Pressure drop

The pressure drop across an ion exchange bed has been represented by an equationt which depends on the average particle diameter, the void fraction in the bed, an exponent and a friction factor dependent on the Reynolds number, a shape factor, the density of the fluid, the viscosity of the fluid and the flow rate. 

While that equation has internally consistent units (English system), the variables are not normally measured in those units. Another disadvantage is that one must check graphs of the exponent and friction factor versus the Reynolds number to use the equation. 

For laminar flow with spherical particles, the equation can be simplified to  

For most ion exchange resins, the void volume is about 0.38, so that (1- ) i = 4.34 and  

Resin Flow Rate (L/min) Mean Bead Diameter (mm) Pressure Drop (bar/cm) Calculated Measured  

The pressure drop corresponds to the decrease of pressure occurring between the inlet and outlet of a duct carrying a fluid. Knowledge of the pressure drop in a duct is needed to sustain an internal flow. In practice, the pressure drop can be split into two distinct contributions  

The pressure drop over a cyclone is normally subdivided in three contributions  

losses in the separation space (the main cyclone body), and 

The losses in the entry are often negligible compared to the other contributions, at least in tangential entry cyclones. For swirl tubes with inlet vanes little information is available, but if the vanes are properly contoured aerodynamically, the losses are generally small. 

The losses in the cyclone body are higher, but, as we shall see later, their main significance is in limiting the intensity of the swirl in the separation space more frictional losses at the walls lead to a less intensive vortex. Such wall losses do not dominate the overall pressure drop. 

The pressm-e drop over a cyclone, Ap, is proportional to—or very close to being proportional to the square of the volumetric flowrate, as it is in all processing equipment with tm-bulent flow. To obtain a characteristic measm-e for pressure drop in a given cyclone, pressm-e drop is often reported in a dimensionless form known as the Euler nmnber  

The total pressure drop across a tray is the sum of the pressure drop across the disperser unit, (diy hole for sieve trays dry valve for valve trays), and the pressure drop through the aerated mass hi, i.e.. 

As the fluid flows through the cooler, there is a pressure drop. Typically this pressure drop is about 35 kPa (5 psi), but clearly it is a function of the cooler design. In preliminary design a value of 35 kPa can be used. Note this has a significant effect on the suction pressure to the low pressure stages. 

During the compression-cooling cycle it is important that the acid gas is not liquefied. Therefore in the design of the compressor it is important to consider the phase envelope. The compression-cooling curve should be plotted on the phase envelope. This allows for rapid interpretation. 

As a safe design the interstage cooling should not be within 5°C of the acid gas dew point. This concept is perhaps best explained by using an example. 

These values meet our first criteria that the discharge temperatures must be less than 180°C. 

Plotting these values on the phase envelope reveals a problem. After cooling on the third stage, the fluid crosses the phase envelope and thus the acid gas is liquefied. This can be seen on figure 6.4a. The saw toothed curve on the figure represents the compression cooling cycle. The suction is at the lowest pressure and temperature (200 kPa and 50°C). In the first stage the gas is compressed to 545 kPa 

Considerable literature has been published on the pressure drop of cocurrent flow through packed columns.46,70-90 100,106,107 Several empirical and semitheoretical correlations are presented. Turpin and Huntington,100 for instance, correlated their downflow pressure gradient results by the relation 

Gg and CL are superficial gas and liquid mass velocities, respectively, dp is the particle diameter, pG is the gas-phase density, e is the bed void fraction, pG and pL are the gas and liquid viscosities, respectively, and Cog is the superficial gas velocity. 

Larkins et al.48 defined the two-phase pressurc radient (AP/AZ)LG as follows  

Abbott et al.1,2 used the form of Eq. (6-3) to correlate hydrodesulfurization and hydroprocessing data. The values of Kx and K2 obtained in their correlation were 0.620 and 0.830, respectively. The liquid holdup was correlated by the expression 

Some unpublished experimental data taken with a nitrogen-butane system at operating pressures between approximately 23.8 and 37.4 atm indicate that the correlation of Abbott et al.1 is applicable over a wide range of practical conditions when the catalyst size is greater than or equal to 0.16 cm. The correlation, however, requires refinement when the catalyst size employed is smaller than 0.16 cm. 

When a liquid flows through a pipe or a channel a pressure drop is observed across the flow geometry due to friction with the wall. The presence of a spacer or turbulence promoter in the pipe or channel will increase the friction and consequently the pressure drop increases. The pressure for a well developed flow can be given by the foDowing correlation. 

In can be observed that the friction factor for channel and tube are rather amilar. Funhermore, in the turbulent region the friction factor is much less dependent on the Reynolds number. The pressure drop is given by the Fanning equation [6] and is related to the flow velocity by 

The next problem is the calculation of the flue gas pressure drop as it crosses the selected finned tube convection section. Using the design information for tubes per row, number of rows, tube spacing, fin and tube geometry and fin pitch, compute the net free volume and friction surface of the convection section. 

determine the gas flow length, L, and the -4T gas density, Pg, at the bulk temperature. 

The TURBULENT DP COEF is the appropriate performance indicator for catalyst pressure drop, and is a better indicator than pressure drop itself, since it is independent of all the known effects of flow rate (both hydrocarbon and steam), gas density, viscosity, catalyst particle diameter, and void fraction. Pressure drop itself is important though, due to the stress it imposes on the catalyst (which raises the potential for crushing) and normally the optimization system has an upper bound on pressure drop. That bound may or may not be active at the solution, depending on the catalyst condition, and whether the solution is maximizing throughput. 

The pressure drop profile illustrated is for a primary reformer when the pressure drop across the catalyst was fairly high. The differential pressure indicator showed a 2.9 kg/cm drop across the catalyst tubes. 

Most packed columns consist of cylindrical vertical vessels. The column diameter is determined so as to safely avoid flooding and operate in the preloading region with a pressure drop of no greater than 1.2 kPa/m of packed height (equivalent to 1.5 in. of water head per foot of packed height). 

It has been found that the pressure drop at flooding is strongly dependent on the packing factor for both random and structured packings. Kister and Gill (1991) developed the empirical expression 

Usually, packed columns are designed based on either of two criteria a fractional approach to flooding gas velocity or a maximum allowable gas-pressure drop. For given fluid flow rates and properties, and a given packing material, equation (4.8) is used to compute the superficial gas velocity at flooding, vGF. Then, according to the 

The dry-packing resistance coefficient (a modified friction factor), 4,o, is given by the empirical expression 

When the packed bed is irrigated, the liquid holdup causes the pressure drop to increase. The experimental data are reasonably well correlated by (Billet and Schultes, 1991a) 

Separation trays and structured and random packings are the prevailing mass transfer internals at choice for rectification columns and, in first deciding between them, a comparative performance design needs to be prepared including examinations on capacity limitations, pressure drop and separation performance. 

Such examinations require a sound knowledge about the following characteristic parameters and physical quantities to permit process engineering calculations and column design. 

In terms of the hydraulic design of columns, the liquid and gas loads are major design parameters to be considered. For the liquid flow, the load characteristic is expressed as the liquid volume flow related on the inner column area  

The gas load is usually characterised by the F-Factor, which is the vapour capacity factor defined as product of superficial gas velocity and square root of vapour density  

For every design approach of rectification columns, the pressure drop is an important physical quantity to be considered. The pressure drop is the resistance offered to the vapour flowing through the column and defined as 

The problem of the optimal particle shape and size is crucial for packed bed reactor design. Generally, the larger the particle diameter, the cheaper the catalyst. This is not usually a significant factor in process design - more important are the internal and external diffusion effects, the pressure drop, the heat transfer to the reactor walls and a uniform fluid flow. 

Hie most commonly found shape of catalyst particle today is the hollow cylinder. One reason is the convenience of manufacture. In addition there are often a number of distinct process advantages in the use of ring-shaped particles, the most important being enhancement of the chemical reaction under conditions of diffusion control, the larger transverse mixing in packed bed reactors, and the possible significant reduction in pressure drop. It is remarkable (as discussed later) that the last advantage may even take the form of reduced pressure losses and an increased chemical reaction rate per unit reactor volume [11]. 

The Ergun equation can be applied to gases by using the density and viscosity of the gas at the arithmetic average of the end conditions. For large pressure drops and temperature changes, it seems better to use Equation 8.38 with the pressure gradient in differential form AP/L should be replaced by -dP/dz, where z is the distance in the direction of flow. 

The superficial velocity can be found if the mass or volume flow rates (G or 4 v) are known  

With this definition, for spheres, the use of Equation 8.39 gives just the diameter of sphere. Expressions of equivalent diameters for different particle shapes as used in packed bed reactors are presented in Table 8.1.  

It is therefore clear that flooding can be caused either by the vapor flow or the liquid flow exceeding certain limitations. Usually the vapor flow is limiting and the column preliminary design is based on it. The column is then checked for its liquid handling capacity. 

The flooding vapor velocity correlations are empirical and specific to the type of tray. For a given tray type, the flooding vapor velocity is a function of the liquid flow, the vapor and liquid densities, and the tray spacing (Section 14.1.4). Corrections for surface tension are included in certain correlations. 

Whereas liquid flow is caused by gravity in vapor-liquid countercurrent columns, a pressure gradient is necessary to induce vapor flow. Pressure drops exist from tray to tray, so the lower trays must be maintained at a higher pressure than the upper trays. One consideration in tray design is to attempt to keep the pressure drop at a minimum. 

High pressure drops can cause the downcomer backup to increase to a point 

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When recycling material to the reactor for whatever reason, the pressure drop through the reactor, phase separator (if there is one), and the heat exchangers upstream and downstream of the reactor must be overcome. This means increasing the pressure of any material to be recycled. 

If the pressure drop available for the stream is known, the expressions of Polley et al. can be used. 

Polley, G. T., Panjeh Shahi, M. H., and Jegede, F. O., Pressure Drop Considerations in the Retrofit of Heat Exchanger Networks, Trans. IChemE, part A, 68 211, 1990. 

A considerable reduction in particle size separation can be achieved at the expense of increased pressure drop using a Venturi scrubber (see Fig. 11.2c). 

Bag filters. Bag filters, as discussed in Chap. 3 and illustrated in Fig. 3.66, are probably the most common method of separating particulate materials from gases. A cloth or felt filter material is used that is impervious to the particles. Bag filters are suitable for use in very high dust load conditions. They have an extremely high efficiency, but they suflFer from the disadvantage that the pressure drop across them may be high. ... 

Inlet pressure and pressure drop (gas-phase reactions)... 

Liquid viscosity is one of the most difficult properties to calculate with accuracy, yet it has an important role in the calculation of heat transfer coefficients and pressure drop. No single method is satisfactory for all temperature and viscosity ranges. We will distinguish three cases for pure hydrocarbons and petroleum fractions ... 

Hydrate formation is possible only at temperatures less than 35°C when the pressure is less than 100 bar. Hydrates are a nuisance they are capable of plugging (partially or totally) equipment in transport systems such as pipelines, filters, and valves they can accumulate in heat exchangers and reduce heat transfer as well as increase pressure drop. Finally, if deposited in rotating machinery, they can lead to rotor imbalance generating vibration and causing failure of the machine. 

This property should also be within precise limits. In fact, a too-viscous fuel increases pressure drop in the pump and injectors which then tends to diminish the injection pressure and the degree of atomization as well as affecting the process of combustion. Inversely, insufficient viscosity can cause seizing of the Injection pump. 

The most common technique for estimating thermal stability is called the Jet Fuel Thermal Oxidation Test (JFTOT). It shows the tendency of the fuel to form deposits on a metallic surface brought to high temperature. The sample passes under a pressure of 34.5 bar through a heated aluminum tube (260°C for Jet Al). After two and one-half hours, the pressure drop across a 17-micron filter placed at the outlet of the heater is measured (ASTM D 3241). 

For Jet Al, the pressure drop should be less than 33 mbar, and the visual observation of the tube should correspond to a minimum of three on the scale of reference. 

The heavy fuel should be heated systematically before use to improve its operation and atomization in the burner. The change in kinematic viscosity with temperature is indispensable information for calculating pressure drop and setting tbe preheating temperature. Table 5.20 gives examples of viscosity required for burners as a function of their technical design. 

Flow measurements for diesel injectors under a pressure drop of 0.6 bar. 

The measurement of a crude oil s viscosity at different temperatures is particularly important for the calculation of pressure drop in pipelines and refinery piping systems, as well as for the specification of pumps and exchangers. 

During production sodium chloride can deposit in layers on tubing walls after partial vaporization of the water due to the pressure drop between bottomhole and wellhead when these deposits become important large enough, the diameter of the well tubing is reduced. 

Using this mixture as an example, consider starting at pressure A and isothermally reducing the pressure to point D on the diagram. At point A the mixture exists entirely in the liquid phase. When the pressure drops to point B, the first bubble of gas is evolved, and this will be a bubble of the lighter component, ethane. As the pressure continues to drop, the gas phase will acquire more of the heavier component and hence the liquid volume decreases. At point C, the last drop of liquid remaining will be composed of the heavier component, which itself will vaporise as the dew point is crossed, so that below... 

The initial condition for the dry gas is outside the two-phase envelope, and is to the right of the critical point, confirming that the fluid initially exists as a single phase gas. As the reservoir is produced, the pressure drops under isothermal conditions, as indicated by the vertical line. Since the initial temperature is higher than the maximum temperature of the two-phase envelope (the cricondotherm - typically less than 0°C for a dry gas) the reservoir conditions of temperature and pressure never fall inside the two phase region, indicating that the composition and phase of the fluid in the reservoir remains constant. 

For both volatile oil and blaok oil the initial reservoir temperature is below the critical point, and the fluid is therefore a liquid in the reservoir. As the pressure drops the bubble point is eventually reached, and the first bubble of gas is released from the liquid. The composition of this gas will be made up of the more volatile components of the mixture. Both volatile oils and black oils will liberate gas in the separators, whose conditions of pressure and temperature are well inside the two-phase envelope. 

Black oils are a common category of reservoir fluids, and are similar to volatile oils in behaviour, except that they contain a lower fraction of volatile components and therefore require a much larger pressure drop below the bubble point before significant volumes of gas are released from solution. This is reflected by the position of the iso-vol lines in the phase diagram, where the lines of low liquid percentage are grouped around the dew point line. 

When fluid flow in the reservoir is considered, it is necessary to estimate the viscosity of the fluid, since viscosity represents an internal resistance force to flow given a pressure drop across the fluid. Unlike liquids, when the temperature and pressure of a gas is increased the viscosity increases as the molecules move closer together and collide more frequently. 

Viscosity is measured in poise. If a force of one dyne, acting on one cm, maintains a velocity of 1 cm/s over a distance of 1 cm, then the fluid viscosity is one poise. For practical purposes, the centipoise (cP) is commonly used. The typical range of gas viscosity in the reservoir is 0.01 - 0.05 cP. By comparison, a typical water viscosity is 0.5 -I.OcP. Lower viscosities imply higher velocity for a given pressure drop, meaning that gas in the reservoir moves fast relative to oils and water, and is said to have a high mobility. This is further discussed in Section 7. 

Reservoirs containing low compressibility oil, having small amounts of dissolved gas, will suffer from large pressure drops after only limited production. If the expansion of oil is the only method of supporting the reservoir pressure then abandonment conditions (when the reservoir pressure is no longer sufficient to produce economic quantities of oil to the surface) will be reached after production of probably less than 5% of the oil initially in place. Oil compressibility can be read from correlations. 

Oil viscosity is an important parameter required in predicting the fluid flow, both in the reservoir and in surface facilities, since the viscosity is a determinant of the velocity with which the fluid will flow under a given pressure drop. Oil viscosity is significantly greater than that of gas (typically 0.2 to 50 cP compared to 0.01 to 0.05 cP under reservoir conditions). 

As the reservoir pressure drops from the initial reservoir pressure towards the bubble point pressure (PJ, the oil expands slightly according to its compressibility. However, once the pressure of the oil drops below the bubble point, gas is liberated from the oil, and the remaining oil occupies a smaller volume. The gas dissolved in the oil is called the solution gas, and the ratio of the volume gas dissolved per volume of oil is called the solution gas oil ratio (Rg, measured in scf/stb of sm /stm ). Above the bubble point, Rg is constant and is known as the initial solution gas oil ratio (Rgj), but as the pressure falls below the bubble point and solution gas is liberated, Rg decreases. The volume of gas liberated is (Rg - Rg) scf/stb. 

If, however, the reservoir pressure drops below the bubble point, then gas will be liberated in the reservoir. This liberated gas may flow either towards the producing wells under the hydrodynamic force imposed by the lower pressure at the well, or it may migrate... 

This parameter is important in the prediction of aguifer response to pressure drops in the reservoir. As for liquids in general, water viscosity reduces with increasing temperature. Water viscosity is in the order of 0.5 -1.0 cP, and is usually lower than that of oil. 

The relationship between the pressure drop across the interface AP, the interfacial tension o, and the radius of the droplet, r, is... 

For direct measurement from core samples, the samples are mounted in a holder and gas is flowed through the core. The pressure drop across the core and the flowrate are measured. Providing the gas viscosity (ji) and sample dimensions are known the permeability can be calculated using the Darcy equation shown below. 

Gas has a much higher compressibility than oil or water, and therefore expands by a relatively large amount for a given pressure drop. As underground fluids are withdrawn (i.e. production occurs), any free gas present expands readily to replace the voidage, with only a small drop in reservoir pressure. If only oil and water were present in the reservoir system, a much greater reduction in reservoir pressure would be experienced for the same amount of production. 

Solution gas drive occurs in a reservoir which contains no initial gas cap or underlying active aquifer to support the pressure and therefore oil is produced by the driving force due to the expansion of oil and connate water, plus any compaction drive.. The contribution to drive energy from compaction and connate water is small, so the oil compressibility initially dominates the drive energy. Because the oil compressibility itself is low, pressure drops rapidly as production takes place, until the pressure reaches the bubble point. 

The material balance equation relating produced volume of oil (Np stb) to the pressure drop in the reservoir (AP) is given by ... 

In the solution gas drive case, once production starts the reservoir pressure drops very quickly, especially above the bubble point, since the compressibility of the system is low. Consequently, the producing wells rapidly lose the potential to flow to surface, and not only is the plateau period short, but the decline is rapid. 

Natural water drive occurs when the underlying aquifer is both large (typically greater than ten times the oil volume) and the water is able to flow Into the oil column, i.e. it has a communication path and sufficient permeability. If these conditions are satisfied, then once production from the oil column creates a pressure drop the aquifer responds by expanding, and water moves into the oil column to replace the voidage created by production. Since the water compressibility is low, the volume of water must be large to make this process effective, hence the need for the large connected aquifer. 

The primary drive mechanism for gas field production is the expansion of the gas contained in the reservoir. Relative to oil reservoirs, the material balance calculations for gas reservoirs is rather simple the recovery factor is linked to the drop in reservoir pressure in an almost linear manner. The non-linearity is due to the changing z-factor (introduced in Section 5.2.4) as the pressure drops. A plot of (P/ z) against the recovery factor is linear if aquifer influx and pore compaction are negligible. The material balance may therefore be represented by the following plot (often called the P over z plot). 

From the above plot, it can be seen that the recovery factor for gas reservoirs depends upon how low an abandonment pressure can be achieved. To produce at a specified delivery pressure, the reservoir pressure has to overcome a series of pressure drops the drawdown pressure (refer to Figure 9.2), and the pressure drops in the tubing, processing facility and export pipeline (refer to Figure 9.12). To improve recovery of gas, compression facilities are often provided on surface to boost the pressure to overcome the pressure drops in the export line and meet the delivery pressure specified. 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

Introduction and Commercial Application Section 8.0 considered the dynamic behaviour in the reservoir, away from the influence of the wells. However, when the fluid flow comes under the influence of the pressure drop near the wellbore, the displacement may be altered by the local pressure distribution, giving rise to coning or cusping. These effects may encourage the production of unwanted fluids (e.g. water or gas instead of oil), and must be understood so that their negative input can be minimised. 

The pressure drop around the wellbore of a vertical producing well is described in the simplest case by the following profile of fluid pressure against radial distance from the well. 

Damage skin Figure 9.3 Pressure drop due to skin... 

The first term (AQ) is the pressure drop due to laminar flow, and the FQ term is the pressure drop due to turbulent flow. The A and F factors can be determined by well testing, or from the fluid and reservoir properties, if known. 

The PIF estimate is only a qualitative check on the potential benefit of a horizontal well. There is actually a diminishing return of production rate on the length of well drilled, due to increasing friction pressure drops with increasing well length, shown schematically in Figure 9.6. 

Having reached the wellbore, the fluid must now flow up the tubing to the wellhead, through the choke, flowline, separator facilities and then to the export or storage point each step involves overcoming some pressure drop. 

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