PTQ Q3 2024 Issue

NG feed model

FG Cons model

Cost

Methane slip model

Steam export model

Figure 5 Steam-to-carbon ratio iterations in models

Regression algorithms have yielded more successful results in predicting the exported high-pressure steam quantity from the HGU. The model has shown promising outcomes across validation techniques such as time-se- ries and holdout validation. Consistent success across different time series underscores the model’s robustness and capability for generalisation (Table 1). This analytical model plays a pivotal role in the optimisation framework by predicting the quantity of high-pressure steam produc- tion based on varying amounts of natural gas and fuel gas corresponding to each adjusted S/C ratio. Given that steam production represents an energy gain, it is a critical input for calculating unit costs, thereby significantly contributing to the optimisation process. Methane slip model Pivotal within the optimisation framework is the methane slip model. A constraint on methane slip values is imposed to delineate the extent of optimisation applicability, ensur- ing that the levels do not exceed a threshold. Methane slip is intricately linked to crucial process parameters, including the natural gas feed and S/C ratio. Interestingly, some fea- tures with low correlation to methane slip have been iden- tified to significantly enhance the model’s performance, notably improving its R² and MAPE metrics. As with other analytical models, regression and tree- based algorithms were subjected to holdout and time- series validation tests to identify the most effective approach for the methane slip model. In this context, robust regression algorithms were employed due to their efficacy. The results of the time-series validation for this model can be seen in Table 1. The outcomes of the methane slip model are fed into the fuel gas analytical model, thus playing a crucial role in understanding variations in fuel gas consumption, one of our key energy components. Objective function The production cost per unit of hydrogen in the HGU var- ies depending on the variables in the unit. The aim is to minimise the cost per unit of hydrogen within the speci- fied S/C limits while meeting the exact amount of hydro - gen demanded by the refinery and not exceeding the 5% methane slip in the pressure swing adsoprtion (PSA) inlet stream. The objective function includes the unit inputs, including feed (natural gas), fuel (fuel gas), other utilities and unit outputs, including hydrogen and high-pressure steam, and the costs of these variables as indicated in the equations:

Although hydrogen is the main output of the unit, since the demand for hydrogen in the refinery is variable and the objective of the unit is to meet the demand, the effect of other variables per unit of hydrogen is considered in the objective function. In this way, the cost spent in the unit per unit of hydrogen can be minimised:

The fuel gas content used in the refinery is variable due to the feeds to the fuel gas header. The fuel gas cost in the refinery is calculated monthly and changes dynami - cally according to the natural gas cost and the feeds to the header. So, instead of using the fuel gas cost in the objec- tive function, a more accurate cost calculation will be made by converting the amount of fuel gas burned to natural gas equivalent over the dynamically changing LHV (calculating how much natural gas corresponds to the fuel gas used; and using the natural gas cost):

The objective function to be maximised in the final case is given as:

Algorithm and iterations The process begins with obtaining the refinery’s hydrogen demand data. Subsequently, the natural gas prediction model generates predictions for the required natural gas quantity to meet this hydrogen demand. These predic- tions are then fed into the methane slip model, resulting in calculated methane slip values. The estimated methane slip and natural gas values are inputted into the fuel gas prediction model to obtain another prediction. Finally, the steam export model’s predictions are supplied to the natu- ral gas and fuel gas models, yielding a forecast. This cycle is completed for each S/C value, and the S/C value that produces the lowest cost function is presented to the user (see Figure 5 ).

PTQ Q3 2024