Plant Models


Just as one can determine the heat interchange between surfaces such as the Nose Ring and the Seals by using an Electrical Analog of this physical problem, to calculate surface Temperatures, we can calculate the interchange of energy between the Induced draft Fan and such kiln components as the seals, the scrubber, and other resistances to the Exhauster fan’s flow by using an electrical analog of the kiln system, shown in Fig 1. The equivalent analog circuit is shown as Fig 7. An important peculiarity of the rotary kiln is that the suction at the top of the hood is more positive than at the bottom. The influx of leakage air is lower at the top than at the bottom of seal #1, prompting the draft measuring connection to be placed at the top of the Firing Hood, only to ensure no puffing at the hood’s top.


We simulate this variation in hood pressure as if it were caused by small fans (batteries) pressing the gas out of the hood. Clearly, the ID fan must pull a little harder to overcome the hood’s stack effect (chimney effect). The flows are positive in the direction shown. Firing Hood leakage is i1+ i4+ i5. Combustion gas flow is i3. Feed end leakage through seal #2 is i2. Process gas flow is i6, while venturi scrubber water is i7. The ID exhaust fan is simulated (accurately) as a battery with an internal resistance, which is determined from the FAN’s curve of Static Pressure vs. CFM. The flow control damper is in series with the fan, totalling to R8. The four unknown flows are i1, i2, i4, and i5, and there are four non-linear loop equations satisfying Kirchoff’s law for voltage (pressure) drops in any loop.

The non-linearity is due to the pressure drop varying as the resistance times the square of the flows, instead of resistance times the flow. The resulting four loop equations is solved by Newton-Raphson’s technique. The known flows i3, i6,and i7 are calculated by APS’s Heat and Mass balances, or is measured in the field. Application of this approach to an 11 ft diameter by 315 ft long calciner (with a combustion chamber) , served as an excellent diagnostic tool. . .leading to 28% fuel reduction, 40% greater production and improved product quality.