responsible for migration of particles to form a close-packed sheet at the fracture center are not understood fully, although second-order fluid calculations for a single neutrally buoyant particle in nonuniform shear flow indicate that the combination of fluid elasticity and shear-rate gradients give rise to particle motion in the observed direction.3 Leal4 offers a result for the non-neutrally buoyant case. The authors are unaware of any literature exploring finite concentration effects on migration in flowing elastic fluids. Complications of fluid leak-off and of shear-thinning suspending-fluid rheology are ignored; we consider a fluid of constant viscosity. Effects of fluid elasticity on static settling are also ignored.
We present a 2D mathematical model for predicting proppant transport in a fracture. Flow within the fracture is described using a set of equations formulated in terms of cross-channel averaged fluxes and solved numerically. This formulation permits investigation of the effects of nonuniform proppant concentration across the fracture width. We use the model to compare proppant settling and convection rates in a slurry in which particles are locally uniform across the fracture width with rates in which all proppant has migrated rapidly to the fracture center forming a close-packed sheet. The latter case is a worst assumption; experiments carried out by Tehrani et al.2 show that concentration of particles in the central core may not reach maximum packing. Although migration of proppant particles across fluid streamlines in viscoelastic fluids with high normal stresses has been observed in pipes and channels, the causes of this phenomenon are not well understood.
Computer simulations are performed using realistic parameter values. In particular, we investigate the effects of suspending-fluid viscosity, fracture width and geometry, and volumetric-injection rate of proppant-laden slurry on settling and convection for homogeneous and sheet flow.
Results show that there are some circumstances where significant vertical motion of proppant can occur within the time scale of a fracturing job. The observation that convection can occur on the time scale of a fracturing job is consistent with other publications.5,6 Convection is slightly enhanced and settling is greatly enhanced if proppant has migrated into a central close-packed core compared with the case when local solids distribution is uniform. A criterion for avoiding gravity-driven rearrangements requires a large suspending-fluid viscosity, short pumping time, and small fracture width.
In elliptic-shaped fractures it is found that, under most fracturing conditions, heavy-proppant slurry can override lighter pumped pad (zero solids).
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