Optimisation of a diesel 
hydrotreating unit

A model based on operating data is used to meet sulphur product specifications at lower DHT reactor temperatures with longer catalyst life

Jose Bird
Valero Energy Corporation

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Article Summary

Meeting product specifications in diesel hydrotreating units is a challenging task requiring ongoing process adjustments as the feed sulphur content can vary significantly during the course of operations. Refinery operations will often run these units at higher reactor temperatures than required to ensure product sulphur specifications are always met but these higher temperatures can negatively impact product yield, energy costs, and catalyst life. This study uses a time series auto-regressive moving average model with explanatory variables (ARMAX) constructed using actual operating data to evaluate the performance of a diesel hydrotreating (DHT) unit at different sulphur operating targets. The optimum sulphur operating target ensures product specifications are consistently met while minimising the detrimental impact of higher reactor temperatures on product yield, energy costs, and catalyst life. The study focuses on the trade-off between sulphur operating target and catalyst life.

The methodology used in this study assumes operating data is available to evaluate the performance of the DHT unit within the sulphur operating target range of interest. The use of a process simulator in combination with Monte Carlo random sampling to evaluate the performance of a distillation unit outside of the current operating range was presented in a previous article.1 The ARMAX model uses transfer functions to capture the relationships between key process variables and the produced diesel sulphur content. The model also contains a noise model to account for the variation in sulphur content not explained by the process variables and to properly represent the autocorrelation structure of model residuals.

The ARMAX model was used to determine the optimum sulphur operating target for the DHT unit by conducting a series of Monte Carlo simulations to model the unit performance under varying process conditions. The variability of the process due to changing conditions in the process variables was modelled using estimated probability distributions. The noise model is superimposed to account for unexplained process variability. Simple control logic was implemented as part of the Monte Carlo simulation that adjusted the reactor weighted average bed temperature (WABT) as necessary to maintain the produced sulphur content within pre-specified operating limits. To capture the effect of running at different WABTs on catalyst life, a term integrating WABT over time was also included. Integrated time on temperature has been previously used in predicting fouling/coking in fired heaters.2 The ability of the process unit to meet diesel product sulphur specifications and the effect on catalyst life in light of reactor pressure drop (dP) and temperature constraints were then evaluated to determine the optimum sulphur operating target.

Figure 1 is a typical process flow diagram of a DHT unit. The raw diesel mixes with recycled hydrogen before entering the heater. The heated mixture enters a reactor where hydrogen reacts with sulphur to produce hydrogen sulphide.3,4 A steam stripper unit then removes the hydrogen sulphide from the diesel. The produced diesel needs to meet a maximum sulphur specification ranging between 10-11 ppm at the delivery point. The refinery configuration specific to this study combined the DHT reactor bottoms stream with the bottoms stream from a light cycle oil (LCO) hydrotreater hydrocracker reactor (HTHC) before entering the H2S steam stripper. The bottoms stream from the steam stripper then goes into a downstream fractionator for final separation.

The following steps summarise the methodology used in this study:
1. Transfer functions for each of the process inputs developed using cross correlation charts between produced diesel sulphur content and the process input
2. Parameters of a noise model determined by examining autocorrelation and partial autocorrelation charts of residuals after accounting for the effect of process variables on sulphur content via the transfer functions
3. Probability distributions generated for input process variables
4. Monte Carlo simulations conducted for different sulphur operating target scenarios.

The simulation results are then used to evaluate the impact of the different sulphur operating targets on the ability of the process to meet the diesel sulphur specification and on catalyst life. A maximum reactor pressure drop (dP) of 90 psia and a maximum WABT of 760°F were assumed to estimate catalyst life.

A detailed description of the construction of the time series ARMAX model is provided below, followed by analysis results and conclusions.

ARMAX time series model construction
The first step in the construction of the ARMAX model is to identify the structure of the transfer function for each of the process inputs.5 The cross correlation function chart (CCF) between the response and the input at different time lags of the input is needed. Quite often the generation of the CCF requires first differencing of both input and output time series. First differencing is calculated by taking the difference between the current value and previous value of a time series. Before building the CCF chart, the input is converted into an uncorrelated time series or white noise by removing any autocorrelation present in the input. This step is known as pre-whitening and the associated pre-whitening filter has an ARMA structure. The pre-whitening filter is also applied to the response prior to calculating the CCF. The SAS Analytics procedure Proc Arima6 performs all of the necessary steps outlined above to generate the CCF for each input. The CCF is then used to identify the statistically significant time lags to consider in the transfer function. One-hour interval data were used in the construction of the ARMAX model.

Of all the variables considered in the study, reactor WABT was found to be the most influential variable impacting produced diesel sulphur content. Other variables considered and found to be statistically significant were DHT reactor weighted average temperature, DHT reactor recycle hydrogen purity, diesel production, and fractionator reboiler duty ratio. Process variables associated with the operations of the LCO HTHC reactor were not found to be statistically significant in predicting sulphur content during the period of operations considered.

Figure 2 gives the CCF chart for the WABT process variable. The CCF chart gives the correlation coefficient between the sulphur content response and WABT input at different time lags of the input. Positive lags represent previous values of input and negative future values of the input. Spikes or 
statistically significant lags in the CCF chart occur when the correlation coefficient value is outside of the 5% significance limits represented as the shaded area. High correlation between these variables at time lags of -1, 0, 1 and 2 periods can be seen in the CCF chart. When identifying the structure of the transfer function for an input, lags greater than or equal to zero are examined as we only consider causal models where the response is affected by previous or current values of the input. The negative spike at the time lag of 1 period indicates that an increase in WABT at time t-1 results in a decrease on sulphur content at time t. Spikes at negative lags such as the one observed at lag -1 represent a feedback control mechanism. In this case, a high sulphur content signal value is followed by an increase in WABT and low sulphur content signal value by a decrease in WABT. This feedback control mechanism was considered in the simulations by using a one-period delay between a sulphur signal and the corresponding adjustment to WABT. Based on this analysis, time lags at 0, 1, and 2 were considered for the WABT transfer function.

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