On the Development of a Model for the Prediction of Liquid Loading in Gas Wells with an Inclined Section

The ability to predict liquid loading in horizontal gas wells is of great importance for determining the time of drainage and optimizing the related production technology.In the present work,we describe the outcomes of experiments conducted using air-water mixtures in a horizontal well.The results show that the configuration with an inclined section is the most susceptible to liquid loading.Laboratory experiments in an inclined pipe were also conducted to analyze the variation of the critical gas flow rate under different angles,pressure and liquid volume(taking the equal liquid volume at inlet and outlet as the criterion for judging on the critical state).According to these results,the related angle of the inclined section ranges from 45°to 60°.Finally,a modified approach based on the Belfroid model has been used to predict the critical gas flow rate for the inclined section.After comparison with field data,this modified model shows an accuracy of 96%,indicating that it has better performances with respect to other models used in the past to predict liquid loading.

Study on Dynamic Prediction of Two-Phase Pipe Flow in Inclined Wellbore with Middle and High Yield

Gas-liquid two-phase flow is ubiquitous in the process of oil and gas exploitation,gathering and transportation.Flow pattern,liquid holdup and pressure drop are important parameters in the process of gas-liquid two-phase flow,which are closely related to the smooth passage of the two-phase fluid in the pipe section.Although Mukherjee,Barnea and others have studied the conventional viscous gas-liquid two-phase flow for a long time at home and abroad,the overall experimental scope is not comprehensive enough and the early experimental conditions are limited.Therefore,there is still a lack of systematic experimental research and wellbore pressure for gas-liquid two-phase flow under the conditions of middle and high yield and high gas-liquid ratio in conventional viscosity,and the prediction accuracy is low.In view of this,this study carried out targeted systematic research,and from the flow pattern,liquid holdup and pressure drop aspects,established the relevant model,obtained a set of inclined wellbore gas-liquid two-phase pipe flow dynamic prediction method.At the same time,firstly,the model is tested by experimental data,and then the model is compared and verified by a number of field measured wells,which proves that the model is reliable and the prediction accuracy of wellbore pressure is high.

Particulate flow analysis in inclined pipes and transfer chutes using tomography imaging,discrete element simulations and continuum modeling approaches

In particulate material transfer systems,traditional shear test based steady state analysis can provide some insight into the strength of the bulk material and subsequent resistive frictional forces during flow.For fast flowing transfer points,dynamic flow conditions dominate and additional modelling techniques are required to improve design guidance.The research presented shows the evolution of a design solution which utilises two distinct processes;a continuum method and a discrete element method(DEM). Initially,the internal structure of dense granular flow,down vertical and inclined pipes was investigated using a twin sensor,12 electrode electrical capacitance tomography device.Subsequently,DEM simulations were conducted using the commercial software,PFC3D.Initially,two particle types and their flow behaviours were analysed:plastic pellets and sand.The pipe angle was varied between 0°and 45°to the vertical.For both the plastic pellets and the sand,good qualitative agreement was found with the spatial particle concentration analysis.Generally,the flow had a dense particle region at its core with the particle concentration reducing away from this core.As expected,at 0°, the core was centrally located within the pipe for both the plastic pellets and sand.At pipe angles 5°or greater,the dense core of particles was located on or near the pipe wall.Average flow velocity analysis was also conducted using the results of wall friction test analysis.The velocity comparisons also showed good agreement between the ECT image analysis and the DEM simulations. Subsequently,the DEM method was used to analyse a complex transfer system(or chute) with the continuum method providing comparative flow analysis with the DEM flow analysis.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Effect of eccentric and inclined loading on the bearing capacity of strip footing placed on rock mass

This paper deals with the bearing capacity determination of strip footing on a rock mass in hilly area by considering the influence of inclined and eccentric loading. Applying the generalized HoekBrown failure criterion, the failure behavior of the rock mass is modeled with the help of the power cone programming in the lower bound finite element limit analysis framework. Using bearing capacity factor(Ns), the change in bearing capacity of the strip footing due to the occurrence of eccentrically inclined loading is presented. The variations of the magnitude of Ns are obtained by examining the effects of the Hoek-Brown rock mass strength parameters(uniaxial compressive strength(sci), disturbance factor(D), rock parameter(mi), and Geological Strength Index(GSI)) in the presence of different magnitudes of eccentricity(e) and inclination angle(λ) with respect to the vertical plane, and presented as design charts. Both the inclined loading modes, i.e., inclination towards the center of strip footing(+λ) and inclination away from the center of strip footing(-λ), are adopted to perform the investigation. In addition, the correlation between the input parameters and the corresponding output is developed by utilizing the artificial neural network(ANN). Additionally, from sensitivity analysis, it is observed that inclination angle(λ) is the most sensitive parameter. For practicing engineers, the obtained design equation and design charts can be beneficial to understand the bearing capacity variation in the existence of eccentrically inclined loading in mountain areas.

A new model for predicting the critical liquid-carrying velocity in inclined gas wells

Based on the assumption of gas-liquid stratified flow pattern in inclined gas wells,considering the influence of wettability and surface tension on the circumferential distribution of liquid film along the wellbore wall,the influence of the change of the gas-liquid interface configuration on the potential energy,kinetic energy and surface free energy of the two-phase system per unit length of the tube is investigated,and a new model for calculating the gas-liquid distribution at critical conditions is developed by using the principle of minimum energy.Considering the influence of the inclination angle,the calculation model of interfacial friction factor is established,and finally closed the governing equations.The interface shape is more vulnerable to wettability and surface tension at a low liquid holdup,resulting in a curved interface configuration.The interface is more curved when the smaller is the pipe diameter,or the smaller the liquid holdup,or the smaller the deviation angle,or the greater gas velocity,or the greater the gas density.The critical liquid-carrying velocity increases nonlinearly and then decreases with the increase of inclination angle.The inclination corresponding to the maximum critical liquid-carrying velocity increases with the increase of the diameter of the wellbore,and it is also affected by the fluid properties of the gas phase and liquid phase.The mean relative errors for critical liquid-carrying velocity and critical pressure gradient are 1.19%and 3.02%,respectively,and the misclassification rate is 2.38%in the field trial,implying the new model can provide a valid judgement on the liquid loading in inclined gas wells.

Numerical Simulation on Production Trials by Using Depressurization for Typical Marine Hydrate Reservoirs:Well Type and Formation Dip

Natural gas hydrate has huge reserves and is widely distributed in marine environment.Its commercial development is of great significance for alleviating the contradiction between energy supply and demand.As an efficient research method,numerical simulation can provide valuable insights for the design and optimization of hydrate development.However,most of the current production models simplify the reservoir as a two-dimensional(2D)horizontal layered model,often ignoring the impact of formation dip angle.To improve the accuracy of production prediction and provide theoretical support for the optimization of production well design,two three-dimensional(3D)geological models with different dip angles based on the geological data from two typical sites are constructed.The vertical well,horizontal well and multilateral wells are deployed in these reservoirs with different permeabilities to perform production trial,and the sensitivity analysis of dip angles is also carried out.The short-term production behaviors in high and low permeability reservoirs with different dip angles are exhibited.The simulation results show that 1)the gas and water production behaviors for different well types in the two typical reservoirs show obviously different variation laws when the short-term depressurization is conducted in the inclined formation;2)the inclined formation will reduce the gas production and increase the water extraction,and the phenomena becomes pronounced as the dip angle increases,particularly in the low-permeability reservoirs;3)and the impact of formation dip on hydrate recovery does not change significantly with the variation of well type.

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

In this paper,we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid.The layer is subjected to a gravitational field and a strictly vertical temperature gradient.Typically,problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer,which prevent these systems from supporting conductive(non-convective)states.The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications.In an earlier work,we carried out a linear stability analysis of the conductive state.It was shown that at any layer tilt angles,the most dangerous type of disturbances are longitudinal rolls.Moreover,a non-zero velocity component exists in z-direction.In the present work,threedimensional non-linear convection regimes are studied.The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v_(z)=v_(z)(x,y).It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles,are in a good agreement with those predicted by the linear theory.The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry.Calculations carried out at low supercriticalities show that a direct bifurcation takes place.With increasing supercriticality,no transitions to other convective regimes are detected.The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient,where the ensuing fluid convection can affect the distribution of oil throughout the layer.

Experimental study on seismic reinforcement of bridge foundation on silty clay landslide with inclined interlayer

A shaking table test for a bridge foundation reinforced by anti-slide piles on a silty clay landslide model with an inclined interlayer was performed.The deformation characteristics of the bridge foundation piles and anti-slide piles were analyzed in different loading conditions.The dynamic response law of a silty clay landslide with an inclined interlayer was summarized.The spacing between the rear anti-slide piles and bridge foundation should be reasonably controlled according to the seismic fortification requirements,to avoid the two peaks in the forced deformation of the bridge foundation piles.The“blocking effect”of the bridge foundation piles reduced the deformation of the forward anti-slide piles.The stress-strain response of silty clay was intensified as the vibration wave field appeared on the slope.Since the vibration intensified,the thrust distribution of the landslide underwent a process of shifting from triangle to inverted trapezoid,the difference in the acceleration response between the bearing platform and silty clay landslide tended to decrease,and the spectrum amplitude near the natural vibration frequency increased.The rear anti-slide piles were able to slow down the shear deformation of the soil in front of the piles and avoid excessive acceleration response of the bridge foundation piles.

Scattering of Water Waves by Dual Symmetric Inclined Floating Porous Barriers Using the DBEM

The scattering of normally incident water waves by two surface-piercing inclined perforated barriers in water with a uniform finite depth is investigated within the framework of linear water wave theory.Considering that thin barriers are zero-thickness,a novel numerical method involving the the coupling of the dual boundary element method(DBEM)with damping layers is applied.In order to effectively damp out the reflected waves,two damping layers,instead of pseudoboundaries are implemented near the two side boundaries of the computational domain.Thus,the modified linearized free surface boundary conditions are formulated and used for solving both the ordinary boundary integral equation as well as the hypersingular boundary integral equation for degenerate boundaries.The newly developed numerical method is validated against analytical methods using the matched eigenfunction expansion method for the special case of two vertical barriers or the inclined angle to the vertical being zero.The influence of the length of the two damping layers has been discussed.Moreover,these findings are also validated against previous results for several cases.After validation,the numerical results for the reflection coefficient,transmission coefficient and dissipation coefficient are obtained by varying the inclination angle and porosity-effect parameter.The effects of both the inclination angle and the porosity on the amplitudes of wave forces acting on both the front and rear barriers are also investigated.It is found that the effect of the inclination angle mainly shifts the location of the extremal values of the reflection and the transmission coefficients.Additionally,a moderate value of the porosity-parameter is quite effective at dissipating wave energy and mitigating the wave loads on dual barriers.

Hydrodynamic characteristics and particle tracking of 90° lateral intakes at an inclined river slope

Lateral intakes are common in rivers.The pump effciency and sediment deposition are determined by the local hydrodynamic characteristics and mainstream division width.The hydraulic characteristics of lateral withdrawal from inclined river slopes at different intake elevations should be investigated.Meanwhile,the division width exhibits significant vertical non-uniformity at an inclined river slope,which should be clarified.Hence,a three-dimensional(3-D)hydrodynamic and particle-tracking model was developed with the Open Source Field Operation and Manipulation(Open FOAM),and the model was validated with physical model tests for 90°lateral withdrawal from an inclined side bank.The flow fields,withdrawal sources,and division widths were investigated with different intake bottom elevations,withdrawal discharges,and main channel velocities.This study showed that under inclined side bank conditions,water entered the intake at an oblique angle,causing significant 3-D spiral flows in the intake rather than two-dimensional closed recirculation.A lower withdrawal discharge,a lower bottom elevation of the intake,or a higher main channel velocity could further strengthen this phenomenon.The average division width and turbulent kinetic energy were smaller under inclined side bank conditions than under vertical bank conditions.With a low intake bottom elevation,a low withdrawal discharge,or a high main channel velocity,the sources of lateral withdrawal were in similar ranges near the local inclined bank in the vertical direction.Under inclined slope conditions,sediment deposition near the intake entrance could be reduced,compared to that under vertical slope conditions.The results provide hydrodynamic and sediment references for engineering designs for natural rivers with inclined terrains.

Research on the mechanism of rockburst induced by mined coal-rock linkage of sharply inclined coal seams

In recent years,the mining depth of steeply inclined coal seams in the Urumqi mining area has gradually increased.Local deformation of mining coal-rock results in frequent rockbursts.This has become a critical issue that affects the safe mining of deep,steeply inclined coal seams.In this work,we adopt a perspective centered on localized deformation in coal-rock mining and systematically combine theoretical analyses and extensive data mining of voluminous microseismic data.We describe a mechanical model for the urgently inclined mining of both the sandwiched rock pillar and the roof,explaining the mechanical response behavior of key disaster-prone zones within the deep working face,affected by the dynamics of deep mining.By exploring the spatial correlation inherent in extensive microseismic data,we delineate the“time-space”response relationship that governs the dynamic failure of coal-rock during the progression of the sharply inclined working face.The results disclose that(1)the distinctive coal-rock occurrence structure characterized by a“sandwiched rock pillar-B6 roof”constitutes the origin of rockburst in the southern mining area of the Wudong Coal Mine,with both elements presenting different degrees of deformation localization with increasing mining depth.(2)As mining depth increases,the bending deformation and energy accumulation within the rock pillar and roof show nonlinear acceleration.The localized deformation of deep,steeply inclined coal-rock engenders the spatial superposition of squeezing and prying effects in both the strike and dip directions,increasing the energy distribution disparity and stress asymmetry of the“sandwiched rock pillar-B3+6 coal seam-B6 roof”configuration.This makes worse the propensity for frequent dynamic disasters in the working face.(3)The developed high-energy distortion zone“inner-outer”control technology effectively reduces high stress concentration and energy distortion in the surrounding rock.After implementation,the average apparent resistivity in the rock pillar and B6 roof substantially increased by 430%and 300%,respectively,thus guaranteeing the safe and efficient development of steeply inclined coal seams.

Exploring mechanism of hidden,steep obliquely inclined bedding landslides using a 3DEC model:A case study of the Shanyang landslide in Shaanxi Province,China

Catastrophic geological disasters frequently occur on slopes with obliquely inclined bedding structures(also referred to as obliquely inclined bedding slopes),where the apparent dip sliding is not readily visible.This phenomenon has become a focal point in landslide research.Yet,there is a lack of studies on the failure modes and mechanisms of hidden,steep obliquely inclined bedding slopes.This study investigated the Shanyang landslide in Shaanxi Province,China.Using field investigations,laboratory tests of geotechnical parameters,and the 3DEC software,this study developed a numerical model of the landslide to analyze the failure process of such slopes.The findings indicate that the Shanyang landslide primarily crept along a weak interlayer under the action of gravity.The landslide,initially following a dip angle with the support of a stable inclined rock mass,shifted direction under the influence of argillization in the weak interlayer,moving towards the apparent dip angle.The slide resistance effect of the karstic dissolution zone was increasingly significant during this process,with lateral friction being the primary resistance force.A reduction in the lateral friction due to karstic dissolution made the apparent dip sliding characteristics of the Shanyang landslide more pronounced.Notably,deformations such as bending and uplift at the slope’s foot suggest that the main slide resistance shifts from lateral friction within the karstic dissolution zone to the slope foot’s resistance force,leading to the eventual buckling failure of the landslide.This study unveils a novel failure mode of apparent dip creep-buckling in the Shanyang landslide,highlighting the critical role of lateral friction from the karstic dissolution zone in its failure mechanism.These insights offer a valuable reference for mitigating risks and preventing disasters related to obliquely inclined bedding landslides.

Evolution of a mining induced fracture network in the overburden strata of an inclined coal seam

The geological conditions of the Pingdingshan coal mining group were used to construct a physical model used to study the distribution and evolution of mining induced cracks in the overburden strata.Digital graphics technology and fractal theory are introduced to characterize the distribution and growth of the mining induced fractures in the overburden strata of an inclined coal seam.A relationship between fractal dimension of the fracture network and the pressure in the overburden strata is suggested.Mining induced fractures spread dynamically to the mining face and up into the roof as the length of advance increases.Moreover,the fractal dimension of the fracture network increases with increased mining length,in general,but decreases during a period from overburden strata separation until the main roof collapses.It is a1so shown that overburden strata pressure plays an important role in the evolution of mining induced fractures and that the fractal dimension of the fractures increases with the pressure of the overburden.

Maximum Force of Inclined Pullout of A Torpedo Anchor in Cohesive Beds

Torpedo anchors have been used in mooring systems for deep-water oil and gas projects owing to their prominent advantages, such as low cost and easy installation. The maximum force of torpedo anchors is crucial not only to the safety and stability of vessels and other marine facilities, but also for an economical design. It is necessary to develop reliable formula for fast predicting their maximum inclined force of a torpedo anchor in cohesive beds. In this study, the maximum inclined force of a torpedo anchor vertically embedded in cohesive beds was extensively investigated. 316 sets of inclined pullout laboratory tests were carried out for 9 differently shaped torpedo anchors which were vertically embedded in different cohesive beds. The loading curves were automatically acquisitioned and their characteristics were analyzed. The load angle relative to the horizontal varied from 20° to 90°. A new formula for fast calculating the maximum inclined force of the torpedo anchor vertically embedded in cohesive beds was obtained based on force analysis and a nonlinear regression on the data from the present and other studies. Effect aspects on the tests are discussed and further studies are highlighted.

Performance of inclined pillars with a major discontinuity

Discontinuities are an inherent part of the rock mass and majorly affect the stability of the excavation skin and pillars.The dip of the discontinuities and their properties also have a significant effect on the strength of the pillars.Empirical approaches are commonly used to determine the pillar strength but can overestimate the strength and don’t consider the inclination of the pillars and the strength reduction caused by discontinuities.Numerical modeling is a powerful tool and if calibrated can be used to evaluate the strength of the pillars with discontinuities having a range of properties.The effect of a discontinuity on inclined pillars was conducted which has been seldom considered in evaluating the pillar strength.Three-dimensional vertical pillars were simulated,and the pillar strength was calibrated to accepted theoretical results and then the discontinuities were introduced in different pillar inclinations with distinct width to height ratios to gain an insight into the effective pillar strength reduction.Based upon the results,it was found that the discontinuities have a significant effect with the increase in the inclination of the pillars even at a higher width to height ratios.

Numerical Simulation on Flow Past Two Side-by-Side Inclined Circular Cylinders at Low Reynolds Number

A series of three-dimensional numerical simulations is carried out to investigate the effect of inclined angle on flow behavior behind two side-by-side inclined cylinders at low Reynolds number Re=100 and small spacing ratio T/D=1.5 (T is the center-to-center distance between two side-by-side cylinders, D is the diameter of cylinder). The instantaneous and time-averaged flow fields, force coefficients and Strouhal numbers are analyzed. Special attention is focused on the axial flow characteristics with variation of the inclined angle. The results show that the inclined angle has a significant effect on the gap flow behaviors behind two inclined cylinders. The vortex shedding behind two cylinders is suppressed with the increase of the inclined angle as well as the flip-flop gap flow. Moreover, the mean drag coefficient, root-mean-square lift coefficient and Strouhal numbers decrease monotonously with the increase of the inclined angle, which follows the independent principle at small inclined angles.

Passive VIV Reduction of An Inclined Flexible Cylinder by Means of Helical Strakes with Round-Section

A series of experimental tests of passive VIV suppression of an inclined flexible cylinder with round-sectioned helical strakes were carried out in a towing tank. During the tests, the cylinder models fitted with and without helical strakes were towed along the tank. The towing velocity ranged from 0.05 to 1.0 m/s with an interval of 0.05 m/s.Four different yaw angles(a=0°, 15°, 30° and 45°), defined as the angle between the axis of the cylinder and the plane orthogonal of the oncoming flow, were selected in the experiment. The main purpose of present experimental work is to further investigate the VIV suppression effectiveness of round-sectioned helical strakes on the inclined flexible cylinder. The VIV responses of the smooth cylinder and the cylinder with square-sectioned strakes under the same experimental condition were also presented for comparison. The experimental results indicated that the roundsectioned strake basically had a similar effect on VIV suppression compared with the square-sectioned one, and both can significantly reduce the VIV of the vertical cylinder which corresponded to the case of a=0°. But with the increase of yaw angle, the VIV suppression effectiveness of both round-and square-section strakes deteriorated dramatically, the staked cylinder even had a much stronger vibration than the smooth one did in the in-line(IL)direction.

Use of Helical Strakes for FIV Suppression of Two Inclined Flexible Cylinders in A Side-by-Side Arrangement

The experimental studies on flow-induced vibrations(FIV) reduction of two side-by-side flexible cylinders inclined at 45° by using the helical strakes were carried out in a towing tank. The main aim of the experiment is to check whether the helical strakes with a pitch of 17.5 D and a height of 0.25 D, which is considered as the most effective vibration suppression device for the isolated cylinder undergoing vortex-shedding, still perform very well to reduce FIV of two inclined flexible cylinders in a side-by-side arrangement. The vibration of two identical inclined cylinders with a mass ratio of 1.90 and an aspect ratio of 350 was tested in the experiment. The center-to-center distance between the two cylinders was 3.0 D. The uniform flow was simulated by towing the cylinder models along the tank.The towing velocity varied from 0.05 to 1.0 m/s with an interval of 0.05 m/s. The maximum Reynolds number can be up to 1.6×104. Three cases were experimentally studied in this paper, including two side-by-side inclined smooth cylinders, only one smooth cylinder fitted with helical strakes in the two side-by-side inclined cylinders system and both two cylinders attached with helical strakes. The variations of displacement amplitude, dominant frequency, FIV suppression efficiency and dominant mode for the two side-by-side inclined cylinders with reduced velocity were shown and discussed.

Dynamic response and optimization of an inclined steel rock shed by the graded energy dissipating method

Blocking rockfalls directly by reinforced concrete(RC) flat sheds with thick sand cushions is an outdated method. Such conventional sheds typically accumulate rock heavily, and become progressively damaged and are difficult to repair, and are very costly. To address these problems, we propose a new structure called a Graded Dissipating Inclined Steel Rock(GDISR) shed that utilizes the graded energy dissipation method. Here, we study the dynamic response of the GDISR shed with model test and numerical simulation, and give its optimization design combining with a practical engineering case. Our results show that the optimized modular E-block and corrugated steel tube can deform to sufficiently absorb the energy of different impact intensities. This efficiently and economically provides GDISR sheds with two security lines. Compared with conventional RC sheds, GDISR sheds with optimal incline have a more efficient anti-impact function, are faster and easier to repair, and are much simpler and cheaper to build.