Applications of Markov chains in chemical processes

Tamir, Abraham

doi:10.1016/b978-044482356-4/50007-9

Cited by 30 publications

(34 citation statements)

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“…This is demonstrated by noticing that the system of equations given by (15) can be seen as the forward equations of a continuous-time markov chain process in which the state space is the n s possible species available in the network reaction system [Lawler, 2006]. This approach has been used in chemical physics to model chemical reactions [Tamir, 1998;Kurtz, 2003]. …”

Section: Species State Transition Probabilitiesmentioning

confidence: 99%

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle‐tracking solution for first‐order network reactions

Henri

Fernàndez-García

2014

Water Resources Research

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Modeling multispecies reactive transport in natural systems with strong heterogeneities and complex biochemical reactions is a major challenge for assessing groundwater polluted sites with organic and inorganic contaminants. A large variety of these contaminants react according to serial-parallel reaction networks commonly simplified by a combination of first-order kinetic reactions. In this context, a random-walk particle tracking method is presented. This method is capable of efficiently simulating the motion of particles affected by first-order network reactions in three-dimensional systems, which are represented by spatially variable physical and biochemical coefficients described at high resolution. The approach is based on the development of transition probabilities that describe the likelihood that particles belonging to a given species and location at a given time will be transformed into and moved to another species and location afterward. These probabilities are derived from the solution matrix of the spatial moments governing equations. The method is fully coupled with reactions, free of numerical dispersion and overcomes the inherent numerical problems stemming from the incorporation of heterogeneities to reactive transport codes. In doing this, we demonstrate that the motion of particles follows a standard random walk with time-dependent effective retardation and dispersion parameters that depend on the initial and final chemical state of the particle. The behavior of effective parameters develops as a result of differential retardation effects among species. Moreover, explicit analytic solutions of the transition probability matrix and related particle motions are provided for serial reactions. An example of the effect of heterogeneity on the dechlorination of organic solvents in a threedimensional random porous media shows that the power-law behavior typically observed in conservative tracers breakthrough curves can be largely compromised by the effect of biochemical reactions.

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Section: Species State Transition Probabilitiesmentioning

confidence: 99%

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle‐tracking solution for first‐order network reactions

Henri

Fernàndez-García

2014

Water Resources Research

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“…The probability of transition to a future state from a current state is given by the transition matrix, , where the value of #$ is the probability of transitioning from state to state . Markov chains were first introduced more than a century ago [40], and have since been used in a number of applications including computer performance evaluation [41], web search [42], chemical processes [43], and design team communications [44,45]. model, and the transition probabilities in describe the probability that one operation will be followed by another.…”

Section: Markov Processesmentioning

confidence: 99%

Capturing Human Sequence-Learning Abilities in Configuration Design Tasks through Markov Chains

McComb¹,

Kotovsky²,

Cagan³

2018

Preprint

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Design often involves searching for a solution by iteratively modifying and adjusting a current design. Through this process, designers improve the quality of the current design as well as learning what patterns of operations are most likely to lead to the quickest future improvements. Prior work in psychology has shown that humans can be adept at learning how to apply short sequences of operations for maximum effect while solving a problem. This work explores the sequencing of operations specifically within the domain of engineering design by examining the results of two human studies in which participants created solutions to configuration design problems. First, a statistical analysis of the data from those studies uses Markov chains to show that meaningful operation sequences exist, and can be accurately described using first-order models. Second, this work uses an agent-based modeling framework in conjunction with Markov chain concepts to simulate the performance of teams with and without the ability to learn sequences. These computational studies confirm the assumption that sequence-learning abilities are helpful during design.Journal of Mechanical Design 2

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“…Tamir's textbook [16], which is an excellent and in-depth source of information on Markov chains model, can help one to apply or extend the method. By applying such a procedure, with Dt equal to 0.44 s, the value of R was found to be 0.5, while the two variances are r 2 exp = 1.125 s 2 and r 2 mod = Figure 3.…”

Section: Model Testingmentioning

confidence: 99%

“…To determine the parameters of the RTD model, it was assumed that the experiment mean residence time and variance have to be identical to those of the theoretical model. (16) where (t m ) exp and r 2 exp can be calculated from the RTD curve that is based on the particles measured in the gasifier exit.…”

Section: Model Testingmentioning

confidence: 99%

Stochastic Modeling of the Particle Residence Time Distribution in an Opposed Multi‐Burner Gasifier

Liang

Guo

et al. 2008

Chem Eng & Technol

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The gasification technology of impinging streams has been extensively applied to chemical production and power generation. Particle residence time distribution (RTD) is an important parameter required for modeling, designing and optimization of an impinging stream gasifier. A stochastic mathematical model based on the Markov chains model is developed for the opposed multi-burner gasifier (OMBG), which closely describes the behavior of the flow pattern and particle RTD in the gasification system. The model simulates the motion of single particle moving in the gasifier using the Markov chains. The predicted results give a reasonable fit to the experimental data. This shows that the flow process of particles in the gasifier has recirculation eddies, which have a downward flow direction near the downflow core and an upward flow direction near the wall, but no short-circuit. Finally, the effect of particle flux rate on the RTD is predicted, and the contrast between gas and particles RTDs at a laboratory scale and in an industrial gasifier are presented.

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Applications of Markov chains in chemical processes

Cited by 30 publications

References 0 publications

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle‐tracking solution for first‐order network reactions

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle‐tracking solution for first‐order network reactions

Capturing Human Sequence-Learning Abilities in Configuration Design Tasks through Markov Chains

Stochastic Modeling of the Particle Residence Time Distribution in an Opposed Multi‐Burner Gasifier

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