Marginal steam pricing

Incremental energy cost AOpEx Increment steam consumption AMsteam 

AOpEx is incremental change in variable energy cost, which consists of fuel and BFW costs but not the fixed cost. The fixed cost does not have an effect on marginal price because the fixed cost is cancelled out in the calculation of AOpEx. In reality, the fixed cost has already taken place no matter how much incremental change occur in steam production. 

By definition, marginal steam price is different from the average steam price as discussed previously  

Let us use the next example to illustrate how marginal steam prices are determined. 

Path 1 Increase HP Steam by 10 klb/h Through Boiler 1 with 75% of Efficiency The incremental fuel consumption for making 10 klb/h of HP steam can be calculated based on equations (15.1) and (15.2) 

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There can be confusion and misunderstanding from plant personnel on steam prices. Are we talking about steam price based on the point of use (marginal steam price) or total steam from the boiler house (average steam price) Should the steam be priced at the point of generation or point of use Does the steam price include both fixed and variable costs Does the average steam price vary for different production rates Why is the steam price obtained based on steam enthalpy instead of costs These are the questions that will become the focus of this chapter. 

The previous discussions demonstrate characteristics with marginal steam prices. The hrst characteristic of marginal steam prices is that they are path dependent. 

The second characteristic of the marginal steam price is that aU incremental steam change must be traced back to the fuel, BFW, and power balances so that the net effects on operating cost can be determined. This is the essence of marginal steam price. 

Clearly, the basis for calculating both the average and marginal steam prices is an overall steam balance including BFW and condensate balances, which is discussed in Chapter 16. The method for calculation of average steam costs follows a top-down approach, while the steam balance corresponds to the most common production scenario and steam system configuration. 

When calculating marginal steam prices, the focus is to find the best way to meet incremental steam demand at a steam header. To do so, individual paths, which can make this incremental steam demand either fully or partially, are identified and the marginal costs for these paths are calculated. As a result, individual paths are differentiated and thus the best path(s) for meeting the incremental steam demand can be identified. 

Marginal steam price should be used as effective cost of stem production because the method considers the entire cycle from generation, distribution, and point of use to condensate recovery. The marginal price depends on the path it follows from the boiler to the point of use and if condensate is recovered or not. In revamp projects, when new boilers and turbines are required, total investment costs should be used as the basis for evaluation. The methods for boiler steam costs and marginal steam prices are provided in Chapter 17. 

The costs in Table 18.7 serve as the average costs for the cost centers. For any increased and reduced steam use from the base demand, marginal steam prices, as discussed in Chapter 17, will be used to cost the incremental amount of steam for the cost center. 

For tackling this challenge, the method based on marginal analysis can indicate true steam costs at point of use. The reason why the marginal price method (Chapter 17) can provide the true steam cost is that it is based on the last incremental amount of steam saved or generated. Determination of marginal steam prices relies on an overall steam and power balance model, which takes into account the effects from steam balances. 

The next step is to obtain equations for the solution of the shadow and marginal prices. This requires the evaluation of various derivatives of the constraint equation matrix. However, because not all the constraints are in algebraic form (those constraints that are functions of steam table properties) numerical derivatives must be evaluated. One other note, there are two condenser costing equations. This means that two separate derivatives must be taken and the derivative corresponding to whichever costing equation is valid for that value of condenser area, is the one that should be used. 

This operating margin mnst cover all charges, such as eqnipment depreciation, and the cost of manpower, and ntilities (power, steam, cooling water, compressed air, etc.). Raw materials of good purity and qnality command a reasonable price in the marketplace. 

Figure 5.4. Long-range marginal costs (LRMC) of gas combined cycle and coal steam turbine with and without C02 costs. (Allowance price 20. Gas/coal price ratio 2. Annual operating hours 5500.)...

The extraction of isoprene from the C, cut of steam-cracked effluents provides one alternative, and its synthesis by different methods an equal number of other possibilities. However, they are all economically marginal due to the price levels of the natural products. 

Calculate the marginal prices for HP, MP, and LP steam if their demands are increased by lOklb/h, respectively. Consider the steam system in Figure 17.1. 

With the additional BFW of 10.2 klb/h in which 0.2 klb/h is the extra blowdown, the marginal price for extra HP steam through path 1 is... 

Path 2 Increase HP Steam by 10 klb/h Through Boiler 2 with 85% of Efficiency Similar to path 1, the marginal price for HP steam through path 2 can be calculated as... 

Application Challenges Eor this steam system, a revamp project requires 40 klb/h of additional HP steam and the limits of steam generation from boilers 1 and 2 are 160 and 140 klb/h, respectively. Since the current loading of both boilers 1 and 2 are at 108 klb/h respectively. Naturally, the hrst 32 klb/h HP steam demand will be provided from boiler 2 since it is more efficient than boiler 1. Thus, the marginal price for 32 t/h from boiler 2 is 11.3/klb, while the last 8 t/h to be made from boiler 2 will be priced at 12.5/klb. 

Path 3 2 Increase MP Steam by 10 klb/h Through the Letdown Valve and Boiler 2 Since the fuel consumption in boiler 2 is increased by 14.6 MMBtu/h and the BFW amount increased by 10.2klb/h for the extra lOklb/h MP steam consumption, the marginal price for the MP steam following this path is... 

Application Remarks The whole set of equations 19.10-19.38 forms the optimization model for steam and power. This optimization strategy allows the fastest dynamic response while always trending to the most economical steady state operating position. Furthermore, the steam marginal prices will be automatically determined from the optimization model (Varbanov et al., 2004). 

There are three boiler forced draft (FD) fans, which are run by medium-pressme to low-pressure (MP-LP) extraction turbines currently with motors in spare. It was identified that motor driving is more economical than turbine due to relatively low electricity price. Based on steam marginal pricing, it is estimated that if one fan can be switched to motor, the benefit would be 738,144 per year. The cost savings would be 2.2MM/year if three fans could be switched to motors. 

From the steam balance point of view, by the end of this implementation sequence, there is no LP dump, but large amount of HP and MP letdown flows. In this case, marginal prices for MP and LP arc the same as HP steam. This may call for optimizing process steam use to reduce both MP and LP steam usage. 

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