*3.1. System Description*

The aforementioned propylene recovery unit is a subunit (a section) of a fluid catalytic cracking (FCC) unit, splitting the liquid propylene–propane fraction from the FCC gas plant into individual products of high purity. Due to low relative volatility of the components (and therefore low temperature difference between the head and bottom of the distillation column), a compression heat pump system can be utilized. However, the small difference in boiling points demands a large reflux ratio (>15) and numerous (>150) separation stages. Hence, such a system (as described in Figure 1) poses not only a technological but also a computational challenge, which once again underlines the pressing need for use of robust simulation software.

Performance of the considered propylene recovery unit was evaluated during an approximately one-year period, from 1 April 2018 to 28 February 2019, and provided the following observations:


Based on the technical documentation, we can state:


#### *3.2. Proposed Change in Steam Drive Type*

Currently, a condensing steam turbine is used as the heat pump compressor drive. Such a situation makes sense if there is excess steam that cannot be utilized for other purposes (process heating, stripping agent, etc.). In the presented industrial study, HPS, used as driving steam, was imported from the CHP. At the same time, enough variability in both HPS and MPS production and transport capacities allowed us to consider condensing steam drive replacement by a backpressure one, targeting fuel savings in the CHP at the expense of a certain loss of CHP power generation. The replacement of condensing mechanical power production by a backpressure unit is economically feasible at most fuel-power price ratios. An additional tangible benefit was the resulting decrease in CO2 and other pollutant emissions in the CHP.

Another steam pressure level, LPS, can be considered as an alternative backpressure steam sink to the MPS, but it is less suitable for this purpose. The reason is an occasional LPS excess in summer and the resulting decrease of LPS export from the CHP to very low values, which negatively a ffects the steam quality in the main LPS pipelines. Additional LPS from a new backpressure steam drive would thus have to be vented into the atmosphere. This situation is well-documented in Figure 4, where occasional drops of LPS export from the CHP can be seen. Sudden one-direction changes in LPS export within a few days or one to two weeks (decrease in April, increase in November) result from switching on/off the space heaters and steam tracing in the refinery. The existing LPS excess in the refinery during summer months is a serious issue that has two consequences: First, lower economic attractiveness of incentives for LPS consumption decrease in the refinery. Second, low LPS export from the CHP leads to reduced backpressure power production. Long-term energy policy of the refinery includes the demand to secure the power supply to critical production units during outer grid outages (severe weather, unexpected events) from the CHP. Thus, a certain minimal power production in the CHP is required regardless of the actual season. As the backpressure power production is insu fficient to cover this demand, additional power is produced in condensing steam turbines during warmer months. The average duration of this period is 40% of the year. Any changes in CHP backpressure power production resulting from the proposed change in the steam drive are reflected in the change of condensing power production in the opposite way during this period of the year.

**Figure 4.** Seasonal fluctuations in low-pressure steam (LPS) export.

Apart from MPS and LPS, other steam pressure levels can be considered with su fficient capacity to absorb the steam produced from the new steam drive. A preliminary analysis of steam consumption in the FCC unit showed no such options, as their steam absorption capacity was only a small fraction of what was needed. Thus, only a backpressure steam drive with HPS as the driving steam and with MPS discharge was considered and further analyzed. A schematic of the analyzed proposal is provided in Figure 5. The FCC unit consumed between 25 to 40 t/h of MPS. During periods of lower MPS consumption, the excess of MPS produced in the new steam drive was exported to other refinery units. The CHP remained the marginal source of both HPS and MPS for the refinery. MPS export from the FCC unit was associated with increased MPS backpressure at the new steam drive discharge, which was considered in the proposed steam drive sizing method. Increase in the HPS export from the CHP increased the steam flow velocities in the HPS network, which was desirable following the outcomes of a study dedicated to HPS network operation [26]. However, transport capacity of both main HPS pipelines as well as those within the FCC unit has to be reviewed.

**Figure 5.** Simplified plant steam network alteration proposal. Legend: Red line = HPS pipelines; orange line = MPS pipelines.

#### *3.3. Key System Analysis and Model Verification*

Prior to designing a new process equipment, it is inevitable to confirm the relevance of the constructed model, based on which the proposal will be carried out. Designing a new process steam drive, the best practice is to prove that the model can predict actual steam consumption precisely. According to the enclosed graph (Figure 6), the model prediction seems to be incorrect though the trend is generally preserved. This was probably caused by the lack of live steam consumption measurement, except for the turbine condensate mass flow, which did not, however, totally correlate with the steam consumption because of the condensate pump by-pass increasing the condensate flow. Moreover, as shown in Figure 7, the calculated compressor shaft speed was in most cases slightly lower than the measured one due to the applied process control: For systems comprising such an enormous recycle stream flow rate (>150 t/h recycle vs. <10 t/h feedstock) it was near impossible to numerically obtain the exact same composition as analytically determined. Rather than that, an automation condition was set, forcing the process control to keep the product quality above 99.6 vol%. Even though real process control can occasionally achieve higher purity, there were numerous cases where the calculated purity was slightly below the measured. As a result, the compressor shaft speed may have, on a small scale, differed from the measured as well.

To account for both effects, the condensate mass flow rate with by-pass valve position was included in the calculation and the measured shaft speed was used for turbine performance assessment. The latter perfectly illustrated the impact of the shaft speed on the turbine efficiency (discussed in detail later). Based on the measured to calculated condensate mass flow rate comparison (Figures 8 and 9), it can be stated that the model provided reliable results and was thus verified.

Subsequently, to design a process drive correctly, it is necessary to:


**Figure 6.** Condensate to steam mass flow comparison.

**Figure 7.** Measured to calculated shaft speed comparison.

**Figure 8.** Comparison of measured and estimated condensate mass flow rate over the evaluated period.

**Figure 9.** Measured to estimated condensate mass flow rate comparison.

Considering the above, process side characteristics (Figure 10) were constructed. Despite expectations, the primary assumption that the feedstock quality affects the process side power requirements was refuted. The best explanation was that the impact of large reflux efficiently suppressed the impact of the feedstock quality and so the characteristics were practically linear, with the feed flow rate as the independent and the power requirement as the dependent variable. The slope of the linear function used to fit the data was later used in results.

**Figure 10.** Process side characteristics.

The installed condensing steam turbine provided 1250 kW of power at nominal conditions, i.e., live steam pressure of 2.95 MPa, live steam temperature of 300 ◦C, exhaust pressure of 25 kPa, and shaft speed of 11,548 rpm, while consuming 2.1 kg/s of HPS. At these conditions, isentropic efficiency of 71.9% was declared. Based on the enclosed technical documentation (correction curves), the effect of alteration of these parameters was studied. The results can be observed in the figures below. It was proven that steam side parameters (Figure 11) affect the turbine isentropic efficiency insignificantly, as even the highest relative parameter deviations caused no more than a 2% difference in isentropic efficiency. Moreover, it is worth mentioning that no such drastic deviations occur in real steam networks, and thus the impact of steam side parameters on the isentropic efficiency can be neglected. However, as it is shown below, the shaft speed affected the isentropic efficiency to a high measure, while a change in shaft speed was a common phenomenon resulting from variations in the system performance and the feedstock throughput. Hence, the effect of shaft speed alteration on turbine isentropic efficiency was normalized (Figure 12) for designing the new turbine.

**Figure 11.** Effect of steam side parameters on isentropic efficiency.

**Figure 12.** Relative isentropic efficiency as a function of relative shaft speed.

The study of actual steam side parameters, however, showed that the installed turbine operates off design as the real steam network measured values differ from the nominal ones. Hence, the parameters measured at the FCC unit battery limit were displayed in histograms (Figures 13–16) to obtain ideal design parameters for the new steam drive.

**Figure 13.** HPS temperature histogram.

**Figure 14.** HPS pressure histogram.

**Figure**MPStemperaturehistogram.

 **15.**

**Figure 16.** MPS pressure histogram.

Temperature and heat losses were studied on a plant-wide scale. Measured values of temperature and pressure of HPS exported from CHP were compared to those measured at the FCC battery limit. The results can be seen in Figure 17. Rather significant differences can be observed namely in temperatures where an almost 50 ◦C decrease was documented. These results illustrate the need for pressure and heat loss assessment prior to any proposals incorporating steam networks.

**Figure 17.** Heat and pressure losses in steam network. Legend: Solid line = conditions at the CHP; dashed line = conditions at the fluid catalytic cracking (FCC) battery limit.

#### *3.4. Variable Approaches in Steam Drive Design*

The steam turbine model was based on steam turbine characteristics well known as the Willan's line [80,81], i.e., linear dependency of the actual turbine's shaft output, *P*, on the actual steam mass flow, .*m*, Equation (1), applied to steam expansion between HPS and MPS, with *I* being the intercept of the linear relationship:

$$P = \, k\dot{m} - I\tag{1}$$

As reported by Mavromatis and Kokossis [80], the slope, *k*, in Equation (1) can be expressed as follows, in Equation (2):

$$k = \frac{1.2}{B} \left(\Delta h\_{IS} - \frac{A}{\dot{m}\_{\text{max}}}\right) \tag{2}$$

Parameters *A* and *B* can be correlated as a function of inlet steam saturation temperature (see [80] for further details); Δ*hIS* represents the isentropic enthalpy difference between inlet and discharge steam, depending on the inlet steam pressure and temperature as well as on the discharge pressure; . *mmax* stands for the maximal (design) steam mass flow through the turbine. As verified in [47], values of k for common steam drive applications do not differ significantly from Δ*hIS* and, thus, Δ*hIS* is used as the slope of the steam drive characteristics in the steam turbine model. Once the nominal turbine steam consumption, the nominal obtained output, and the slope of the characteristics are known, the steam turbine characteristics can be constructed. Following the engineering practice of steam turbine vendors, when depicting the given relationship, the inlet steam mass flow is located on the *y*-axis and the obtained output on the *x*-axis. Thus, an inverse function to Equation (1) is depicted in Figure 18, with its slope being equal to <sup>Δ</sup>*hIS*−1, as seen in Equation (3):

$$
\dot{m}\_s = \frac{1}{\Delta h\_{IS}} P + \frac{I}{\Delta h\_{IS}} = \frac{1}{\Delta h\_{IS}} P + K \tag{3}
$$

**Figure 18.** Illustrative example of turbine characteristics.

Varying inlet steam conditions and discharge pressure impact the Δ*hIS* value and thereby affect the actual turbine's steam consumption necessary to achieve the desired output. The analysis of process side characteristics revealed the maximum power requirement of 1278 kW to be supplied by the turbine. For the new turbine, the design power output was thus set to 1300 kW. According to numerous publications on isentropic efficiency of industrial steam drives [30,82], an isentropic efficiency of 65% was assumed, which is typical for mid-size industrial steam drives operating at full load with a low-steam pressure ratio. Mechanical efficiency of such equipment can be estimated to be 85% [81]. While the mechanical efficiency changed in a very short interval and thus could be considered constant for a reasonable operational window [81], the isentropic efficiently changed significantly regarding the turbine load. The dependence between turbine power and isentropic efficiency has been well documented before [80]. It can be calculated directly from the Willan's line and described in the form of a parabolic function (Figure 19).

**Figure 19.** Isentropic efficiency as a function of power output.

To find the design point and subsequently construct the turbine characteristics, several approaches are available (Table 1). These vary depending on the number of variables considered, i.e., on the number of system properties that are neglected and/or simplified. To provide a comprehensive overview, a variety of possible approaches was exploited to illustrate the main differences in the resulting design (Table 3). These cases were subdivided into three groups: Cases 1–6 considered the properties and topology of the existing propylene recovery unit, with only cases 1–3 considering the features of the

pipeline; cases 7–9 illustrated the changes in results for a steam drive located ten times farther (in means of pipeline length) from the battery limit; and case 10 was a standalone case considering only the basic enthalpy balance and constant values of all parameters.

**Table 3.** Steam drive design approach variations. Real insulation conductivity of 0.080 <sup>W</sup>·m<sup>−</sup>1·K−1, calculated previously by Hanus, et al. [26], was considered. Design insulation conductivity of 0.038 W·m<sup>−</sup>1·K−<sup>1</sup> was considered as a common value for new steam pipeline insulations.


Pressure drop calculations for each segmen<sup>t</sup> of the pipeline came from the Bernoulli's equation, which can be generally written as Equation (4):

$$z\_1 \mathbf{g} + \frac{w\_1^2}{2\alpha\_1} + \frac{\mathbf{p}\_1}{\rho} = z\_2 \mathbf{g} + \frac{w\_2^2}{2\alpha\_2} + \frac{\mathbf{p}\_2}{\rho} + \varepsilon\_{\text{dis}} \tag{4}$$

where *z* is the geodetic height, *g* the gravitational acceleration, *w* the mean steam transport velocity, *P* absolute pressure, ρ fluid density, ε*dis* specific dissipated energy, and the dimensionless parameter, α, has the value of 0.5 or 1 for laminar or turbulent flow, respectively. Subscripts 1 and 2 refer to inlet and outlet of the pipe segment, respectively. For each segment, the inner pipe diameter remained constant. Thus, based on the continuity equation, the transport velocity remained constant as well. Furthermore, the difference in geodetic heights can be sensibly neglected and Equation (4) can be transformed into Equation (5):

$$
\Delta P = \rho \varepsilon\_{\text{dis}} \tag{5}
$$

The overall specific dissipated energy comprises dissipation due to friction and local energy dissipation. Based on the Darcy's law, Equation (6) is deduced:

$$
\Delta P = \rho \left( \lambda \frac{Lw^2}{2D} + \sum \xi \frac{w^2}{2} \right) \tag{6}
$$

where λ is the friction factor, *L* the length of the pipeline segment, *D* the inner diameter of the pipeline segment, and ξ is the coefficient of local dissipation. A generalized ready-to-use approach for friction factor estimation was proposed by Brki´c and Praks [83].

Assuming that the only significant heat transfer resistances are that of the insulation and that of the ambient space, the following Equations (7) and (8) apply:

$$T\_F \approx T\_W \tag{7}$$

$$\dot{q}\_L = \frac{\pi (T\_F - T\_I)}{\frac{1}{2\kappa} \ln \frac{D\_l}{D\_W}} = \frac{\pi (T\_F - T\_A)}{\frac{1}{2\kappa} \ln \frac{D\_l}{D\_W} + \frac{1}{\alpha\_A D\_l}}\tag{8}$$

where *TF* is the temperature of transported fluid, *TW* temperature of outer pipeline wall, *TI* the outer temperature of insulation, *TA* the ambient temperature, .*qL*the length-specific heat flux, κ the heat conductivity of the insulation, *DW* the outer diameter of the pipe, *DI* the outer diameter including insulation, and α*A* is the combined radiation and convective heat transfer coefficient.

Therefore, the length-specific heat loss from a segmen<sup>t</sup> can be iteratively calculated for *f* = 0 from Equations (9)–(12) [84]:

$$a\_A = \; 9.74 + 0.07(T\_{I,1} - T\_A) \tag{9}$$

$$\dot{q}\_L = \frac{\pi (T\_F - T\_A)}{\frac{1}{2\kappa} \ln \frac{D\_l}{D\_W} + \frac{1}{\alpha\_A D\_l}}\tag{10}$$

$$T\_{I,2} = T\_F - q \frac{\ln \frac{D\_I}{D\_W}}{2\pi\kappa} \tag{11}$$

$$f = \,^T T\_{W,2} - T\_{W,1} \tag{12}$$

where *TW*,<sup>1</sup> is the primary estimate of the temperature of the pipeline wall (under insulation).
