Horizontal Bed Research Articles

Experimental Study of Proppant Transport in Complex Fractures with Horizontal Bedding Planes for Slickwater Fracturing

Summary The use of hydraulic fracturing has taken off over the past decade, and the importance of efficient proppant placement in fractures has increased accordingly. Connection with weak-formation bedding planes brings about distinctive fracture propagation and development. This might hinder hydraulic fractures from extending in a vertical direction, yet they might instead propagate in a horizontal direction after the existing bedding planes. The bedding plane introduces additional hydrocarbon flow path during the recovery process. This naturally leads to proppants traveling in the horizontal section of the fractures. Optimal proppant delivery and conductivity in bedding planes directly relate with effective fracture height and well performance. This paper focuses on understanding horizontal movement and delivery of proppants and their distribution in vertical and horizontal fractures on the basis of experimental work. The size of proppants is one of the key determining parameters when calculating uplift and settling velocity. They travel farther into the fracture because they settle slower with less gravitational effect. Fine mesh is highly recommended to effectively deliver proppant to the horizontal bedding plane. Large proppants have to rely on the critical bed height to move into the bedding plane sitting on top of the vertical fracture. A higher injection rate promoted bedding-plane proppant delivery in the inverted T-shape case because it opened up a longer and larger area for particles to settle. Excessively strong turbulent flow generated by two inlet cases prevented proppants from settling and seeping into the bedding plane. Continuous mixing and agitation disturb proppants from settling. They limited additional coverage area expansion in the bedding plane. Moreover, inlet design shows little effect in the T-shape, yet having more injection points improves proppant placement in the bedding plane. Direct injection to the bedding plane surprisingly did not affect much in the T-shape case. Overall, only a small percentage of proppant can travel into the bedding plane for both T-shape and inverted T-shape-fracture geometries.

Influence of process variables on spray agglomeration process in a continuously operated horizontal fluidized bed

Experiments on continuously operated spray fluidized bed agglomeration are presented in this work. The process is conducted with glass beads and water-based binder hydroxypropylmethylcellulose (HPMC). By varying the process parameters, the results show that by the decrease of air temperature or feed rate and by the increase of binder concentration, larger particles can be achieved. Larger particle size also results in higher bed mass and more fluctuations in the process. Besides parameters variations, different internal and outlet weir configurations are used. Tracers are used in the experiments to characterize the particle residence time distribution. The separation effect can be decreased and the particle residence time can be optimized by the installation of internal weirs and lower height of outlet weir. The results show that the jets from the spray nozzles are increasing the motion and mixing of particles significantly.

Impact of the stress state and the natural network of fractures/faults on the efficiency of hydraulic fracturing operations in the Goldwyer Shale Formation

Cost-effective hydrocarbon production from low-permeability unconventional reservoirs requires multi-stage hydraulic fracturing (HF) operations. Each HF stage aims to generate the most spatially extended fracture network, giving access to the largest volume of reservoir possible (stimulated volume) and allowing hydrocarbons to flow towards the wellbore. The size of the stimulated volume, and therefore, the efficiency of any given HF stage, is governed by the rock’s deformational behaviour and presence of pre-existing natural fractures/faults. Naturally elevated pore pressures at depth not only help to reduce the injection energy required to generate hydraulic fractures but can also induce slip along pre-existing fractures/faults, and therefore, enhance production rates. Here we analyse borehole image, density, resistivity and sonic logs available from a vertical exploration well in the Goldwyer Shale Formation (Canning Basin) to (i) characterise the pre-existing network of natural fractures; and (ii) estimate the in-situ pore pressure and stress state at depth. The aim of such an analysis is to evaluate the possibility of fracture/fault reactivation (slip) during and following HF operations. Based on this analysis, we found that an increase in the formation's pore pressure by only a few MPa (typically ~5–10 MPa) could lead to slip along pre-existing fractures/faults, provided they are favourably oriented with respect to the prevalent stress field for future production. We also found that slip along the horizontal or sub-horizontal bedding of the Goldwyer Formation is unlikely in view of the prevalent strike-slip faulting regime, unless an extremely large overpressure exists within the reservoir.

Multi-stage and multi-compartment model for dynamic simulation of horizontal fluidized bed granulator

This work presents a multi-chamber and multi-compartment model of a horizontal fluidized bed apparatus for layering granulation, coating, and drying. Each chamber is designed individually and process conditions, such as spray rate, particle feed or gas temperature, can be adjusted for each chamber separately. Particle growth is described by population balance modeling. The characteristics of the particle exchange rates between the individual process chambers are determined by separation functions to account for different weir configurations. Additionally a drying model is presented that takes initial droplet size and contact angle as well as partial wetting of the particle surface into account. Because of the great variety of parameters that influence this model, a parametric study is carried out to identify how construction or process parameters affect the product quality. The influence of different separation functions, thermal process conditions, and initial droplet properties on key product quality features such as particle size distribution, product moisture content, and degree of surface wetting are presented and discussed. The developed model can be used to describe product quality and particle transport in complex horizontal fluidized bed apparatuses.

A Regression Analysis Result for Water Waves on Irrotational Flow over a Horizontal Bed

A Regression Analysis Result for Water Waves on Irrotational Flow over a Horizontal Bed

Continuously-fed gravity currents propagating over a finite porous substrate

We present the results of laboratory investigations of continuously-fed density currents that propagate first over a smooth horizontal bed and then over a porous substrate of limited length. Inflow discharge, initial excess density, and substrate porosities are varied. Density measurements, acquired through an image analysis technique, are performed above the porous layer simultaneously with quasi-instantaneous vertical velocity profiles. After a first phase in which the current sinks into the substrate, freshwater entrainment from the bed begins and, gradually, a mixing layer forms at the interface between the surface flow and the porous bed. Shear-driven and Rayleigh-Taylor instabilities rule the dynamics of this mixing layer. The porous boundary effects are observed in the vertical distributions of both density and velocity, especially in the near-bed region. Here, larger flow velocities are recorded over porous substrates. We argue that these are due to the presence of a longitudinal pressure gradient, which in turn is a consequence of the current mass loss. Its presence over the porous substrate is proved by the current interface longitudinal slope. However, other effects of the presence of the porous substrate, such as the relaxation of the no-slip boundary condition and the bed-normal momentum exchange, also affect the velocity field. The turbulent structure changes significantly over the porous substrate: while streamwise turbulence decreases, shear and bed-normal Reynolds stresses increase in large part of the current depth. Buoyancy instabilities further enhance the bed-normal momentum flux and, in the near-bed region, contribute to turbulent kinetic energy generation together with shear.

An experimental and numerical study on solitary wave loads at cylinders near the bed

The present study describes an experimental and numerical investigation on the horizontal and vertical hydrodynamic forces given by solitary waves on horizontal circular cylinders placed near a rigid horizontal bed. The experimental campaign was conducted in the wave channel of the University of Calabria in which twelve pressure sensors were installed along the external surface of a cylinder located at gap-to-diameter ratios equal to 0.25 and 0.1. The numerical modeling was carried out using the open source OlaFlow model, based on the OpenFOAM solver, in order to simulate the wave forces, also extending the range of experiments. The resulting force field was defined by the dominance of the horizontal inertia force along the flow direction and by the lift force along the transversal one. The values of the hydrodynamic forces and the free stream kinematics were adopted to calibrate the hydrodynamic coefficients (drag, lift and horizontal and vertical inertia) involved in the Morison formula and in a proposed version of the transverse equation through the use of the weighted least square approach. For practical aims, semi-analytical relationships to determine the hydrodynamic coefficients as a function of wave amplitude and water depth are presented.

Crack propagation and dynamic properties of coal under SHPB impact loading: Experimental investigation and numerical simulation

To investigate the crack propagation and dynamic mechanical properties of coal under high strain rate loading, 24 sets of Brazilian disk (BD) coal specimens with vertical and horizontal beddings were made, and tests were conducted by a split Hopkinson pressure bar (SHPB) system. Under different impact velocities, a high-frame and high-resolution camera was employed to capture the fracture process, and two high-dynamic strain gauges were used to record the stress pulse signals simultaneously. Using one-dimensional stress wave theory, the dynamic mechanical properties of coal with different bedding directions under different impact velocities were analyzed and discussed. Experimental results indicate that bedding directions not only have a major influence on dynamic mechanical properties such as dynamic tensile strength, strain rate and strain energy but also have a great influence on the crack propagation path. Then, based on the image processing technique and fractal method, cracks conforming to the fractal have been proven, and the results further illustrate that the fractal dimension of cracks on the coal surface increased in the fracture process under SHPB loading. Finally, a numerical model based on bond-based Peridynamic theory was proposed to simulate crack propagation and dynamic mechanical properties of coal under the SHPB test, and the displacement-strain-stress fields were also calculated, which further reveal the fracture mechanism and dynamic behavior of coal under different impact loading conditions.

Investigation on the effect of confining pressure on the geomechanical and ultrasonic properties of black shale using ultrasonic transmission and post-test CT visualization

Knowledge of the influence of confining pressure on the geomechanical and ultrasonic characteristics is essential to exploration and development of gas shale reservoirs. In contrast to the extensive studies on the physical and mechanical properties of shale, the velocities of P-wave and S-wave during continuous deformation are not thoroughly understood. In this study, a suite of triaxial compression tests were done on the shale samples collected from the Sichuan Basin and were cored with horizontal bedding structure under various confining pressure. In-situ ultrasonic transmission technique combined with post-test CT imaging analysis was used to reveal the velocity-pressure characteristics and crack patterns. The experimental results indicate that strength, elastic parameter, P- and S-wave velocities, and failure pattern are influenced by the applied confining pressure. At the pre-peak stage on the stress-strain curve, the P-wave velocity increases with elevated stress; however, the S-wave velocity first increases and then decreases, which is related to the crack damage evolution. The meso-structural changes during deformation are considered to be the main factor controlling the pressure sensitivity of the velocities. Under compression, the relatively soft pores, micro-cracks and minerals were compacted gradually, and it is the primary reason leading to the increment of velocities. Based on the CT scanning technique, the crack pattern was obtained after triaxial testing, the crack pattern analysis suggests that the fractal dimension of fracture distribution almost increases with confining pressure. What is more, the stimulated fracture density increases with increasing confining pressure. It suggests that, for the Longmaxi black shale, a high confining pressure condition is beneficial to form a complex fracture network.

Studying effect of entrainment on dynamics of debris flows using numerical simulation

This paper studies entrainment phenomenon in debris flows using full flow (non-depth-averaged) equations and an Incompressible Smoothed Particle Hydrodynamics (ISPH) method. A viscoplastic constitutive relationship is adopted for both the overlying fluid and bed material. Collapse of a two-dimensional dry granular column on a horizontal bed consisting of entrainable dry granular material is considered as a benchmark problem. The adopted ISPH method for simulation of collapse over rigid and entrainable beds is validated using available numerical and experimental data. To quantify the effects of entrainment on dynamics of flow, the initial aspect ratio of granular column (a) is varied and the variations in momentum and energy of moving materials are investigated.

Modeling of yield-power-law fluid flow in an eccentric annulus with fixed horizontal cuttings bed

ABSTRACT Inclination and horizontal wells are commonly used to develop petroleum and natural gas reservoirs. Cuttings bed buildup is inevitable in an eccentric annulus because of the high inclination angle (>60°), which affects the drag and torque as well as the downhole pressure. To accurately and conveniently predict the pressure gradient in an eccentric annulus with fixed horizontal cuttings bed, a simplified model was established in this study to predict the pressure gradient by using the effective hydraulic diameter. In addition, simulation experiments were carried out to investigate the pressure gradient in the eccentric annulus with a cuttings bed using the computational fluid dynamics (CFD) software ANSYS Fluent. The simplified model was validated by comparing the results with those obtained from CFD simulations. The results show that the average shear stress of the cuttings bed wall first decreases and then increases with increasing cuttings bed height. The simplified is in good agreement with the results of existing numerical and CFD simulations (within an error of ±10%). The proposed simplified model provides a shortcut for the prediction of the pressure gradient in an eccentric annulus with a cuttings bed.

Experimental study on fracture propagation induced by supercritical CO2 jet fracturing in artificial samples with prefabricated bedding planes

The propagation characteristic of fractures under the influence of bedding during SC-CO2 jet fracturing remains value to be studied. In order to avoid the large dispersion of natural rock property, seven types of artificial rock samples (Φ100 mm × 100 mm) with prefabricated different positions and numbers of bedding were prepared. A multifunction SC-CO2 jet system was used to conduct the SC-CO2 jet fracturing with ambient pressure. The main fractures on the surface were observed through vertical and side view after the experiment. In addition, five fracture propagation modes were summarized systematically. Finally, the fracture tortuosity parameters were obtained by quantitative analysis, and it was found that for horizontal bedding, the farther the vertical distance from the casing, the larger the fracture tortuosity formed by SC-CO2 jet fracturing; if a single fracture penetrates the bedding, the fracture tortuosity will increase.

Prediction Characteristics of Free and Submerged Hydraulic Jumps on Horizontal and Sloping Beds using SVM Method

Doubtlessly hydraulic jump is a useful phenomenon in open channel flow such as rivers and spillways. As the most important characteristics of hydraulic jump, length, and sequent depth ratio play a key role in designing of hydraulic structures. The hydraulic jump length is one of the most important parameters, which cannot be calculated by mathematical analyses directly. In this context, several relations have been proposed to estimate the length and sequent depth ratio of the hydraulic jumps, but the results of the mentioned equations are not general and acceptable due to the uncertainty of the functions. Achievements of this study follows three aims; firstly to develop and examine support vector machine (SVM) for estimating characteristics of five types of free and submerged hydraulic jumps; secondly to compare the results of SVM models with analytical and semi-empirical equations; and finally to perform a sensitivity analysis to investigate the effect of each input parameter on the output in terms of root mean square error (RMSE), correlation coefficient (R) and Nash-Sutcliffe or determination coefficient (NS or DC). The meteorological data sets used herein to develop the models are obtained from previous credible researches. Performance of the models appoints dominant parameters for predicting the characteristics of the different types of hydraulic jumps As Also based on the comparisons among the SVM models, analytical and semi-empirical equations, it can be seen that, SVM models depict better results than those equations.

Flood propagation modeling with the Local Inertia Approximation: Theoretical and numerical analysis of its physical limitations

Attention of the researchers has increased towards a simplification of the complete Shallow water Equations called the Local Inertia Approximation (LInA), which is obtained by neglecting the advection term in the momentum conservation equation. This model, whose physical basis is discussed here, is commonly used for the simulation of slow flooding phenomena characterized by small velocities and absence of flow discontinuities. In the present paper it is demonstrated that a shock is always developed at moving wetting-drying frontiers, and this justifies the study of the Riemann problem on even and uneven beds. In particular, the general exact solution for the Riemann problem on horizontal frictionless bed is given, together with the exact solution of the non-breaking wave propagating on horizontal bed with friction, while some example solution is given for the Riemann problem on discontinuous bed. From this analysis, it follows that drying of the wet bed is forbidden in the LInA model, and that there are initial conditions for which the Riemann problem has no solution on smoothly varying bed. In addition, propagation of the flood on discontinuous sloping bed is impossible if the bed drops height has the same order of magnitude of the moving-frontier shock height. Finally, it is found that the conservation of the mechanical energy is violated. It is evident that all these findings pose a severe limit to the application of the model. The numerical analysis has confirmed the existence of the frontal shock in advancing flows, but has also demonstrated that LInA numerical models may produce numerical solutions, which are unreliable because of mere algorithmic nature, also in the case that the LInA mathematical solutions do not exist.Following the preceding results, two criteria for the definition of the applicability limits of the LInA model have been considered. These criteria, which are valid for the very restrictive case of continuously varying bed elevation, are based on the limitation of the wetting front velocity and the limitation of spurious total head variations, respectively. Based on these criteria, the applicability limits of the LInA model are discouragingly severe, even if the bed elevation varies continuously. More important, the non-existence of the LInA solution in the case of discontinuous topography and the non-existence of receding fronts radically question the viability of the LInA model in realistic cases. It is evident that classic SWE models should be preferred in the majority of the practical applications.

Piloted Ignition of Cylindrical Wildland Fuels Under Irradiation

Recent mega wildfires have become one of the most dangerous and devastating hazards, with a wide range of negative impacts on the economy, society and environment. As cylindrical shrubs and twigs are typical fuel loads in wildfires, it is important to understand how the diameter and arrangement of cylindrical fuels affect ignition behaviors. In this work, the piloted ignition of cylindrical wood rods with different diameters (3.2 ~15.9 mm) are conducted under the irradiation up to 50 kW/m2. Three fuel groups are tested: (I) single vertical rod, (II) single horizontal rod, and (III) horizontal rod bed attached to the ground. For a single vertical rod, the measured ignition time decreases as the diameter is decreased from 15.9 mm to 6.4 mm, showing a thermally-thin behavior. However, the ignition of the 3.2-mm rod is more difficult than the 9.5-mm rod, because of the enhanced convective cooling by the smaller curvature. Nevertheless, when the rod fuels are placed horizontally on the ground, the curvature-enhanced convective cooling becomes limited. For a single rod, when both the fuel diameter and the irradiation are small, only smoldering ignition occurs, and eventually the sample collapses. For the rod bed, flaming ignition always occurs, and it is easier to ignite because of a smaller convective cooling. For both horizontal configurations, the fuel ignition temperature increases almost linearly with the diameter from 270℃ (3.2 mm) to 330℃ (15.9 mm) but is insensitive to the irradiation level. This research quantifies the effect of fuel diameter and arrangement on the piloted ignition and reveals that the traditional classification of thermally thin and thick fuel for flat materials may not be suitable for cylindrical wildland fuels.

Comparison between Numerical, Analytical, and Field Solutions with Experimental Data for 90º Open Channel Junctions

Junction in open channel flow points out any side water secession from natural or artificial channels. In the last decades, comprehensive theoretical and experimental investigations on the dividing flow in open channel junctions have been executed to understand the characteristics of this separating flow. In this research, a three-dimensional turbulence model by fluent software used to replicate the flow characteristics of a 90o open channel junctions for two geometries. One is with equal width and horizontal bed and the other is field canal junction with irregular section. The modeling is based on the Navier-Stokes equation and κ-ω turbulent model. Comparing prepared to the numerical solution, the analytical model and the field works with published experimental data. The comparison showed that the numerical solution gave good agreements with maximum discrepancy 1.620% for rectangular sections and 0.718% for irregular sections than the published experimental data. The analytical solution gave a large error than numerical with a maximum discrepancy of 2.95% for the rectangular section and 11.485% for irregular sections than the published experimental data. A proposed relation between discharge ratio with upstream Froude number and depth ratio for the irregular section is suggested. The proposed equation has a maximum discrepancy equal to 0.433% with reference to the field data recorded.

Effect of hydrodynamic forces on sandy sediments in oscillatory boundary layer flow

In the present work, the forces exerted on spherical sand particles by oscillatory boundary layer flows at Re=25,000 and Re=55,000 are examined by means of Large Eddy Simulations. The particles move within the carrier fluid under the influence of the Stokes Drag, Gravity, Added Mass, Pressure Drag and Basset forces. The model has been validated for the cases of a particle accelerating within a stagnant fluid under the influence of gravity and for a particle within an oscillatory flow. The Basset force is computed in an efficient way, by calculating the Basset integral only for a specific time in the particle’s immediate history, called “window time”. In order to define the window time, existing literature approaches have been implemented. The rest of the particle’s history is calculated by an efficient second order methodology suitable for a large number of particles moving within the carrier fluid. The importance of each of the hydrodynamic forces has been examined when the particles are released far from the horizontal bed and when they are released in the boundary layer region, in the absence of gravity. The results indicate that Stokes Drag, Basset force and Pressure Drag are equally important. The contribution from the Added Mass force was found to be orders of magnitude smaller and the acceleration components in the other directions are also negligible. Furthermore, in the boundary layer region, a near-wall zone of negative mean Stokes Drag and positive mean Basset force has been identified. Moving away from the wall but still in the boundary layer region, another zone of positive mean Stokes Drag and negative mean Basset have been identified.

Prediction of particle size and layer-thickness distributions in a continuous horizontal fluidized-bed coating process

To predict the particle size and layer-thickness distributions (LTDs) in a continuously operated horizontal fluidized-bed granulation process, two alternative models were considered. A one-dimensional two-zone model was proposed, which describes with population-balance equations the particle growth in a spraying zone that is separated from the drying zone. The residence-time distribution (RTD) was calculated from a literature correlation and was coupled with a population-balance model via a tank-in-series model with reflux. A two-dimensional, one-zone population-balance model, which was based directly on the RTD and the feed particle-size distribution (PSD) was also used. Granulation experiments were conducted and analyzed microscopically and with a camera optical device to determine the sample PSDs. LTDs over the particle population were derived from the PSDs and were analyzed directly by micro-computer-tomography. To compare the simulated data with the experimentally determined distributions, the PSDs were converted to LTDs. The good agreement shows that both methods are suitable to determine the PSD from an RTD of an arbitrary granulation process in a horizontal fluidized bed. Improvement appears necessary with regards to the LTD spread.

Wave-Induced Oscillatory Flow Over a Sloping Rippled Bed

In this paper, the findings of an experimental analysis aimed at investigating the flow generated by waves propagating over a fixed rippled bed within a wave flume are reported. The bottom of the wave flume was constituted by horizontal part followed by a 1:10 sloping beach. Bedforms were generated in a previous campaign performed with loose sand, and then hardened by means of thin layers of concrete. The flow was acquired through a Vectrino Profiler along two different ripples, one located in the horizontal part of the bed and the second over the sloping beach. It was observed that, on the horizontal bed, near the bottom, ripple lee side triggered the appearance of an onshore directed steady streaming, whereas ripple stoss side gave rise to an offshore directed steady streaming. On the sloping bed, a strong return current appears at all positions, interacting with the rippled bottom. The turbulence is non-negligible within the investigated water depth, particularly when velocities were onshore directed, due to flow asymmetry. Turbulence caused a considerable flow stirring which, above a non-cohesive bed, could lift the sediment up in the water column and give rise to a strong sediment transport.

Experimental study on high temperature damage of anisotropic sandstone

Rocks often have certain bedding structures under long-term geological conditions, which leads to different performances. In this paper, ultrasonic analysis of horizontal bedding and vertical bedding is carried out by high temperature tests on anisotropic red sandstone samples to obtain data on mass, density, porosity and longitudinal wave velocity as a function of temperature. Then through the apparent morphology analysis of the sample, data processing and image analysis, the high temperature damage law of the anisotropic sandstone is finally obtained, which provides theoretical support for underground resource development and underground engineering construction.