Flow of fluids

When the radial flow of fluid towards the wellbore comes under the localised influence of the well, the shape of the interface between two fluids may be altered. The following diagrams show the phenomena of coning and cuspingoi water, as water is displacing oil towards the well. 

The previous sections have considered the flow of fluid to the wellbore. The productivity index (PI) indicates that as the flowing wellbore pressure (Pwf) reduces, so the drawdown increases and the rate of fluid flow to the well increases. Recall... 

R. E. Collins, Flow of Fluids through Porous Materials, Reinhold, New York, 1961. C. Dyhowski and R. L. Lichter, eds., NMR Spectroscopy Techniques, Marcel Dekker,... 

R. E. Collins, Flow of Fluids Through Porous Materials, Reinhold, New York, 1961. 

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

Convective heat transfer is classified as forced convection and natural (or free) convection. The former results from the forced flow of fluid caused by an external means such as a pump, fan, blower, agitator, mixer, etc. In the natural convection, flow is caused by density difference resulting from a temperature gradient within the fluid. An example of the principle of natural convection is illustrated by a heated vertical plate in quiescent air. 

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

Flow of Fluids tliroiigli Valves, Fittings, and Pipe, Tech. Pap. 410, Crane Co., 1969. 

Lansford, Loss of Head in Flow of Fluids thr-ough Various Types of IVs-in. Valves, Univ. Eng. Exp. Sta. Bull. Ser. 340, 1943. 

Gate valves are used to minimize pressure drop in the open position and to stop the flow of fluid rather than to regulate it. The problem, when the valve is closed, of pressure buildup in the bonnet from cold liquids expanding or chemical action between fluid and bonnet should be solved oy a relief valve or by notching the upstream seat ring. 

Constant Flow into Protected Equipment For the steady-state design scenario with a constant, steady flow of fluid from a pressure source that is above the maximum aUowed pressure in the protected equipment, volume is being generated within the equipment at a rate RV = F/ f. Substituting into Eq. (26-21) and noting that the specific volume of the vent stream is l/p, gives the required mass flow rate ... 

Motorized sluice valve - To throttle the flow of fluid Figure 6.38 Conventional throttle control... 

Variable-speed drives are essential for many industrial applications requiring variable operating parameters during the course of operation. Such variations can be in the flow of fluid and pressure of air or gas etc. The con-... 

Moderate to accurate, depending upon the accuracy of controls. Stepless up to 20% of V, at constant h.p. and up to 33% of N, at constant torque is possible. Pumps, ID fans etc., that call for speed variation during a process need may not necessarily be too accurate. Or variation in flow of fluid, gas or temperature etc. not calling for very accurate controls, that such drives find their extensive use. It may be made more accurate, but at higher cost of controls... 

The economics would depend upon the smoother flow of fluid without exce.ssive friction loss. A smaller section of pipe may not only require a higher h.p. for the same suction and lifting head due to greater frictional losses, but may also cause the pipe to deteriorate quickly as a result of the additional load on its surface. Losses due to bends ami valves should also be added in the total friction loss. 

The D Arcy equation is the accepted equation for the flow of fluid through a packed bed and its derivation will be found in most physics textbooks. If a capillary column... 

Single gas bubbles in an inviscid liquid have hemispherical leading surfaces and somewhat flattened wakes. Their rise velocity is governed by Bernoulli s theory for potential flow of fluid around the nose of the bubble. This was first solved by G. I. Taylor to give a rise velocity Ug of ... 

The axial dispersion model also gives a good representation of fluid mixing in paeked-bed reaetors. Figure 8-34 depiets the eorrelation for flow of fluids in paeked beds. 

Bulk flow is expressed as the material or energy carried by the bulk flow of fluid into or out of the control region. 

Consider first the steady flow of fluid through a control volume CV between prescribed stable states X and Y (Fig. 2.1) in the presence of an environment at ambient temperature Tj, (i.e. with reversible heat transfer to that environment only). The maximum work which is obtained in reversible flow between X and Y is given by... 

The following semi-empirical equation relates the (hindered) settling velocity of a slurry of particles to the settling velocity of a single particle, known as the Richardson and Zaki (1954) (RZ) equation. The RZ equation is also used for liquid fluidization whereby particles are supported by an up-flow of fluid. 

For laminar flow of fluid through a pipe experieneing viseous drag. Carman (1937, 1956) applied the Flagen-Poisseuille Equation... 

Crystals suspended in liquors emerging from crystallizers are normally passed to solid-liquid separation devices such as gravity settlers or thickeners that may subsequently feed filters to remove yet more liquid prior to drying. Here the transport processes of particle motion and the flow of fluids through porous media are important in determining equipment size, the operation of which may be intensified by application of a centrifugal force. 

Figure 2-2. Change in AT over distance, counter-current flow of fluids.

The flow of fluid leaving a choke is in the form of a high-velocity jet. For this reason it is desirable to have a straight run of pipe of at least ten pipe diameters downstream of any choke prior to a change in direction, so that the jet does not impinge on the side of the pipe. 

The process described above is usually called osmosis and this usually imphes a flow of fluid in one direction or the other. If the permeating species, usually called the solvent, flows from the pure compartment to the mixture compartment then it is called osmosis pure and simple. This seems the natural process since the solvent dilutes the solution and this involves an increase in entropy and/or a decrease in free energy, so the resultant flow is spontaneous and the system tends to equihbrium. However, the starting conditions may be such that the difference of pressure... 

Flow of Fluids Tlirough Valves, Fillings, and Pipes , Teclmical Paper 4I0M. Crane Co, New York, 1981. 

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