Stresses Around a Wellbore Due to Internal Pressure and Unequal Principal Geostatic Stresses

1962 ◽  
Vol 2 (02) ◽  
pp. 145-155 ◽  
Author(s):  
E.M. Galle ◽  
J.C. Wilhoit
Keyword(s):  
Numerical Solutions ◽  
Stress Component ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Petroleum Industry ◽  
Analytical Investigation ◽  
Structural Failure ◽  
Overburden Pressure ◽  
Lost Circulation ◽  
Good Agreement

Abstract A three-dimensional photoelastic study was made to determine the stress state around the wall and bottom of a wellbore due to fluid pressure within the wellbore and unequal principal geostatic stresses. Models simulating the wellbore were made from a phthalic anhydride-cured epoxy resin. The frozen stress technique of three-dimensional photoelasticity was used to determine the stresses within the model. Two separate problems were solved:hydrostatic pressure on all sides of the model with the exception of the inside of the hole, anduniaxial compression perpendicular to the center line of the hole. The results are presented in the form of contour curves for each stress component. The curves cover a region which extends several hole radii from the bottom and wall of the hole. By proper use of these results, the state of stress may be calculated for any point on the wall or bottom of the hole, as well as for any point within the material that surrounds the hole. A systematic method is given for calculating these stress components for any combination of fluid pressure within the wellbore and system of unequal principal geostatic stresses, provided one of the principal geostatic stresses is parallel with the wellbore. The results show that stresses around the wall and bottom of a wellbore induced by an unequal system of principal geostatic stresses, are appreciably different from those induced by geostatic stresses that are hydrostatic. For unequal principal geostatic stresses, the experimentally determined stresses on the wall of the hole several radii from the bottom are in good agreement with the stresses calculated by elastic theory. Introduction Interest in the problem of determining the stresses around and near the bottom of a wellbore, due to geostatic loading and fluid pressure within the wellbore, originated in the petroleum industry. The stresses on the wall of the wellbore are of interest due to their relation to lost circulation during drilling, the fracturing of formations during squeeze cementing and hydraulic fracturing of producing formations. The stresses on the bottom of the hole are of interest to the drilling segment of the industry because to produce a hole in the earth it is necessary to remove material from the bottom of the hole. This removal of material is produced by structural failure of the rock, whatever the criterion for failure may be. Cunningham and Eenink have shown that for certain conditions the effect on drilling rate of the bottom-hole stresses caused by a hydrostatic overburden pressure is small compared to other effects. This question, however, needs further experimental and analytical investigation. Much information concerning the stresses on the walls of wellbores has been published considering both equal and unequal principal geostatic stresses. The problem of determining the stresses around the bottom of the wellbore is considerably more complicated. However, previous investigators have obtained numerical and experimental solutions to the problem for equal principal geostatic stresses. Whitworth and Woods have obtained numerical solutions. Word obtained a three-dimensional photoelastic solution, Durelli and Deily obtained surface stresses only by photoelastic means, and Cheatham and Wilhoit determined the stresses around the bottom of a short cylindrical cavity. While Miles and Topping, McGuire, Harrison and Kieschnick, and Hubbert and Willis obtained the stresses on the wall of a wellbore for unequal principal geostatic stresses, they did not concern themselves with the stresses near the bottom of the hole. The estimates made by Hubbert and Willis of the differences between the principal geostatic stresses indicate that, to obtain a satisfactory solution for the stresses around the bottom of a wellbore, unequal principal geostatic stresses should be considered. This work is directed toward obtaining such a solution. The materials in the earth's crust are nonhomogeneous, permeable and anisotropic. SPEJ P. 145^

scholarly journals Edge behaviour in the glass sheet redraw process

2015 ◽  
Vol 785 ◽  
pp. 248-269 ◽  
Author(s):  
D. O’Kiely ◽  
C. J. W. Breward ◽  
I. M. Griffiths ◽  
P. D. Howell ◽  
U. Lange
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Sheet Thickness ◽  
Glass Block ◽  
Final Thickness ◽  
Thin Glass ◽  
Boundary Layer Problem ◽  
Sheet Width ◽  
Good Agreement ◽  
Layer Problem

Thin glass sheets may be manufactured using a two-part process in which a sheet is first cast and then subsequently reheated and drawn to a required thickness. The latter redrawing process typically results in a sheet with non-uniform thickness and with smaller width than the cast glass block. Experiments suggest that the loss of width can be minimized and the non-uniformities can be essentially confined to thickening at the sheet edges if the heater zone through which the glass is drawn is made very short. We present a three-dimensional mathematical model for the redraw process and consider the limits in which (i) the heater zone is short compared with the sheet width, and (ii) the sheet thickness is small compared with both of these length scales. We show that, in the majority of the sheet, the properties vary only in the direction of drawing and the sheet motion is one-dimensional, with two-dimensional behaviour and the corresponding thick edges confined to boundary layers at the sheet extremities. We present numerical solutions to this boundary-layer problem and demonstrate good agreement with experiment, as well as with numerical solutions to the full three-dimensional problem. We show that the final thickness at the sheet edge scales with the inverse square root of the draw ratio, and explore the effect of tapering of the ends to identify a shape for the initial preform that results in a uniform rectangular final product.

scholarly journals Predicting fluid pressure in sedimentary basins from seismic tomography

2019 ◽  
Vol 219 (2) ◽  
pp. 1421-1430
Author(s):  
Brian M O’Reilly ◽  
Manel Prada ◽  
François Lavoué ◽  
Sergei Lebedev
Keyword(s):  
Hydrological Cycle ◽  
North Atlantic Ocean ◽  
Fluid Pressure ◽  
Petroleum Industry ◽  
Sedimentary Basins ◽  
Depth Scale ◽  
Porcupine Basin ◽  
Seismic Images ◽  
Volume Decrease ◽  
Good Agreement

SUMMARY Gravitational compaction of thick (2–10 km) sediment accumulations in sedimentary basins is controlled by the interplay of mechanical and chemical processes that operate over many orders of magnitude in spatial scale. The compaction of sediments into rock typically involves a density increase of ≈500 to 1000 kg m−3, occurring over a depth-scale of several kilometres. The volume decrease in the compacting sediments releases vast volumes of water, which plays an important part in the global hydrological cycle and also in tectonic and geochemical processes; including the formation of hydrocarbon and mineral deposits. This study utilizes recently developed tomographic seismic images from the Porcupine Basin, which lies in the deep-water North Atlantic Ocean. A generic method for predicting fluid pressure variations that are driven by gravitational compaction is developed over the scale of the entire sedimentary basin. The methodology is grounded upon both observational evidence and empirically based theories, relying on geophysical measurements and relationships between sediment porosities and densities. The method is based upon physical concepts that are widely used in the petroleum industry and applied extensively in models of overpressure development in sedimentary basins. Geological and geophysical data from exploration wells are used to test the predictions of the method at two locations within the basin and are found to be in good agreement with the theory.

scholarly journals Three-Dimensional Investigation of the Stokes Eigenmodes in Hollow Circular Cylinder

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Adil El Baroudi ◽  
Fulgence Razafimahery
Keyword(s):  
Present Method ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Finite Depth ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Element Analysis ◽  
Fluid Medium ◽  
Stokes Eigenmodes ◽  
Good Agreement

This paper studies the influence of boundary conditions on a fluid medium of finite depth. We determine the frequencies and the modal shapes of the fluid. The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced.

A Free Energy Perturbation Approach to Estimate the Intrinsic Solubilities of Drug-like Small Molecules

2019 ◽  
Author(s):  
Sayan Mondal ◽  
Gary Tresadern ◽  
Jeremy Greenwood ◽  
Byungchan Kim ◽  
Joe Kaus ◽  
...  
Keyword(s):  
Solid State ◽  
Small Molecules ◽  
Three Dimensional ◽  
Aqueous Solubility ◽  
Computational Approach ◽  
Free Energy Perturbation ◽  
Perturbation Approach ◽  
Energy Perturbation ◽  
State Form ◽  
Good Agreement

<p>Optimizing the solubility of small molecules is important in a wide variety of contexts, including in drug discovery where the optimization of aqueous solubility is often crucial to achieve oral bioavailability. In such a context, solubility optimization cannot be successfully pursued by indiscriminate increases in polarity, which would likely reduce permeability and potency. Moreover, increasing polarity may not even improve solubility itself in many cases, if it stabilizes the solid-state form. Here we present a novel physics-based approach to predict the solubility of small molecules, that takes into account three-dimensional solid-state characteristics in addition to polarity. The calculated solubilities are in good agreement with experimental solubilities taken both from the literature as well as from several active pharmaceutical discovery projects. This computational approach enables strategies to optimize solubility by disrupting the three-dimensional solid-state packing of novel chemical matter, illustrated here for an active medicinal chemistry campaign.</p>

scholarly journals Experimental studies on the transformation from firn to ice in the wet-snow zone of temperate glaciers

1997 ◽  
Vol 24 ◽  
pp. 181-185 ◽  
Author(s):  
Katsuhisa Kawashima ◽  
Tomomi Yamada
Keyword(s):  
Experimental Studies ◽  
Ice Formation ◽  
Compression Tests ◽  
Densification Rate ◽  
Overburden Pressure ◽  
Proportionality Constant ◽  
Wet Snow ◽  
Water Saturated ◽  
The Relationship ◽  
Good Agreement

The densification of water-saturated firn, which had formed just above the firn-ice transition in the wet-snow zone of temperate glaciers, was investigated by compression tests under pressures ranging from 0.036 to 0.173 MPa, with special reference to the relationship between densification rate, time and pressure. At each test, the logarithm of the densification rate was proportional to the logarithm of the time, and its proportionality constant increased exponentially with increasing pressure. The time necessary for ice formation in the firn aquifer was calculated using the empirical formula obtained from the tests. Consequently, the necessary time decreased exponentially as the pressure increased, which shows that the transformation from firn in ice can be completed within the period when the firn aquifer exists, if the overburden pressure acting on the water-saturated firn is above 0.12–0.14 MPa. This critical value of pressure was in good agreement with the overburden pressure obtained from depth–density curves of temperate glaciers. It was concluded that the depth of firn–ice transition was self-balanced by the overburden pressure to result in the concentration between 20 and 30 m.

Thermal Performance Analysis of a Rectangular Longitudinal Finned Solar Air Heater With Semicircular Absorber Plate

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Satyender Singh ◽  
Prashant Dhiman
Keyword(s):  
Thermal Performance ◽  
Numerical Solutions ◽  
Solar Air Heater ◽  
Duct Flow ◽  
Balance Equations ◽  
Absorber Plate ◽  
Ansys Fluent ◽  
Air Heater ◽  
Glass Cover ◽  
Good Agreement

Thermal performance of a single-pass single-glass cover solar air heater consisting of semicircular absorber plate finned with rectangular longitudinal fins is investigated. The analysis is carried out for different hydraulic diameters, which were obtained by varying the diameter of the duct from 0.3–0.5 m. One to five numbers of fins are considered. Reynolds number ranges from 1600–4300. Analytical solutions for energy balance equations of different elements and duct flow of the solar air heater are presented; results are compared with finite-volume methodology based numerical solutions obtained from ansys fluent commercial software, and a fairly good agreement is achieved. Moreover, analysis is extended to check the effect of double-glass cover and the recycle of the exiting air. Results revealed that the use of double-glass cover and recycle operation improves the thermal performance of solar air heater.

scholarly journals Simulation of Thermal and Electric Field Distribution in Packaged Sausages Heated in a Stationary Versus a Rotating Microwave Oven

Foods ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1622
Author(s):  
Wipawee Tepnatim ◽  
Witchuda Daud ◽  
Pitiya Kamonpatana
Keyword(s):  
Temperature Distribution ◽  
Electric Field ◽  
Three Dimensional ◽  
Development Stage ◽  
Microwave Oven ◽  
Computational Time ◽  
Plastic Package ◽  
Heating Uniformity ◽  
The Cost ◽  
Good Agreement

The microwave oven has become a standard appliance to reheat or cook meals in households and convenience stores. However, the main problem of microwave heating is the non-uniform temperature distribution, which may affect food quality and health safety. A three-dimensional mathematical model was developed to simulate the temperature distribution of four ready-to-eat sausages in a plastic package in a stationary versus a rotating microwave oven, and the model was validated experimentally. COMSOL software was applied to predict sausage temperatures at different orientations for the stationary microwave model, whereas COMSOL and COMSOL in combination with MATLAB software were used for a rotating microwave model. A sausage orientation at 135° with the waveguide was similar to that using the rotating microwave model regarding uniform thermal and electric field distributions. Both rotating models provided good agreement between the predicted and actual values and had greater precision than the stationary model. In addition, the computational time using COMSOL in combination with MATLAB was reduced by 60% compared to COMSOL alone. Consequently, the models could assist food producers and associations in designing packaging materials to prevent leakage of the packaging compound, developing new products and applications to improve product heating uniformity, and reducing the cost and time of the research and development stage.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

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