This presentation introduces a novel multi-model operability-based approach for design and intensification of processes described by high-dimensional and nonlinear models. This novel approach is applied to membrane reactors (MRs) for the direct methane aromatization (DMA) conversion to benzene and hydrogen. In the last decades, MRs have emerged as examples of intensified processes as they combine reaction and separation unit operations in one process improving the system efficiency and lowering the cost1,2,3. Specifically, in the DMA-MR process, higher methane conversion than in conventional reactors is enabled due to the selective hydrogen removal from the reaction side through the membrane. This removal shifts the reaction equilibrium towards the products, thus increasing methane conversion and benzene production rate. The nonlinear and multivariable nature of the DMA-MR system associated with the reaction-transport phenomena interplay make this system challenging to design and optimize.
Process operability was developed as an approach for the design and control of complex chemical processes4. In particular, process operability enables the verification of a design’s ability to achieve the feasible region of operation associated with process specifications, considering the physical limitations of the process design. Operability describes the relationship between the input (manipulated and/or disturbance) and output variables through a linear/nonlinear mapping obtained by employing the process model5. This approach has been applied to chemical processes that are described by high-dimensional linear models6. For the design of nonlinear systems, a low-dimensional operability implementation for the DMA-MR was analyzed using a subset of the system variables, including: membrane selectivity and permeance, reactor pressure and diameter, methane conversion and benzene production rate7,8. The results of this previous study demonstrated the promising capabilities of the operability approach to provide guidelines for experimental research, in terms of determining the set of membrane characteristics that should be obtained to achieve desired process specifications. However, the DMA-MR process intensification analysis using process operability and the full set of process variables has not been addressed, especially due to the limitation of current operability methods for nonlinear systems in terms of the problem size that they can address.
In this research, we first explore the extension of previously formulated operability algorithms for large-scale linear systems9 to develop a multi-model operability approach for high-dimensional and nonlinear models. This approach employs sensitivity calculations and linear programing tools to quantify the output space as a function of the input space using the minimum number of linearized models that are necessary to adequately describe the nonlinear process operating envelope. The proposed approach is then applied as a tool for process intensification of complex high-dimensional systems. The performed operability calculations consider the multivariable nature of the DMA-MR process, by including the following variables: (i) reactor: diameter, length, temperature, pressure, and input flows; (ii) membrane: area, permeability, and selectivity; and (iii) economics: membrane and catalyst costs. Preliminary results on the application of the operability method as a tool for process intensification show reduction of the DMA-MR footprint (reactor volume and membrane surface area) for an equivalent level of performance. This case study indicates that operability can be a powerful tool for process intensification of membrane reactors and other complex chemical processes.
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