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 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.
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)
...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.
...make the equations work and come up with an appropriate answer. From these equations, other ones can be created to solve many other problems on heat transfer. Anywhere that temperature exists, there is some sort of heat transfer happening. By predicting, analysing, and testing any equation in thermodynamics, we can learn how to conserve heat and energy for when we actually do need it.
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
... model for the thermodynamics and fluid mechanics calculations for this system need to be presented.
Enclosures are frequently encountered in practice, and heat transfer through them is of practical interest. Heat transfer in enclosed spaces is complicated by the fact that fluid in the enclosure, in general, does not remain stationary. The fluid adjacent to the hotter surface rises and the fluid adjacent to the cooler one falls, setting off a rotationary motion within the enclosure that enhances heat transfer through the
For gas, the MBE is defined as the relationship between the original gas in place, initial pressure (pi), cumulative gas production, and the current average reservoir pressure. The basis of the MBE for gas flow is the volumetric balance of all the fluids at a given time. The following equation proposed by Ramagost and Farshad (1981) is used to calculate the average reservoir pressure for gas systems. This equation considers that gas is the only mobile phase in the presence of residual fluid saturations (oil and water) in a compressible formation.
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