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Introduction to Optimization Modeling for Petroleum Refineries

1.1 Background

The topological optimization problem for determining an optimal configuration of a petroleum refinery can be addressed by a logic-based modeling approach within a mixed-integer superstructure optimization framework. The focus lies in investigating and advancing existing optimization approaches and strategies of employing logical constraints to conceptual process synthesis and design problems within the framework of conventional mixed-integer linear programming (MILP) (Nemhauser and Wolsey 1988) and alternate generalized disjunctive programming (GDP) (Grossmann and Trespalacios 2013). This work attempts to address the following considerations:

• How the formulation of design specifications in a synthesis problem can be accomplished using logical constraints in a mixed-logical-and-integer optimization model to enrich the problem representation by way of incorporating past design experience, engineering knowledge, and heuristics;
• How structural specifications on the interconnectivity relationships by space (states) and function (tasks) should be properly formulated using logical constraints within a mixed-integer optimization model.

The resulting modeling technique is illustrated on a numerical example, which is based on a case study involving alternative processing routes of naphtha in a refinery.

Process synthesis or conceptual process design is concerned with the identification of the best flowsheet structure to perform a given task. The following variants are mainly available in the literature to address this class of problem: (1) the heuristics method, notably the hierarchical decomposition of design decisions procedure; (2) the technique based on thermodynamic targets and physical insights as exemplified by pinch analysis; and (3) the algorithmic approach that utilizes optimization based on the construction of a superstructure that seeks to represent all feasible process flowsheets (Seider et al. 2009).

The intricate complexities associated with process synthesis problem in general and the refinery design problem in specific necessitates the development and implementation of a systematic and automated approach that efficiently and rigorously integrates the elaborate interactions involving the design decision variables. This work aims to extend the superstructure optimization-based approach of using logical constraints (Raman and Grossmann 1991, 1992, 1993a,b) within a MILP to incorporate qualitative design knowledge based on engineering experience and heuristics in modeling the major process flows in a refinery. These constraints adopt discrete integer decision variables of the binary 0-1 type to model the existence of a refinery process unit and the associated stream piping interconnections (which are effectively pipelines) in a network structure, in which a value of one for a 0-1 variable designates that a unit is present in the optimal structure while the converse is true for a value of zero.

Our work serves to further substantiate that the use of 0-1 decision variables offers a more natural and powerful modeling approach compared to the conventional linear programming technique that employs only continuous decision variables. It also affords the convenience of representing fixed-cost charges in the objective function formulation. A variation in the use of integer variables in optimization model formulations has been widely reported (Williams 1999).

Optimization is the core objective of chemical process design as exemplified through the synthesis of petroleum refinery configurations (Khor and Varvarezos 2017). Selecting the best among a set of possible solutions requires good engineering judgment to critically analyze the process with respect to the desired performance objectives. It is crucial to identify and strike a balance between the competing objectives of realizing the largest production, the greatest profit, the minimum cost, the least energy usage, and so on. This ensures improved plant performance through improved yields of valuable products, higher processing rates, longer time between shutdowns, and reduced maintenance costs. In order to find the best solution within the given constraints and flexibilities, a trade-off usually exists between capital and operating costs.

Although the design stage only takes up about 2% or 3% of a project expenditure, decisions made during this phase have an immense impact on plant economic performance because approximately 80% of the capital and operating expenses of the final plant are fixed during the design stage (Biegler et al. 1997). Hence, the necessity of developing systematic methods in chemical process design has led to two major strategies for process synthesis in determining an optimal configuration of a flowsheet and its operating condition.

In the first strategy, the problem can be solved in a sequential form involving decomposition, fixing some elements in the flowsheet, and then using heuristic rules to determine changes in the flowsheet that may lead to an improved solution. An example of such a strategy is the sequential hierarchical decomposition strategy by Douglas (1985, 1988). However, the sequential nature of the decisions and the heuristic rules that are used can lead to suboptimal designs. Douglas claims that only 1% of all designs are ever implemented in practice and hence this screening procedure avoids meticulous evaluation of most alternatives. It is not possible to rigorously produce an optimal design because the sequential nature of flowsheet synthesis cannot take all interactions among the design variables into consideration. Furthermore, the exponential number of possible topologies coupled with the multitude of process technology options decrease the chances of realizing the best design.

The second strategy that can be applied to solve a process synthesis problem is based on simultaneous optimization using mathematical programming (Grossmann 1996). This strategy requires the postulation of a superstructure, which includes a set of equipment that are potentially selected in the final flowsheet and their interconnections. The equations pertaining to the equipment and their interconnectivity in addition to the operating condition constraints are formulated in an optimization model with an objective function that typically minimizes cost or maximizes profit. In particular, such a formulation requires discrete variables to represent the choices of equipment besides continuous variables on the process parameters (e.g. flow rates) with which the model becomes a mixed-integer linear or nonlinear program (MILP or MINLP). In this regard, Grossmann (1996) states that an advantage of mathematical programming strategy is that they can perform simultaneous optimization of the configuration (as described by the discrete decisions) and operating conditions (as described by the continuous decisions).

Designing a petroleum refinery configuration is challenging and complex. Many factors such as design specifications and structural specifications have to be considered and incorporated at the conceptual design stage to arrive at an optimum configuration of the refinery flowsheet (Khor et al. 2011). Hierarchical decomposition uses heuristics, shortcut design procedures, and engineering experience to develop an initial base case, but doing so is possibly time-consuming, whereas the result may not necessarily guarantee an optimal solution. Thus, developing or adopting an automated systematic procedure in the refinery configuration design endeavor can significantly improve the decision-making process. The task can be achieved via optimization or mathematical programming approach by representing the problem through a superstructure and formulating the corresponding optimization model, which is solved to obtain an optimal configuration based on inputs of crude oils to be processed and final products to meet market demands while complying with the requisite constraints.

Figure 1.1 shows the rapidly rising downstream capital cost index from 2005 to 2019. Thus, an automated approach that can guarantee an optimal refinery design is increasingly important and sought after in the face of increased capital costs, higher energy costs, and depleting resources. At the same time, heightened fuel consumption leads to raised demand for petroleum products despite tight supplies with the consequential need to construct new grassroots petroleum refineries.

With increasingly stricter environmental regulations and emphasis on clean fuels, new refineries need to adhere to narrower operating margins and more stringent product specifications. This situation adds to the degree of complexity in designing refineries, which at present is already time-consuming with the intricacies of the interplay among the various factors including public opinions and permitting processes. All these considerations give rise to an exponential number of possible refinery topologies or configurations that can adequately meet current economic, operating, and environmental requirements.

We consider the following superstructure optimization problem for a refinery topology design. Given the following data: fixed production amounts of desired products, available process units and ranges of their capacities, and cost of crude oil and process units, we wish to determine an optimal configuration in terms of the...