377210 Recent Results and Insights into Using Graphics Processors (GPUs) for Attainable Regions Computations
The task of computing the limits of achievability for a system of reactions and associated kinetics finds special importance in the design of efficient chemical reactors, used in industrially relevant processes. Knowledge of these limits helps us to understand what potential improvements could be made to an existing reactor design, and further assists in setting performance targets for new, potentially novel, reactor designs.
For the past three decades, computation of these limits for chemical reactor networks specifically has been made possible by the idea of the Attainable Region (AR). The AR for a system of reactions represents the collection of all states achievable by the system for a given set of kinetics and initial conditions. The AR is represented as the set of all compositions achievable in a reactive system. It is commonly plotted as a convex polytope in n-dimensional composition space. The dimension and complexity of this space is determined by the number of components participating in the reactions as well as the number of independent reactions associated with the system. From this it follows that problems in AR theory revolve around understanding the nature of convex polytopes in higher dimensional spaces, understanding the characteristic structure of these regions, and also understanding how to compute the AR for a given set of component reactions, and feed points.
Recently, a large interest in AR theory has focussed towards developing novel computer algorithms which help to construct the AR via numerical means. Due to the higher dimensional and geometric nature of Attainable Regions, computation of the AR for a system of moderate complexity is often not easy to perform by hand. Rather, one must rely on automated AR construction techniques to assist in finding these regions.
Automated AR construction is often difficult in itself. The problem of determining a higher dimensional convex polytope, associated with a system of non-linear reaction kinetics and reactor models, is a complex procedure. Additionally, the large amount of data generated by the AR imposes a large computational workload even for problems of moderate complexity. Computation of the AR has hence only been achieved for relatively small systems, residing in two or three dimensions usually.
In roughly the same timeframe as the development of AR theory, rapid advances in computer architecture and high performance computing (HPC) have also been made. The increase in computational power has allowed researchers to investigate increasingly complex problems in science and engineering. More specialised technologies and techniques used in computer science have not always been widely adopted in mainstream chemical engineering research - HPC applications are often more widely noticed in fields of computational fluid dynamics (CFD) and catalysis rather than in the fields of computational reactor and process synthesis for instance.
More recently, the use of graphics processing units (GPUs) in general purpose computations has allowed for computationally demanding scientific discovery to be carried out on the computer. GPUs are highly powerful devices which are able to throughput a large number of floating point operations per cycle. Current GPUs are often considered to be an order of magnitude more powerful and are considered to be far more energy efficient when compared to traditional CPUs. It is for this reason that many HPC applications and computer codes have recently directed focus towards implementation on GPUs. Nevertheless, adoption of GPUs to computationally strenuous problems in chemical engineering has been predominantly in CFD-related fields - little research into the use of GPUs to reactor network synthesis problems has been achieved thus far. Unlike CPUs however, which are fast highly generalised processors, GPUs rely on parallel computation.
In this work, we highlight a number of advancements and insights gained, specifically to AR construction techniques, using GPUs to carry out computations. The computationally demanding tasks required by current AR construction algorithms warrants the use of GPUs. Recent results have shown how large gains in construction time and computational efficiency can be obtained using GPUs when the algorithm can be interpreted in a parallel manner. Dependent on the complexity and type of AR problem investigated, speed ups in construction time of 2x to 60x have already been observed. However, additional improvements and advances are still possible with adequate understanding of how to better exploit GPU performance in AR applications. This allows for more complex and industrially relevant systems to be considered which would have been computationally prohibitive in the past.
Furthermore, existing AR construction algorithms, which were in the past implemented on a serial CPU, may also be adapted for use with GPUs. The success and challenges of these implementations is also a topic of discussion in this work. A number of GPU implementations, both to existing algorithms, as well as to entirely new algorithms are currently being investigated. We wish to highlight a number of these issues in this work, discuss implementation challenges currently being faced with recent methods, and reflect on possible future directions using GPUs specifically in AR research.
The information generated by understanding the AR for a system may be valuable in the design of more efficient chemical reactors, however its computation has been limited to relatively small systems currently. The use of GPUs to accelerate AR computations has already shown to be beneficial, although greater performance may be gained with further research in this field. This may lead to more robust and computationally efficient AR construction methods in the future.
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