The effective placement of proppant in a fracture has a dominant effect on well productivity. Existing hydraulic fracture models simplify proppant transport calculations to varying degrees and are often found to over-predict propped or effective fracture lengths by 100 to 300%. A common assumption is that the average proppant velocity due to flow is equal to the average carrier fluid velocity, while the settling velocity calculation uses Stokes' law. To accurately determine the placement of proppant in a fracture, it is necessary to rigorously account for many effects not included in the above assumptions. In this study, the motion of particles flowing with a fluid between fracture walls has been simulated using a coupled CFD-DEM code that utilizes both particle dynamics and computational fluid dynamics calculations to rigorously account for both. These simulations determine individual particle trajectories as particle to particle and particle to wall collisions occur and include the effect of fluid flow and gravity. The results show that the proppant concentration and the ratio of proppant diameter to fracture width govern the relative velocity of proppant and fluid. Further, the dependencies of settling velocity on apparent fluid viscosity, proppant diameter and the density difference between the proppant and fluid predicted by Stokes' law were found to apply. However, additional effects have been quantified and shown to substantially alter the predictions from Stokes' law. Proppant concentration and slot flow Reynold's number were both shown to modify the settling velocity predicted by Stokes' law, as does the ratio of proppant diameter to slot width. The effect of leak-off was found to be negligible in terms of altering either the settling velocity or the relative velocity of proppant and fluid. The models developed from the direct numerical simulations have been incorporated into an existing fully 3-D hydraulic fracturing simulator. This simulator couples fracture geomechanics with fluid flow and proppant transport considerations to enable the fracture geometry and proppant distribution to be determined. Unlike all previous studies, these effects are included together and so are shown to be inter-dependent, allowing us for the first time to accurately model proppant transport. As noted above, proppant velocities have been accurately determined without simplifying approximations and with all relevant effects included, showing inter-dependence between the different effects. Two engineering fracture design parameters, injection rate and fluid rheology, have been varied to show the effect on proppant placement in a typical shale reservoir. This allows for an understanding of the relative importance of each and optimization of the treatment to a particular application.

No abstract

Summary The effective placement of proppant in a fracture has a dominant effect on well productivity. Existing hydraulic-fracture models simplify proppant-transport calculations to varying degrees. A common assumption applied is that the average proppant velocity caused by flow is equal to the average carrier-fluid velocity, while the settling-velocity calculation uses Stokes’ law. To more accurately determine the placement of proppant in a fracture, it is necessary to account for many effects not included in previous assumptions. In this study, the motion of particles flowing with a fluid between fracture walls is simulated with a coupled computational-fluid-dynamics/discrete-element method (CFD/DEM) code that uses both particle dynamics and CFD calculations to account for both particles and fluid. These simulations (presented in metric units) determine individual particle trajectories as particle-to-particle and particle-to-wall collisions occur, and include the effect of fluid flow. The results show that the ratio of proppant diameter to fracture width governs the relative average velocity of proppant and fluid. A proppant-transport model developed from the results of the direct numerical simulations and existing correlations for particle-settling velocity has been incorporated into a fully 3D hydraulic-fracturing simulator. This simulator couples fracture geomechanics with fluid-flow and proppant-transport considerations to enable the fracture geometry and proppant distribution in the main hydraulic fracture to be determined. For two typical shale-reservoir cases, the proppant placement and width distribution have been determined, allowing comparison at the hydraulic-fracture scale, including effects observed at the particle scale. This allows for optimization of the treatment to a specific application, and the results are presented in oilfield units, considered more familiar to our readers.

In conventional reservoirs, pressure communication between wells is ascribed to hydraulic diffusion through the rock matrix. In this work we show that in unconventional (low-permeability) reservoirs, pressure communication due to matrix diffusion is insignificant, and pressure changes observed in an offset monitor well during stimulation of a nearby well are primarily due to poroelastic effects. We quantify the pressure transient response observed through external downhole gauges in monitor wells, when an adjacent well is fractured. Our goal is to model this poroelastic response and obtain important reservoir mechanical and flow properties, as well as hydraulic fracture geometry. A fully-coupled, 3-D, poroelastic, compositional, reservoir-fracturing simulator was used to simulate dynamic fracture propagation from a treatment well and compute the resulting pressure changes at one or more monitor wells. The pressure transient response is shown to depend on the reservoir fluid and formation properties (permeability, Biot's coefficient, stress anisotropy) and reservoir mechanical properties (Young's modulus). The impacts of hydraulic diffusivity versus poroelastic pressure response are compared. Type curves are presented that allow the pressure transient response to be interpreted for any general reservoir and well configuration. These type curves can be used to obtain reservoir mechanical and flow properties and the geometry of the propagating fracture. We show that modeling the fracture as a discrete discontinuity (as opposed to high permeability grid- blocks) is essential to obtain good agreement with field pressure observations. The pressure observed in the monitor well first decreases and then increases over time as the growing fracture interacts poroelastically with the monitor well. It is shown that this pressure transient signature is dominated by poroelastic effects for most unconventional reservoirs. The poroelastic response depends on the reservoir fluid type (gas, oil) and the mechanical properties of the reservoir. To simplify the quantitative interpretation of the pressure transient response we have developed type curves that allow us to determine the rock elastic and flow properties and the evolving geometry of the propagating fracture. If multiple monitor wells are utilized, the relative communication between different vertically separated reservoirs and the effects of the altered stresses in the reservoir induced by prior production / depletion can clearly be observed. We present, for the first time, general type curves for interpreting the pressure transient response of monitoring wells when an adjacent well is being fractured. Our representation of the propagating hydraulic fracture as an explicit discontinuity in a poroelastic medium is crucial to capture the poroelastic response observed. The impacts of reservoir heterogeneity (layering), fracture geometry, reservoir mechanical properties, hydraulic diffusivity and prior depletion on the pressure response are quantified. The interpretation of inter-well pressure interference data using the methods described in this paper presents a powerful new fracture diagnostic method.

No abstract