Water-fracs, consisting of proppant pumped with un-gelled fluid are the type of stimulation used in many low-permeability reservoirs throughout the United States. The use of low viscosity, Newtonian, fluids allows the creation of long narrow fractures in the reservoir without the excessive height growth often seen with cross-linked fluids. Proppant transport is a central issue in all these treatments because of the low viscosity of the fracturing fluid. New models for proppant transport and settling in hydraulic fractures were developed and implemented in a 3-d hydraulic fracturing code. It is shown that a simple Stokes settling model is grossly inadequate. The proppant settling models developed in this paper account for the effects of fracture walls, changes in settling velocities and rheology caused by changes in proppant concentration, turbulence effects due to high fluid velocities and inertial effects associated with large relative velocities between the proppant and the fluid. Narrower fractures, higher proppant concentration and smaller proppant size reduce settling whereas turbulence leads to an increase in settling. Results are presented to show how the settling velocities are impacted by fluid velocity, proppant size, fluid rheology and fracture width. In most instances settling velocities differ significantly from the Stokes settling velocity. The new proppant settling model was incorporated into a 3-D hydraulic fracture simulator (UTFRAC-3D). Simulation results show that when settling is accounted for, significantly shorter propped lengths are obtained. The narrow fractures associated with water-fracs alter settling and thereby alter the proppant placement significantly. Although increasing fluid viscosity can reduce settling rates, increased height growth reduces the distance to which proppant can be placed. This clearly suggests a need to optimize fluid rheology. The improved fracture simulator can be used to better design fracture treatments (fluid rheology, injection rates, proppant concentration and size) for better proppant placement under a given set of in-situ stress conditions. Introduction Water-fracs are commonly applied in low permeability gas reservoirs. These treatments involve pumping low viscosity ungelled fracture fluids. The low viscosity of the slick water leads to long created fracture lengths. However, due to high settling velocities of the proppant in the low viscosity fluid, the propped lengths achieved can be very small. Modifications to the water-frac stimulation design are needed to transport proppant further out into the fracture. This requires suspending the proppant until the fracture closes without generating excessive fracture height. Proppant transport clearly is a central issue in all these treatments. An improved proppant transport model is presented that can accurately model proppant transport when either un-gelled or cross-linked fluids are used to place the proppant. The use of this proppant transport model will allow engineers to customize treatment designs for individual wells. The complete model for proppant transport in hydraulic fractures was incorporated into UTFRAC-3D, a fully three-dimensional hydraulic fracture simulator. The proppant transport equations were solved on an adaptive finite element mesh. The settling of the proppant was modeled taking into account the change in settling velocities and rheology due to changes in proppant concentration, turbulence effects due to high fluid velocities, and inertial effects associated with large relative velocities between the proppant and the fluid. Inertial effects become significant at high settling velocities (Rep>2) and are discussed in the next section. The effects of particle concentration, fracture width and turbulence are discussed in the following sections. An example calculation is shown to demonstrate the importance of each of the correlation factors applied to the Stoke's settling velocity. Finally, the settling correlations are incorporated into a proppant transport model in a fully 3-D fracture simulator (UTFRAC-3D). Results from the model are discussed in the last section. The project is co-funded by the US Department of Energy - National Energy Technology Laboratory.
Neutrally buoyant particles in low-Reynolds-number pressure-driven suspension flows migrate from regions of high to low shear, and this migration is a strong function of the local concentration. When the particle density differs from that of the suspending fluid, buoyancy forces also affect particle migration. It is the ratio between the buoyancy and viscous forces, as quantified by a dimensionless buoyancy number, which determines the phase distribution of the suspension once the flow is fully developed. Although several experiments have verified shear-induced particle migration in neutrally buoyant suspensions, data for particle migration when buoyancy effects are important are scarce. Electrical impedance tomography (EIT) is used here to non-invasively measure particle concentration across a pipe arising from the low-Reynolds-number flow of heavy conducting particles and light non-conducting particles in a viscous suspending fluid. A range of buoyancy numbers was investigated by varying the flow rate. In all of the experiments, a significant fraction of the particle phase was observed to migrate towards the top or bottom of the pipe, depending on the relative density of the particles. The amount of migration away from the centre of the pipe increased with increasing magnitude of the buoyancy number. Furthermore, observations of the phase distribution at several positions downstream of the inlet indicate that these suspension flows become fully developed earlier than that observed for neutrally buoyant particles. A scaling analysis for the prediction of the fully developed length is presented, which predicts shorter lengths for higher buoyancy numbers and is consistent with experimental observations. The experimental data were compared to an isotropic suspension balance model, and it was found that the particle phase distributions predicted by this model agree fairly well with the experimental observations.
The phase distribution of a bimodal distribution of negatively buoyant particles in a low-Reynolds-number pressure-driven flow of a suspension in a horizontal pipe is measured using multi-frequency electrical impedance tomography (EIT). Suspensions of heavy silver-coated particles and slightly heavy PMMA particles exhibit different effective conductivities depending on the frequency of an applied electrical current. This difference allows the separate imaging of the phase distribution of each particle type and the composite suspension. At low flow rates the dense particles tend to distribute in the lower half of the pipe The particles are resuspended toward the centre as the flow rate is increased. The slightly heavy particles tend to accumulate closer to the centre of the pipe. The presence of the nearly neutrally buoyant particles enhances the resuspension of the heavy particles compared to that of a suspension of heavy particles alone at the same volume fraction. A suspension balance model is used to theoretically predict the distribution of particles in the flow assuming an ideal mixing rule for the particle partial pressures. The agreement between the predictions and the experimental observations is qualitatively correct and quantitatively fair.
Neutrally buoyant particles in low Reynolds number, pressure‐driven suspension flows migrate from regions of high to low shear. When the particle density differs from the suspending fluid, buoyancy forces affect this particle migration. The ratio between the buoyancy and viscous forces, as quantified by a dimensionless buoyancy number, determines the phase distribution of the fully developed suspension. Electrical resistance tomography (ERT) was used to visualize and quantify particle migration in low Reynolds number pressure‐driven pipe flows of dense and light particles suspended in a viscous fluid. The measured phase distributions are compared to the predictions of a modified suspension balance model.
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