Bài giảng Computer-aided chemical engineering - Chương 1: Computer simulation in process engineering
1/25/2014
Computer-Aided Chemical
Engineering
An Introduction to Process Simulation
C1. Computer Simulation
in Process Engineering
Computer Simulation in Process Engineering
1. Computer Simulation in Process Engineering
2. An Historical View
3. Approach of A Simulation Problem
3.1. Definition
3.2. Input
3.3. Execution
3.4. Results
3. 5. Analysis
4. Architecture of Flowsheeting Software
4.1 Computation Straegy
4.2 Sequential-Modular Approach
4.3 Equation-Oriented Aproach
4.4 Simultaeous-Modular Aproach
5. Integrated systems (pen Technology; Hyprotech; Simulation Sciences)
6. Selection of A Smulation Software (Functional Analysis; Computer
Science Analysis; ommercial Analysis)
7. Summary
1
1/25/2014
1. Computer Simulation in Process Engineering
Simulation is a fundamental activity in Process Engineering. The following
definition captures its essential features (Thomeù, 1993):
Simulation is a process of designing an operational model of a system and
conducting experiments with this model for the purpose either of
understanding the behaviour of the system or of evaluating alternative
strategies for the development or operaton of the systemIt has to be able
to reproduce selected aspects of the bhaviour f the system modelled to an
accepted degree of accuracy.
Simulation implies modelling, as well as tuning of models on experimental
data. A simulation model seves to conduct 'virtual experiments'. Almost
invisible in most cases, eing incorporated in the software technology,
modelling is the key feature in every simulation. It is important to keep in
mind that the simulation is only an apprimate representation of the reality,
at a certain level of accuracyand not the reality itself. That is why the user
must always be able to evaluate te reliability of the results delivered by a
simulator.
Simulation in Process Engineering requires specific scientific knowledge
among we may e accurate description of physical properties of pure
components ad compx mixtures, models for a large variety of reactors
and unit operations, as well as numerical techniques for solving large
systems of algebraic and differential equations.
1. Computer Simulation in Process Engineering
The main simulation activity in process engineering is flowseeting. Following a
previous definition (Westerberg et al., 1979) flowsheeting is the use of
computer aids to perform steady state heat and mass balancing, sizing and
costing calculation for a chemical process.
Taking into account the evolution in the last decades, we may formulate a
more extended definition as:
Flowsheeting is a systemic description of material and energy streams in a
process plant by means of computer simulation with the scope of designing a
new plant or improving the performance of an existing plant. Flowsheeting
can be used as aid to impleent a plntwide control strategy, as well as to
manage the planoperation.
2
1/25/2014
1. Computer Simulation in Process Engineering
Figure 1: The new paradigm of Process Engineering: Simulation as core
activity in Research & Development, Design ad Operation
1. Computer Simulation in Process Engineering
Table 1: Process Simulation applications in Chemical Process Industries
Chemical Process Industries
Oil & Gas
pplications
Offshore exploration, Surface eatment,
Pipeline trsport, Undergrond storage,
Gas processing
Refining
Petrochemicals
Gasoline and fuels
Hydrocarbon based hemicals, Methanol,
Monomer
Basic Organic Chemicals Intermediates, Solvents, Detergents, Dyes
Inorganic Chemicals
Fine Chemicals
Biotechnology
Metallurgy
Ammonia, Sulhuric Acid, Fertilisers
Pharmaceuicals, Cosmetics
Food and bio products
Steel, Aluminium, Copper, etc.
Polyethylene, PVC, Polystyrene, fibres, etc.
Paper pulp
Power plants, Coal gasification
Waste treatment, Safety
Water cleaning, Biomass valorisation
Polymers
Paper & Wood
Energy
Nuclear industy
Environment
3
1/25/2014
Figure 2: Applications of steady state and dynamic Plant Simulation Models
2. An Historical View
The story of process simulation began in 1966, when Simulation Science, a
small company located in Los Angeles/USA, had the dea to commercialise
a generic computer program for simulating distillation columns. This was
the heart of a flowsheeting package, PROCES (prersor of PRO II,
Simulation Science), which might be consideed the ancestor of process
simulators. Three years later ChemSre (Huston/USA) released
DESIGN (continued with DESIGN II and WINSIM), a capable flowsheeting
program for gas & oil applications. At that time, the expansion of the refining
and petrochemical industries motivated the advent of computer packages.
The first world oil crisis in 1973 has greatly stimulated the interest in
simulating processes with alternatie raw materials, as coal and biomass. In
1976, US Dept. of Engy and MIT launched jointly the ASPEN project
(continued by ASPEN PLUS, ASPEN Tech). The advent of high-speed
computation systems boosted the business of small companies specialised
in modelling and simulation. More generally, the scientific computation
evolved from individual programs to large packages designed as industrial
products.
4
1/25/2014
2. An Historical View
Personal Computer arrived in 1982. Although the power of PC's was weak
for flowsheeting, the idea of a 'personal' tool was stong enough to incite
enthusiasts (development of ChemCADChemStations and Hysys,
Hyprotech). The challenge of leaving thelitist environmnt of mainframes
was launched.
At the beginning of 1990's the dominatin of Pproducts was a fact. The
relative stabilisation in operaing systems, dominated nowadays by UNIX
and Windows, enabled thdevelopment of new generation of simulation
software. The Graphical User nterface became a central part in the
software development. The power of the former super-computers was
available on desktos.
3. Approach of A Simulation Problem
Figure 3: Methodological levels in steady-state siulation
5
1/25/2014
3. Approach of A Simulation Problem
3.1. Definition
A real Process Flow Diagram (PFD) must be translated in a scheme
compatible with the software capabilities anwith the simulation goals. The
flowsheet scheme built up for simulation purposs will e called Process
Simulation Diagram (PSD). PSD is in generdifferet from PFD. For
example, some simple units, as for pressuor temperature change, may
be lumped in more complex units (from simulatin viewpoint). Contrary,
complex units, as distillation columns or hemil reactors, may need to be
simulated as small flowshees. Hence, a preliminary problem analysis is
necessary. The steps in dining a simulation problem are:
- Convert PFD in PSD. Split the owshet in several sub-flowsheets, if
necessary.
- Analyse the simulation model for ach flowsheeting unit.
- Define chemical comnents, ncluding user-defined or petroleum
fractions.
- Analyse the thermodynamic modelling issues regarding the global
flowsheet, subflowsheetand key units.
- Analyse the specification mode (degrees of freedom) of complex units.
3. Approach of A Simulation Problem
3.2. Input: The input of a flowsheeting problem dependon the software
technology. This activity is normally supported by a Graphical User Interface
(GUI). The steps are:
- Draw the flowsheet.
- Select the components, from standard database or ser defid.
- Specify the input streams.
- Specify the units (degrees of freedom analysis
- Select the thermodynamic model. Check odel pameters.
- Determine the computational sequence.
- Initialise tear streams and difficult units. Note that correct specifications do not
always mean feasible specification.
3.3. Execution: The simulation is successful when the convergence criteria
are fulfilled both at the flowsheet and units' level. The user should pay
particular attention to vergence history for troubles shootings. Here the
steps involved are:
- Check the convence algorithms and parameters, and change them if
necessary.
- Check the convergence errors and the bounds of variables.
- Follow-up convergence history.
6
1/25/2014
3. Approach of A Simulation Problem
3.4. Results
A simulation delivers a large amount of results. The most important are:
- Stream report (material and heat balance), incluing flowsheet
convergence report.
- Unit report, including material and heat bnce, as well as unit
convergence report.
- Rating performances of units.
- Tables and graphs of physical properties.
The graphical presentation results may take various forms. Generally,
advanced software provides their wn analysis tools, but the exchange of
data with all-purpose seadsheets is usually available. Detailed results, as
internal flows or tables of properties, may be exported to specialised design
packages.
3. Approach of A Simulation Problem
3. 5. Analysis
Flowsheeting analysis tools enable to get more value from the simulation
results. The most used is the sensitivity analysis. This consists usually of
recording the variation of some 'smpled ariableas function of
'manipulated variables'. The interprtation of reslts can be exploited
directly, as trends, correlation or pre-optiisatio. Case studies can be
employed to investigate combinations (scenaios) of several flowsheet
variables. Finally, the simulation wrk mabe refined by multi-variable
optimisation.
A more advanced use of owsheeing capabilities is the controllability
analysis of standlone units, or the tudy of a plantwide control strategy.
7
1/25/2014
4. Architecture of Flowsheeting Software
4.1 Computation strategy
The architecture of a flowsheeting software is determined by the strategy of
computation. Three basic approaches have been devloped over the years:
- Sequential-Modular;
- Equation-Oriented;
- Simultaneous-Modular.
A. In Sequential-Modular (SM) achitecture, the omputation takes place
unit-by-unit following a calculation sequence. A rocess with recycles must
be decomposed in one or several calculation sequences. Each of these
begins at a certain place, where the incoming streams have to be known
either as inputs, or initialised as tear streams. The computation sequence of
units involved in a recycle dfines a convergence loop. When tear streams
are present, the inal steady sae solution is obtained by iterative
calculations. Tear streams are modified (accelerated) after successive
iterations by applyinan ppropriate convergence algorithm. The
computation stops when both the units and the tear streams satisfy some
convergence critea, usually the closure of the material and heat balance.
The SM architcture ws the first used in flowsheeting, but still dominates
the technology of steady state simulation.
4. Architecture of Flowsheeting Software
Among the advantages of the SM architecture we may cite
- Modular development of capabilities.
- Easy programming and maintenance.
- Easy control of convergence, both at the units and floweet level.
There are also disadvantages, as for exampe:
- Need for topological analysis and systmatic itialisation of tear streams.
- Difficulty to treat more complex computation sequences, as nested loops
or simultaneous flowsheet and design specification loops.
- Difficulty to treat specifications regardg internal unit (block) variables.
- Rigid direction of computaon, normally 'outputs from inputs'.
- Not well suited for dynamic simulation of systems with recycles.
Some modificatiohave been proposed to improve the flow of information
and avoid redndant cmputations. Among these we may mention the bi-
directional transmission of information implemented in HysysTM
.
8
1/25/2014
4. Architecture of Flowsheeting Software
B. In Equation-Oriented (EO) approach all the modellig equations are
assembled in a large sparse system producing Non-linear Algebraic
Equations (NAE) in steady state simulationand stiff Differential Algebraic
Equations (DAE) in dynamic simulation. Thus, the soluton is obtained by
solving simultaneously all the modelling equatios.
Among the advantages of the equation-solving architecture we may
mention:
- Flexible environment for specificationwhicmay be inputs, outputs, or
internal unit (block) variables.
- Better treatment of recyles, and no need for tear streams.
- Note that an object oriented mdelling approach is well suited for the EO
architecture.
However, there re also substantiadrawbacks, as:
- More programming ert.
- Need of substanil computing resources, but this is less and less a
problem.
- Difficulties ihandlinarge DAE systems.
- Difficult convergence follow-up and debugging.
4. Architecture of Flowsheeting Software
C. In Simultaneous-Modular approach the solution strategis a combination
of Sequential-Modular and Equation-Oriented aproaches. Rigorous
models are used at units' level, which are olved sequentially, while linear
models are used at flowsheet level, solved globaly. The near models are
updated based on results obtained wh rigoros models. This architecture
has been experimented in some academic ducts.
It may be concluded that Sequential-Modular appoach keeps a dominant
position in steady state simulation. The Equaton-Oriented approach has
proved its potential in dynamic simulation, and real time optimisation. The
solution for the future generations of flowsheeting software seems to be a
fusion of these strategies. The relese 11.1 of Aspen Plus (2002)
incorporates for the first tie EO features in the environment of a SM
simulator.
9
1/25/2014
4. Architecture of Flowsheeting Software
4.2 Sequential-Modular approach
Sequential-Modular approach is mostly used n steady state flowsheeting,
among we may cite as major products AspePlus, ChemCad, Hysys, ProII,
Prosim, and Winsim (see Table 2.2 for information). Hwever, there are
some dynamic simulators built on this architecure, the most popular being
Hysys.
The basic element in a modulsimultor is he unit operation model. A
simulation model is obtained by meanof coservation equations for mass,
energy and momentum. These lead finally to a system of non-linear
algebraic equations as:
f(u,x,d,p)=0
(1)
Here the notations signify:
- u, connectivity varias formally classified in input and output variables;
- x, internal (state) aiables, as temperatures, pressures, concentrations;
- d, variables defing the geometry, as volume, heat exchange area, etc;
- p, variables defining physical properties, as specific enthalpies, K-factors,
etc.
4. Architecture of Flowsheeting Software
Figure 4: General layout of unit operation model
10
1/25/2014
4. Architecture of Flowsheeting Software
Note that the system (1) has a strong non-linear character, particularly due
to the interdependence between physical properties and state variables. It
is important to keep in mind that physical roperties may consume up to
90% from the computation time. The above system suld be seen as
completed with equations for constrains.
The difference between the total numbeof nonredundant variables in the
system (1) and the number of indepndent algebraic equations gives the
degrees of freedom. Thee are usually specifications that a user must
supply to run a simulation.
In SM approach ach simulation ut (block) is treated by the rule:
output variables = funcn {input variables, unit variables, unit parameters}
The functional relatois specific for each unit, as flash, pump, reactor,
distillation columntc. Because of a large variety of physical situations, it is
rational to incorporate art of the algorithm in the routine that solves the
unit. From programming point of view it is said that the approach is
procedural.
4. Architecture of Flowsheeting Software
The architecture of software is a matter of computer science. However, as
with every complex system, the user should be aware about the main
elements. Figure 5 presents a generic archecture of a Sequential-Modular
simulator. The heart of the system is the Executive Progm. Its function is
to manage both computation and da exchnge tasks, as for example
calculation sequence, retrieval of paraers for physical properties,
routines for unit operations, convergence follow-upand management of the
data file system. Other essential components ar
- Databases with physical parameters for pure components and mixtures.
- Librarian for computing physical propertes of components and mixtures.
- Librarian for physical and cemical equilibrium calculations.
- Librarian for uit operations and eactors.
- Librarian with mathetical Solvers.
- Graphical User Ineface (GUI).
11
1/25/2014
4. Architecture of Flowsheeting Software
Figure 5: Software architecture of a Sequential-Modular simulator
4. Architecture of Flowsheeting Software
From the above description, we may conclude that
flowsheeting software is a very sophisticated computer-based
system, and not a collection of algorithms for solving different
unit operations. A process simulator must bdesigned with
computer science development anmanagement tools. It is
interesting to note that n the total cost the software
maintenance (typically more han 70 %) is by far more
important than the cosof programming (typically under 10 %).
12
1/25/2014
4. Architecture of Flowsheeting Software
4.3 Equation-Oriented approach
In Equation-Oriented (EO) approach the software architecture is close to a
solver of equations. EO is more suited for dnamic simulation since this can
be modelled by a system of differential-algebraic equatns (DAE) of the
form:
dx
--- = f (u,x,d,p) (2)
dt
The steady state solution is obtaind by setting the derivatives to zero. The
overall DAE system (2) is sparse and st, its size varying between 103 and
105 equations.
Dynamic simulation is ore demanding as its steady state counterpart.
Firstly, it needs muh more sizing elements. Then, the pressure variation
cannot be negled or lumped in the specification of simulation unit.
However, in general te specification of variables is more flexible. Any
flowsheet variable could be set as input or output streams, or internal unit
variables.
4. Architecture of Flowsheeting Software
The software architecture built with an EO approach is presented in Fig. 6.
The input of the simulation problem can be formulateby means of a meta-
language, or be supported by an intelligenGUI. In Aspen Dynamics, the
problem definition starts at steady state in Aspen Plus in an SM
environment. Adding accumulation terms the equations of units
generates the DAE system.
In an EO simulator the algorithmitreatment includes not only the
mathematical solution, but also problem debugging, compilation/linking, as
well as correction and addition of equatins. An important feature is the
post-processing of results, as timeecordings and plots of different
variables.
13
1/25/2014
4. Architecture of Flowsheeting Software
Figure 6: Software architecture of an Equation-Oiented simulator
5. Integrated Systems
Three major integrated simulation systems will be shortly presented.
Update information may be found by consulting the respective web sites.
5.1 Aspen Technology
The integrated system includes both all-puose flowsheeting system, and
specialised packages. Different packages commnicate via specific files,
but share the same physical property methods nd datHere we mention
only the major components.
- Aspen Plus: steady state simulation environmet with mprehensive database
and thermodynamic modelling; feasibility studies of nw designs, analysis of
complex plants with recycles, optimisation
- Aspen Dynamics: dynamic flosheeting nterfaced with Aspen Plus.
- Aspen Custom Modeller: mdelling environment for user add-on units and
programming in dynamic simulatin.
- Aspen Pinch: Pinch analysis, optimal desin of heat exchanger networks.
- Aspen Split: synthesis and deign of non-ideal separation systems.
- Polymer Plus: simulation of polymeration processes.
- Aspen Properties: physl property system including regression capabilities and
estimation method.
- Aspen OLI: simulatin of aqueous electrolyte systems.
- Batch Plus: recipeoriented batch process modeling.
- Batchfrac: batch reactioand separation processes.
- RTO: real time plant optimisation based on rigorous models.
- Aspen Zyqad: database environment for engineering projects.
14
1/25/2014
5. Integrated Systems
5.2 Hyprotech
The special feature of the flowsheeting system proposd by Hyprotech is
that steady state and dynamic simulation ae avaiable in the graphical
environment. Other products have beedeveloped as stand-alone
applications for engineering or operation purposesThe sstem is designed
for complete customisation. The main components are:
- Hysys.Concept: conceptual design pacage for design and retrofit applications,
with two components:
DISTIL: distillation column sequences,
HX: heat integration projects by Pinch analysi
- Hysys.Process: steady state flowsheeting for opimal new designs and modelling
of existing plants, evaluatretrofits and improve the process.
- Hysys.Plant: steady state and dynamic simuation to evaluate designs of existing
plants, and analyse safety and control prlems.
- Hysys.Operator Training: sta-up, shutown or emergency conditions, consisting
of an instructostation with DCS (Distributed Control System) interface, and
combined with Hysys.nt as calculation engine.
- Hysys.RTO+: real-timmultivarible optimisation; on-line models may be used
offline to aid maintnnce, scheduling and operations decision-making.
- Hysys.Refinery: orously modelling of complete refining processes, integrating
crude oil database and a set of rigorous refinery reactor models.
- Hysys.Ammonia: full plant modelling and optimisation of ammonia plants.
5. Integrated Systems
5.3 Simulation Sciences
The integrated system proposed by Simsci is built around a database
environment (PROVISION), and can be in pinciple interfaced with third-
party components. The system is orienteto applications in oil & gas
industries, as described below.
Process Engineering: tools for process engineeng desn and operational
analysis.
- Pro/II: general-purpose process flowsheeting ad optimisation.
- Hextran: Pinch analysis and desin of heatransfer equipment.
- Datacon: plant gross error detection andata reonciliation.
- Inplant: multiphase, fluid flow simulation for plant piping networks.
- Visual Flow: design and mdelling osafety systems and pressure relief networks.
Upstream Optimisation: decision-suppotools designed for oil and gas
production.
- Pipephase: multphase fluid flow simlator for pipelines and networks.
- Tacite: multiphase simuor for complex transient flow phenomena.
- Netopt: optimisation of oil and gaproduction operations.
On-line Performance: Advanced Process Control (APC) and on-line
optimisation.
- ROMeo: on-lie lant melling and optimisation, off-line analysis tool.
- Connoisseur: APC multivariable controls several via the plant's DCS (Distributed
Control System).
15
1/25/2014
6. Selection of A Simulation Software
The selection of a simulation system is a strategic decision for an
organisation. It implies a medium/long term co-ordnation policy, both in
hardware platforms and in scientific software, as well as in the training of
personnel, compatibility with third parties environment, etc. The procedure
described below may be applied for low-risk choicof any scientific
software. The evaluation procedure tkes the orm of a questionnaire, as
given hereafter.
1. Functional Analysis
- Typical applications.
- Capabilities and options.
- User interface.
- Algorithms and numerical metods.
- Complementary products.
- Databases" size, applications, qualitof data.
- Post-treatment of resul
- Typical benchmarks ad library of examples.
- User manual
6. Selection of A Simulation Software
2. Computer Science Analysis
- Hardware: platforms and operating systems.
- Resources: hard disk space, typical user spacmemory.
- Software analysis: architecture, file structure, programming laguages.
- Graphical User Interface: functions, portaility.
- Use of standards: graphics, communicaton, poability.
- Software development tools and qualiy control
- Interface with known scientific or -purpossoftwae.
- Customisation.
3. Commercial Analysis
- Social reason, shareholders, financial rep.
- Commercial politics: market, ents, prices.
- Training and usr support.
- Maintenance and upda
- Communication polics: users group meetings, newsletter
- Academic and scntific contacts, publications.
16
1/25/2014
6. Selection of A Simulation Software
Each question is quoted by a mark and weighted by a factor. Consequently,
this procedure will produce a list of two or three good candidates. The final
choice will imply a finer assessment of the above aspects. More information
may be asked by experts, as benchmarks, customised demonstrations,
programming samples, quality assurance documents, etIn this respect it
is important to test the product on prblems ose to the user application
area.
Despite similar functionalities among generalist uppliers, every system has
capabilities where it performs better than othrs. This could have historical
reasons, or could come frm the profile of clients. The reliability of physical
properties and of parameters in hermodynamic models is an essential
feature in design. That is why the qualy of thermodynamics is a peculiar
feature in selecting a simulatn system for process design purposes. Other
important features are customisaon of units, programming capabilities,
transmission of information and control structures, as well as debugging
convergence problems ith recycles. A system in which the user has the
control on all the asets of the modelling background should be preferred.
As mentione, the ocess simulation market has known severe
transformations in the 1985-1995 decade. Relatively few systems have
survived. Table 2 presents a sample of the main commercial software at the
end of 2001.
6. Selection of A Simulation Software
Table 2: Process Design & Simulation commercial software
Supplier
1 Aspen Tech
Cambridge-MA/USA
Software
Appcations
Flowsheeting, sizng, costing
Dynamic Sition, Real time systems
Energy Integration
Aspen Plus
Aspen Dynamics
Advent
Split
Bijac
Non-ideaDistillation Sytems
Heaxchanger den
Polymer Plus
Batchfrac
ChemCad
CC-ReACS
Hysys
Pomer procese
atch and continuous rocesses
Flowsheetingsizing, cos
Batch rector simulaor
2 Chemstations
Houston-USA
3 Hyprotech
Combid steady e and dynamic simulation
Noideal Disttion Systems
hermodynamics
Calgary-Canada
Concept
Hyprop
ProSim
4 Prosim
Flowsheeting
Toulouse-France
5 Simulation Science
Los Angeles-USA
Pro II
Flowseting, sizing
Graphial environment
Egy Integration
Povision
Hextran
Datacon
ROMeo
De
Data reconciliation
Rigorous on-line modelling
Flowsheeting, sizing
6 WinSim
Houston-USA
7 Imperial College
London-UK
_ROMS
Dynamic Simulation
8 Bryan Research &
Engineering
Prosim
Tsw
Superget
BatchPro Designer
Flowsheeting
Gas purification
9 KBC/Linnhoff March
10 Intelligen, Scotch Plains,
NJ-USA
Energy integration
Scheduling and Design of batch processes
17
1/25/2014
7. Summary
Process Simulation is a key activity in Process Engineering covering the
whole life cycle of a process, from Research & Development to Conceptual
Design and Plant Operation. In this context, flowseeting is a systemic
description of material and energy streams n a process plant by means of
computer simulation with the scope of designing the plant or understanding
its operation.
Steady state flowsheeting is an eveyday toof the hemical engineer. The
generalisation of the dynamic simulation in the design practice is the next
challenge. By means of a capable commerciaflowsheeting system, it is
possible to produce a comprehensive computer image of a running
process, a Plant Simulatin Model, which can combine both steady state
and dynamic simulation. This tool is partiularly valuable in understanding
the operation of a complex plant, and ohis basis can serve for continuous
improving the process desigor for dveloping new processes.
Process simulation is bed on models. A model should mirror the reality at
the degree of accuracy required by application. Having a good knowledge
of the modelling bakground is compulsory for getting reliable results and
using the softwarffectively. The difference between successful and failed
computer-aideproject hould be attributed more to an insufficient capacity
of the user to take advantage from the modelling environment than to
inadequate performance of the simulator. That is why a problem simulation
must be carefully prepared.
7. Summary
Flowsheeting is still dominated by the Sequential-Modulaarchitecture, but
incorporates increasingly features of the Equation-Oiented solution mode.
A limited number of systems can offer both steady state and dynamic
flowsheeting simulators.
The integration of simulation tools is ecessry to cope with the variety of
needs in process engineering. It is desable to open the access to
simulation technology to a larger number of modl suppliers. This can be
realised by a cooperative approach between thcommunity of users and of
software producers. The avaability osimultion systems on Internet can
boost the use of simulation technology in a global environment.
18
Bạn đang xem tài liệu "Bài giảng Computer-aided chemical engineering - Chương 1: Computer simulation in process engineering", để tải tài liệu gốc về máy hãy click vào nút Download ở trên
File đính kèm:
bai_giang_computer_aided_chemical_engineering_chuong_1_compu.pdf

