(475c) Formulation of Closed-Form Mathematical Expressions Applied to Chemical Engineering Processes Using the Bayesian Machine Scientist

Chemical engineering is a vast research field that includes experimental and more theoretical (mathematical) approaches such as process simulation and machine learning. The transition from laboratory to pilot or industrial scale is not always straightforward and scientists often struggle to compare the performance of a novel technology or approach to the business as usual scenario at the early development stage.

We assume that those researchers who are specialized in experimental work do not have access to process design and simulation tools or that a detailed process modeling would be too time-consuming. In this scenario, the availability of simple closed-form mathematical expression comes in handy to take decisions during the planning and design research phases or to determine the reference costs.

The vast majority of the research on chemical processes is focused on implementing novelties and improvements. On the other side, machine learning aims to provide relationships to describe black-box models, although the expressions obtained are generally rather complex and not easy to handle. Very little attention is given to symbolical regression, which tries to find those simple mathematical expressions, which can relate process inputs and outputs. One recent publication in this direction is the Bayesian machine scientist[1], which has been proven to perform better than previous machine learning approaches. This Markov chain Monte Carlo (MCMC) algorithm is a good balance between fit and model complexity and it can explore a vast space of mathematical models. The Bayesian machine scientist not only provides simple closed-form mathematical models, but it can also recover the true model with just 100 points, decreasing the computational time noticeably.

Here we propose an application of the Bayesian machine scientist that provides the closed-forms of preselected key process indicators of a first principle chemical process implemented in Aspen HYSYS V11. The case study presented refers to the natural gas sweetening with CO₂ sequestration and storage. The natural gas sweetening process includes the natural gas at extraction, the absorption and desorption columns using a monoethanolamine (MEA) aqueous solution and the CO₂ compression stage. The sweet natural gas is purified in the absorber and collected at the top, while the MEA solution leaving at the bottom is sent to the stripper, regenerated and recycled. The natural gas is assumed to be a binary mixture of CH₄ and CO₂, 80% and 20% mol., respectively. The selection of this binary mixture is justified by the numerous applications in literature studies about membrane technologies, which are not yet ready to be a large-scale technology. In the nominal case, the sweet natural gas is produced at 99.5% mol. CH₄ and is ready for pipeline injection and distribution. A stream of 99% mol. pure CO₂ is compressed to 110 bar for pipeline transportation and injection at a selected storage site. Capital and operating expenditure are calculated for the base case scenario. Given the most significant influence of operating expenditures, the variables of interest for the process are the amount of MEA, cooling and heating utilities and electricity consumption. The utilities are calculated as minimum utilities from the grand composite curve.

The optimized flowsheet is sampled for 1000 points using Latin Hypercube Sampling (LHS). These points are used to train the Bayesian machine scientist. The independent variables are the feed temperature and pressure, composition and product purity, while the dependent variables are minimum cooling utilities, minimum heating utilities, electricity consumption and amount of MEA. The range of the sampling variables is defined based on literature data[2]–[4], where each variable is perturbed by approximately 30% of its nominal case value. The Bayesian machine scientist samples the space of equations using an MCMC algorithm and addresses the complexity of the model by considering priors over expressions commonly used in physics, engineering, and other scientific fields. The objective function is to minimize the description length, which is calculated from the Bayesian Information Criterion (BIC) and the priors. The inputs to the BMS are the data, the hyperparameters of the priors, and the number of MCMC steps. A number of 5000 steps were chosen based on the observation of the description length throughout the MCMC steps. The algorithm returns closed-form mathematical expressions for each output variable of interest as a function of the input variables and a number of parameters provided by the algorithm.

This case study proved that the application of the Bayesian machine scientist to determine key process indicators will allow experimental researchers to compare their product to the business as usual scenario, without the need of process simulation tools to determine for example the minimum utilities and energy consumption. Additionally, the application of the Bayesian machine scientist can be extended to other variables of interest or even to single process units.

[1] R. Guimera et al., “A Bayesian machine scientist to aid in the solution of challenging scientific problems,” Sci. Adv., vol. 6, no. 5, Apr. 2020, doi: 10.1126/sciadv.aav6971.

[2] M. Hoorfar, Y. Alcheikhhamdon, and B. Chen, “A novel tool for the modeling, simulation and costing of membrane based gas separation processes using Aspen HYSYS: Optimization of the CO2/CH4 separation process,” Comput. Chem. Eng., vol. 117, pp. 11–24, 2018, doi: 10.1016/j.compchemeng.2018.05.013.

[3] L. Peters, A. Hussain, M. Follmann, T. Melin, and M. B. Hägg, “CO 2 removal from natural gas by employing amine absorption and membrane technology-A technical and economical analysis,” Chem. Eng. J., vol. 172, no. 2–3, pp. 952–960, Aug. 2011, doi: 10.1016/j.cej.2011.07.007.

[4] C. Song, Q. Liu, N. Ji, S. Deng, J. Zhao, and Y. Kitamura, “Natural gas purification by heat pump assisted MEA absorption process,” Appl. Energy, vol. 204, pp. 353–361, Oct. 2017, doi: 10.1016/j.apenergy.2017.07.052.