Horizontal Friction Research Articles

Considering Wellbore Friction in Planning Horizontal Wells (includes associated papers 28646 and 29095 )

Abstract The importance of friction pressure loss within the completed section of horizontal wells, under some reservoir conditions, has been analyzed. The phenomena were studied both analytically and experimentally with sub sequent implementation in a commercially available 3-D,3-phase reservoir simulation model. Based on simulation studies, criteria for the selection of appropriated imensions for horizontal wells under different reservoir conditions are outlined. A field example from the Troll Field offshore Norway where these results were applied during the planning of a horizontal test well, is presented. Introduction The Troll field, located in 300m water depth offshore Norway (Fig. 1), contains 0–26 m thick oil rims sandwiched between a large gas cap and active aquifers. In the westernmost fault block of the field, the Troll WestOil Province, the oil zone is at its thickest; 22–26 m. The oil in place of this province is estimated at 121x10 6 Sm3.The reservoir contains several highly permeable, unconsolidated sands separated by low permeability micaceous sands. Impermeable calcite cemented horizons with imperfectly known spatial disposition and extensions occur within the high permeability sands. The oil production from Troll may be limited by gas coning, resulting in a limited available drawdown for the well. Since the oil rim is only 22–326 m thick, the drawdown can only be in the range of 1.5 to 2 bar in order to avoid the production of free gas-cap gas. The recoverable oil in the Troll West Oil Province is located in high-quality sands with permeabilities ranging from3000 to 10 000 md, so high liquid rates were expected(Fig. 2). With the combination of limited drawdown and high rates, wellbore friction pressure loss was considered to be of importance [1].The subject has been studied analytically by Dikken [1]. However, implementation of the effect of horizontal well friction in simulators with subsequent application for well planning and design purposes has previously not been reported. Horizontal well friction was given due attention during the planning of a 500 m horizontal well in the Troll field. The well was drilled and completed in late1989, and has been on production since January 10th 1990. The cumulative oil production as of early June1990 was 500 000 Sm [2]. Background The Troll field covers an area of 700km2 . The estimated gas and oil in place is 1670x10 9 Sm3 and 615x10 6 Sm3respectively (Fig. 3). Two main north-south bound faults divide the field into three provinces: Troll West Oil Province, Troll West Gas Province and Troll East(Fig. 3).Concession Block 31/2 (Fig. 3), operated by A/SNorske Shell, was awarded in 1979. Blocks 31/3, 31/5, and 31/6 were awarded in 1983 with shared operatorship between Norsk Hydro a.s, Den norske stats oljeselskapa.s, and Saga Petroleum a.s.

Measurement of the properties of sand in a calibration chamber by the cone pressuremeter test

The cone pressuremeter is a new site investigation device which incorporates a pressuremeter behind a standard cone penetrometer tip. This Paper seeks to develop an understanding of the new device, and to establish a procedure to allow the test to be used to determine the engineering properties of cohe-sionless soils. A series of calibration chamber tests is described, in which three cone pressuremeter prototypes of different cross-sectional areas were used. A programme of calibration designed to examine the influence of relative density, stress level and stress ratio on the values of limit pressure obtained from the cone pressuremeter test and the cone resistance values obtained from the cone test is presented. A procedure for deducing the in situ horizontal stress, density and friction angle is described, and is used to back-analyse the test data. Le cÔne pressiomètre est un nouvel appareil de reconnaissance de sols qui incorpore un pressiomètre placè derrière un cône classique. Cet article cherche à dèvelopper notre connaissance de ce nouvel appareil et à ètablir une nouvelle procèdure peremettant à l'essai d'être utilisè pour dèterminer les propriètès mècaniques des sols sans cohèsion. Une suite d'essais faits dans une enceinte de calibration est dècrite dans laquelle 3 prototypes de cône pressiomètre de diffèrentes sections furent utilisès. On prèsente dans cet article un programme de calibration conçu pour examiner l'influence de la densitè relative, du niveau des contraintes et du rapport des contraintes sur les valeurs de pression limite obtenues à partir de l'essai au cône pressiomètre et les valeurs de rèsistance de pointe obtenues à partir de l'essai au cône. Une procèdure pour dèduire les contraintes horizontales in-situ, la densitè et l'angle de frottement interne est dècrite et est utilisèe pour l'analyse rètrospective des rèsultats des essais.

Eddy Dynamics in a Primitive Equation Model: Sensitivity to Horizontal Resolution and Friction

A primitive equation model of an idealized ocean basin, driven by simple, study wind and buoyancy forcing at the surface, is used to study the dynamics of mesoscale eddies. Model statistics of a six-year integration using a fine grid (1/6° × 0.2°), with reduced coefficients of horizontal friction, are compared to those using a coarser grid (1/3° × 0.4°), but otherwise identical configuration. Eddy generation in both model cases is primarily due to the release of mean potential energy by baroclinic instability. Horizontal Reynolds stresses become significant near the midlatitude jet of the fine-grid case, with a tendency for preferred energy transfers from the eddies to the mean flow. Using the finer resolution, eddy kinetic energy nearly doubles at the surface of the subtropical gyre, and increases by factors of 3–4 over the jet region and in higher latitudes. The spatial characteristics of the mesoscale fluctuations are examined by calculating zonal wavenumber spectra and velocity autocorrelation functions. With the higher resolution, the dominant eddy scale remains approximately the same in the subtropical gyre but decreases by a factor of 2 in the subpolar areas. The wavenumber spectra indicate a strong influence of the model friction in the coarse-grid case, especially in higher latitudes. Using the coarse grid, there is almost no separation between the energetic eddy scale and the scale where friction begins to dominate, leading to steep spectra beyond the cutoff wavenumber. Using the finer resolution an inertial subrange with a k−3 power law begins to emerge in all model regions outside the equatorial belt. Despite the large increase of eddy intensity in the fine-grid model, effects on the mean northward transport of heat are negligible. Strong eddy fluxes of heat across the midlatitude jet are almost exactly compensated by changes of the heat transport due to the mean flow.

FRICTION MECHANISM OF SADDLE WITH HORIZONTAL FRICTION PLATE IN SUSPENSION BRIDGE

An experimental investigation on friction behavior of saddle with horizontal friction plate was done using a prototype. On basis of the results, an analysis model was constructed. Friction mechanism of the saddle of a real suspension bridge was analyzed by the model. As the result, the mechanism was made clear. Furthermore, the result was adopted for the design of Tokyo Port Link Bridge. As an example, a reasonable design frietion coefficient was established for the bridge.

EFFECT OF HORIZONTAL FRICTION PLATE AS A METHOD TO INCREASE FRICTION RESISTANCE OF SADDLE OF SUSPENSION BRIDGE

An experimental investigation on effect of horizontal friction plate as a method to increase friction resistance of saddle of suspension bridge was performed. As a result, it became clear that whole maximum friction resistance was less than total of maximum friction resistances on each contact surface. Furthermore, behaviors of friction between wire and steel galvanized with pure zink, between zink plates, and between wire and zink plate were made clear.

The motion of a finite mass of granular material down a rough incline

Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses, which typically are in the form of innumerable discrete blocks or granules, initially accelerate down the slope until the angle of inclination of the bed approaches the horizontal and bed friction eventually brings them to rest. The present paper describes an initial investigation which considers the idealized problem of a finite mass of material released from rest on a rough inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth-averaged equations of motion are derived; they bear a superficial resemblance to the nonlinear shallow-water wave equations. Two similarity solutions are found for the motion. They both are of surprisingly simple analytical form and show a rather unanticipated behaviour. One has the form of a pile of granular material in the shape of a parabolic cap and the other has the form of anM-wave with vertical faces at the leading and trailing edges. The linear stability of the similarity solutions is studied. A restricted stability analysis, in which the spread is left unperturbed shows them to be stable, suggesting that mathematically both are possible asymptotic wave forms. Two numerical finite-difference schemes, one of Lagrangian, the other of Eulerian type, are presented. While the Eulerian technique is able to reproduce theM-wave similarity solution, it appears to give spurious results for more general initial conditions and the Lagrangian technique is best suited for the present problem. The numerical predictions are compared with laboratory experiments of Huber (1980) involving the motion of gravel released from rest on a rough inclined plane. Although in these experiments the continuum approximation breaks down at large times when the gravel layer is only a few particle diameters thick, the general features of the development of the gravel mass are well predicted by the numerical solutions.

Parasitic Seismic Response of Equipment in Base Isolated Structure Mounted on Sliding Bearings

Abstract All the implementations of seismic base isolation of structures until today—except for one (1982)—have used laminated rubber bearings inserted at foundation level which transfer simultaneously both horizontal and vertical forces. The double function of these bearings and the buckling problem resulting from it have led designers to restrict the fundamental period of the isolated structure to values less than 1.5–2 s in order to avoid large displacements, and this has caused a limitation of isolation efficiency. On the contrary, when the transfer of vertical forces is uncoupled from the transfer of horizontal forces, i.e., when these two functions are accomplished by independent components (for example, sliding bearings and steel or rubber springs, respectively), the buckling problem is overcome. The present study deals with equipment installed in an isolated structure mounted on such a dual support. It carries out a parameter analysis of the parasitic response of the equipment produced by horizontal friction force transferred to the structure through the sliding bearings. The parameters considered are: 1) the fundamental period of the isolated structure (1.5 to 7 s), 2) the stiffness of the sliding bearings, 3) the friction coefficient μ (2 to 15 percent), 4) the ratio σ of equipment mass to the whole structure mass (σ = 0.125 to 50 percent), 5) the frequency content of the ground seismic motion, 6) its intensity (0.3 to 3.0g GPA), and 7) the fundamental frequency of the equipment (3 to 30 Hz).

Vibration isolation system with adjustable constant force, all-directional, attenuating seismic restraint

A vibration isolation system includes a seismic restraint assembly that attenuates forces above a chosen magnitude transmitted to a unit from a support during a seismic event. Vertical friction elements on a vertical frame engage and support a vertical damper element. Horizontal friction elements on a horizontal frame engage and retain a horizontal damper element. One frame is connected to the unit, the other to the support. The vertical and horizontal damper elements interconnect, but lost motion spacing between these elements ordinarily prevents low level vibrations being communicated therethrough. Each of the vertical and horizontal friction elements is spring biased into a predetermined frictional engagement with its associated damper element. The force of the engagement is adjustable to adjust the level at which higher than ordinary forces that are being transmitted through the assembly will begin to be attenuated by slippage of the frictionally engaged elements.

A nested numerical tidal model of the southern New England Bight

A nested, barotropic numerical tidal model has been applied to the southern New England Bight to include Long Island Sound (LIS), Block Island Sound (BIS), Rhode Island Sound (RIS), Buzzards Bay (BB) and a portion of the southern New England shelf. An explicit finite difference representation of the two-dimensional vertically averaged equations of motion and continuity, employing forward time and centered spatial differences with the bottom friction term being evaluated at both time levels, is applied to the study area to predict tidal circulation dynamics. Horizontal friction and advective terms have been neglected. Tidal height data along the open boundaries is specified from available data. Model predictions of corange and high and low cophase lines agree with available data and show the strongly co-oscillatory behavior of LIS. Tidal current ellipses agree reasonably well with available data showing rectilinear motion in LIS, BIS and BB and rotary motion in RIS.

M2Baroclinic Tides in Johnstone Strait, British Columbia

Tide, current and water property data collected in the western basin of Johnstone Strait, British Columbia, are compared with analytical models for M2 semidiurnal motions in a stratified, rotating channel of uniform depth. We show that, for a rectangular basin in which there is a depth-independent mean flow, the tidal fluctuations are readily expressible in terms of a landward (eastward) propagating Kelvin wave and exponentially damped, seaward (westward) propagating baroclinic Kelvin waves. The internal M2 tide appears to be generated through interaction of the surface tide with the shallow sill at the eastern end of the basin and is dominated by a first-mode baroclinic wave whose amplitude undergoes attenuation over an e-folding distance of one wavelength (∼26 km). Near the sill the baroclinic current speed may exceed 50% of the barotropic flow speed. The along-channel energy flux (power) of the barotropic tide is comparatively uniform at ∼1.4×109 W throughout the western portion of the Strait but decreases by a factor of 2 across the sill. Less than 0.3% of this power loss is needed to account for the baroclinic energy flux of ∼2×106 W near the sill; dissipation due to bottom friction is the main sink for the barotropic tidal energy. Attenuation of the baroclinic waves appears to result from a combination of turbulent horizontal friction and bottom boundary layer friction. Based on the first mode amplitudes, we find a horizontal eddy viscosity of ∼4×106 cm2 s−1 and a vertical eddy viscosity of ∼103 cm2 s−1. Our analysis further indicates that higher modes may be subject to attenuation by critical-layer absorption in the presence of the mean estuarine circulation in the basin. The M2 tides and currents are shown to possess considerable variability over periods of weeks and to have seasonal trends that, qualitatively at least, are related to changes in the mean density structure.

Dissipation Mechanisms and the Importance of Eddies in Model Ocean Energy Budgets

Abstract The importance of mesoscale eddies in the basin energy budgets of closed-basin numerical model oceanic systems that attempt to resolve such motions varies greatly from calculation to calculation. In existing calculations, eddy importance has been found to depend strongly on the dissipation mechanism(s) selected. These energy budget results can be understood by examination of how eddy and mean flow kinetic energy are dissipated in the long-time mean in the different regions of the model flow. Scale analysis arguments are presented, assuming that the characteristics of the flows satisfy certain mild quasi-oceanic constraints, to investigate these dissipation terms. From these scale. estimates it appears that many of the model ocean results can he understood in terms of a nondimensional parameter that measures the relative importance of horizontal and bottom friction dissipation. When horizontal friction dissipation dominates, eddies can only be of modest importance in basin energy budgets, but when...

Time scales in wind‐driven lake circulations

The effect of turbulent friction on transient three‐dimensional wind‐driven circulation in large lakes is studied. Horizontal friction is neglected, and vertical friction is modeled by a constant eddy viscosity. The linearized Ekman equations are used in a constant depth lake model which is assumed deep (of small Ekman number). High‐frequency transients due to acoustic, internal, and surface gravity wave modes are eliminated through assumptions of incompressibility, homogeneity, and rigid lid surface, respectively. The initial value problem arising from a suddenly imposed wind stress on an initially quiescent lake is analytically solved, and significant time scales are identified. It is found that the manner in which transient currents adjust to temporal variations in wind stress depends not only on a lake's physical parameters but also on the wind stress spatial pattern. While the inertial period is always significant, the spin‐up time is significant only when the wind stress has a nonzero curl.

A Numerical Study of Somali Current Eddies

Abstract A three-dimensional numerical ocean model is used to study the transient response of the western boundary region of a tropical ocean to the sudden onset of winds parallel to the boundary. In particular, the behavior of resulting western boundary current eddies is studied as a function of various parameters of the model. Alongshore eddy movement is found to decrease and vanish as the horizontal orientation of the western boundary is changed from northward to northeastward. A similar retarding effect is produced upon increasing the nonlinearity of the flow by using weaker vertical turbulent friction or stronger wind stress. Little sensitivity is found to the magnitude of the horizontal turbulent friction coefficient. A term-by-term evaluation of the vorticity balance in the region of the eddies is used to analyze their behavior. A case is run in which the western boundary configuration and applied wind stress approximate that of the northwestern Indian Ocean. An eddy structure evolves which is simi...

Formation of discontinuities in a stratified rotating atmosphere

The formation of discontinuities within internal gravity waves in a rotating Boussinesq atmosphere is investigated with a numerical model. The motion is bounded between two rigid horizontal boundaries, and heating and friction are neglected. Special sinusoidal initial conditions are used. The equations are integrated for a range of values of the initial Rossby (Ro) and Froude (Fr) numbers. Discontinuities are found when the following conditions are satisfied: Fr ≥ 0.2 and Ro ≥ 0.2. These results are substantially different from those obtained for a one-layer fluid with a free upper surface.

ON WAVE DEFORMATION AFTER BREAKING

Waves will dissipate their energy rapidly after breaking. In this paper, the three factors , (i) formation of a horizontal roller,(11) bottom friction, and (in) turbulence with air entrainment, which will contribute to the energy dissipation, are dealt with experimentally and theoretically The horizontal roller formed by a plunging breaker is approximated as a Rankme-type vortex by experiments, and it is calculated that 15$-30%of wave energy is dissipated due to the formation of horizontal roller alone from a breaking point to a point of the roller disappearance. A bottom shear stress due to a breaker is measured by the shear meter deviced by the authors and it is clarified that the energy dissipation due to bottom friction is a little Mam part of the energy dissipation is taken to be caused by the turbulence with air entrainment. It is indicated that an incident monocromatic wave is transformed into a higher frequency wave due to the turbulence. Furthermore, a new basic equation for breaking waves with a turbulence term expressed by a Reynolds stress is presented The theoretical curves computed numerically have a consistent agreement with the experimental results.

Specificity of Individual Differences in Arm Movement Fatigue within Two Levels of Work Load

Abstract Fifty subjects were given fatiguing tests at two work loads on a horizontal arm-crank friction ergometer.2 The initial speed was 120 rpm; the test continued for 10 min. Both fatigue curves were S-shaped—the rate of work dropped off slowly at first, then went through a rapid drop-off phase followed by a slow drop-off phase that approached an asymptotic steady state. The mathematical form was a two-component exponential equation which fitted the observed data very closely. Using a 2-k. work load, there was 22 percent decrement at the end of the test. Using a 3.45-k. work load (1 week later), the decrement was 48 percent. Test-retest reliability of individual differences in drop-off was moderately high (r = .86 and .85 for the two work loads). However, the correlation between drop-offs for the two work loads was only r = .61 and even after correction for attenuation was only .71. Thus only 50 percent of the individual difference variance in fatigability was common to the two work loads, while 50 per...