The design of optimal processing materials (molecules) and optimal process variables for a given process is referred to as Computer Aided Molecular and Process Design (CAMPD). Processing materials used to achieve process goals include mass separating agents (such as solvents for absorption, extraction, leaching and adsorbents), catalysts, heat transfer fluids and reaction medium solvents. Choosing processing molecules influences the optimal process variables and vice versa. Molecular and process decision variables are linked, interacting with each other in a complex manner. Hence, neither of these decisions can be made in isolation.

The CAMPD problem involves continuous decisions such as process operating conditions (examples include pressure, temperature) and discrete decisions (examples include number of groups of a given kind in the molecule to be designed, connectivity between the groups and process topology). The objective is a process/plantwide one. The process model is a coupled nonlinear system of equations. The process model also involves numerous calls to property prediction models to obtain thermophysical properties such as density, enthalpy and chemical potentials. Property models can also be highly complex. Hence, the CAMPD problem is a MINLP problem with a large number of equality constraints.

While the evaluation of the objective is numerically challenging, an even bigger challenge is that a given molecule may be infeasible in the process. Consider a process molecule to be used as a solvent in a separation system. This molecule may or may not exist in the liquid state for a given choice of process variables. The choice of a non-liquid solvent molecule (and the corresponding process conditions) will not only result in a physically infeasible process but may also result in numerical failure when attempting to simulate or optimise the process. Hence, due to infeasible regions in the domain, failure to converge is frequently encountered in these design problems. The domain is not only discontinuous but also non convex and made more challenging from combinatorial explosion that results from the presence of discrete variables. A set of 10 functional groups in the molecular design space can generate 184755 potential “molecules” of utmost 10 groups [1]. These problems are not usually amenable to solution by general purpose MINLP solvers.

To overcome this challenge, heuristics and knowledge based screening of all molecules in the search space has been previously used [2]. This large MINLP has also been reformulated as a NLP [3, 4]. An approach based on determining a range of target properties of molecules using process requirements and then finding molecules whose properties lie within the range has been proposed [5]. A Multi objective optimisation (MOO) framework based on physical properties to identify promising molecules has also been developed [6, 7]. More recently, the HiOpt approach has been put forward in which MOO based on the performance of a simplified process has been used to identify initial guesses for the optimization of the CAMPD problem [8]. While this latter work tackles the full CAMPD problem, it does not fully address the numerical challenges posed by the simultaneous variation of molecular and process variables.

With a focus on solvent based separation systems we present an alternative screening embedded in optimisation algorithm to solve this MINLP. As mentioned before, a challenge in solving the CAMPD problem is that many molecules may be infeasible in the process based on their properties and phase behaviour in presence of the feed to be separated. Our screening methodology exploits this to reduce the solution domain and solve the problem efficiently. However, we do not generate and test molecules but choose to embed screening steps within an MINLP optimisation framework, such as previous work in the context of molecular design [9, 10]. We have proposed a series of new screening tests that help to eliminate solvents that fail the tests, but can also be used to reduce the continuous domain of process variables. These tests are implemented within the outer approximation (OA) framework [11].

A test of feed phase stability restricts the process domain to one where the feed has the desired phase (gas/liquid). This test is independent of the solvent chosen. As a solvent molecule is generated at each iteration of the OA algorithm by the master problem it goes through a series of tests. The molecule is first tested based on its pure component properties. This test is used to check if the molecule exists in the liquid state at its handling and storage temperature. Its ease and safety of usage are also tested.

A test of separation feasibility is used to checks if an infinitely long separation column with the molecule as solvent can achieve any separation of the feed. This test is equivalent to checking if the feed and the solvent can form a two phase mixture on contacting. This test is posed as an NLP optimisation problem to determine the region of the process domain where this is possible. If no feasible region is found for the problem, the solvent is rejected from the search space.

A test of purity feasibility is used to determine if the required degree of separation (or purification of the feed) may be achieved by the solvent. This test is a check on the two-phase boundary of the solvent and feed. This test is posed as an NLP optimisation problem to determine the range of the process variables where this condition is satisfied.

Molecules that fail any of the tests are eliminated from the search space. Molecules that pass are provided as input to the primal problem. Information obtained from the tests and the primal problem is progressively added to the master problem whose solution generates a new molecule.

We have implemented this algorithm in C++, with gPROMS [12] as the simulation engine and NLP solver and Gurobi [13] as the MILP solver. We demonstrate it on the design of a separation system for the absorption of carbon dioxide from natural gas. The property prediction model employed is a group contribution based version of the statistical associating fluid theory (SAFT) -γ Mie [14]. This provides a single consistent thermodynamic model across the entire fluid region. This equation of state is predictive for both pure compounds and mixtures. However, this complex and nonlinear model makes solving the CAMPD problem more challenging. The case study is solved successfully, without numerical failures, and leads to the identification of a promising solvent. The performance of the algorithm is discussed in the context of the proposed tests.

References:

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