*Energy Targeting Using Algebraic Method*

*Energy Targeting Using Algebraic Method*

*“Given a unit with a list of hot streams to be cooled and cold streams to be heated”*

*Constructing Temperature Interval Diagram*

*Constructing Temperature Interval Diagram*

*Draw two temperature scales one for the hot streams and another for the cold streams**Select a reasonable minimum temperature approach between the hot streams and the cold stream, (for instance, 10ºC)**Draw all the hot streams (in the table hot section) to be cooled according to the hot steam scale as arrows that start at the supply temperatures and end at the target temperatures.**Repeat step 1.3 for all cold streams in the cold section of the table**Start at the highest temperature of any hot stream in the hot section and draw a horizontal line that spans across the two sections of the table, the hot and the cold.**Draw horizontal lines again at the start and the end of any arrow representing the hot streams in the hot section of the table.**Repeat step 1.6 for any arrow representing cold stream in the cold section (at the start and the end of any arrow).**Count the number of segments generated and number them starting at the highest temperature (they are called temperature intervals)**Make sure that each temperature interval has now temperature value on both the hot temperature scale and cold temperature scale. The difference is the desired minimum temperature approach (for instance the 10ºC used in this example).*

*These procedures are depicted in the figure below.*

**Note:** This structure means that within any temperature interval it is thermodynamically

*feasible to transfer heat from the hot streams to cold streams. It is also feasible to*

*transfer heat from a hot stream in an interval “x” to any cold stream which lies in an*

*interval below.*

*The Temperature Interval Diagram*

*Note: The temperature symbol T* is the interval inlet temperature used later on constructing what is **known as grand composite curve for selecting the suitable energy utility mix. To calculate T*.*

*we take the average interval inlet temperature of the hot and cold temperature scale.*

*Constructing Tables of Exchangeable Heat Loads and Cooling Capacities.*

*Determining individual heating loads and cooling capacities of all process streams for all*

*temperature intervals using this formula:*

*Qnm = F1Cp1* (Ts-Te) in energy units (kW)*

*Ts is the interval start temperature and*

*Te is the interval end temperature*

*“n” is stream number and “m” is the interval number*

*Example 1*

*Example 1*

*Interval # 1 in the hot section:*

*The interval start temperature is 560 K*

*The interval end temperature is 520 K*

*Q11 (Q for stream #1 in interval #1)= F1Cp1*(560-520)*

*Since there is no H1 stream in this interval, hence, F1Cp1=0.0*

*Q stream # 1(exchangeable load) in this interval = 0.0*(560-520) = zero*

*Example 2:*

*Example 2:*

*Interval # 2 in the hot section:*

*The interval start temperature is 520 K*

*The interval end temperature is 390 K*

*The flow specific heat F1Cp1= 10 kW/K*

*Then,*

*Q stream #1(exchangeable load) in interval #1= 10*(520-390) = 1300 kW*

*Example 3*

*Interval # 1 in the cold section:*

*The interval start temperature is 550 K*

*The interval end temperature is 520 K*

*The flow specific heat of this cold stream is F1Cp1= 10 kW/K*

*Then,*

*Q stream #1(cooling capacity) in interval #1= 10*(560-520) = 400 kW*

*Upon the completion of this step we can now obtain the collective loads (capacities) of the hot (cold) process streams.*

*These collective loads (capacities) are calculated by summing up the individual loads of the hot process streams that pass through that interval and the collective cooling capacity of the cold streams within the same interval.*

*These calculations for the above problem are shown in the following tables:*

*Exchangeable Loads for Process Hot Streams Intervals*

*Cooling Capacities for Process Cold Stream Intervals*

**Constructing Thermal Cascade Diagrams**

**Constructing Thermal Cascade Diagrams**

*This diagram is constructed using the total hot loads and cooling capacities obtained in the **previous step for each temperature intervals.[1,2,3]*

*The temperature intervals are drawn as “rectangular” with two inlets and two outlets.*

*The inlet from the left is the total hot load available in this interval (for instance,*

*1300 kW in case of interval # 2).*

*The inlet from above is the utility input load, in case of the first interval, or the input from **interval above in case of second, third,……,N intervals.*

*The output from the right is the total cooling capacity of this interval (for instance,*

*1300 kW in case of interval #2).*

*The output from the bottom is the difference between the total inputs and the cooling*

*capacity of the interval.*

*The heat balance around each interval will be conducted as follows:*

*Subsequent Intervals Heat Balance:*

*Figure 5.8 – Numerical Example of First Interval Heat Balance*

*Numerical Example for Subsequent Intervals Heat Balance*

*For instance; Interval # 3*

*The reader is encouraged to do the calculations for interval number 2 and see that in*

*interval number 2 the hot side input is equal to the cold side output and hence the final*

*output of the interval will be the same as interval number one ,-400 energy unit.*

*Upon the completion of the heat balance around each interval the following energy*

*deficiency diagram will be produced.*

*Thermal Cascade Diagram (Un-Balanced)*

*Thermal Cascade Diagram (Un-Balanced)*

*Note: During this step, the input from Hot Utility to the first interval is equal to zero.*

*The maximum difference between the available hot loads and cooling capacities from the*

*heat balances of these intervals is – 550 kW. This deficiency in heat will be supplied via an **outside hot utility. This value will be the input (from the top of the first interval) and the **same heat balance calculation conducted above will be repeated to produce the energy **balanced thermal cascade diagram below.*

*Balanced Thermal Cascade Diagram*

*Balanced Thermal Cascade Diagram*

*With the completion of this step, the minimum heating utility and minimum cooling utility*

*required are 550 kW and 50 kW respectively.*