New Analytical Solutions for Predicting Pressure Distribution and Transient Behavior in Wedges and Truncated Wedges

2001 ◽  
Author(s):  
N.M. Anisur Rahman ◽  
Ramon G. Bentsen
Keyword(s):  
Pressure Distribution ◽  
Analytical Solutions ◽  
Transient Behavior

An Engineering Approach to Non-Hertzian Contact Elasticity—Part II

2000 ◽  
Vol 123 (3) ◽  
pp. 589-594 ◽  
Author(s):  
Luc Houpert
Keyword(s):  
Pressure Distribution ◽  
Analytical Solutions ◽  
Curve Fitting ◽  
Numerical Solutions ◽  
Companion Paper ◽  
Hertzian Contact ◽  
Line Contact ◽  
Correction Factors ◽  
Analytical Development ◽  
Single Radius

Roller/race misalignment and deformation are used for calculating analytically the pressure distribution along the roller/race contact and the final roller/race load and moment. Use is made of the surface crowns and race undercuts for calculating contact dimensions with their possible truncations at large misalignment or loads. The pressure distribution is not symmetrical when misalignment occurs. This analytical development was possible by using a slicing technique in which the local roller/race geometrical interference was calculated in each slice of the contact. A mix of point and line contact Hertzian solutions developed in a companion paper “Part I” is used for obtaining the final load per slice. The final analytical solutions (load, moment and pressure) are successfully compared to two numerical solutions described briefly. The analytical model has been slightly fine-tuned using correction factors obtained by curve-fitting for matching the results to the numerical ones. In the curve-fitting, the single radius profile and multi-radius profile are distinguished.

Contact Area Variation in Elastic Indentation Problems

2009 ◽  
Author(s):  
Roman Riznychuk
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Half Space ◽  
Analytical Solutions ◽  
Contact Area ◽  
Elastic Half Space ◽  
Exact Expression ◽  
Rigid Punch ◽  
Contact Pressure Distribution ◽  
Area Variation

Contact problem of the frictionless indentation of elastic half-space by smooth rigid punch of curved profile is investigated. An exact expression of the contact pressure distribution for a curved profile punch in terms of integral involving the pressure distribution for sequence of flat punches is derived. The method is illustrated and validated by comparison with some well-known analytical solutions.

Hydrodynamics of Wire-Drum Contact

1987 ◽  
Vol 109 (4) ◽  
pp. 679-683
Author(s):  
A. Magnin ◽  
J. M. Piau ◽  
J. Frene ◽  
D. Bois ◽  
M. Godet
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Wire Tension ◽  
Active Pressure ◽  
Tension Level ◽  
Foil Bearing ◽  
Pressure Zone ◽  
Minimum Film Thickness

The hydrodynamics of a wire-drum contact is analyzed using theoretical techniques developed in foil bearing studies. Analytical solutions and numerical solutions are obtained. Results show that: when for a given minimum film thickness the wire tension increases, the pressure arc extent decreases and reaches a minimum for certain wire tension level; the pressure distribution is independent of wire tension for large values of tension; and the active pressure zone depends strongly on film thickness.

scholarly journals Contact Analyses for Anisotropic Half Space: Effect of the Anisotropy on the Pressure Distribution and Contact Area

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Caroline Bagault ◽  
Daniel Nélias ◽  
Marie-Christine Baietto
Keyword(s):  
Pressure Distribution ◽  
Contact Mechanics ◽  
Half Space ◽  
Analytical Solutions ◽  
Contact Area ◽  
Anisotropic Material ◽  
Analytical Methods ◽  
Numerical Techniques ◽  
Recent Developments ◽  
Space Effect

A contact model using semi-analytical methods, relying on elementary analytical solutions, has been developed. It is based on numerical techniques adapted to contact mechanics, with strong potential for inelastic, inhomogeneous or anisotropic materials. Recent developments aim to quantify displacements and stresses of an anisotropic material contacting both an isotropic or anisotropic material. The influence of symmetry axes on the contact solution will be more specifically analyzed.

Decline Curves of a Vertical Well in Stress-Sensitive Reservoir

2013 ◽  
Vol 772 ◽  
pp. 781-788
Author(s):  
Zhang Zhang ◽  
Shun Li He ◽  
Hai Yong Zhang ◽  
Shao Yuan Mo ◽  
Shuai Li
Keyword(s):  
Pressure Drop ◽  
Analytical Solutions ◽  
Transient Behavior ◽  
Stress Sensitivity ◽  
Variable Pressure ◽  
Well Testing ◽  
Type Curves ◽  
Vertical Well ◽  
Constant Rate ◽  
Decline Curves

Stress-sensitivity effects have been recognized to have impact on the pressure/rate transient behavior of wells in several reservoirs. Although the effects of stress-sensitivity have been considered in well testing theory in the past thirty years, little has been done to determine their influence on rate decline behavior. This paper presents a single phase flow model considering stress-sensitive formation permeability to investigate the characteristic of production rate decline of a vertical well. The stress-sensitive permeability is considered as an exponential form. The permeability changes with pressure drop are described by a permeability modulus. By introducing two pseudo functions, the equations of the mathematical model are linearized and approximate semi-analytical solutions are obtained. The analytical solutions are carefully verified through numerical simulation. Two sets of new decline type curves are diagramed on a log-log plot for constant rate case and constant bottomhole pressure case respectively. The influence of stress-sensitive permeability on decline curves are analyzed and compared. From this work, we recognized that the rate decline characteristics of stress-sensitive reservoir under constant rate and constant bottomhole producing condition are different. New analysis method should be developed to analyze field variable rate/variable pressure drop data.

scholarly journals Thrust Bearing with Rough Surfaces Lubricated by an Ellis Fluid

2014 ◽  
Vol 19 (4) ◽  
pp. 809-822
Author(s):  
A. Walicka ◽  
E. Walicki ◽  
P. Jurczak ◽  
J. Falicki
Keyword(s):  
Pressure Distribution ◽  
Analytical Solutions ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Plastic Fluid

Abstract In the paper the influence of bearing surfaces roughness on the pressure distribution and load-carrying capacity of a thrust bearing is discussed. The equations of motion of an Ellis pseudo-plastic fluid are used to derive the Reynolds equation. After general considerations on the flow in a bearing clearance and using the Christensen theory of hydrodynamic rough lubrication the modified Reynolds equation is obtained. The analytical solutions of this equation for the cases of a squeeze film bearing and an externally pressurized bearing are presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. A thrust radial bearing is considered as a numerical example.

Pressure Studies in Bounded Reservoirs

10.2118/50-pa ◽  
1961 ◽  
Vol 1 (04) ◽  
pp. 223-228 ◽  
Author(s):  
S.A. Hovanessian
Keyword(s):  
Pressure Distribution ◽  
Analytical Solutions ◽  
Constant Pressure ◽  
Theoretical Method ◽  
Reservoir Pressure ◽  
Production Well ◽  
Numerical Examples ◽  
Rectangular Pattern ◽  
Flow Boundaries ◽  
Rectangular Field

Abstract Analytical solutions are obtained for calculating the pressure distribution in rectangular fields due to injection and/or producing wells located anywhere within the field. The field is assumed to be homogeneous with either constant pressure or no-flow boundaries. These solutions are extended to include the calculation of average reservoir pressure and permeability from pressure build-up curves. Numerical examples are given to illustrate the application of equations to practical problems. Introduction Pressure distribution analyses are of considerable importance in the field of reservoir mechanics. A number of papers dealing with this subject have appeared in the petroleum literature. Perrine in 1956 presented a summary of the methods available for pressure build-up calculations and discussed the applicability of each in some detail. More recently (1958), Hazebroek, et al, discussed a theoretical method for obtaining pressure distribution in a radial field. Also in 1958, Nisle gave a theoretical solution of the pressure distribution in a field extending to infinity with a partially penetrating line source at the origin. Mathews, et al, applied the method of images to existing solutions for pressure distribution in radial fields and obtained expressions for calculating pressures in bounded reservoirs. However, a literature survey revealed that a general analytical solution for the pressure distribution in a rectangular field, with injection and/or production wells located anywhere within the field, was not available. Such a solution could be used to approximate the pressure distribution in a field the shape of which is nearly rectangular. Furthermore, it could be applied to pressure calculations pertaining to a single well taken from a system of wells which were drilled in a rectangular pattern. In this case the boundaries of the well drainage area are considered to be the perpendicular bisectors of the lines joining the well and its nearest neighbors. The basic problem considered in this paper consists of a rectangular field with either constant pressure or no-flow boundaries and with either an injection or production well located anywhere within the field. The physical properties of the rock and fluids present are considered to be constant. Analytical expressions are obtained for the pressure distribution within the field during the production or injection periods. These expressions, which are infinite series, can be used to evaluate pressure at any point within the field as a function of time and position. For fields containing more than one well (production and/or injection), the solutions for each well acting independently are superposed. That is, at any point in the field, the pressures due to each injection or production well acting alone can be algebraically added to give the pressure resulting from all wells acting simultaneously. Evaluation of the series solutions given in this paper is readily accomplished by means of an electronic digital computer; and, in most cases, sufficient accuracy is obtained by setting the upper limits of summation at 20. These solutions are extended to include the calculation of average reservoir pressure and permeability from build-up data. A number of numerical examples are given to illustrate application of the solutions to actual field problems. ANALYTICAL SOLUTIONS The partial differential equation representing the pressure distribution in a homogeneous rectangular field (see Fig. 1), having a single source or sink of strength, can be written: ............................(1) where x, y = space coordinates, ft, (l, q) = location of source or sink, ft, p = pressure at (x, y), psi, 0 = porosity, fractional SPEJ P. 223^

Damped waves generated by a moving pressure distribution

2001 ◽  
Vol 12 (3) ◽  
pp. 357-366 ◽  
Author(s):  
J. -M. VANDEN-BROECK
Keyword(s):  
Free Surface ◽  
Pressure Distribution ◽  
Analytical Solutions ◽  
Lower Layer ◽  
Free Surface Flows ◽  
Two Dimensional ◽  
Surface Flows ◽  
Short Waves

Free surface flows generated by a moving distribution of pressure are considered. The fluid consists of two superposed layers in a two-dimensional channel. The upper layer is inviscid and the lower layer, which is introduced as a damping mechanism, is modelled by the mathematically convenient lubrication equations. Numerical and analytical solutions are presented. Special attention is given to solutions for which there is a train of waves on each side of the distribution of pressure. It is shown that, depending on the values of the parameters, the short waves can appear on either side of the distribution of pressure.

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