Resistance curves

Fig. 4. Selection of fan size where the soHd line represents a typical setting and the dashed lines the operating extremes, (a) Desirable sizing. The system resistance curve intersects the fan curve near its maximum efficiency. Changes in system resistance from a flow-control element also intersect the fan curve at desirable points for good flow control. The dashed curves also intersect system resistance curves at desirable locations, (b) A fan essentially too large for the system. The intersection of the system curve near the peak of the fan curve results in poor system flow control and perhaps surging.

For air-flow control, the system may contain a control valve or damper that automatically or manually modulates system pressure drop. The dotted curves in Figure 4a on each side of the system resistance curve might represent operating extremes of the system resistance as the control valve is varied from maximum to minimum opening. These curves also intersect the fan curve at desirable operating portions of its range both for efficiency and flow control. 

Fig. 7. Control of fan performance with inlet vane control. SoHd lines marked A and N show normal performance without vanes (vanes wide open). As vanes are progressively closed, static and power curves are modified as indicated by dashed lines. Intersection ( - ) of the system resistance curve with these reduced pressure curves at points B, C, D, and E shows how imparting more spin to the inlet air reduces flow. Projecting points A to E vertically downward to the corresponding power curve locates fan power points A through E7 Power savings achieved over throttling control can be estimated by projecting points B through E vertically downward to the A power curve and comparing the value with that from the proper reduced power curve. To...

The fan will now have a system resistance Curve A-B and operate at Point 2. As an alternate approach to securing a system balance at the point required, the motor speed can be changed by a suitable means. If the fan speed is reduced by 13,000/13,600, the new speed should be (0.889) (600) = 573 rpm. A new fan Curve E-E will go through the desired point conditions. The new horsepower for this operation will be (3.87) (573/600)" = 3.35 hp. 

Figure 12-143 shows the individual static pressure curve Pf and total pressure curve Pff If pressure losses between the two fans are neglected (and they should he very low for good design), the combined total pressure curve is twice the value of curve Pft, 2 Pff The new operating static pressure also should be twice the individual total pressure value minus the velocity pressure, 2 p — p for identical fans, the new operating static pressure is equal to 2 p + Pf. The operation of the series fans will be along the system resistance curve, and the resultant point of operation will be at the intersection of the system curve with the curve for (2 pa — Pfv). 

Figure 12-143 shows the curves for identical fans. When unlike fens are placed in series, the individual static and total pressure curves are placed on the graph. The individual curves for assumed fans No. 1 and No. 2 and the system resistance curve define the system. The combined total pressure curve is the sum of the individual values at the same capacity. Then total combined pressure curve = Pft (No. 1) + Pft (No. 2). The new combined operating static pressure curve is the sum of the individual static pressure valves at the same capacity and exists only at the oudet of the second fan then, the total combined static pressure = Pfti + Pftg — Ps. Any losses in connections between the fans will reduce the values of the total static and system total pressures. 

Note that the total static pressure curve of Figure 12-145 is limited by the lowest output pressure of the multifan system. The limit curve is established using the fan curve (No. 1 in this example) having the smallest volume increment to the system resistance curve. In this situation fen No. 2 cannot add to the system until its pressure-volume relation reaches the peak point on its curve. 

The drill collar acts as a series of elongated electrodes in a way similar to the laterolog 3 wireline sonde. The lower electrode, which is the drill bit, is used to get the forward resistivity curve. A lateral resistivity measurement is made between the two toroid receivers. An example of toroid logs is shown in Figure 4-279. 

According to chart in Figure 4-304, d, = 40 in. with the wireline logs. The d, cannot be calculated with the MWD/LWD logs since we have only two resistivity curves. 

The true porosity <1> is determined with the neutron-density Pe logs. R is generally given by the deep investigation resistivity curve. R equals R, in the water formations. It increases rapidly in hydrocarbon saturated formations. 

FIGURE 18.12 Typical resistivity curve For FCC catalyst. (With permission from Hamon.)... 

Many local regulatory agencies require the ESP to be energized whenever the FCC main blower is in operation. Some units have found that steam/moisture injection is useful at temperatures lower than 400°F as a form of resistivity modification. This is because the unit is in the surface conduction phase of the resistivity curve. At this temperature, the moisture improves surface conduction of the particles. 

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