Total Site Heat Integration: Utility Selection and Optimisation Using Cost and Exergy Derivative Analysis

This paper presents a new Total Site Heat Integration utility temperature selection and optimisation method that can optimise both non-isothermal (e.g. hot water) and isothermal (e.g. steam) utilities. None of the existing methods addresses both non-isothermal and isothermal utility selection and optimisation incorporated in a single procedure. The optimisation affects heat recovery, the number of heat exchangers in Total Site Heat Exchanger Network, heat transfer area, exergy destruction (ED), Utility Cost (UC), Annualised Capital Cost (CC), and Total Annualised Cost (TC). Three optimisation parameters, UC, ED, and TC have been incorporated into a derivative based optimisation procedure where derivatives are minimised sequentially and iteratively based on the specified approach. The new optimisation procedure has been carried out for three different approaches as the combinations of optimisation parameters based on the created derivative map. The merits of the new method have been illustrated using three case studies. These case studies represent a diverse range of processing types and temperatures. Results for the case studies suggest the best derivative optimisation approach is to first optimise UC in combination with ED and then optimise TC. For this approach, TC reductions between 0.6 and 4.6% for different case studies and scenarios are achieved.

228 utility for TSHR because as it is generated and consumed, the final temperature of the utility 229 is uncertain. Return utility flows from multiple processes may then be mixed together 230 resulting in an unknown average temperature. A higher quality utility is needed to heat or 231 cool the return utility flow to the intended supply temperature of the reverse utility (e.g. a 232 hot utility loses heat to become a cold utility). Hard utility target temperatures refer to 233 temperature constraints that must be met. These utility temperatures have an opportunity 234 to be optimised to increase HR.
235 TSP in Figure 1 can be divided into three different regions. The process heat deficit region sits 236 above the hottest TSP source temperature, which is derived from the Grand Composite 237 Curves (GCC) in each process (or plant) before the TSP is constructed. The process heat surplus 238 region is below the coldest TSP sink temperature and is again derived from the GCCs. The 239 region in between may be in process heat deficit or surplus depending on the balance 240 between utility generation and consumption. Those utilities that occur within this middle 241 region, which may be generated and consumed, are optimisable to maximise TSHR, Utility C 242 and D in Figure 1.
243 When Combined Heat and Power (CHP) generation is exploited, more complex utility options 244 are available. Rejected heat from gas turbines and/or boilers with steam turbines may be used 245 to generate or supply hot utility, e.g. steam. In such systems, the utilities that are in the upper 246 region of Figure 1 may provide the potential for SWG through a turbine. These hot utilities 247 can also be considered as optimisable to maximise shaft work, e.g. Utility B. Similarly, for 248 processes which require sub-ambient utility in the lower region of Figure 1, the cold utility 249 requires compressors in refrigeration cycles to generate the needed cooling, Utility F. As a 250 result, the appropriate utility temperature selection, which is considered as optimisable, may 251 lead to minimum work consumption.
252 In short, any utility that is either connected to a turbine, linked to a refrigeration cycle, or 253 both generated/consumed, is a candidate for temperature optimisation.
254 UC can be calculated considering hot utility, cold utility, and power generation/consumption 255 prices and targets. Equation 1 presents the UC calculation method.

256
(1) Where UP is utility price, Q is utility target, PP is power price, W is power target, and OP is 258 operating period of the plant. Subscripts h,ut is hot utility, c,ut is cold utility, and gen is 259 generation. The final term is an offset but not total power cost.
260 Total Annualised Cost (TC) is calculated using UC and CC as presented in Equation 2.

275
(3) Where T 0 is the reference temperature. As it can be seen ED is a positive quantity for any 277 actual process and becomes zero for a reversible process.

280
(4) 1 ln 0 0 0 281 Exergy can be calculated using Equation 4 when the specific heat capacity has been assumed 282 constant with respect to temperature in the range from T to reference T 0 . The factor in the 283 square bracket is called exergetic temperature (T x ) and has units of Kelvin. Exergetic 284 temperature is a function of stream temperature in K and the selected zero state 285 temperature, T 0 , in K. This equation determines the change in exergy as a process flow heats 286 or cools from its supply to its target temperature.
287 Figure 2 shows the exergy potential of a single heat exchanger where the hot stream as a heat 288 source has an exergy relative to the T 0 , and the cold stream as a heat sink has a lower exergy 289 relative to the T 0 . For the ED, it can be said that: The same concept applies to a process plant.

304
(6) Figure 4 shows how ED applies to a TS. Figure 4a illustrates the ED region in the TSP. Figure   306 4b shows that by shifting utility temperatures, ED has been increased for small regions on 307 both sides of TSP while it has decreased for most other regions. In Figure 4b, shifted utility 308 temperature levels are illustrated in solid lines and original utility temperature levels from 309 Figure 4a are illustrated in dashed lines. In summation, total exergy destruction has been 310 reduced because of the utility temperature change. Equation 3 can be applied to analyse TS 311 which determines utility-process ED for entire TS due to heat transfer.
312 Figure 4c shows the work generation potential using the Site Utility Grand Composite Curve 313 (SUGCC). When the HR increases (solid utility lines), power generation often decreases. While 314 in the Figure 4d, the same concepts of ED reduction apply. Shifting utility temperatures 315 towards the Total Site Pinch region shows an effect on ED resulting in increased HR across the 316 TS and slightly higher power generation for this example. There is a complex trade-off 317 between power generation, HR, and ED that must be considered when analysing the selection 318 of utility temperatures.
319 The smaller temperature difference between the hot and cold available utilities in the TS may 320 offer lower ED and a reduction in UCs through improved HR. Improved temperature selection 321 in the TS may provide the opportunity to reduce energy consumption within the TS as the 322 result of a decrease in ED (i.e. shifting utility temperatures towards the Total Site Pinch will 323 cause a reduction in ED). There is a trade-off between hot and cold utility temperature 324 difference in the TS and total heat transfer area, which affects CC and finally TC. TC is normally 325 the final objective function in the optimisation of TS targets. To select utility temperatures, a 326 temperature range may be considered for each required utility.
Where subscript, i is representing each individual utility temperature for either supply or 338 target temperature (hot or cold sides of the utility) and ΔT is a small change in temperature 339 (step change).
340 In this approach, the TC derivative is minimised given the initial utility temperature selection.
349 This approach includes a two-step process: first, minimise the derivative of UC iteratively, 350 then, second, minimise the derivative of TC. But the UC function tends to be more continuous can be presented as: 358 The third approach, similar to the second approach, includes a two-step process: first, 359 minimise the derivative of UC iteratively and, when constant (flat), minimise the derivative of 360 ED, then, second, minimise the derivative of TC. It is important to understand that UC 361 functions tend to be continuous with many flat sections where a change in temperature has 362 no impact on UC. In this region, it becomes necessary to apply the derivative of ED as the 363 objective, which is not flat. The logic for initially minimising UC with ED is to help select 364 temperatures that are more likely in the proximity of the global optimum, from which starting 365 point a TC minima may be located. The TC local minimum is not guaranteed to be the global 366 optimum. is applied in this study as opposed to conventional TSHI. UTST 376 performs utility targeting at the process level using the GCC. This method considers more 377 constraints around meeting supply and target temperatures of utilities, especially for non-378 isothermal utilities, within individual processes. As a result, the UTST method restricts any 379 inter-dependency of utility use between processes, which is important for non-isothermal 380 utilities as well as non-continuous processing clusters that often operate independently with 381 different schedules. By adding this new constraint, the calculated targets become more 382 achievable and realistic.

383
Step 1: Objective function derivatives calculation 384 A derivative map can be constructed using the framework presented in Table 1 for each utility. Step 5 if the iteration is not the first iteration.

404
Step 3: Selection of appropriate value from the derivative map 405 The most negative value, i.e. a reduction in cost, utility, or ED, for the objective function is 406 located on the derivative map, which shows the highest potential for improvement, and 407 identifies the utility, its temperature and the direction that it should be changed. The utility 408 corresponding to this value must be selected in this step.

409
Step 4: Utility temperature re-selection 410 After identifying the best utility temperature to change, whether utility generation turns to 411 utility consumption or vice versa, ∆T s must be divided by half and the shift backwards or 412 forwards to converge to the optimum; i.e. new ∆T s can be added or subtracted to the utility 413 temperature. After changing the utility temperature, the process is re-targeted according to 414 the TSHI targeting method which is used, and the derivative map is re-calculated. This 415 procedure may be repeated unless the result converges.
416 After the first iteration, the optimisation procedure may lead to step 5: 417 Step 5: Objective function check 418 The value obtained for the objective function (UC or ED) from the derivative map should be 419 checked. If the value is negative it means there is a potential to improve the objective function 420 by increasing or decreasing its supply/target temperature by ∆T s . Therefore, the procedure 421 goes back to Step 3; otherwise, it should be checked that if ED is the optimised objective 422 function and/ or if it is targeted that ED be an objective function. The answer may lead the 423 procedure either to Step 6 or Step 7.
465 Where A is the heat transfer area in m 2 , and a, b, and c are cost coefficients and exponent 466 relating to the heat exchanger type, as given in Table 3 Table 7. SWG is not considered in this case study.
497 As can be seen in Figure 7a Table 8. Targeting results are presented in Table 9. In this case, optimisation based on TC 504 as an individual objective function has a lower reduction in TC (-2.52 %) while other two 505 criteria show identical TC reduction (-3.36 %). This means that when the TS is optimised 506 considering UC as the objective function, the optimal temperatures are used as the starting 507 point for the next optimisation step where TC is the objective function. The dual optimisation 508 function approach requires fewer iterations and enables an improved target to be achieved.
509 However, in this case, the benefit of including ED in the procedure is negligible since the 510 UC+TC approach and UC+ED+TC approach achieve the same final results.

512 4.3 Case study III: New Zealand Dairy Processing Factory
513 A large dairy factory in New Zealand has been chosen for the last case study and details are 514 illustrated in Table 2. All processes in the factory, which is considered as TS, have recently 515 been investigated and integrated to industry best practice. However, further improvements 516 have been achieved by using UTST method [19]. Table 10 presents initial utilities which are 517 used in the plant. As it is illustrated in Table 10 only LTHW has the conditions to be optimisable 518 utility.
519 Figure 8a shows TSP comparison between the Base Case targets using original utility 520 temperatures as a starting point, in dashed lines, and optimised targets in solid lines using the 521 same starting points. As can be seen hot utility targets, utility heat surplus, are identical 522 before and after optimisation but in cold utility side, utility heat deficit, LTHW has been 523 slightly improved. The similar comparison is illustrated for SUGCCs in Figure 8b which shows 524 TSHR has been increased about 100 kW.
525 Surprisingly, Tables 11 and 12 show that the optimisation results of all three criteria are 526 identical in this case study. This might be due to a couple of reasons, first, the LTHW is a non-527 isothermal utility that has only 9.5 % of total heat load in both heat surplus and heat deficit 528 sides of TS which after optimisation is fully balanced. This means the utility has the exact 529 amount of generation and consumption as shown in Figure 8.  Figure 9. This means the optimal utility temperatures are weakly 543 dependent on the utility price for the utility price range that has been studied.
544 Figure 10 illustrates the changes of the UC and TC based on the optimisation results, and the 545 TC saving in each case with the different hot utility unit price. For each unit price, the 546 optimisation result has been compared to its original unit price based on the case study's 547 targets. As it can be seen in Figure 10, by increasing the hot utility price in the plant, the 548 reduction in the UC and TC may decrease based on the initial results. However, the net annual 549 cost saving increases from NZD 664,574 /y, which is a 7.1 % cost reduction for NZD 25 /MWh 550 to NZD 960,804 /y, which is 2.6 % cost reduction for NZD 45 /MWh.  Table 13.
559 The new scenario of four utility mains has been targeted with and without optimisation.
560 Results are presented in Table 14. After optimisation for the four utility mains case, TC has 561 decreased by 4.59 %, which offers NZD 773,406 /y of TC savings. As a percentage, this 562 reduction is not significantly higher than the previous analysis using five utility mains including 563 HTHW and LTHW. In terms of absolute TC, the optimised four utility mains case is 2.6 % higher 564 than the optimised five utility mains case, NZD 406,031 /y ( 583 valuable information about potential utility mains temperatures. As can be seen in Figure 6, 584 the heat sink profile has a flat region around 157 °C and a steep slope in temperature range 585 immediately below 157 °C. If an isothermal utility, i.e. LPS, temperature is chosen below 586 157 °C, the optimal temperature may not converge above the region's higher boundary. As a 587 result, a logical initial temperature for LPS is >157 °C, as selected in the Base Case. 588 Different step sizes have been considered to study the sensitivity of the presented 589 optimisation procedure. The procedure has been carried out using initial 16 °C step size. It 590 has been repeated for 0.1, 1.0, 8.0, and 24.0 °C. Table 17 shows the optimal temperatures for 591 different step sizes. The original temperatures are considered as the utility temperature 592 starting points and targets are repeated for each step size. As it can be seen in Table 17, for 593 8.0 °C and 24.0 °C step size, the same optimal temperature can be achieved. For the 1.0 °C, 594 only cold side of HTHW converged 1.8 °C lower than the optimal case. For the very small step 595 size (0.1 °C) final temperatures did not converge as it may be due to the local optimums of 596 the optimisation function.
597 Table 18 presents TS targets deviation from the initial 16 °C optimal temperature results after 598 optimisation carried out using different step sizes. Only the deviation of the 0.1 °C step size 599 can be taken into an account as it is not converging the optimal utility temperature. It means, 600 it is not easy to adjust utility temperatures by very small amounts due to operational 601 uncertainties such as heat loss and hydraulic difficulties. Therefore, from both Table 17   Step 1 Step 2 Step 6 A B Step 5 Step 3 Step 4 Step 7