(102b) Novel Hybrid Plant Modelling Paradigm That Provides Consistent Solutions from Control to RTO to Scheduling and to Planning

Currently there are three main paradigms for plant modelling: rigorous plant models for design and optimization, simplified models for scheduling and planning, and data-driven MPC models.

Since the late 1960s plant modelling for process design and optimization of operating conditions has been based on describing process streams by mole fractions of individual components, total molar flow, temperature and pressure (moles & fractions paradigm). That enabled use of thermodynamic methods to calculate phase conditions of any stream, as well as development of first-principles based models of unit operations. Resulting plant models are highly nonlinear; they require good initialization of individual unit models and of streams in the flowsheet model in order to converge.

Production planning started to use mathematical models in the early 1950s by using linear programming models to blend gasoline and then proceeded to address the entire refinery production planning (Bodington et al, 1990). These models were based on bulk properties and total stream flows (volumetric or mass). Operation of process units was represented by linearized models, which enabled solution of large-scale multi-period planning models. Planning models today still use the same paradigm, with some modifications to accommodate nonlinear models. Similarly, production scheduling employs models based on bulk flows and properties of streams.

In the late 1970s dynamic matrix controller (DMC) was introduced (Cutler et al, 1979), bringing data-driven plant models into industrial practice. That is the third widely deployed plant modeling paradigm. DMC controller models are the most successful, most widely applied data driven models up to now.

During the last one or two decades more and more attention has been devoted to hybrid models which combine first principles with data-driven models. These efforts have accelerated recently with wide attention given to machine learning and AI methods in the process systems field. Not surprisingly, companies producing plant modelling software view hybrid unit models as just another variation of equipment models and promote that they be integrated as node models in moles & fractions paradigm flowsheet models. Unfortunately, that will not enable moles & fractions based software to be used for anything else beyond what it does already, i.e. process design and detailed optimization of single plant instances.

This work introduces a new paradigm for plant modelling which has two main components:

1. Replace mole flows and fractions by component mass flows. Change from mole to mass enables use of simplified, locally approximated thermodynamic properties (e.g. enthalpy per unit of mass), since [property/mass] is a lot less sensitive to changes in composition than [property/mole], which means that the thermodynamic properties retain their accuracy even if the stream composition is somewhat inaccurate, i.e. it changes due to variations in operating conditions.

Use of locally approximated bulk stream properties means that there is no need to carry mole fractions for each stream since there is no need to invoke a rigorous thermodynamic properties calculations. Combined with using component mass flows, this enables us to build process flowsheets that eliminate a vast majority of nonlinearities which appear in the current generation of rigorous flowsheet models.

2. Introduce detailed plant flow diagram as a common topological structure that is a basis for all plant models (from optimization to scheduling to planning).

An immediate question that arises from that is e.g. how can a scheduling model or multi-period planning model include e.g. all heat exchangers, pumps, etc. and still be solve reliably and quickly? That is possible if each node in a plant network can be instantiated at different levels of abstraction. For instance, a heat exchanger model instantiation for a planning or for a scheduling model may be comprised of only mass balance equations. Such model is linear and its presence in the planning model will not hinder the convergence.

Therefore, we introduce different levels on node and stream abstractions, depending on the purpose of a specific plant model. If one is to optimize operation (or plan or schedule) of a plant, there are different options. Optimization based on mass balances only has the lowest cost since it does not account for energy costs. If one adds energy balances at fixed stream unit enthalpies, the minimal cost increases and the optimum may lie at somewhat different point. Inclusion of energy balances brings us to the vicinity of the true optimum, since the bulk material and energy costs determine the vicinity of the true optimum. If we go one step further and include local approximation of stream unit enthalpy (and other properties), the optimum solution is likely to change but not very far. Note that in the above abstraction hierarchy, the nonlinearity of the plant model depends on the nonlinearities of the node models, since at the flowsheet level streams representation is linear.

In addition to plant models being instantiated at different levels of stream abstraction from one business application to another, different levels of stream abstraction are also needed at different sections of a flowsheet in order to make them easier to solve and meet the business purpose for which the model is built. Similarly, node models need to be able to be instantiated at different levels of abstraction (e.g. material balance only, or material end energy balances, or...).

Please note that moving from coarser (mass balance only) to finer (mass and energy balances) abstractions results in solutions at a coarser level that can be used as initial points for the more detailed abstraction of the model. The unified modeling paradigm proposed by this work enables such inheritance through construction of composite solution algorithms that successively solve the models that are based on the same plant topology.

Use of mass instead of moles also (sometimes) leads to conversion-based (or yield-based) reactor models that are (more) linear vs. nonlinear mole based reactor models. For instance, RGIBBS model of autothermal reactor converting methane to hydrogen and CO is linear if based on mass units and is highly nonlinear if based on mole fractions.

It is proposed that at the node models be linear or almost linear (surrogate) models which are updated from more detailed rigorous or hybrid models. That ensures rapid convergence of large plant models, making the suitable for RTO or for planning or for scheduling. Once the entire model is converged, if an increased accuracy is required, the approximate stream properties or approximate node models are updated and the entire model is resolved.

Above approach requires construction of multi-phase composite algorithms, which converge successively plant models at different abstraction levels until the desired accuracy is attained. We illustrate this via optimization of a blue hydrogen plant model, showing that the results obtained are very close to the rsults from rigorous simulations and at the same time the solutions times are such that solving rapidly multi-period models is not a challenge.