The challenge is deceptively simple to state but brutally hard to solve. Optimizing a crude oil distillation unit, or CDU, means simultaneously tuning structural variables, such as the number of trays in each section of the column, and operating variables, including feed temperature, pressure, reflux ratio, and steam flows. The search space mixes continuous and discrete decision variables, and it is fenced in by a large number of constraints tied to product quality specifications. Worse still, every candidate design must be evaluated with a rigorous simulation model built on the MESH equations, the mass balance, enthalpy balance, equilibrium, and summation equations applied stage by stage. For a column with multiple components and stages, the total number of equations can easily exceed a thousand, making each evaluation a time-consuming task that can bring an evolutionary optimization algorithm to its knees.

Historically, engineers have attacked this problem with three main categories of models. Rigorous models, built from first principles, provide the most accurate predictions of column behavior, but they are notoriously difficult to embed in an optimization loop because of their large systems of non-linear equations and their need for a perfect initial guess to avoid convergence failures. Simplified models converge faster and are more robust, but they often carry large errors and cannot faithfully predict the behavior of complex distillation units. Statistical models, including polynomial regression, support vector regression, and artificial neural networks, have become popular because they are straightforward and robust, but their quality depends entirely on the sampling data used to train them, and poor-quality samples translate directly into poor optimization results.

The Ningbo University team, led by Yingjian Xiong and Xuhua Shi, took a different path. They proposed a method called Bi-level Surrogate column model Aided Constrained Optimization Design, or Bi-SACOD, which combines the best of two worlds: fast statistical surrogate models and accurate rigorous simulations. The key insight is that a single surrogate model is not enough. Local surrogate models, while accurate near known points, cannot help an optimization algorithm escape from local optima, those deceptive valleys in the fitness landscape where a search can become trapped. Bi-level models, pairing a global surrogate with a local one, are expected to outperform most individual surrogates in both accuracy and efficiency for complex optimization problems.

Bi-SACOD consists of three tightly integrated components. The first is bi-level surrogate model construction, which builds and updates the two-tier statistical model. In the global tier, the team uses Kriging models, also known as Gaussian process regression, which have excellent global statistical characteristics and are used to smooth out local optima and speed up the search. In the local tier, radial basis function networks with linear spline kernels are constructed from the best 20 percent of the global dataset to approximate the fitness landscape accurately near the most promising regions. The second component is bi-level model management, which cleverly combines the fast surrogates with occasional rigorous CDU simulations to ensure that the search stays on track. The third is a particle swarm optimization mixed-integer constrained evolutionary search strategy, or PSO-MICE, which handles both continuous and discrete decision variables while respecting the problem’s constraints.

One of the most ingenious aspects of Bi-SACOD is its use of a support vector machine as a feasibility classifier. Every new individual generated by the particle swarm is sorted into one of two families: feasible or infeasible solutions. Only winner individuals that satisfy the constraints are eligible to update their velocity and position, which prevents the algorithm from wasting precious evaluations on designs that would never converge in the rigorous simulator. This SVM-feasibility approach is applied to both the global and local searching processes, dramatically reducing the number of time-consuming rigorous model evaluations needed to reach a successful optimization outcome.

The team tested their approach on a realistic industrial CDU consisting of a main column with 60 stages, one condenser, three side strippers, and three pump-around systems. The unit processes 0.16 cubic meters per second of crude oil into light naphtha, heavy naphtha, light gas oil, heavy gas oil, and residue. The optimization objective was to maximize economic profit, with 15 decision variables spanning operating conditions like feed inlet temperature, pressure, reflux ratio, and pump-around duties, as well as structural variables like the number of trays in each of the column’s five sections. The rigorous simulations were facilitated through an interface between the commercial platform Aspen Plus and MATLAB.

The results are striking. Over 20 independent runs, Bi-SACOD achieved a success rate of 96.31 percent, the highest among all comparative approaches, including a rigorous-model-only method, single-surrogate methods using only Kriging or only RBF models, and a recently proposed ANN surrogate combined with SVM feasibility handling. Just as importantly, Bi-SACOD required only about 2,820 rigorous model evaluations to reach successful conditions, considerably fewer than the roughly 3,620 evaluations needed by the rigorous-model-only approach and the 4,000 evaluations of the ANN-based method. Although the Kriging-only surrogate approach required a similar number of evaluations, its success rate was remarkably lower, demonstrating that the bi-level combination is what delivers the best of both speed and reliability.

In terms of pure economics, the optimized design reached a profit of 2.88 times 10 to the fifth US dollars per day, which is remarkably close to the 2.99 times 10 to the fifth dollars per day achieved by the rigorous-model-only method, while requiring significantly fewer expensive simulations. The profit profiles of Bi-SACOD over the course of optimization were also remarkably more consistent with those of the rigorous-model-only method, indicating that the surrogate-assisted search tracks the true optimization landscape faithfully rather than chasing phantom gains predicted by an inaccurate statistical model.

The implications reach far beyond a single distillation column. As refineries face mounting pressure to squeeze more value from every barrel of crude while reducing energy consumption and emissions, tools like Bi-SACOD offer a way to redesign complex process systems automatically, reliably, and affordably. The team notes that their follow-up research will further improve the method and extend it to other types of distillation units. If successful, the bi-level surrogate paradigm could become a standard weapon in the arsenal of process engineers, marrying the raw power of evolutionary computation with the precision of rigorous physics-based simulation, all while keeping the computational bill manageable.

Subject of Research: crude oil distillation unit, surrogate model, optimization, evolutionary algorithm, particle swarm optimization, Kriging, RBF, support vector machine, refinery, process control

Article Title: Optimization design of crude oil distillation unit using bi-level surrogate model

Article References: Xiong, Y., Shi, X., Ma, Y., & Chen, Y. (2023). Optimization design of crude oil distillation unit using bi-level surrogate model. Frontiers in Control Engineering, 4, Article 1162318. https://doi.org/10.3389/fcteg.2023.1162318

Image Credits: AI Generated

DOI: 10.3389/fcteg.2023.1162318

Keywords: Optimization, design, crude, distillation, unit, bi-level, surrogate, model, scientific research