Use trial and error to find X2. P f See Polymath program Pf. This is what is observed at small values of X. The reactor volumes are absurdly large. P Problem involves estimating the volume of three reactors from a picture. The door on the side of the building was used as a reference. It was assumed to be 8 ft high. P No solution necessary. See Polymath program P The area of the rectangle is approximately The area of the rectangle is approximately 7.
The necessary catalyst weight is approximately 22 kg. The necessary catalyst weight is approximately 13 kg. P f P g For different -rA vs. X curves, reactors should be arranged so that the smallest amount of catalyst is needed to give the maximum conversion. One useful heuristic is that for curves with a negative slope, it is generally better to use a CSTR. Similarly, when a curve has a positive slope, it is generally better to use a PBR.
P a Individualized Solution P b 1 In order to find the age of the baby hippo, we need to know the volume of the stomach. The Levenspiel Plot is shown: Autocatalytic Reaction 5 4. For the intestine, the Levenspiel plot for the intestine is shown below.
The outlet conversion is 0. We first plot the inverse of the reaction rate versus conversion. For now, we will assume that conversion X will be less that 0.
CDP2-A g Critique the answers to this problem. The rate of reaction for this problem is extremely small, and the flow rate is quite large.
To obtain the desired conversion, it would require a reactor of geological proportions a CSTR or PFR approximately the size of the Los Angeles Basin , or as we saw in the case of the batch reactor, a very long time. P a Note: This problem can have many solutions as data fitting can be done in many ways. See Polymath program Pfireflies. See Polymath program Pcrickets. See Polymath program Pants. So activity of bees, ants, crickets and fireflies follow Arrhenius model.
So activity increases with an increase in temperature. Activation energies for fireflies and crickets are almost the same. Insect Activation Energy Cricket Firefly Ant Honeybee P d There is a limit to temperature for which data for any one of he insect can be extrapolate. Data which would be helpful is the maximum and the minimum temperature that these insects can endure before death.
Therefore, even if extrapolation gives us a value that looks reasonable, at certain temperature it could be useless. The temperature increases as we go from top to bottom of the column and consequently the rate of corrosion should increase.
There is virtually no HCN in the bottom of the column. These two opposing factors results in the maximum of the corrosion rate somewhere around the middle of the column. Therefore doubling the temperature will not necessarily double the reaction rate, and therefore halve the cooking time. When you bake the potato, the heat transfer coefficient is smaller, but the temperature can be more than double that of boiling water.
Therefore, So, option 4 is correct. For any reaction, the rate law cannot be written on the basis of the stoichiometric equation. It can only be found out using experimental data. In the evaluation of the specific reaction rate constant at o C the gas constant that should have been used was 8.
In the same equation, the temperatures used should have been in K rather than oC. The units for calculated k at oC are incorrect. The dimension of the reaction rate obtained is incorrect.
This is due to the fact that the rate law that has been taken is wrong. P c Example For the concentration of N2 to be constant, the volume of reactor must be constant. Therefore the reverse reaction decreases. The units of the rate constant, k, will differ depending on whether partial pressure or concentration units are used.
See below for an example. This can be done with mass balances on each element involved in the reaction. Once all the coefficients are found, you can then calculate the yield coefficients by simply assuming the reaction proceeds to completion and calculating the ending mass of the cells.
The rate law is to be obtained from the experimental data. It has been mentioned as an elementary reaction in the problem statement but in the proposed solution the rate law is based on the reaction equation that has been divided by stoichiometric coefficient of A. P a Example There would be no error! The initial liquid phase concentration remains the same. P h Individualized solution. P i Individualized solution. So, we get 0.
But actually it is a second order reaction. Also when we increase the particle size from position A, we reach at point B, again there is a decrease in the conversion. Assume the reaction temperature is K. P f The points of the problem are: 1 To note the significant differences in processing times at different temperature i. One minute to react and to fill and empty. It does not matter if the reactor is red or black.
In case of a , For a batch reactor. PFR with pressure drop: Alter the Polymath equations from part c. See Polymath program Pf-pressure. CB 0 L 10 ft lb mol P psig Assume that the reactions are irreversible and first order. Case 1: gal v0 X 0. Also, the reverse reaction begins to overtake the forward reaction near the exit of the reactor. See Polymath program Pc. The cost of this storage could prove to be the more expensive alternative. A cost analysis needs to be done to determine which situation would be optimal.
What is the maximum number of moles of ethylene glycol CH2OH 2 you can make in one 24 hour period? The feed rate of ethylene cholorhydrin will be adjusted so that the volume of fluid at the end of the reaction time will be dm3. Now suppose CO2 leaves the reactor as fast as it is formed.
First try equal number of moles of A and B added to react. See Polymath program Pb. This results in a conversion of. CDGA d We must reexamine the mole balance used in parts a-c. ICE ebooks.
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Google eBookstore. PDF Books World. C Programming ebooks. JAVA ebooks. It is thus necessary to understand where are the bottlenecks, both in terms of fundamental knowledge and technological aspects, limiting the possibility to realize the challenges related to this transition and reach the target to make sustainable and economic these novel technologies. These two aspects should be developed in an integrated manner, rather than sequential, as exemplified from the development of photoelectrocatalytic materials and devices [ 13 ].
In addition, still often the specific research directions are not based on an analysis of how the technology should be implemented. For example, producing H 2 and O 2 from water splitting, without generating them in physically separated zones, creates major issues of safety due to the formation of H 2 -O 2 explosive mixtures and relevant costs for downstream separation to reach the required purity.
There are also often relevant aspects underestimated. Materials development should be related to engineering and operations of the device. There are several of such a type of examples, in which research, even if excellent from the scientific perspective, is not put in the right technological perspective. While progresses in fundaments are always necessary, there is the need to accelerate the development of the technologies enabling to meet the necessary targets, in the case of energy and chemistry in transition.
Note also that a successful transitional strategy requires identifying critical processes in a timeline perspective, with solutions for short-, medium- and long-term [ 14 ]. The crucial point is that cost-effective solutions are only those integrating within the current systems and value chains, to minimize investments and thus reduce the initial cost barriers.
A proper synchronism between technological capabilities and socio-economic context is the decisive issue. We feel that today the limiting factor is the capability to identify properly the key aspects on which focus development areas from the timeline perspective of a fast evolving scenario for chemistry and energy in transition.
This review will thus analyze, from a personal perspective, the possible impact on chemical reaction technologies deriving from the transition in energy and chemistry, with focus on needs, gaps and opportunities. There are various motivations indicating the need to decrease this very high dependence.
Among them: i decrease greenhouse gas emissions in order to contribute to climate change mitigation and to reach CO 2 emission targets, ii security and diversification of resources, iii promote rural development by using the local resources, and iv use of C-sources less depending on fluctuations and uncertainty in future costs of fossil raw materials.
It is often argued that cheap oil will be still available in the future to make useless the development of alternative routes. The same argument was used up to few years ago to indicate that energy from fossil fuels would remain also in the future the most competitive one. Recent reports like that by IRENA [ 4 ] have demonstrated that instead already today this is no long valid. In the area of petrochemistry, uncertain in predicting future costs is already a major factor determining investments in new plants, with a panorama where very few new technologies have been put on the market in the last decade.
The future decade for chemical companies is market from the need to reinvent their interface with oil refining and manage the transition to a circular economy [ 18 ]. In fact, the last decade has been characterized for petrochemical companies from an erosion in the product margin, due to low-cost of feeds. Consequently, new models for value creation are necessary [ 18 ], because the advantaged-feedstock-opportunity window is closing.
Crude-to-chemicals COTC , i. Silura OCM oxidative coupling of methane process is one example of technology under development attracting increasing interest. On the other hand, these technologies are interesting for countries with low fossil fuel costs and one major challenge is the expected high capital investment required to construct the plants.
In fact, an opposite tendency for chemical industry is to reduce the rising CAPEX costs [ 18 ], even more critical when cost forecast are difficult, and thus to adopt strategic agility [ 22 ], i. Olefins and aromatics could be produced alternatively from CO 2 and H 2 , also in direct processes [ 23 ], and these technologies are instead suitable for distributed, small size, productions. There are additional benefits in terms of incentives for CO 2 reduction: i promotion of bioeconomy CO 2 could derive from biogas or fermentation processes and integration with renewable energy sources [ 24 , 25 ], ii integration within local economy, iii promotion of circular economy, etc.
Thus, it may be argued whether COTC and OCM technologies will be game changer for chemicals industry, as announced, or instead, more likely, just a piece in the puzzle for transition in economy.
The main difference between the two approaches, apart from large vs. Distributed processes allow instead a much better integration into local economies, including aspects related to circular economy [ 26 ].
It is evident that there are two different approaches, with the latter producing raw materials for chemicals from waste and renewable energy being based on a different, more sustainable economic model of development. The analysis of the two production models should be thus not based on the traditional economic models and concepts, such as scale-economy. It is necessary to use new assessment tools, which include the capability to analyze socio-economical macro-trends, market evolution, competitiveness related to entire ecosystems, sustainability and integration into territory rather than globalization , non-linear dynamic of changes and costs evolution, extended life-cycle cost and social analysis [ 18 , 27 , 28 ].
Therefore, new techno-economic engineering assessment tools should be developed. In transition periods, new conceptual assessment modes, including to evaluate the feasibility from a chemical engineering viewpoint, are necessary and it is historically demonstrated that in the absence of this approach a company may rapidly lose their market positions being their innovation capacity a crucial aspect in chemical production rapidly lost [ 17 ].
Waste-to-Chemicals WtC , as argued from above analysis, is an important element of the strategy to diversify carbon sources for chemical production. Biomass use is another relevant component of this strategy [ 25 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ]. However, when based on dedicated biomass i. From a process engineering perspective, the major issues are related to the presence of a complex matrix, which should be transformed to high purity chemicals in the presence of several contaminants, which can influence the use of catalysts.
Solutions have been identified and made possible, but in general terms, this translates to high costs of production. Therefore, differently from a decade or more ago, when a large optimism was present, today the general perception is that the production of chemicals directly from dedicated biomass sources is applicable in some selected cases, but is not a general solution. To be competitive to fossil fuels use for chemical production, it is necessary to i use quite cheap raw materials, ii integrate well into a regional strategy also in terms of plant size , including circular economy, iii use technologies flexible in handling a variety of biomass sources, and iv be flexible in the production of different chemicals, minimizing costs for operations, especially purification and separation [ 36 ].
The use of waste biomass, which includes, but is not limited to, the organic fraction of municipal solid waste — MSW, which is called in different ways, one of them being RdF refuse-derived fuel , is clearly an opportunity as a low cost raw material. In fact, it is a side production with a cost for disposal.
Its valorization is often limited to thermal incineration. There are various attempts for alternative valorization methodologies to create a waste biorefinery [ 37 , 38 ], but reuse is limited to very specific type of biomass waste.
For general purpose technologies, following above indications, it is necessary a process technology able to handle a variety of waste sources, including MSW, to reach the necessary dimension for a regional waste biorefinery, but minimizing the transport of raw materials from long distances, i. There are essentially two routes to produce chemicals from organic waste, particularly from MSW and excluding reuse or recycling technologies which are tailored for specific waste and not suited for mixed wastes: pyrolysis [ 39 , 40 , 41 ] and gasification [ 42 , 43 , 44 ].
By fast pyrolysis a liquid fuel and a gas component, with the former especially characterized by a large range of products and quite low quality, are produced with eventually also a solid residue.
Severe upgrading treatments are necessary, and the pyrolysis liquid product can be essentially used only as fuel. The syngas instead produced in the gasification process can be easier purified and further processed to produce, in a flexible way, different chemicals or fuel components [ 36 ], by using essentially available technologies.
This flexibility is an important added-value term allowing a much better tailoring to different demands. This is a crucial aspect to minimize developing costs for WtC, by adapting to the large variety of locals demands. We thus limit the further discussion to waste gasification as the first step, to produce syngas to be further converted to different chemicals. Options in gasifiers for the WtC process. The latter produces a hot gas to be used only for electrical energy generation or heat recovery.
In gasification, instead, a syngas a CO-CO 2 -H 2 mixture , with CO x to H 2 ratios depending on operation conditions and feed, is produced by using a controlled air or O 2 feed.
The oxygen is typically one-fifth to one-third of the stoichiometric amount. Steam and CO 2 , in some cases, are also co-fed. The heat for gasification derives from the partial biomass combustion in the gasifier.
Biomass gasification has been extensively analyzed and discussed [ 44 , 45 , 46 ], but the used of mixed feeds, particularly containing the organic fraction of MSW, determines specific issues [ 47 , 48 , 49 ]. There are various crucial aspects in the design of the reactor: i the gasifier should be designed to produce a tar-free syngas, because otherwise downstream cleaning is costly, ii the formation of CO 2 should be minimized, iii the inorganic part of the biowaste should be eliminated in a form allowing an easy disposal, and iv pretreatment of the biowaste should be minimized as much as possible.
Fluidized beds for gasification processes allow high conversion and low tar yields, due to high heat and mass transfer rates, excellent gas-solid contact and good control of temperature. Besides the higher reactor costs and operations, biowaste should be grinded and sieved to small particles of uniform size, requiring additional costs. Plasma gasification is of rising interest, for the possibility to obtain complete cracking of tar compounds and high gas yields [ 50 ].
Microwave plasma shows various advantages with respect to alternative ways to produce the plasma [ 51 ], but still there are many challenges to solve for industrial implementation. Gasification in supercritical or near-to-supercritical water [ 52 , 54 , 55 ] is another valuable option, but also having main challenges related to cost, thermal efficiency, plugging and corrosion problems. The general question is that may be often unclear when and for which cases these different options should be applied.
There are clear scale-up and cost issues, and different situations for which one technology should be preferable over the other [ 56 ]. Most of the considerations, however, refer to either gasification for energy purposes, or for H 2 production, with the production of optimal syngas production and integration with downstream processing to valuable chemicals scarcely considered. There are specific, but interesting cases to consider, as the MSW treatment in small touristic islands, where the produced MSW actually needs to be costly transported by ship to remote areas for disposal.
The gasification in supercritical water allows to have compact reactors, and reduce downstream cleaning processes.
The syngas could be upgraded to methane for local use, being these islands not reached by the natural gas grid. This is an example of a case when a technology otherwise too costly can be instead considered. The missing knowledge are thus in suitable multicriteria assessment tools able to guide selection along the different solutions and technologies, and to identify the engineering aspects limiting the overall performances. Robustness, minimization of downstream operations, flexibility in variable composition feed handling, minimization of sludges downstream treatment, safety aspects are some of the keyword to consider for the selection.
We believe that based on these aspects, the use of a high temperature HT converter as that presented in Fig. The biowaste RdF is fed from the side. A relevant advantage is that the reactor allows to feed relative large particles, and thus avoiding grinding costs. Reproduced with permission from ref. Copyright Elsevier, The use of RdF and other biowaste is possible, with influence on the composition of the syngas.
Temporal variations in the syngas flowrate and composition derive from the non-uniformity of the reactor bed, related to the use of large and non-uniform in size RdF particles. The partial clogging of the bed bridge formation later collapsing, is also another mechanism causing variations of syngas. However, a dimensioned downstream gasometer and operations with multiple parallel units, can avoid that this could be a problem in operations. There are some main issues in this reactor.
The first is that the very high-temperature operations create problems of lifetime of the refractory materials used for the reactor walls, with thus the need of frequent maintenance. The second, is that modelling of this type of gasifier is difficult and thus of its optimization. The third issue is related to the possibility of using catalysts to increase conversion and reduce the temperature of operations. Catalytic gasification is a valuable option to promote energy efficiency [ 45 , 59 , 60 ], but only in few cases it is applied to improve MSW gasification.
Ni-based catalysts [ 61 , 62 ] could be used, but they cannot be utilized in a gasifier as that shown in Fig. Low costs catalysts should be used to be continuously co-fed with RdF, remaining then in the molten slug. Olivine or similar natural materials, which are available in large amount at low cost, could be used [ 63 , 64 ]. Alternatively, a catalytic bed at the top of the gasifier could be used to improve the polishing of the syngas, but catalysts stable at high temperature and to the presence of fly ashes, tars, metals and salts should be developed.
Among other aspects, these three areas evidence who new chemical reaction technologies challenges are opened from the development of new technologies for using biowaste as carbon source. These impurities should be removed before the downstream catalytic processes Fig.
Downstream operations to upgrade syngas to chemicals are in principle similar to those already available, but with catalysts and operations that should be specifically tailored for four aspects: i the typical higher CO 2 content with respect to current operations, ii the higher presence of impurities, iii the need of optimal operations in smaller reactor units and iv fluctuations in the feed flow rate and composition.
These fluctuations can be minimized by a downstream gasometer, but remain higher than in conventional reactors, for example for methanol synthesis. Also in this case, thus new dedicated engineering solutions have to be developed.
They are feasible from a techno-economic perspective [ 36 , 57 , 58 ]. The use of mixed RdF and biowaste from agro-food production is also possible. In addition, with respect to incineration of the same waste, there are environmental advantages. For example, in waste-to-urea process, a reduction of about 0. This short excursus on some aspects of the development of novel routes for the use of alternative carbon sources evidences thus that many scientific and technological questions are opened by addressing this possibility.
The aspects discussed are examples, and will thus not exclude other areas. However, already they remark the complexity of the problem to be addressed in a short term. It is thus very important to focus the analysis on the most critical aspects, and guide scientific advances by using a more holistic view of the full problems. The direct use of renewable energy sources RES in chemical production, i.
Rather than use heat produced from fossil fuels to run operations, electrical energy deriving from renewable sources should be used. This is not only a technological change in supplying the energy for the chemical transformation, but determines a full change in the engineering of chemical processes design, where heat recovery and transfer is a major designing element and one of the key factors determining the need to have large plants.
Moving in this direction will allow passing to plants optimal for small-medium size distributed productions. Even more important, the scale-up in electrocatalytic processes is by parallel units, differently from the conventional approach.
Parallelized production will permit a much greater flexibility in production to follow better market demands and fluctuations and especially a faster time to market. CAPEX is higher, but compensated from above advantages. Thus, electrification of the chemical industry is not only a technological change, but a full transformation in the engineering, design and marketing of chemical processes. As commented earlier, conventional techno-economics assessment models are not able to consider these aspects.
This is one of the reasons why in these transitional periods, several of the conservative predictions fail to be correct and determine relevant marked losses in several companies. Thus, it integrate RES in the chemical production requires major technological and scientific changes, because catalysts, reactors, operations have to be fully redesigned. There are different ways by which RES can be coupled to chemical production: use of electrons electrical energy produced from renewable sources in electrocatalytic or non-thermal plasma processes, and use of photons in photocatalytic processes [ 65 ].
We omit here to consider instead processes, where concentrated solar power CSP is used to heat the reactor, or instead radiations like microwave are used for heating the reaction medium. Between photo- and electro-driven processes, we consider the latter closest to industrial exploitation [ 66 ], although both are clearly relevant. Their combination in a single photo-electrocatalytic PEC reactor is the basis to develop artificial-leaf type devices in the future [ 67 , 68 , 69 ].
For example, 2-butene has four carbon atoms and eight hydrogen atoms; however, the atoms in this compound can form two different arrangements. Therefore, we consider them as two different species, even though each has the same number of atoms of each element.
When has a We say that a chemical reaction has taken place when a detectable num- chemical reaction ber of molecules of one or more species have lost their identity and assumed a taken place? In this classical approach to chemical change, it is assumed that the total mass is neither cre- ated nor destroyed when a chemical reaction occurs. The mass referred to is the total collective mass of all the different species in the system. However, when considering the individual species involved in a particular reaction, we do speak of the rate of disappearance of mass of a particular species.
The rate of disappearance of a species, say species A, is the number of A molecules that lose their chemical identity per unit time per unit volume through the breaking and subsequent re-forming of chemical bonds during the course of the reac- tion. There are three basic ways a species may lose its chemical identity: decomposition, combination, and isomerization.
In decomposition, the mole- cule loses its identity by being broken down into smaller molecules, atoms, or atom fragments. A second way that a molecule may lose its chemical identity is through combination with another molecule or atom. In the above reaction, the propylene molecule would lose its chemical identity if the reaction were carried out in the reverse direction, so that it combined with benzene to form cumene. The rate at which a given chemical reaction proceeds can be expressed in several ways.
To illustrate, consider the reaction of chlorobenzene and chloral to produce the banned insecticide DDT dichlorodiphenyl-trichloroethane in the presence of fuming sulfuric acid. What is —rA? The rate of reaction, —rA, is the number of moles of A e. Example 1—1 Chloral is being consumed at a rate of 10 moles per second per m3 when reacting with chlorobenzene to form DDT and water in the reaction described above. The symbol rj is the rate of formation generation of species j.
If species The convention j is a product, then rj will be a positive number. The rate of reaction, —rA, is the rate of disappearance of reactant A and must be a positive number. Heterogeneous reactions involve more than one phase. In heterogeneous reaction systems, the rate of reaction is usually expressed in measures other than volume, such as reaction surface area or catalyst weight. For a gas-solid catalytic reaction, the gas molecules must interact with the solid catalyst sur- face for the reaction to take place, as described in Chapter It is the number of moles of species j generated per unit volume per unit time.
We can say four things about the reaction rate rj. The chemical reaction rate law is essentially an algebraic equation involving concentration, not a differential equation. Crynes and H. Fogler, eds. Equation states that the rate of disappearance of A is equal to a rate constant k which is a function of temperature times the square The convention of the concentration of A.
As noted earlier, by convention, rA is the rate of for- mation of A; consequently, —rA is the rate of disappearance of A. Throughout this book, the phrase rate of generation means exactly the same as the phrase rate of formation, and these phrases are used interchangeably.
The volume enclosed by these boundaries is referred to as the system volume. We shall perform a mole balance on species j in a system volume, where species j represents the particular chemical species of interest, such as water or NaOH Figure Figure Mole balance on species j in a system volume, V. If all the system variables e.
Figure Dividing up the system volume, V. The total rate of generation within the system volume is the sum of all the rates of generation in each of the subvolumes. The reactor can be charged i. Section 1. It is referred to as the continuous-stirred used for?
Equipment on the CRE Web site. It is normally operated at steady state and is assumed to be perfectly mixed; consequently, there is no time dependence or position dependence of the temperature, concentration, or reaction rate inside the CSTR. That is, every variable is the same at every point inside the reactor. Because the temperature and concentration are identical everywhere within the reaction vessel, they are the same at the exit point as they are elsewhere in the tank.
Thus, the temperature and concentration in the exit stream are modeled as being the same as those inside the reactor. In systems where mixing is highly nonideal, the well-mixed model is inadequate, and we must resort to other modeling techniques, such as residence time distributions, to obtain meaningful results. This topic of nonideal mixing is discussed in Chapters 16, 17, and 18 on nonideal reactors. We note that the CSTR is modeled such that the conditions in the exit stream e.
It consists of a cylindrical pipe and is When is a tubular normally operated at steady state, as is the CSTR. Tubular reactors are used reactor most often used? A schematic and a photograph of industrial tubular reactors are shown in Figure In modeling the tubular reactor, we assume that the concentration varies continuously in the axial direction through the reactor. Consequently, the reaction rate, which is a function of con- centration for all but zero-order reactions, will also vary axially.
Figure b Tubular reactor photo. Longitudinal tubular reactor. McGraw-Hill, Inc. That is, there is no radial variation in reaction rate, and the reactor is referred to as a plug-flow reactor PFR. Plug flow—no radial variations in velocity, concentration, temperature, or reaction rate Also see PRS and Visual Encyclope- dia of Equipment.
However, we see that by applying Equation , the result would yield the same equation i. As the reac- tants proceed down the reactor, A is consumed by chemical reaction and B is produced.
The greater the mass of a given catalyst, the greater the reactive surface area. Consequently, the reaction rate is based on mass of solid catalyst, W, rather than on reactor volume, V. Figure shows a schematic of an industrial catalytic reactor with vertical tubes packed with solid catalyst. Figure Longitudinal catalytic packed-bed reactor.
The derivation of the design equation PBR Mole Balance for a packed-bed catalytic reactor PBR will be carried out in a manner analo- gous to the development of the tubular design equation. To accomplish this der- ivation, we simply replace the volume coordinate in Equation with the catalyst mass i.
Example 1—2 How Large Is It? Solution 1. Sketch CA as a function of V. CA0 CA 0. Calculate V. Again using Equation E We see that a reactor volume of 0. The more species A consumed and converted to product B, the larger must be the reactor volume V. The purpose of the example was to give a vision of the types of calculations we will be carrying out as we study chemical reaction engineering CRE. There are also links to view reactors on different Web sites.
Susan Montgomery and her students at the University of Michigan. Chapter 1 Summary 23 The CRE Web site describes industrial reactors, along with typical feed and operating conditions. The goal of this text is to weave the fundamentals of chemical reaction engineering into a structure or algorithm that is easy to use and apply to a variety of problems. By convention, —rA is the rate of disappearance of species A and rA is the rate of formation of species A.
Mole balances on species A in four common reactors are shown in Table S Summary Notes 2. Web Material A. Problem-Solving Algorithm B. Getting Unstuck on a Problem This Web site gives tips on how to overcome mental barriers in problem solving. Smog in L. Web module includes a Living Example Problem.
Getting Unstuck C. Interactive Computer Games A. Quiz Show I 4. The reactor portion of this encyclopedia is included on the CRE Web site.
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