Structure and Content of BEng Chemical Engineering Programmes in the UK, Relative to the Frontiers in Chemical Engineering Education Model

The Frontiers in Chemical Engineering Education initiative in the USA in the early 2000s proposed a reformed chemical engineering curriculum organised around the three themes of Molecular transformations, Multiscale analysis and a Systems view. It was subsequently observed that few departments in the USA had adopted this structure for their programmes, although several UK programmes appeared already to feature this structure. Therefore, the objective of the current work was to analyse BEng chemical engineering programmes in the UK relative to this tripartite structure, in order to evaluate to what extent the Frontiers model was already represented within UK chemical engineering education. From the 28 UK universities offering IChemE-accredited programmes, the structure and content of 24 BEng programmes were analysed against the tripartite Frontiers structure. All 24 programmes broadly followed the Frontiers structure. The greatest variation between programmes was in the amount of content contributing to the Molecular transformations theme, which varied from 1.4 to 26%. This was also the smallest of the three themes, contributing on average around 10%, compared with 37% for Multiscale analysis and 38% for Systems, with 10% coming from Supporting Competences (such as laboratory and professional skills) and 5% from Other subjects (such as mechanical or electrical engineering or electives). Molecular transformations was generally most prominent in the first year, the second year tended to contribute the most Multiscale analysis content and the final year was dominated by Systems. The Institution of Chemical Engineers’ Accreditation guidance tends to encourage the high Systems emphasis and low Molecular transformations component, in contradiction to the recommendations of the Frontiers initiative. Optional electives and MEng specialisms feature Molecular transformations emphases, the latter less so than in the 2000s, since when the drivers for curriculum development have moved from biosciences and nanotechnology towards energy and sustainability.


Introduction
Chemical engineering has been described as "the broadest and most scientific of the engineering disciplines" (Perkins 2003) and chemical engineering graduates are amongst the best paid of all graduates and better paid than any other engineering discipline (Armstrong et al. 2008;The Engineer 2014;Dwyer 2016).One reason that chemical engineers are highly valued and well paid is that they can view problems holistically, by applying their understanding of the molecular nature of matter over multiple scales and viewing processes and products as complex systems.Their holistic and multiscale perspective, informed by their broad scientific base, means that they tend to rise to managerial levels, hence the high salaries they earn relative to other engineers (Campbell and Belton 2016b;Sadd 2018).
The historical development of chemical engineering education gives insight into the features that made chemical engineering a distinctive discipline as it emerged and evolved.These features include the first and second paradigms of chemical engineering education that underpin the fundamentals of the discipline today: the unit operations concept of chemical engineering, which brought together the concepts of chemistry and physics common to all chemical processes (Perkins 2003;Favre et al. 2008;Flavell-While 2012;Varma and Grossmann 2014); and the engineering science paradigm with at its heart the transport phenomena concept, which recognised that different unit operations draw on the same principles of heat, mass and momentum transfer, and led to a unifying and powerful synthesis of the underlying mathematics, allowing chemical engineers to deal with simultaneous phenomena (Perkins 2002(Perkins , 2003;;Favre et al. 2008;Varma and Grossmann 2014).Transport phenomena is by nature highly mathematical; as the famous book by Bird, Stewart and Lightfoot states in its Preface, "the language of transport phenomena is mathematics" (Bird et al. 1960); consequently, chemical engineering education became highly mathematical, a common feature within chemical engineering programmes today.
Chemical engineering programmes generally feature unit operations and transport phenomena in some form and to varying degrees, and these paradigms have served the discipline well (Armstrong 2005).However, the broad nature of chemical engineering, which is its strength (Perkins 2003), nevertheless raises concerns that the breadth of content covered in chemical engineering programmes may be at the expense of depth, while the emphasis on mathematical analysis, empowered by the transport phenomena paradigm, has been at the expense of synthesis, which is arguably more distinctively the remit of the chemical engineer (Perkins 2002;Stephanopoulos and Reklaitis 2011;Campbell and Belton 2016a).
Chemical engineers work in a varied range of industries, which is also intrinsically linked to the broad nature of the discipline.However, according to Armstrong (2003Armstrong ( , 2006)), the curriculum in the USA at that time did not reflect the varied range of industries in which chemical engineering graduates work.He also observed that the connections between different modules are only revealed to students when they carry out a design project in the final years of the degree.Thus, students may struggle to connect concepts in a coherent manner until their final year.
Recognising the opportunity to re-organise the curriculum such that chemical engineering is taught in a coherent manner throughout the degree programme, Armstrong led the Frontiers in Chemical Engineering Education initiative in the USA, a series of workshops that aimed to define a new undergraduate chemical engineering curriculum and develop the materials needed to support the new curriculum (Zukoski et al. 2002;Armstrong 2003Armstrong , 2004Armstrong , 2005Armstrong , 2006;;Armstrong et al. 2008).After consultation with a number of universities and companies in the USA, the outcome of the initiative concluded that "Among the engineering disciplines, chemical engineering is unique in coupling understanding of molecular transformations, multiscale analysis and a systems view of problems" (Armstrong et al. 2008), the latter described elsewhere as "systems analysis and synthesis" (Armstrong 2006).It was therefore proposed that the new curriculum be organised around the three themes of Molecular transformations, Multiscale analysis and a Systems view.Armstrong (2006) summarised that "chemical engineers leverage knowledge of molecular processes across multiple-length scales in order to synthesize and manipulate complex systems comprising processes and the products they produce."Campbell and Belton (2016a) observed that the chemical engineering programme in Manchester broadly followed the tripartite structure of the Frontiers model.They then described how the new BEng programme in Huddersfield was also consciously structured around these three themes.However, and by notable contrast, it has been observed that universities in the USA did not appear to have changed their chemical engineering curricula to fit the model proposed by Armstrong (Wood 2010;Varma and Grossmann 2014).
In an earlier article written after the 2005 World Congress of Chemical Engineering in Glasgow, Wood (n.d.) writes scathingly about chemical engineering programmes in the USA and EU being stuck in the 1960s and 70s, writing "the message from Glasgow applies in all countries [that] chemical engineering education is in drastic need of reform."Wood quotes the introduction from Cussler and Moggeridge's 2001 Chemical Product Design book: …in terms of responding to the changing requirements of Industry, we believe that chemical engineering education has done almost nothing… A glance at an old syllabus or textbook or a consultation with retiring academics reveals that the basic structure of chemical engineering curricula is essentially unchanged in the past 30 years.
Wood also quotes Armstrong (2006): …the curriculum for 1965 is very nearly the same as that used today.Why is this?It is possible that after 60 years of hard work on the curriculum the discipline arrived at a more or less timeless implementation.But this seems hard to believe in the face of all of the change that has taken place over the past 40 years outside of the curriculum.On the other hand it is possible that we have simply not paid the attention we should to curriculum development over this period.

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Wood then endorses the Frontiers model as providing "chemical engineering educators worldwide with an excellent model for curricula reform." This is an intriguing observation, that on the one hand, the Frontiers initiative identified the distinctive power of chemical engineering as deriving from its "unique coupling" of these three themes (Armstrong et al. 2008), while on the other hand, it appears many programmes in the USA at least do not follow these themes and, presumably, are therefore missing out on the full and distinctive power of chemical engineering and, in the alarming terms of Wood (n.d.), "face being cast into insignificance."

Frontiers in Chemical Engineering Education
Frontiers in Chemical Engineering Education was an initiative lead by Professor Armstrong from MIT to propose possible changes to the structure and content of the core chemical engineering curriculum (Armstrong 2003(Armstrong , 2004(Armstrong , 2005(Armstrong , 2006;;Armstrong et al. 2008).This was because the core curriculum had not changed in over 40 years, however during this time the chemical industry was rapidly expanding due to the leaps being made in chemical engineering research (Perkins 2003;Armstrong 2006;Byrne 2006;Armstrong et al. 2008;Favre et al. 2008;Wood n.d.).In addition, other industries not typically thought of as chemical industries started to realise the benefits of process engineering, such that many chemical engineering graduates were working in industries outside of the traditional petrochemical industries (Armstrong 2003).
To ensure that students left university with the necessary tools and skills to apply their knowledge to the broad range of industries in which they could work, the Frontiers discussions identified that the core curriculum needed changes.Through a series of workshops involving 53 universities and five companies, it emerged that the power of chemical engineering arose from its unique combination of skills and knowledge from three areas: understanding of Molecular transformations, Multiscale analysis and Systems analysis and synthesis.It was therefore proposed that the chemical engineering curriculum should be organised around these three themes (Armstrong 2003).
The Frontiers conclusion was that an understanding of Molecular transformations would give the chemical engineer a good understanding of what happens either naturally or when an outside force causes changes to a system at the molecular scale.These changes can be physical, chemical or biological and the "molecules" can range in scale from the micro-to the macro-scale.This organising principle arose because it was determined that chemical engineers need to understand what happens at the molecular scale in order to design, operate and control processes (Armstrong 2003(Armstrong , 2005)).Examples of Molecular transformations identified in the Frontiers documentation include the molecular basis of thermodynamics, of reactions and of properties and constitutive equations.
Multiscale analysis would give the chemical engineer sound analytical skills and an understanding of computational methods and mathematical techniques required to aid problem solving (Armstrong 2003(Armstrong , 2005).An understanding of what happens at the molecular scale is required to design, operate and control large scale processes, meaning that chemical engineers need to have the ability to understand what happens at all scales and how changes at one scale affect other scales.The heart of Multiscale analysis is transport phenomena, which brings together the core topics of momentum, heat and mass transfer.
A Systems approach aids in solving problems, because chemical engineering problems frequently arise from or interact with external influences.Chemical processes are "complex systems," which means, formally, that they have social, economic, environmental and technical factors that need to be considered when designing, operating and controlling them (Agnew et al. 2003;De Weck et al. 2011).An example of the Systems approach is understanding how to control process plants, which is also closely connected to process safety.Armstrong (2006) argues that the traditional Systems content of chemical engineering programmes is primarily tied to large-scale chemical processes, and that this theme needs to be extended to additional scales and to encompass complexity and uncertainty; nowadays the acronym VUCA -volatility, uncertainty, complexity and ambiguity -might capture the required new scope of Systems thinking more fully.
The Frontiers group recommended that organising the chemical engineering curriculum around these three areas, Molecular transformations, Multiscale analysis and Systems analysis and synthesis, suitably integrated, would ensure that chemical engineering graduates are equipped to meet the demands of producing products in increasingly complex environments (Armstrong 2003(Armstrong , 2006;;Armstrong et al. 2008).It was argued that these changes would benefit students by exposing them to the breadth of chemical engineering applications through solving realistic example problems that integrate these themes over the years of the programme.Figure 1 shows Armstrong's example curriculum structured around the three themes.Note that this was presented by Armstrong as an illustrative draft only, not intending to be at all prescriptive.Note too that the three themes were envisaged to be developed somewhat equally across each of the three years of the programme, and vertically integrated within each year through, for example, laboratory classes, seminars and case studies that cut across all three themes.
Alongside the organising principle of the three themes, Armstrong (2006) acknowledges that programmes should also cultivate in chemical engineering graduates attributes of critical thinking, problem solving, communication skills, the desire for lifelong learning, and an awareness of the social impacts of engineering and technology.
Interestingly, the Frontiers documentation and Armstrong's 2006 paper do not mention sustainability (although it is prominent in Armstrong et al. 2008).The driver for the Frontiers model is much more from the molecular end, both of chemistry and, even more so, of molecular biology and nanotechnology (Zukoski et al. 2002).May (2003) similarly argues that "a Chemical Engineering curriculum must include a basic grounding in what once could have been called simply 'biochemistry', but which today must be interpreted to extend from molecular biology and genomics all the way through physical, organic and inorganic chemistry."Varma and Grossman (2014) also emphasise "with the incorporation of biotechnology and nanotechnology in the ChE discipline, it may be claimed that the current paradigm of our discipline is molecular engineering," although they go on to note "trends for energy and sustainability are likely to swing the pendulum back toward engineering fundamentals." The Frontiers initiative arose in the USA.Since much of the development in chemical engineering education in the UK has historically taken place in parallel with developments in the USA (Wood n.d.), it follows that universities in the UK might similarly be stuck in the 1960s, and might similarly benefit from following the Frontiers model.Therefore, the current work analyses the structure and content of chemical engineering programmes in the UK to elucidate whether and how the Frontiers model is followed in the UK, and whether the concerns of Wood and others are indeed reflected in the UK's chemical engineering provision.
The current work systematically quantifies the content of each of the three Frontiers themes within UK BEng chemical engineering programmes, to reveal the distinctive emphases of each university's programme and the overall pattern for the UK.The balance of content implied by the Institution of Chemical Engineers' accreditation guidance, which influences programme content, is also analysed.The current work then considers the issue of diversity in the curriculum, as encouraged by, for example, Perkins (2002), Shott et al. (2015) and Brown et al. (2019), by looking at the range of MEng specialisms on offer in UK chemical engineering programmes.

Methodology
The methodological challenges of creating a framework of analysis were twofold: i) To clarify the type of content to be allocated to each of the three Frontiers themes; ii) To judge from the available information the type of content in each taught module at each university.
The Frontiers documentation describes the envisaged content of the three themes in reasonable but not comprehensive or definitive detail.The broad scope of each theme is summarised in Sect."Frontiers in Chemical Engineering Education" above and illustrated in Fig. 1.The documentation expands on each, but retains some ambiguity (Armstrong 2003(Armstrong , 2005)).The documentation also describes the four-year structure operated in the USA in terms of Freshman, Sophomore, Junior and Senior years; the latter three broadly correspond to Years 1-3 of a BEng programme in England, Wales and Northern Ireland, and to Years 2-4 in Scotland.(2006), with permission Within a given programme, there is also content that does not contribute to any of the three Frontiers themes.Often this is in the form of modules that cover other technical topics that are not part of core chemical engineering, or that develop other skills such as communication or employability.Two further categories were therefore identified to account for content that did not sit within the three Frontiers themes.These categories were Supporting Competencies (for things like laboratory skills, groupwork, presentations and employability skills) and Other (for technical topics from other disciplines such as electrical engineering, or optional modules for which the uncertainty of option choices precluded quantifying the allocation to a particular Frontiers theme).Both of these categories proved to be small and did not significantly alter the dominance of the Frontiers themes for categorising programme contents.
The Frontiers documentation notes that "Traditional chemical engineering curricula have not involved direct exposure of freshmen to their chosen discipline.The first course has come in the sophomore year, and is often a course in mass and energy balances" (Armstrong 2003).The documentation then proposes that the Freshman year could introduce some chemical engineering content including mass balance principles.Interestingly, it places this within Multiscale analysis.We concur that a material and energy balance module is generally one of the first encountered by chemical engineering students in the UK, generally in the context of a foundational module entitled something like "Process Engineering Fundamentals" (e.g.Lancaster, Manchester) or "Introduction to Process Engineering" (Leeds) or "Chemical Engineering Design 1" (Huddersfield), in which material and (usually) energy balance calculations are introduced in the context of chemical process flowsheets and terminology.In our judgement, however, this material belongs more properly to the Systems theme; it is typically where whole processes are first encountered, while material balances are frequently set up and solved as systems of equations.However, continuum-based description of mass, energy and momentum transfer, the basis of transport phenomena, is rightly placed in the Frontiers documentation under Multiscale analysis.
Thermodynamics presents another categorisation challenge, arising in part from the different perspectives of this topic across the disciplines of physics, chemistry, chemical engineering and mechanical engineering (Smit 2017).According to the Frontiers documentation, the study of the laws of thermodynamics contributes to Molecular transformations whilst the study of heat transfer contributes to Multiscale analysis (Armstrong 2004).Often universities combine the study of thermodynamics and heat transfer.Understandably these topics are interlinked, however heat transfer is not the same as thermodynamics and the terminology is used somewhat interchangeably or with overlap.Some universities differentiate by referring to thermodynamics as "chemical thermodynamics" and heat transfer as "engineering thermodynamics."The ambiguous terminology was recognised during the analysis, and modules that combined the two topics were carefully analysed to make sure that allocations aligned with the descriptions proposed in the Frontiers model.In the few cases where a description of the module content was not available to clarify the content, if the module was titled "engineering thermodynamics" it was assigned to Multiscale analysis; if titled "chemical thermodynamics" it was assigned to Molecular transformations.
Although it could be argued that, for a chemical engineer, Mathematics is a tool and therefore a supporting competency, maths modules were assigned to Multiscale analysis, as transport phenomena is a highly mathematical subject and the one most supported by mathematical modules (Campbell and Belton 2016a).
Although chemical reaction engineering on the face of it deals with Molecular transformations, it was assigned to Multiscale analysis because its content is predominantly mathematical (and often uses only symbolic chemicals as in A + B → C + D), as undergraduate reaction engineering textbooks, such as Coulson and Richardson's chemical engineering series (Ravi et al. 2017), Levenspiel (1998) and Schmal (2014) demonstrate.
The same policy was adopted for more advanced chemical reaction engineering modules, often comprising catalytic reaction engineering, as these also predominantly comprise mathematically bridged connections between the molecular scale behaviour and reactor design, linked with transport phenomena.Enzyme catalysis arose in different contexts, either within biotechnology or biochemistry modules without a mathematical emphasis, in which case the allocation was to Molecular transformations, or within catalytic reaction engineering with a more mathematical focus, in which case the allocation was to Multiscale analysis.Catalysis introduced within the context of early Physical Chemistry modules were retained within Molecular transformations, as in this context the topic is more conceptual than mathematical.Straightforward chemistry modules (including physical, organic and inorganic chemistry) were allocated to Molecular transformations.
Particle technology is a further topic that poses some ambiguity regarding its allocation.The Frontiers documentation only mentions particles in the context of Multiscale analysis, which we agree is its most appropriate home.
Design projects tend to be large in terms of credit weighting, the categorisation of which is therefore highly influential to the analysis, and integrative, such that they are likely to combine material from all three themes.However, for this analysis it was considered that the integrative nature of the Design Project makes it fall most defensibly into the Systems theme.
Labs are sometimes part of a module, sometimes they are separate modules; in either case, they could be considered contributing to teaching core knowledge, or to developing supporting competencies in the form of lab skills, report writing and group work.For the purposes of this analysis they were considered to contribute to Supporting Competencies.An alternative categorisation might consider that labs contribute 50:50 to Supporting Competences and to strengthening knowledge and understanding of the subject of the lab, which most often falls into the Multiscale analysis theme (e.g. chemical reaction engineering, heat transfer, fluid flow, particle technology), such that some of the allocation would enhance this theme.In general, however, labs form a small component that does not influence the allocation much, and it was felt more useful to separate out lab work in its entirety as a qualitatively different element of the student learning experience and as a further basis for identifying differences between programmes.
Where modules indicated a lab component but not how much it contributed to the module, a standard allocation of 20% of the module credits was implemented.
Research projects are generally located in the final year of an MEng programme; however, a few programmes (those at Queen's University Belfast, Edinburgh, Heriot-Watt and Loughborough) featured a Research Project within the BEng programme.Given the nature and diverse topics of Research Projects, it was decided that they were mostly safely viewed as contributing to Supporting Competences.Teesside has a 40-credit Chemical Engineering Project that can be either research or design; for comparability with other programmes, it was assumed this was usually a Design Project and allocated as Systems.
Other Supporting Competencies included groupwork, presentations, employability and computing skills, unless part of the Design Project in which case they were retained within Systems.However, process simulation and modelling, which might be considered to develop computing skills, was judged more appropriately to contribute to Systems, along with process control and safety.
Modules or components of modules that were related to the study of electrical engineering, electronics, programming, mechanical engineering, or structural/civil engineering were all assigned to Other.
Materials science was allocated to Molecular transformations, but topics such as mechanics of materials were considered more closely aligned with mechanical engineering and assigned to Other.
Optional elective modules were also assigned to Other on the bases that (a) some options may not align with any of the three themes; and (b) what proportion of students might select an option is not known.The prevalence of optional modules was sufficiently low not to affect the analysis greatly.
Where substantial information about the module content was available, and the content fell into more than one category, the detailed information was used to estimate the number of credits contributing to each category.In some instances, instead of the percentage weighting of different topics or tasks, the module specification indicated the number of hours students spent on topics, which was converted into the number of credits, where one UK credit is nominally equivalent to 10 h of student effort.
Table 1 summarises the guidance for the allocation of module content.
Having clarified the bases for allocating material, the actual content of UK programmes was accessed and analysed.The website of each IChemE-accredited UK university was accessed during the period October-December 2018 and information obtained about the BEng and MEng chemical engineering courses offered.Following the analysis, all departments were contacted to give them the opportunity to check that our analysis was accurate and a fair representation; the several who responded endorsed our analysis of their programmes as fair and representative.
Most universities gave a caveat on their websites that the list of modules was not definitive of future programme content and was there for illustrative purposes.Websites reported the content that the universities offered at the time of publication, and typically the modules that had been taught in the previous academic year; students entering the course in the following academic year would not necessarily study the modules that were listed.The modules analysed were those found on the website of each university during the time period October-December 2018; it is likely that since then, universities have introduced new modules or made changes to the content of existing modules, which means that the analysis that follows is not definitive over time.
The categorisation of module content into the five themes involved necessarily an element of informed judgement.Having been through the first three years of an undergraduate chemical engineering programme, the first-named author was able to recognise descriptions and "read between the lines" to make (literally) educated guesses about the likely content, guided through discussions with the other two authors who had designed the Huddersfield programme based on a thorough consideration of the chemical engineering education literature (Campbell and Belton 2016a).It is acknowledged that the resulting classifications are not completely objectively precise or definitive.However, they suffice to paint a valid national picture and to discern broad trends as well as some distinctive differences between programmes.
It is also acknowledged, as did Campbell and Belton (2016a, b) when comparing programmes at Huddersfield and Manchester, that equivalent proportions of content, or content similarly described, does not imply equivalent depth of coverage or challenge of assessment.
It is further acknowledged that, just because the existing content of a curriculum largely fits into these themes, this does not imply that it covers the extended scope of those themes envisaged in the Frontiers model.Thus, for example, Systems would ideally encompass problems with VUCA characteristics -volatility, uncertainty, complexity and ambiguity -sometimes called (with less precision) "wicked" problems, which are particularly well exemplified with respect to sustainability issues (Byrne and Fitzpatrick 2006;Byrne 2010).A strong Systems score within a particular programme does not necessarily imply the depth and scope advocated by the Frontiers vision.Similarly, Molecular transformations or Multiscale analysis may be well represented but still conventional in their content and/or limited in their scope.Nevertheless, the argument of the Frontiers proposal is over the unique coupling of these three components rather than the scope of any one, which is necessarily constrained by the need to attain an integrated balance with the other two and by the total content that can be reasonably squeezed into a programme.The current analysis is just for the three years of BEng programmes; these extensions into greater depth and breadth more naturally arise within the MEng year.
A further analysis was undertaken of the IChemE Accreditation Guide (Version 2.1, February 2019), to elucidate what balance of content is implied by this Guide.(Note that IChemE revised its accreditation guidance in 2021; however, the analysis was undertaken using the Guide in operation at that time.The new Guide is not so different in its emphases as to alter the analysis substantially.)By definition the programmes analysed, which were all accredited by IChemE, had met the criteria specified in the Guide, which undoubtedly had influenced their construction and content.Appendix 1 presents this analysis, in which each of the learning outcomes listed in Appendix 1 of the Guide was allocated to one of the five themes.(Subsections A2.6.1 and A2.7.1 were excluded, to avoid double counting and excessive weighting of the Safety and Ethics components elaborated under those subsections.)Each learning outcome was then equally weighted to calculated the balance of programme content implied by the prominence of each theme.The Guide specifies an overall minimum core chemical engineering content of 85 European Credits (1 EC = 2 UK credits, hence 170 UK credits) plus at least 10 ECs of Chemical Engineering Practice (interpreted as Supporting Competencies) and 10 ECs of Chemical Engineering Design Practice and Design Projects (interpreted as Systems), plus "sufficient" underpinning mathematics, science and associated engineering disciplines (which was distributed between Molecular transformations, Multiscale analysis and Other).In previous versions of the Guide, 20 ECs of this underpinning material had been specified, so for the current analysis "sufficient" was interpreted as 20 ECs.Thus a minimum of 125 ECs of a 3-year, 180-EC programme are specified; the breakdown between the five categories was then scaled to a 360 UK credit programme, to judge the balance of material in a full programme implied by the prominence of the themes in the learning outcomes specified by the Guide.
Following the analysis of BEng content and IChemE accreditation guidance, the scope of MEng specialisms was also reviewed to gauge the extent of diversity of chemical engineering provision offered through MEng programmes, and the extent to which the MEng year gives scope for extended depth and breadth within the three Frontiers themes.

Results and Discussion
In October 2018, there were 29 accredited BEng programmes listed on the IChemE website, two of which are taught within the same institution, University College London's chemical engineering and biochemical engineering programmes.Out of the 29 BEng programmes, 24 were analysed; the programmes not included in the analysis were: • University College London Biochemical Engineering, as it is unique and somewhat different from standard chemical engineering programmes.• Bath, as the University of Bath website had limited information about the course structure, providing only a list of module titles, with no indication about module content, module credits, or which modules were taken in each year of the programme.• Nottingham, as the University of Nottingham website did not provide module credits and only provided a list of modules which they explicitly stated was only a sample of typical modules.• Oxford; the programme offered at the University of Oxford is different from other chemical engineering programmes in the UK.This is a 4-year programme that leads to an MEng Engineering Science degree.The first two years of the programme involve the study of general engineering and the last two years focus on chemical engineering.Due to the unique nature of the programme at Oxford, and the unavailability of information about module content and credits on the university website, the Oxford programme was not included in the analysis.• Cambridge; the Cambridge programme also has an unusual structure, in which students enter into the second year of chemical engineering from a first year of either natural sciences or engineering.There was also limited availability of module content and credits on the website.A direct request to a staff member, who is gratefully acknowledged, yielded the required information; however, the module content was not presented in terms of credits which, combined with the inability to include a common first year in the analysis, led to the decision that it was not possible to present the Cambridge programme comparably with other UK programmes.
In some instances, the module descriptors were not provided on the university websites or were brief and lacking detail.In those instances, educated guesses were made from the title of the modules as to which category the modules were best suited.Descriptors for the modules of the University of Hull were incomplete, and for Imperial College London and Queen's University Belfast were absent, such that the analysis of these programmes is less precise than for others.The University of Aston also had limited information on its website; however, a direct request resulted in the required information being provided.
Since the analysis, several other new chemical engineering providers have entered the UK scene, including the universities of Wolverhampton, Sheffield Hallam, Greenwich, Brunel, Queen Mary and Canterbury Christ Church, with Southampton also planning to introduce chemical engineering programmes.

Analysis of Core BEng Chemical Engineering Content
Supplementary Information A lists the programmes and information obtained from university websites and presents the assignment of module content to the three Frontiers themes, Molecular transformations, Multiscale analysis or Systems, or to Supporting Competencies or Other.
Table 2 summarises the UK credit allocations for the BEng programme at each university, from which some immediate patterns emerge.In terms of the three Frontiers themes, on average Molecular transformations contributed 10.2% of the overall content (36.6 credits), Multiscale analysis 36.6% (131.7 credits) and Systems 38.1% (137.3 credits), with Supporting Competencies and Other contributing on average 10.0% (35.8 credits) and 5.2% (18.6 credits), respectively.Overall, the picture in the UK is that all three themes of the Frontiers model are represented, but with Molecular transformations much less prominent than the other two.
The ranges of content within each theme vary from 1.4 to 25.8% (5-93 credits) for Molecular transformations, 26.9 to 45.8% (97-165 credits) for Multiscale analysis, 24.1 to 46.7% (87-168 credits) for Systems, 2.8 to 15.6% (10-56 credits) for Supporting Competencies, and 0 to 16.7% (0-60 credits) for Other.In relative terms (range/average), the greatest variation is for Other, reflecting different proportions of either optional modules or material from other disciplines, with ten of the 24 programmes being entirely specified (no options) and entirely chemical engineering (zero Other).In absolute terms, the greatest variation is in the Molecular transformations theme, while Multiscale analysis shows slightly less variation than Systems in both absolute and relative terms.
The lower variation between the extremes for both Multiscale analysis and Systems content, compared with the variation for Molecular transformations, arises from the evident collective agreement regarding essential content by all providers and by the IChemE.Transport phenomena, the second paradigm of chemical engineering, contributes to the Multiscale analysis theme.All the programmes analysed included the study of heat and mass transfer and fluid mechanics, some to more depth than others, and all programmes had modules that taught reaction engineering and the design of separation systems such as distillation, absorption and drying.While the details differed, the general prominence of these topics exhibited a somewhat inevitable uniformity.
Regarding the relative uniformity of the Systems component, all the programmes included modules covering material and energy balances, process control, safety and sustainability, and all had a Design Project, with a broadly uniform credit budget again inevitably needed to address these topics.
The IChemE Accreditation Guide also obliges a degree of uniformity between programmes, although with only 125 out of 180 European credits specified (69%), one might hope for more ambitious and creative use of the remaining 31%.But a combination of caution, inertia and reluctance to abandon cherished topics appears to be suppressing ambitious programmes that push and extend the boundaries of chemical engineering education (May 2003;Brown et al. 2019).
Programmes in the USA and a number of other countries are accredited by the Accreditation Board for Engineering and Technology, ABET (Voronov et al. 2017)  around 16%.This brief analysis supports the finding for UK programmes that the Systems theme dominates, followed by Multiscale analysis, with Molecular Transformations much less represented in chemical engineering programmes all three countries.Figure 2 shows bar charts of the 24 programmes in order of highest to lowest content of the three themes, while Fig. 3 shows the relative contributions of the three Frontiers themes in the form of a ternary diagram, where the fraction of content contributing to each of the three themes is represented.The proportions of the three themes in Fig. 3 have been normalised to omit the, on average, 15.2% of Supporting competencies and Other components.This diagram must be interpreted with care and with reference to Table 2 and Fig. 2, to understand distortions arising from the different amounts of Supporting and Other in each programme, such that a higher relative proportion of one of the three themes in a programme may not reflect a higher absolute content of that theme if the programme contains a lot of Supporting or Other material.Figure 3 must also not be overinterpreted at the level of small differences between programmes.
Those caveats stated, Fig. 3 immediately gives a clear visual confirmation of the main conclusions from Table 2 and Fig. 2, that in general UK BEng Chemical Engineering programmes are relatively balanced between Multiscale analysis and Systems content, but much weaker on the Molecular transformations theme encouraged by the Frontiers model.The average proportions of the three themes with the Supporting competencies and Other content omitted become 11.9%Molecular transformations, 43.1% Multiscale analysis and 45.0% Systems.
Relative to these proportions, the most average or representative programmes in the UK, in terms of being most central within the cluster of programmes (having the smallest sum of squares of differences across all five categories and across just the three Frontiers themes), are Strathclyde and Swansea.Perkins (2002) observes, "It is unlikely that there is such a thing as a 'typical' chemical engineering course these days"; these programmes appear to offer the most typical examples from the UK range of provision.
Figure 3 also shows the position implied by the prominence of the three themes within the learning outcomes specified in the IChemE Accreditation Guide which, normalised to exclude Supporting or Other, falls at 10.2% Molecular transformations, 38.4% Multiscale analysis and 51.4% Systems.Interestingly, the average Systems content on the ternary diagram was much lower at 45% (equivalent to nearly 20 credits difference), with all but two programmes featuring less than 50% Systems.It is important to acknowledge that the balance of content "implied" by the content of the learning outcomes in the Accreditation Guide does not mean that this balance is consciously encouraged by IChemE.For the sake of the analysis, the listed learning outcomes were equally weighted, but this does not mean they were formulated within the Guide as intentionally equal in size and scope.
That being said, the 20-credit discrepancy in Systems emphasis between the accreditation guidance and the implementation in practice is due in large part to the Safety component of the Accreditation Guide.Safety is elaborated quite extensively in the Guide, to underline its importance from IChemE's perspective, and most of the learning outcomes were allocated to this theme (one was allocated to Molecular transformations, as it related to risks such as toxicity and explosion that arise from the chemistry).Safety, although rightly prominent in IChemE's attempts to influence programme content, is frequently covered within a single 10-credit module (supported by an underpinning Safety culture as prescribed in Section A2.6.1 of the Guide), a much lower proportion than the 35 credits implied by the prominence of this topic in the learning outcomes specified in the Guide (Appendix 1).Chemical engineering academics are frequently neither particularly keen nor competent to teach safety, preferring to pull programmes towards the more academically interesting and educationally demanding theme of Multiscale analysis or the more research-aligned theme of Molecular transformations.As well as training graduates for industry, departments have an educational obligation to "teach at university what cannot be taught elsewhere" (Campbell and Belton 2016a) and thus to structure and deliver programmes that maintain the educational obligation in healthy tension with industry and professional body priorities.The undoubted importance of safety nevertheless remains a topic not necessarily best taught in universities and for which industry has its own training obligations, and the departure of programmes from the gravitational pull of the guidance in this respect is perhaps not surprising.
The minimal IChemE emphasis on Molecular transformations content, at 10.2%, no doubt also contributes to the low 11.9% average content of this theme across UK programmes, in contradiction to the Frontiers recommendations and the urging of commentators such as Cussler andMoggridge (2001), May (2003), Varma andGrossman (2014), Shott et al. (2015) and Wood (n.d) who says, "if the chemical engineering fraternity fails to embrace change the opportunities for the future, particularly in the biomolecular and nanotechnology fields, will be passed to others." Turning to the extremes, the University of Huddersfield has the highest content of Molecular transformations material; its position near the centre of the ternary diagram means that it can claim to offer the most balanced chemical engineering programme in the UK(!), and also the most distinctive.This reflects the deliberate intention to design this programme around the Frontiers model, including a distinctive emphasis on chemistry (Campbell and Belton 2016a, b).Also, the Huddersfield programme is the only IChemEaccredited programme in the UK located within an Applied Sciences school; other UK programmes are within either dedicated chemical engineering departments, engineering schools or joint engineering and science schools.Campbell and Belton (2016a) state that, when introducing chemical engineering at Huddersfield, the programme was consciously constructed to leverage the strength of the school's chemistry context, because this was considered attractive to students and to employers.Note that even with this high chemistry content, the Huddersfield programme nevertheless delivers 240 UK credits of core chemical engineering material, well in excess of the IChemE minimum of 170 credits, plus a substantial 30-credit Design Project.Despite the IChemE accreditation guidance favouring the other two themes, there is plenty of scope for increasing the Molecular transformations content of programmes while retaining more than adequate core chemical engineering material.
However, the high chemistry content qualifies the Huddersfield programme, within the University's naming regulations, to be awarded with a "with" designation; a recent development, therefore, has been to introduce BEng and MEng programmes in Chemical Engineering with Chemistry, and to revise the straight BEng and MEng programmes to replace the organic chemistry modules in the 2nd and 3rd years with modules from the School of Computing and Engineering, which will increase the engineering content and move the balance back towards that of other UK programmes.
Sheffield, Leeds, Chester, Edinburgh and Aberdeen also feature quite large Molecular transformations components.In Sheffield's case this is due to its Department of Chemical and Biological Engineering having 1st and 2nd year modules on "Engineering with Living Systems," with two chemistryheavy 1st year modules and a 3rd year "Science of Formulated Products" module also helping to boost its Molecular transformations content to 65 credits in total.
By contrast, London South Bank University appears to have almost no Molecular transformations content (scrutiny of the LSBU module descriptions gave very little indication of material that might be considered fundamental chemistry, biology or biochemistry).Loughborough University, UCL and Lancaster also appear to contain little content contributing to Molecular transformations.One reason may be the home of the programme.At LSBU chemical engineering is taught within an engineering school (and there is no Chemistry department within the university), while Lancaster chemical engineering is similarly within an engineering department, with Chemistry in a separate (and relatively young) department.
Loughborough University has a separate Chemical Engineering Department that sits within the School of Aeronautical, Automotive, Chemical and Materials Engineering, with Chemistry in a separate School of Science.UCL similarly has a standalone Chemical Engineering Department sitting in the Engineering Sciences Faculty, with Chemistry a department within the Faculty of Mathematical and Physical Sciences.A chemical engineering department within an engineering school or faculty is likely to result in a greater emphasis on mathematical/engineering content relative to chemistry.
Interestingly, the programmes at Queen's University Belfast and Aston, which are the only combined chemistry and chemical engineering departments in the UK, do not contain large proportions of Molecular transformations content.
Looking at the other axes of Fig. 3, Multiscale analysis appears most prominent in the programmes at Bradford, Teesside, UCL and Lancaster, while Chester and Aston have the lowest proportion of this material.However, there is some distortion here, as Bradford and Lancaster have high components of Supporting Competencies and Other (95 and 101 credits, respectively) such that in absolute terms, the Multiscale analysis content of these programmes is more average, with the highest absolute contents featuring in the programmes of Newcastle, Teesside, Queen's University Belfast and the University of the West of Scotland (Fig. 2b).At the other end, Aston, Huddersfield, Birmingham and Leeds have the lowest absolute amounts of Multiscale analysis.The differences between the extremes are not as great as the differences between the extremes of Molecular transformations; at Newcastle 161 credits (44.7% of 360 credits) contributes to Multiscale analysis compared with 97 credits (26.9%) at Aston.
Systems is highest in absolute terms at Aston, London South Bank, University of the West of Scotland and Heriot-Watt (Fig. 2c).Allocation of the Design Project to Systems tends to inflate this theme, and for the LSBU and West of Scotland the high Systems score is in part the result of a large 40-credit Design Project (although still lower than the 60 credits at Manchester and Strathclyde).Aston has just a 30-credit Design Project, with its high Systems score coming from a broader range of modules across all three years, covering design, control, simulation, HSE, energy systems and sustainability.Systems content is lowest at Aberdeen, due in part to a small 15-credit Design Project, and Huddersfield, due its high Molecular transformations content.At Aston 168 credits (46.7%) of the content contributes to Systems compared with 87 credits (24.2%) at Aberdeen.
Figure 4 shows the credits contributing to Multiscale analysis and Systems plotted against the credits contributing to Molecular transformations and against each other (with the data for Huddersfield and Aberdeen excluded as their very high Molecular transformations and low Systems content, respectively, tended to skew the graphs excessively).Clearly in a constrained dataset, there must be negative correlations.Even so, Fig. 4 clarifies that the trade-off tends to be between Molecular transformations and Multiscale Analysis, with Systems more consistent.However, the scatter is the more dominant element of the graphs, reflecting the diversity of balance between programmes, not to mention the diversity of specific module content within each of the three broad themes.

Supporting Competencies and Other Content
Supporting competencies was primarily aimed at separating out laboratory and, to a lesser extent, computing skills, while modules that enhanced students' soft skills such as employability were also assigned to this category.Although these modules are not fundamental chemical engineering modules, they develop students' professional skills and ensure that students become well-rounded, professional chemical engineering graduates, aligning more with the IChemE's Chemical Engineering Practice requirement.As well as specifying a minimum of 20 UK credits of Practice, the IChemE recommends that programmes should support students in developing soft skills.Some universities embed such skills within core chemical engineering modules, whilst other programmes deliver separate modules that develop soft skills.
Figure 5 shows the credit counts contributing to Supporting competencies and Other, in order from most to least of the former.A word of caution is needed, that although the overall national picture is probably reasonably accurate, judging the amount of Supporting competencies material within specific modules was not always straightforward, and the precise ordering within Fig. 5 is unlikely to be significant.Some programmes have dedicated labs modules, which are easier to allocate, while others embed labs within taught modules, in which case a standard assumption was applied that 20% of the module credits were Supporting competencies.
Those caveats noted, the perception from the available information is that Hull has a noticeably strong Supporting competencies component to its programme.This arises predominantly from two 20-credit "Engineering Global Challenge" modules in 1st and 2nd year, aimed at helping students to "Develop and enhance a range of professional skills as a basis for professional registration as an Incorporated or Chartered Engineer, [focussing] on areas such as team working, leadership, project planning, data collection, measurement, business skills, and self-reflection."Loughborough Fig. 2 Proportions of content in UK BEng chemical engineering programmes, in order from greatest to least credits of a Molecular transformations, b Multiscale analysis and c Systems ◂ also scores well in this aspect of their programme, in this case boosted by a 20-credit labs module in 1st year and a 20-credit Research Project in 3rd year.Huddersfield's high score arises from high practical labs content across numerous chemical engineering and chemistry modules, reflecting the general focus on good lab skills within the School of Applied Sciences.
At the other end, the low score for the University of the West of Scotland arises in part because some of this programme's Supporting competencies material arises in Year 1 (including some labs and a 10-credit "Technical Communication in Engineering" module) and has not been counted in the analysis, while some lab classes in later years in the area of engineering mechanics have been allocated under Other.Sheffield's low Supporting competencies score apparently arises from no labs in Year 1 and a single dedicated 15-credit "Experimental Investigation" module in Year 2 (however the curriculum structure was in transition at the time and moving towards a model with labs embedded into modules in both years).Surrey has a 15-credit "Transferable Skills and Laboratory Skills" module in 1st year and a small lab component in 2nd year.

Other Engineering Disciplines
Overall Other content (other engineering disciplines or electives) accounted for 18.6 credits or 5.2% of programmes on average.But ten of the programmes analysed were entirely specified with zero Other content; the remaining 14 programmes thus had an average of 31.8 credits or 8.8% of their

S y s t e m s V i e w M u l t is c a l e A n a l y s i s
programmes made up of Other content, equivalent to around one 10-credit module in each year of the programme.The programmes featuring the most Other content, at Aberdeen, Bradford and Lancaster (Fig. 5), all deliver a common first year to a range of engineering disciplines.
Table 4 lists the Other content: either compulsory modules drawn from other disciplines (electronics/electrical engineering, mechanics/mechanical engineering, engineering materials, transport, manufacturing, programming); or Electives, the topics of which are listed in Table 4.Of the total Other content in all these 14 programmes, 35.6% was compulsory material from other disciplines, while 35.9% was named electives and 28.5% was unspecified electives.The named elective module topics were unique to a programme with a few exceptions (nanomaterials/nanotechnology was on offer at two universities and petrochemical/ petroleum engineering at three universities).There were a few themes within the electives; bio-topics were most prominent (biomaterials science/biochemical engineering/ biopharmaceutical engineering/biorefineries), with energy and renewables/sustainability/environmental engineering also making appearances, as might be expected.
Elective modules can, of course, contribute to one of the three Frontiers themes.Table 5 shows the distribution of the elective module topics from Table 4 between the three themes and those that remain either as Supporting Competencies or Other.Of the 27 modules listed in Table 4, eight are in topics contributing to Molecular transformations, eight in Multiscale analysis, five in Systems and six in Other.
Thus the exclusion of these elective topics from the main analysis has had the effect of very slightly shifting the balance in the ternary diagram of Fig. 3 towards Systems.The prominence of Molecular transformations electives aligns with Armstrong's structure in Fig. 1 that suggests final year material in this theme might be in the form of electives.
The current work did not extend to core and elective modules in the 4th year MEng programmes, for which IChemE Accreditation required at least 10 ECs each of Advanced Depth, Breadth and Practice plus 5 ECs of Advanced Design (the former two combined in the new Guide into 20 ECs of Advanced Principles).Some of the 4th year MEng modules lead to specialisms indicated by the title of the programme, which Sect. "MEng Chemical Engineering with Specialisms" considers.

Scottish Universities
Analysis of the Scottish programmes, as noted above, omitted the first year, as the structure in Scotland means that Years 2-4 are more comparable with Years 1-3 of BEng programmes elsewhere in the UK.This created a concern over possible distortion of the picture for the Scottish programmes.However, Fig. 3 shows the Scottish programmes falling largely within the main cluster of programmes, with Aberdeen's lower Systems content taking it out to one side.Table 6 summarises the average content of each of the five categories for the Scottish programmes and for the rest of the UK, confirming a very comparable picture.

The Home of the Programme
A further interesting question is whether the home of the programme -whether it is in a dedicated chemical engineering department or a joint department, or within a more general engineering school -influences the balance of content.
Table 7 lists all 28 institutions offering IChemE-accredited chemical engineering programmes in the UK, showing the institutions that have their own distinct chemical engineering departments, those that have larger departments or schools (either just engineering or combined with other disciplines) within which chemical engineering is taught, and  those where chemical engineering is a major component of a joint department.(Note that terminology for university structures varies, some using Departments as the smallest unit, within a School or College, some using Schools as the smallest unit, within a College or Faculty.The headings in Table 7 use "Department" to indicate the smallest unit in which the chemical engineering teaching is located, although some of these units are called Schools within their own university's terminology.Categorising the homes of programmes is made more difficult by the apparent trend of many university websites to hide or obscure the internal organisational structure in order to allow taught programmes or research groupings to be more prominent to the external world.However, this table of departmental names was sent to all departments to check that they were correct.It is acknowledged that university restructuring may have altered department names and homes since then.)On a departmental level, 11 programmes are taught within chemical engineering departments, five are taught within joint departments where chemical engineering is the major component of the joint department, seven programmes are taught within engineering departments or schools, and five in schools that are not restricted to engineering.The range of titles is interesting.The first category features all combinations of Department or School with Chemical Engineering or Chemical and Process Engineering.The five joint departments are with Chemistry, Biotechnology, Analytical Science, Environmental Engineering and Biological Engineering, these titles often reflecting research themes more than undergraduate course content (Byrne 2006); that all of these are in the Russell group is probably not a coincidence.Programmes taught without a distinct chemical engineering department are either in engineering schools or in large schools not exclusively devoted to engineering (or, in Huddersfield's unique case, in an Applied Sciences school).Because titles are not entirely definitive, these two were grouped together in the analysis of content (with the Huddersfield programme omitted, as its very high Molecular transformations content would have skewed the averages).
Table 8 reports the average credit and percentage content of the five themes for each of the three groupings.No substantial differences emerge, and the variation between programmes within a grouping is greater than the variation between groupings.Nevertheless, it is reasonable to conjecture that Molecular transformations content might be lower in more general engineering schools, and the data does suggest that these programmes have on average around 6 credits less of this material than dedicated chemical engineering departments, and over 15 credits less than the three joint departments.These appear to be leveraging their chemistry, analytical science and biological engineering expertise into their BEng programmes, although most of the difference is due to Sheffield's 65 credits of Molecular transformations content, the second highest after Huddersfield.
What is perhaps surprising is how small the Systems difference is.Since systems thinking is one of the distinctive skills that chemical engineers supposedly have (Stephanopoulos and Reiklatis 2011), it might be expected to be noticeably more prominent in dedicated chemical engineering departments where there may be more flexibility and focus as to what can be taught relative to other departments, whereas the data shows it to be on average slightly less.
Where chemical engineering sits within an engineering school/department, in several cases there is a common first year or shared modules, where students from all engineering disciplines are taught together.On the one hand, this strengthens the programme because chemical engineering students are exposed to other engineering disciplines and are able to recognise the interfaces where other engineering disciplines interact with chemical engineering.However, while increasing the understanding of other engineering disciplines, such shared teaching could weaken the chemical engineering focus of the programme, as the common material may be less bespoke (heat transfer for chemical engineering is arguably different in emphasis to that for mechanical, civil or electrical engineering, for example).
Although recognising the interactions that chemical engineering has with other engineering disciplines is important, equally important is recognising the interactions that chemical 1 3 engineering has with chemistry, as the discipline of chemical engineering arose primarily from industrial chemistry (Perkins 2003;Foley 2016).It is also important that the coherence of chemical engineering and the features of its own identity, and from which it gets its unique power, are clearly understood from within chemical engineering and not diluted through confusion (in the literal sense) with other disciplines.

Distribution of Core Chemical Engineering Content from First to Final Year
As well as the content of programmes in terms of the three Frontiers themes, it is also of interest to see how the balance between the themes evolves over the years of the programme.Figure 6 shows the distribution of content contributing to each of the three themes, for a representative selection of universities.Universities were chosen to represent regions of the UK based on the number of student enrolments in 2016-2017; the university with the greatest enrolments in a particular region of the UK was chosen to represent that region, with data for the number of student enrolments taken from the Higher Education Statistics Agency website (2018).The University of Surrey was also chosen to represent the South of England in addition to UCL representing the London region.Huddersfield was included for our own interest and because of its distinctiveness, and the figure also shows the average data for all 24 programmes analysed.The general pattern is that Molecular transformations content is mostly taught within the first year and decreases from the first to the final year, by which time it has often disappeared completely (and sometimes by Year 2, leading to a concern that any learning on this theme in 1st year may be long forgotten by graduation).By contrast, Systems content tends to increase from the first to the final year, where it dominates, while in general programmes emphasise Multiscale analysis content in the second year.The Design Project, which is taken in the final year of all programmes, contributes to the increase in the Systems theme in the final year.These trends are not surprising.Molecular transformations content in the form of chemistry and perhaps biology is a natural topic to locate in first year, because this provides a familiarity with school-level material and eases the transition to university.On the other hand, Multiscale analysis topics such as heat transfer and fluid flow are less familiar and it is reasonable to allow students to settle into university life before introducing these more demanding topics (although some programmes introduce these topics in the first year).Meanwhile, a Systems perspective requires a depth of knowledge and maturity to synthesise, which is developed in later years as more knowledge is gained.
However, this unsurprising pattern is at odds with the proposed Frontiers structure, which envisaged a more even development of the three themes across the three years of the programme (Armstrong 2003(Armstrong , 2005(Armstrong , 2006)), although Fig. 1 does seem to acknowledge a diminishing of Molecular transformations to mainly electives in the final year.The data from the UK indicates a collective judgement that Molecular transformations material is most appropriate for the earlier years of a programme, Multiscale analysis becomes a natural focus in the second year, and Systems requires a scope of knowledge and maturity of perspective that is only adequately developed by the final year.Thus it appears that UK chemical engineering programmes reflect the content of the Frontiers model, but less so its structure.However, while recognising the natural predominant location for each the three themes -Molecular transformations in Year 1, Multiscale analysis in Year 2, and Systems in Year 3 -it may be that there is an opportunity to strengthen programmes by having at least some material from each theme in each of the three years.

MEng Chemical Engineering with Specialisms
From the 28 institutions that offered IChemE-accredited chemical engineering programmes in the UK in 2018, 13  offered between them a total of 29 MEng programmes with a specialism, compared with 13 institutions listed by Byrne (2006) that offered between them a total of 35 MEng programmes with a specialism (Table 9), suggesting a slight narrowing in the scope of specialisms now offered.Figure 7 shows the number of MEng specialisms that were available for 2019-2020 entry compared with those indicated by Byrne (2006), illustrating the nature of this narrowing.
Programmes with a language/year abroad remain the most popular, but are now only offered by six UK chemical engineering departments compared with ten in 2006.Programmes with Industrial Experience are up to four from just two in 2006 (although many programmes have a sandwich year).Energy is now more popular (combined with Environment at Manchester), reflecting Varma and Grossman's (2014)  As noted from Fig. 7, offerings in management have disappeared and in study abroad have reduced considerably since 2006, as have the Molecular transformations-themed programmes, in opposition to the direction of travel encouraged by the Frontiers initiative and by Varma and Grossman (2014) who noted "an added benefit of the proposed cur-riculum… wherein the molecular level is connected through multiscale analysis to the systems level, is that it reconnects undergraduate education with contemporary ChE research, which has largely been absent for the last several decades."Energy has gained prominence, as predicted by Varma and Grossman (2014), while formalised industrial experience programmes are also slowly on the rise.

General Discussion
It appears that BEng chemical engineering programmes in the UK deliver a significant amount of Systems content, despite laments that university programmes do not contain enough Systems material such as process design, control and safety.Stephanopoulos and Reiklatis (2011) voiced this concern, writing: Today, Process Systems Engineering is well established as core capability in chemical engineering.Unfortunately, its educational foundation remains fragmented and a significant number of educational institutions do not recognize it as foundational component of the chemical engineering curriculum.Teaching of process design, process dynamics and control, process operations safety, are frequently "outsourced", if they are part of the curriculum at all.(Italics added.)However, the data from UK programmes does not appear to support this concern at the BEng level; most UK programmes cultivate a Systems perspective, including in-house teaching of design, control and safety, that is ultimately reinforced by the Design Project, while a number of MEng specialisms also aim to extend the Systems perspective.
Multiscale analysis is also prominent in UK programmes, with all programmes covering unit operations and transport phenomena to greater or lesser degrees of scope and sophistication.Perkins (2002) identified "the ability to synthesise as well as analyse" as the distinctive power of chemical engineering and, like Stephanopoulos and Reiklatis (2011) encouraged a balance between these two in chemical engineering programmes.The above analysis gives encouragement that, across the UK as a whole, these two legs of chemical engineering are indeed balanced.
However, the Frontiers model encourages a three-legged stool, and arguably the UK's chemical engineering provision could be strengthened by a greater prominence of Molecular transformation material.One must remember the basis of Perkin's (2003) claim that chemical engineering is the broadest and most scientific of the engineering disciplines, precisely because it has "a deep involvement with chemistry in addition to the application of physics and mathematics common to all engineering."The unique power of chemical engineering, according to Perkins and according to Armstrong, is its grasp of chemistry, and its unique opportunities are lost if chemical engineers are not distinguished from other engineers by having a "deep" knowledge of chemical and biochemical transformations in their toolbox.Perkins (2003), reviewing the origins of chemical engineering and the 1908 formation of the American Institute of Chemical Engineers, notes that "a society composed of men who can be called strictly engineers" was considered necessary to allow the new discipline to escape from the paradigms and preconceptions of industrial chemistry.While this separation at birth was needed in order to establish the new discipline's own identity and technical content in its early years, in this year of the centenary of the IChemE, perhaps the time has come to be more accepting of chemistry's legitimacy as a core element of chemical engineering, and to extend the embrace to biology.
Even so, the description of the Frontiers model as a "radically different curriculum" (Armstrong 2006;Wood n.d.) does not appear so radical from the UK perspective; the content of UK programmes seems consistently recognisable as aligned with the Frontiers proposals.There is, however, considerable scope to push the boundaries and enhance the distinctiveness of programmes, in order to create a greater coverage across the UK as a whole of the full scope of chemical engineering, and greater diversity of provision of graduates with strongly overlapping but not too uniformly identical skills.
As noted above, when the Frontiers model was being developed, its main driver appeared to be developments in molecular level understanding in both chemistry and, even more so, biology, along with the promises of nanotechnology, but with sustainability largely absent from the discussion; the proposals for new curriculum material were mainly within the Molecular transformations theme, and arguably rightly so, given its distinct third place even within UK programmes.Since then, however, sustainability has emerged as a more urgent driver of curriculum change (Favre et al. 2008;Byrne and Fitzpatrick 2009;Byrne 2010).Thus, writing several years later, Varma and Grossman (2014) identified that "the current paradigm of our discipline is molecular engineering," but went on to anticipate that "given the future needs for addressing sustainability and energy issues, we anticipate that the next paradigm is likely to be one involving the integration of multiscale and systems analysis."

Conclusions
Quantitative analysis of the relative proportions of the three components of the Frontiers model showed that chemical engineering programmes in the UK contain much less Molecular transformations content, relative to Multiscale analysis and Systems content, with more variation between the amount of Molecular transformations content compared with the other two themes.The average content for the 24 programmes analysed, contributing to each of the three themes of Molecular transformations, Multiscale analysis and Systems, was around 10%, 37% and 38%, respectively, with the remaining coming from Supporting competencies (10%) and Other (5%).
In terms of the structure of programmes, a general pattern was that first year contributed most Molecular transformations content, which decreased or disappeared in subsequent years, while the second year was dominated by Multiscale analysis and the final year emphasised Systems.
Programmes taught within chemical engineering departments appear to deliver slightly more Molecular transformations content relative to those that are taught within general engineering which, unsurprisingly, tend to have more material from other engineering disciplines.Joint departments delivered on average around 15 credits more of this theme than programmes taught from within general engineering, probably reflecting research themes in those departments.However, there are not extensive differences between programmes, suggesting that the IChemE accreditation criteria appear to provide some level of consistency between programmes or, more negatively, to constrain what Brown et al. (2019) consider to be a valuable diversity.
There is an opportunity to extend the current work and evaluate the structure and content of chemical engineering programmes worldwide relative to the tripartite structure of the Frontiers model, to identify distinctive differences between programmes and to develop a clear picture of the international pattern.

Appendix 1 IChemE Accreditation Credit Analysis
The learning outcomes for a BEng programme were extracted from sections A1 to A4 of Appendix 1 of the IChemE Accreditation Guide, Version 2.1, February 2019.
The number of credits for each section is based on minimum levels specified in the Guide of 85 European Credits of Core Chemical Engineering, 10 ECs of Chemical Engineering Practice, 10 ECs of Design Practice and Design Projects, and "sufficient" (interpreted as 20 ECs) of Underpinning material, a total of 125 out of 180 ECs for a 3-year BEng programme.
Each learning outcome was given equal weighting.
Each learning outcome was coded on the basis of methodology outlined in the main paper.
The total credits for each theme was calculated using the credit weightings for each section and proportion of learning outcomes for each theme under each section.Students graduating from an accredited programme will: • Have a knowledge and understanding of mathematics necessary for the analysis of and to support applications of key chemical engineering principles and processes.

Fundamentals -Level B
Students graduating from an accredited programme will: • Understand the principles of material and energy balances.Systems *Assuming that credit distribution for specified content is representative of entire course Molecular transformations fraction of credits = 0.102 Multiscale analysis fraction of credits = 0.384 Systems fraction of credits = 0.514 • Understand the thermodynamic and transport properties of fluids, solids and multiphase systems.Multiscale analysis • Understand the principles of momentum, heat and mass transfer, and be able to apply them to problems involving flowing fluids and multiple phases.Multiscale analysis • Be able to apply thermodynamic analysis to processes with heat and work transfer.Multiscale analysis • Understand the principles of equilibrium and chemical thermodynamics, and be able to apply them to phase behaviour, and to systems with chemical reaction.Molecular transformations • Understand the principles of chemical reaction and reactor engineering.Multiscale analysis

Mathematical Modelling and Quantitative Methods -Level B
Students graduating from an accredited programme will: • Be familiar with, and able to apply, a range of appropriate tools such as dimensional analysis and mathematical modelling.Multiscale analysis • Understand the role of empirical correlation and other approximate methods.Multiscale analysis • Be competent in the use of numerical and computer methods, including industry-standard chemical engineering software, for solving chemical engineering problems (detailed knowledge of computer coding is not required).

Process and Product Technology -Level B
This is a broad heading that includes the "unit operations" of separation and mixing; particle technology; equipment sizing and performance.Students graduating from an accredited programme will: • Understand and be able to apply methods to analyse the characteristics and performance of a range of typical mixing, separation, and similar processing steps for fluids, particulates and multi-phases.Multiscale analysis • Understand the principles on which processing equipment operates, and be able to apply methods to determine equipment size and performance of common items such as reactors, exchangers and columns.Multiscale analysis • Understand and be able to estimate the effect of processing steps upon the state of the material being processed, and on the end product in terms of its composition, morphology and functionality.Systems

Systems -Level B
Students graduating from an accredited programme will: • Understand the principles of batch and continuous operation and criteria for process selection.Systems • Understand the inter-dependence of elements of a complex system and be able to synthesise such systems by integrating process steps into a sequence and applying analysis techniques such as balances (mass, energy) and pinch.Systems • Understand system dynamics, be able to predict the response to changes in a dynamic system, and be able to design and determine the characteristics and performance of measurement and control functions.Systems

Process Safety -Level B
Students graduating from an accredited programme will: • Understand the inherent nature of safety and loss prevention, and the principal hazard sources in chemical and related processes -including flammability, explosivity and toxicity (including biological hazards).Molecular transformations • Understand the principles of risk assessment and of safety management, and be able to apply techniques for the assessment and abatement of process and product hazards.Systems • Understand methods of identifying process hazards (e.g.HAZOP), and of assessing environmental impact.Systems • Be aware of specialist aspects of safety and environmental issues, such as noise, hazardous area classification, relief and blowdown, fault tree analysis.Systems • Have knowledge of the local legislative framework and how it is applied to the management of safety, health and environment in practice and in the workplace, from the perspectives of all involved, including operators, designers, contractors, researchers, visitors and the public.Systems Safety Culture -Level B and Level F Not taught material, so not included in the credit analysis In addition to the above "taught" outcomes, it is expected that students' learning and teaching will be undertaken in an environment (Department, School, etc.) where there is an obviously strong and effective safety culture and where the students will learn by example.
Thus, students graduating from an accredited programme will understand that an effective Safety, Health and Environment (SH&E) culture includes: • Leadership -Head of Department and Senior Management take an active part in SH&E.• Visibility -clear and relevant signage and information; good standards of housekeeping in laboratories.• Behaviour -staff, students and visitors behave in a careful, risk averse manner; Personal Protective Equipment is available and usage is enforced; there are systems for incident reporting, follow-up, feedback and improvement.

Sustainability and Economics, Ethics -Level B
Students graduating from an accredited programme will: • Understand the principles of sustainability (environmental, social and economic) and be able to apply techniques for analysing, throughout the lifecycle, the interaction of process, product and plant with the environment.Systems • Understand and be able to apply the main methods of minimizing the environmental impact on air, water, land, and integrated eco-systems, including waste minimization at source and "end-of-pipe" methods.Systems • Be able to apply the principles of process, plant and project economics.Systems • Understand the need for high ethical and professional standards and understand how they are applied to issues facing engineers.Systems

Fig. 1
Fig. 1 An example layout of a curriculum.From Armstrong (2006), with permission

Fig. 4 Fig. 5
Fig.4The relationships between content contributing to Molecular transformations, Multiscale analysis and Systems

Fig. 6
Fig. 6 Content contributing to each of the themes of Molecular transformations, Multiscale analysis and Systems in each year of the BEng programme

Table 1
Allocation of module content across the Molecular transformations, Multiscale analysis, Systems, Supporting Competencies and Other themes Voronov et al. (2017)a are accredited by the China Engineering Education Accreditation Association, CEEAA(Yao et al. 2021); the accreditation guidance from these boards no doubt exerts a similar constraining influence on programmes in these countries.Voronov et al. (2017)analysed the credits of 158 USA chemical engineering programmes against 19 categories of content (noting that USA credits are different from UK and European credits, with one USA credit roughly equal to 1.5 European credits or 3 UK credits).Yao et al. (2021) simplified Voronov et al.'s categories into 13, and similarly analysed 79 Chinese programmes and compared them with the USA pattern.Table 3 allocates the categories proposed by Yao et al. (2021) into the three Frontiers themes plus combined Supporting Competencies/Other, and summarises the average credit balances of the USA and Chinese programmes.On average the breakdown in the USA and China is nearly 40% Systems, around 30% Multiscale Analysis, and around 15% Molecular Transformations, with Supporting Competencies/Other contributing

Table 2
Credit content (out of 360 credits total) of Molecular transformations, Multiscale analysis, Systems, Supporting Competencies and Other in UK BEng chemical engineering programmes

Table 3
Allocation of the chemical engineering programme categories proposed byYao et al. (2021)into the Frontiers themes, and the resulting USA and China credit averages, relative to a total average of 129.6 credits (USA) and 180.6 credits (China)

Table 4
Other

Table 5
Distribution of elective modules between Molecular transformations, Multiscale analysis, Systems and Supporting Competencies or Other

Table 6
Average credit contents and percentages of Molecular transformations, Multiscale analysis, Systems, Supporting Competencies and Other in Scottish BEng chemical engineering programmes compared with programmes from the rest of the UK

Table 7
Universities that have chemical engineering departments, joint departments, or teach chemical engineering within engineering departments or larger schools.(Italicised universities not included in the current analysis)

Table 8
Average credit contents and percentages of Molecular transformations, Multiscale analysis, Systems, Supporting Competencies and Other in university programmes from Chemical Engineering departments, Joint Departments and programmes with no separate department, being part of a larger school.(The fractions, 10/11, 3/5 and 10/12, indicate how many of the programmes listed in Table 7 are included in the averages.)

Table 9
Byrne (2006)l engineering programmes with a specialism in 2018, compared with those listed byByrne (2006) Byrne (2006)f the swing back to this topic, with nuclear also offered at Imperial, Leeds and Sheffield.Programmes with a bio or environmental flavour have halved compared with 2006.Single offerings with specialisms in pharmaceutical engineering, materials, petroleum, oil and gas, process control and sustainable engineering are now available.Meanwhile, losses since 2006 include business/ management, chemistry, computer science, fuel technology, environmental biotechnology and fine chemicals processing.Table10attempts a broad categorisation of the MEng specialisms into the three Frontiers themes and Supporting Competencies/Other, for the 2006 and 2018 data.Bio-themed specialisms along with chemistry and pharmaceutics have been considered probably developing additional knowledge and skills most strongly in MEng Chemical Engineering specialist programmes in 2018, compared with those listed byByrne (2006)

Table 10
Distribution of MEng specialisms from 2018 and 2006 between Molecular transformations, Multiscale analysis, Systems and Supporting Competencies or Other.(Specialisms in italics cross over two themes.)

Underpinning Mathematics, Science (Chemistry, Physics, Biology) and Associated Engineering Disciplines -20 ECs Learning Outcomes -Level B
• Have a knowledge and understanding of basic mathematical models relevant to chemical engineering.Multiscale analysis • Have a knowledge and understanding of scientific principles, namely the relevant aspects of physics, chemistry, biochemistry, biology and materials science, to enable the understanding of chemical engineering principles.20% Other/80% Molecular transformations • Have a basic understanding of relevant elements from engineering disciplines commonly associated with chemical engineering, such as electrical power and motors; microelectronics; mechanics of pressure vessels; structural mechanics.Other • Legislative Compliance -there is a sound understanding of, and compliance with, applicable SH&E legislation.• Risk Assessment and Management -Risk Assessment and Permit to Work systems are in place; those who use them are fully conversant with their roles and responsibilities.