|How To Calculate The True Cost of Steam - Calculating the Cost of Steam Generation|
|Written by USDOE Office of Industrial Technologies|
|Wednesday, 30 June 2010 13:49|
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Calculating the Cost of Steam Generation
The first step, which has several components, is to calculate the cost of generating steam from the boiler(s):
Calculating the cost of generating steam is relatively easy. The total variable cost of raising steam, CG, is the sum of all these individual contributions, expressed as dollars per thousand pounds ($/Klb) of steam generated:
CG = CF + CW + CBFW + CP + CA + CB + CD + CE + CM
Fuel cost is usually the dominant component, accounting for as much as 90% of the total. It is given by:
CF = aF x (HS – hW)/1000/ηB
where aF = fuel cost, ($/MMBtu)
HS = enthalpy of steam, Btu/lb
hW= enthalpy of boiler feedwater, Btu/lb
ηB = overall boiler efficiency, fractional.
Overall boiler efficiency is based on combustion air supply at ambient temperature, and boiler feedwater makeup temperature to the deaerator. It is assumed that boiler feedwater preheat from ambient to condensate temperature (usually about 200°F) will be done by heat exchange against a process stream, outside the boiler island battery limits, with only some “top-up” heat recovery against hot boiler blowdown. The use of steam to preheat boiler feedwater was common when energy was cheap, but using surplus process heat instead (from below the “process pinch” temperature) represents a significant opportunity for improved cycle efficiency. Overall boiler efficiency becomes primarily a function of the final flue gas temperature, and will typically be in the range of 80 to 85% when the excess air ratios are near optimal.
In principle, one should calculate the individual cost components rigorously for the site-specific conditions. In practice, it is usually sufficient to use an approximation:
CG =CF (1+0.30)
The number 0.30 represents a typical value for the sum of cost components 2 through 9 above (in oil- and gas-fired facilities). However, it could be more in smaller facilities, or in those that use coal and biomass. Normally, maintenance costs could be considered fixed, rather than variable. If the plant has multiple boilers, however, and there is an option to shut down one or more of them as the steam production rate is reduced, then maintenance costs should more properly be considered to be variable.
The second step is to calculate the cost of steam at lower pressure levels. This is not easy, as the cost depends upon the path that the steam follows from the point of generation to the point of use. Low-pressure steam that is produced through a pressure letdown station, usually a pressure-reducing valve (PRV), has substantially the same enthalpy as the higher-pressure steam from which it was made. Therefore, it will be superheated, and the normal practice is to desuperheat it using condensate. The low-pressure steam cost is then calculated from the high-pressure steam cost as:
CL =CH x(HSL –hW)/(HSH –hW)
where HSL = enthalpy of low-pressure steam, Btu/lb
HSH = enthalpy of high-pressure steam, Btu/lb.
Making low-pressure steam through a PRV is inefficient. For steam flows over 50,000 lb/h, it is usually far more cost effective to extract by-product power by passing the steam through a backpressure steam turbine. When the low-pressure steam is produced through a turbine, its cost is calculated as:
CL = CH – 1000 x aE x (HSH – H*SL)/3413/ηT/ηG
where aE = electrical power cost, $/kWh
H*SL= enthalpy of low-pressure steam from isentropic expansion of high-pressure steam, Btu/lb
ηT = isentropic efficiency of steam turbine, fractional
ηG = generator efficiency, fractional.
The difficulty is to assign the correct cost to the increase or decrease in low-pressure steam consumption, which depends on the path followed by steam from the point of generation to the point of use (for example, PRV or turbine). The only way to determine the correct value is to develop a heat and material balance simulation model of the system.
Setting Up the Model
The model accounts for the significant flows into and out of each subsystem, as well as for the boiler system as a whole. For the system shown in Figure 1, the inputs and outputs across the boiler- house boundaries are:
Inputs = Condensate return from process + boiler feedwater makeup
Outputs = Steam to process + blowdown from flash drum + vents to atmosphere (A, B, and C)
For material balance, neglecting losses, we set inputs = outputs (however, for many systems, losses can be significant and need to be tracked).
There are several internal subsystem balances that have to be satisfied as well.
For the boiler itself:
Steam generation + boiler blowdown (before flash) = boiler feedwater
For the steam header:
Steam generation = steam to process + steam to PRV + steam to turbogenerator + steam for soot blowing
For the condensate tank:
Deaerator feed = boiler feedwater makeup + combined process condensates – vent A
Boiler blowdown will be at the boiler temperature, and will flash when the boiler feedwater is let down to atmospheric condition. This flash vapor can be recovered for use in the deaerator. Normally, the blowdown is let down to the deaerator (DA) pressure, and the vent flow labeled “C” in Figure 1 is zero. Thus, for the blowdown flash drum, the balance is:
Blowdown from boiler = blowdown from drum + flash vapor to deaerator
For the deaerator,
Boiler feedwater = deaerator feed + steam to the deaerator from the PRV + steam to the deaerator from the turbine + blowdown flash vapor – vent B
In addition to the material balances, we must also develop the heat (enthalpy) balance equations for each subsystem. The combined set of equations is solved algebraically. Examination of the overall balance shows that there is one more unknown variable than there are equations, so it is necessary to solve the problem iteratively. This is not a problem, and the calculations tend to converge fairly rapidly in a unique solution. The recommended computational strategy is to assume a trial value of steam generation rate, and proceed to solve the equations for boiler feedwater makeup, condensate return, blowdown, and boiler feedwater.
The individual subsystem balances are then solved in a “top-down” sequence: steam header, blowdown flash drum, condensate tank and deaerator. The new calculated steam rate is then compared with the assumed trial rate, and this is repeated until the two values converge to within an acceptable difference.
The net cost of operating the system is equal to the cost of steam generation less the credit for power generation in the turbine.
For simple systems with steady steam demand, the calculation only needs to be done once, and then adjusted periodically when external circumstances or assumptions change. A computer-based model may not even be necessary.
Most large industrial steam systems are typically much more complex: with multiple boilers, multiple fuels, multiple pressure levels, and alternative connection paths (for example, PRVs and turbines) between the different steam headers, as in Figure 2. For them, it is particularly important that an accurate computer-based model is developed, and that the model is run frequently, perhaps as often as three times per day.
Methodology for Marginal Steam Pricing
The average steam generation cost can be calculated quite easily, but how can the consumption cost be calculated?
Before going further, we need to understand the distinction between average costs and marginal, or incremental, costs. The essential definitions are:
Average Cost = Total Operating Cost = Co
Marginal Cost = Incremental Operating Cost = ∆Co
For evaluating energy conservation and/or efficiency improvement projects, it is the marginal cost that should be determined.
The first step is to decide on basic operating parameters for the combined heat and power system, including condensate return rate, boiler blowdown, deaerator pressure, fuel mix, condensate temperature, boiler feedwater makeup supply temp, the process steam demand profile, PRV, and steam turbine flows. The model is then used to calculate the total operating cost for this base case scenario, as in Table 1.
Figure 2. Simplified Schematic Flowsheet of Combined Heat and Power System for a Sugar Refinery
Table 1: Base-Case Steam Generation Costs from Model
How does the total operating cost change if the consumption of low-pressure steam, at 12 pounds per square inch gauge (psig), in the process either increases or decreases by some amount, Y lb/h? To determine this, we manually change the input value of the low-pressure process steam consumption by the appropriate amount, and make a note of the new operating cost calculated by the model. However, the model should accurately incorporate the plant operating policy for fluctuations in the process-steam demand. For example, important information includes whether the reduction in steam input to the low-pressure header is through a PRV or through a steam turbine, whether the required degree of superheat is being maintained, whether the correct boiler and fuel are being scaled back, whether the equipment capacity constraints are being observed, and whether the correct boiler and turbine efficiencies are being used at the new flow conditions.
This procedure is repeated for several additional perturbations, and the results are tabulated and illustrated in Table 2 and Figure 3.
Table 2 shows that the marginal cost of low-pressure steam varies significantly with operating rate, because the low-pressure steam follows different paths through the combined heat and power system. At the low end, when the process steam demand is 152.8 Klb/h, the gas boiler (#1) is being operated at its minimum rate (30% of capacity). Under these conditions, gas is the more expensive fuel, and the coal boilers (#2 through 6) are operated to provide the balance of steam demand. Turbogenerators #2 and #3 are at their minimum operating rates, 20 and 40 Klb/h respectively. As the process steam requirement increases the load on the coal boilers increases, as well as the amount of steam passed through turbogenerator #3 up to its maximum capacity of 110 Klb/h. As the steam demand increases, further, the flow through turbogenerator #2 starts to increase. At some point the preferred operating rate of 85% for the coal boilers is reached.
Further increases in steam demand must now be supplied from the gas boiler. Once the flow through turbogenerator #2 reaches its maximum capacity of 60 Klb/h, further demand for low- pressure steam can now only be provided by passing high-pressure steam through a PRV. The marginal cost of low-pressure steam therefore takes a dramatic rise. As low-pressure steam demand continues to increase, the maximum capacity of the gas-fired boiler is reached, and the coal-fired boilers need to be used, pushing them to their maximum safe operating limit of approximately 95%. Notice that the marginal fuel starts out as coal, then switches to gas, and then switches back to coal. The marginal low-pressure steam cost depends not only on the marginal fuel; it also depends on the path that the incremental steam flow follows between the point of generation and the point of use.
Table 2: Results of Perturbation Analysis for Marginal Cost of Low-Pressure Steam
The results of Table 2 are plotted graphically in Figure 3, and show that the net steam cost is not constant. In fact, the net steam cost varies significantly with consumption rate, depending on the path being followed. The operating policy, as described above, is implicit in these curves. The same approach can be taken to determine the marginal cost curves for medium- and high-pressure steam.
Figure 3. Variation of Net Low-Pressure Steam Cost (Marginal) with Consumption Rate