(460c) A Spatial Superstructure Approach to the Optimal Design of Modular Processes and Supply Chains

Modular technologies can be easily transported to different geographical locations to exploit changing market patterns and to enable the recovery of resources that are highly distributed and potentially short-lived [1, 2, 3]. This decentralized approach contrasts with the more traditional monolithic approach in which a large processing system is installed at a fixed location over its entire lifetime [4]. The centralized approach involves investments that can reach billions of US dollars and face significant risk due to changing markets and climate, shortages of resources at a specific location (e.g., water), and changes in the policy landscape (e.g., carbon emissions). Moreover, the mass deployment of small modular units facilitates experimentation, learning, and sharing of best practices that can reduce operational costs (compared to large facilities, in which experimentation is more difficult) [5, 6]. On the downside, economies of scale benefit large systems due to the favorable scaling of throughput with equipment size [7]. Due to complex trade-offs between costs and flexibility, industrial systems will likely evolve into a mixed state in which certain processing tasks are performed in small modular systems while others are performed in large centralized systems. Therefore, identifying optimal spatial process design that involves both centralized and modular technologies is complicated due to complex product interdependencies and varying geological information.

Maximal p-graph structures and superstructures have been widely used in the design of chemical processes, supply chains, and of mass and energy recovery networks [8, 9]. We propose to investigate a new class of hierarchical algorithms to identify optimal configurations and geographical placement of modular systems. These algorithms will be based on a new concept for modular system design that we call a spatial superstructure. We recall that a maximal p-graph structure encodes all possible feasible pathways between raw materials, processing tasks, and intermediate and final products [10]. A superstructure encodes all possible configurations of equipment units and product flows that perform tasks defined by the maximal p-graph (i.e., multiple units might perform the same task) [11, 12]. A spatial superstructure is a superstructure under which equipment units and flows encode positional (geographical) context. This allows us to represent a standard single-site process (under which equipment units are located at the same geographical location) and a spatially distributed process (under which units are distributed over multiple geographical locations) by using the same graph topology. The only distinction between these representations is the transportation modes for the product flows. For instance, short-range transport might use a pipeline while long-range transport might use truck hauling. Spatial superstructures will guide hierarchical branch & bound strategies that search over feasible pathways and modular configurations. This approach contrasts with standard superstructure optimization approaches that search over individual equipment units. With this, we seek to drastically reduce the search space and thus accelerate the search.

Therefore, we propose to derive a computational approach that outputs the connectivity of the spatial superstructure and then, based on such connectivity, it identifies an optimal spatial design that involves both a combination of small-modular and large technologies. Our approach is cast as a mixed-integer multi-objective formulation takes the economy of scales and modularity into account and that considers complicated interdependencies between raw material, intermediate products, and final products. We consider both the annualized cost and the modularity measure as objectives and analyze the trade-offs between these objectives through case studies.

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