The prediction and mitigation of annular pressure build up in a wellbore during injection and production are recurring challenges in petroleum engineering. The annular pressure build up has been studied continuously over the past decades because the understanding and underlying APB mechanism is essential for developing any mitigation technology.
The first step of understanding the APB mechanism is to predict temperature profiles in the wellbores accurately. Almost all practical methods for calculation of temperature profiles in the wellbores go back to the work by Ramey (1962) on wellbore heat transmission published in early 1960’s.
In that paper, Ramey presented an analytical equation for wellbore temperatures based on a simplified heat balance. Assuming steady-state flow of an incompressible single phase fluid, he dropped the kinetic energy term.
Edwardson et al. (1961) developed methods to calculate formation temperature disturbances attributable to mud circulation during drilling operations. The method was mathematically expanded by solving of the differential equation of heat conduction and the calculated results reasonably confirmed field data. It was concluded that, in general, the temperature disturbances caused by circulating mud are small beyond 10ft from the wellbore, but are quite significant near the wellbore.
In 1989, Mitchell et al. presented a model to predict downhole temperature during the operations by reducing the differential equations of energy and momentum conservation to algebraic equations, and by solving these algebraic equations subject to the appropriate boundary using a numerical solution process. They indicated that wellbore simulation can provide more reliable estimates of well loads and flowing fl...
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...the Grashof number were studied starting from the solution for mixed convection without viscous dissipation. It was reported that viscous dissipation enhances the effects of buoyancy and vice versa.
The effects of viscous dissipation and the yield shear stress on the asymptotic behavior of the laminar forced convection in a circular duct for a Bingham fluid were investigated by Khatyr et al. (2002). Three types of wall boundary conditions, namely: variable heat flux distributions, constant wall temperature and convection with an external isothermal fluid were considered. The same asymptotic values of the the Nusselt number were reported for the boundary conditions of constant wall temperature and convection with an external isothermal fluid. It was illustrated that in the convective boundary conditions, the value for Nusselt number is independent of the Biot number.
Thermodynamics is essentially how heat energy transfers from one substance to another. In “Joe Science vs. the Water Heater,” the temperature of water in a water heater must be found without measuring the water directly from the water heater. This problem was translated to the lab by providing heated water, fish bowl thermometers, styrofoam cups, and all other instruments found in the lab. The thermometer only reaches 45 degrees celsius; therefore, thermodynamic equations need to be applied in order to find the original temperature of the hot water. We also had access to deionized water that was approximately room temperature.
The purpose of this lab was to calculate the specific heat of a metal cylinder
According to his Jamaica Letter, Simon Bolivar's desired outcomes was to have the people break away from the civil state, and create a new Civil State and declare independence. The reason he had wanted the people to break away was because he had felt they were treated unfairly. But it was not going to be that easy to just declare independence there were some challenges that they had to face. According to his Jamaican Letter the outcome that Simon Bolivar desired for Latin America was for the people to break away from the civil state a create their own form of the social contract he wanted them to separate from Spain and be independent. The conditions Latin America had been expressed by the people, and how Spain had kept them in a lock. “The veil has been torn asunder, we [South America] have already seen the light and it is not our desire to thrust back into the darkness” (Bolivar 201). When Bolivar said this he is emphasizing his desire to have them separate from Spain he said “it is not” their desire to go “into the darkness” [There original state]. Therefore is emphasizing the fact that the desire for Latin America was to have the people separate from Spain. He also said this directly when Bolivar says “light” he is referring to being separated from Spain, they have already experienced separation from Spain, and the “darkness” Bolivar talked primarily being dependent on Spain. Overall Bolivar directly showed his desire for Latin America was to have the people separate from Spain entirely.
The data which was collected in Procedure A was able to produce a relatively straight line. Even though this did have few straying points, there was a positive correlation. This lab was able to support Newton’s Law of Heating and Cooling.
...he principle numbers of Froude, Reynolds and Weber. Mathematical model predicts the heat and mass transfer in numerical framework for both transports phenomena of relevance to the industry continuous casting tundish system. Additionally, it has an excellent agreement outlet temperature respond the step input temperatures in the inlet stream of water in the tundish model. The simulations of 8x8 grid and 16x16 grid are applied to obtain significant difference between the TAV maps in which both grids are computed by software represent the specific flow of the fluid in the model and the steel caster as the actual size system. Therefore, the physical and mathematical modeling is used as a guidance to build a model before the prototype is constructed in terms of calculation, measurement and determination of specific fluid flow, heat and mass transfer in the water model.
The range of application of the original Boltzmann equation has grown way beyond just dealing with a rarefied gas with one constituent and as a result, several generalizations of the Boltzmann equation have been developed and this includes the reactive Boltzmann
...a producing well is significantly lower than at other areas where no well is drilled. The driving force could be either natural or created by engineering design involving fluid injection through certain wells placed optimally to achieve the best results. Experimental data suggests that reservoir rocks are abundantly permeable in both vertical and horizontal directions. Among a myriad of factors related to geological and geochemical processes, the permeability of a rock is influenced by the slit, shape, configuration, and connectivity or a porous network.
Convection occurs when warmer areas of a liquid or gas ascend to cooler areas in the liquid or gas. Cooler liquid or gas then takes the place of the warmer areas which have risen higher. The fluid above a hot surface expands, becomes less dense and rises. This results in a continuous circulation pattern. At the molecular level, the molecules expand upon introduction of thermal energy. As temperature of the given fluid mass increases, the volume of the liquid must increment by same variable. This impact on the liquid cause dislodging as the quick hot air rises, it pushes denser and colder air down. This is happened in this parabolic solar cooker. Figure 2.0.8 shows place where convection application occurs in this solar
Bruce R. Munson, Theodore H. Okiishi, Wade W. Huebsch, Alric P. Rothmayer, Fluid mechanics 7th edition, Willey, (2013)
Kreith, Frank, and Mark S. Bohn. Principles of Heat Transfer, 6th ed. New York: Brooks/Cole, 2001
Let us consider the heat flow in a bar or rod along the x-axis. Consider a rod of homogeneous material of density is ρ (gm⁄〖cm〗^3 ) and having a constant cross-sectional area A (〖cm〗^2 ). Let c be the specific heat and k be thermal conductivity of material. We suppose that the sides of the bar are insulated and the loss of heat from the sides by conduction or radiations is negligible. Take an end of the bar as the origin and the direction of heat flow as the positive x-axis.
Finally a recent phenomenon that has been encountered is the increased seismic activity in areas surrounding hydraulic fracturing well sites. Induced seismic activity is used to describe the transfer of utilized hydraulic fracturing liquids as a part of profound infusion wells either at too high a pressure or to close to a current geologic flaw causing disruptions that can be felt as
Well development occurs after exploration has located an economically recoverable field and involves the construction of one or more wells from the beginning (called spudding) to either abandonment if no hydrocarbon are found or to well completion if hydrocarbons are found in sufficient quantities.
In this present work the CFD simulation of heat sink is carried out for two different velocity magnitudes. The heat sink is modelled as a combination of Copper and Aluminium materials. The base of the heat sink is taken as Copper and the fins are modelled as Aluminium. A conjugate heat transfer analysis is carried out for this fluid – structure case. Two cases are simulated with a velocity of flow as 4 m/s and 10 m/s. The base of the heat sink is given with heat flux boundary. The results of both the scenarios are showing good coherence with the physical phenomenon. As velocity increases the temperature of the heat sink decreases, so the heat generated in the heat sink will become less. The rate of heat transfer will be