## 3 Problem Statement
### Debutanization Process  
The debutanization process is a fractional distillation process that aims to recover the light gases (\(C1-C4\)) and the Liquefied Petroleum Gas (\(LPG\)) from the overhead distillate coming from the distillation unit [26]. This distillation process aims to separate liquid components by heating a liquid to vapor, condensing the vapor back to liquid to purify or separate it. To that end, three components are required: (1) a distillation column (used  
Figure 1: High-level schematic diagram of some of units found in crude oil refineries. In this research we focus on one of the LPG debutanizer units. to separate a liquid mixture into its fractions based on the differences in volatilities); (2) a reboiler (used to provide the necessary vaporization of the distillation process); (3) a condenser (used to cool and condense the overhead vapor). The \(CH4\) (methane) component exists in the feedstock with the other alkane compounds, with the \(C4H10\) (butane) fraction only gaining its freedom when the vaporized gas condenses inside the array of valve trays that line the interior of the debutanizer column. Based on thermal unit conversion technology, the butane is efficiently siphoned from the raw feed. To achieve this, the boiling point of butane is used as a reference point to determine temperature and pressure conditions. Pure butane condenses in the debutanizer column when the architecture of the column locks in the mandated variables, so few impurities can form. Similarly, propane, ethane, and methane are liberated and refined as valuable fuel sources in the other alkane processing columns. Pressure is frequently considered the most relevant distillation control variable since it affects column temperatures, product relative volatilities, condensation (and therefore the distillate composition), and cooling and energy requirements [68]. Pressure controls are usually integrated into the condensation system, and therefore both need to be considered simultaneously. The satisfactory operation of the distillation column requires steady pressure, and pressure changes must be introduced slowly and steadily. In a mass balance control, higher distillation column pressures reduce the relative volatility between the components, increasing the molar flow rates, the condensation rate, and therefore the amount of reflux [69]. Conversely, low pressures can prevent condensation and thus prevent a successful distillation. In atmospheric distillation columns, the condensation rate can be controlled through the temperature too [70]. The control of condensate temperature enables additional control over vapor and liquid product split. Changes in the temperature usually correlate with changes in the product composition [71]. In particular, differential temperature control considers that given temperature measurements at two different points of the distillation column, the temperature difference between both remains constant regardless of the pressure changes. Variations in the temperature difference thus signal changes in the composition profile of the product [72]. It must be noted that vapor enters the distillation condensers at a saturation temperature. Given the importance of the pressure and temperature variables in the distillation process, it is critical to determine the best placement of the sensors to enable adequate and timely insights into the process. The distillation column pressure is usually measured in vapor spaces at the reflux accumulator and the top of the column. The column temperature is usually measured nearby the condenser to avoid a dynamic lag associated with the reflux drum. The temperature sensor placement follows two criteria: the linearity of the response (where the steady-state responses to a positive and negative change in the corrective action are most similar), and the maximum sensitivity to product composition. In addition, experts consider that the best temperature control points are where the most extensive and symmetrical temperature variations are observed [70].