Numerical modeling of non-Newtonian fluid flow in fractures and porous media

Non-Newtonian fluids having Bingham or power-law rheology are common in many applications within drilling and reservoir engineering. Examples of such fluids are drilling muds, foams, heavy oil, hydraulic-fracturing and other stimulation fluids, and cement slurries. Despite the importance of non-Newtonian rheology, it is rarely used in reservoir simulators and fracture flow simulations. We study two types of non-Newtonian rheology: the truncated power-law (Ostwald-de Waele) fluid and the Bingham fluid. For either of the two types of non-Newtonian rheology, we construct relationships between the superficial fluid velocity and the pressure gradient in fractures and porous media. The Bingham fluid is regularized by means of Papanastasiou-type regularization for porous media and by means of a simple hyperbolic function for fracture flow. Approximation by Taylor expansion is used to evaluate the fluid velocity for small pressure gradients to reduce rounding errors. We report simulations of flow in rough-walled fractures for different rheologies and study the effect of fluid parameters on the flow channelization in rough-walled fractures. This effect is known from previous studies. We demonstrate how rheologies on different domains can be included in a fully-unstructured reservoir simulation that incorporates discrete fracture modeling (DFM). The above formulation was implemented in the open-source MATLAB Reservoir Simulation Toolbox (MRST), which uses fully implicit discretization on general polyhedral grids, including industry standard grids with DFM. This robust implementation is an important step towards hydro-mechanically coupled simulation of hydraulic fracturing with realistic non-Newtonian fluid rheology since most hydraulic fracturing models implemented so far make use of oversimplified rheological models (e.g., Newtonian or pure power-law).acceptedVersio

Anomalously large oxygen-ordering contribution to the thermal expansion of untwinned YBa2Cu3O6.95 single crystals: a glass-like transition near room temperature

We present high-resolution capacitance dilatometry studies from 5 - 500 K of untwinned YBa2Cu3Ox (Y123) single crystals for x ~ 6.95 and x = 7.0. Large contributions to the thermal expansivities due to O-ordering are found for x ~ 6.95, which disappear below a kinetic glass-like transition near room temperature. The kinetics at this glass transition is governed by an energy barrier of 0.98 +- 0.07 eV, in very good agreement with other O-ordering studies. Using thermodynamic arguments, we show that O-ordering in the Y123 system is particularly sensitive to uniaxial pressure (stress) along the chain axis and that the lack of well-ordered chains in Nd123 and La123 is most likely a consequence of a chemical-pressure effect.Comment: 4 pages, 3 figures, submitted to PR

Million node fracture: size matters?

Transmissivity of self-affine fractures was computed numerically as a function of the grid size. One-million-node fractures (1024 × 1024 nodes) with fractal dimensions of 2.2–2.6 were cut into successively smaller fractures (“generations”), and transmissivities computed. The number of fractures in each generation was increased by a factor of 4. Considerable scatter in transmissivity was observed for smaller grid sizes. Average transmissivity of the fractures in the generation decreased with the grid size, without approaching any asymptotic value, which indicates no representative elementary volume (REV). This happened despite the average mean aperture being the same in each generation. The results indicate that it is not possible to estimate the transmissivity of a large fracture by cutting it into smaller fractures, running flow simulations on those and averaging the results. The decrease in transmissivity with the grid size was found to be due to an increase in the flow tortuosity

Discrete-element model of electrophoretic deposition in systems with small Debye length: effective charge, lubrication force, characteristic scales, and early-stage transport

Electrophoresis was recently proposed as a new method for controlling properties and structure of the interface between cement and steel elements in petroleum and construction industries (Lavrov A et al., 2018). Cement slurries typically contain a wide range of particle sizes (micron to hundred micron), and the particles have small Debye lengths (nanometer). The relative magnitude of different forces acting on particles in such systems was examined. A formulation based on the DLVO theory was used to calculate van der Waals forces and electric repulsion forces between particles. It was shown that the following forces need to be included in a discrete-element model of electrophoretic deposition in this case: viscous drag force, force due to the external electric field, gravity + buoyancy force, lubrication force, van der Waals force, and direct mechanical contact force. The recommended cut-off gaps for van der Waals and lubrication forces are equal to the radius of the larger particle participating in the interaction. An example DEM simulation has revealed that deposition starts with deposing finer particles. Shortly after, larger particles are deposited on the finer substrate. This is due to the larger speed-up time of larger particles. The difference in the speed-up time leads to some size segregation at the early stage of deposition, even though the particle mobility is independent of the particle size. The model enables some insight into the processes that take place during the earlier stages of electrophoretic deposition that are difficult to capture and analyze in laboratory experiments

Manipulating cement-steel interface by means of electric field: Experiment and potential applications

Good shear bonding and hydraulic bonding between cement and steel play a crucial role in well integrity of oil and gas wells. In this experimental study, we investigate the effect that constant electric field may have on the bonding at cement-steel interfaces. Constant voltage (18 V) was applied between two stainless-steel electrodes immersed into a cement slurry. It was found that bonding was significantly improved at the positive electrode, while it was significantly worse at the negative electrode. The effect was due to the negatively-charged cement particles being attracted to the positive electrode. The effect may potentially be used for manipulation and control of casing-cement and reinforcement-concrete bonding strengths in oil & gas and construction industries, respectively. Side-effects that might reduce the applicability of this technology, are gas production at both electrodes (and especially at the negative one) and significant corrosion at the positive electrode due to electrochemical reactions at metal surfaces. Poor bonding at the negative electrode may potentially be used for cleaning of cement equipment, such as cement pumps, pipes, tanks, and mixers used on the rigs to perform well cementing jobs in oil & gas industry

Experimental and numerical study of the Kaiser effect in cyclic Brazilian tests with disk rotation

Sensitivity of the Kaiser effect to the deviations of the directions of sigma(1)-principal stress experienced by rock in Successive loading cycles has an important impact on the application of this effect for stress measurements in rocks. The paper presents an analysis of the gradual Kaiser effect degradation with increasing deviation of the principal stress axes between loading cycles in Brazilian experiments. An experimental study was carried out to investigate the Kaiser effect in cyclic loading tests of disk specimens of a brittle limestone in diametrical compression With acoustic emission measurement. Tests were performed in which disks were loaded in two cycles without of with rotations between successive cycles. The rotation angle varied between 0degrees and 90degrees. The Kaiser effect became gradually less pronounced with increasing rotation angle, but remained detectable for angles < 10degrees. Rotation by more than 10degrees resulted in complete disappearance of the effect. These experimental results were confirmed by numerical simulations using the displacement discontinuity method. (C) 2002 Elsevier Science Ltd. All rights reserved.status: publishe

Electrophoresis-induced structural changes at cement-steel interface

Applying positive potential to a steel electrode immersed into a cement changes the packing of cement particles in the vicinity of the electrode surface. The electrophoresis-induced packing enhancement at anode has promising applications in oil &amp; gas and CO2 storage industries since it could be used to improve the mechanical and hydraulic cement-casing bonding in wells and thereby improve the well integrity, both in short and long term. In this experimental study, we use synchrotron radiation microtomography (µ-CT) and X-ray diffraction (XRD) analyses of the interfacial transition zone (ITZ, a 20–100 µm wide near-wall zone depleted of large particles) to find out what structural changes are responsible for different cement-steel adhesion at anode and cathode. Particle size distribution analysis reveals that the ITZ is enriched with large (equivalent diameter &gt; 10 µm) cement particles near anode. On the contrary, near cathode, cement is depleted of large particles, which results in poor adhesion to the electrode. XRD analysis reveals that cement near anode is enriched with tricalcium silicate (Ca3SiO5). These findings suggest that electrophoresis-enhanced cement-steel adhesion is due to large (&gt;10 µm) negatively-charged tricalcium silicate particles being attracted to anode