Solid-State Fermentation Bioreactors

by Mitchell, David A.; Krieger, Nadia; Berovic, Marin

• ISBN13: 9783540312857
• ISBN10: 3540312854
• Format: Hardcover
• Copyright: 2006-06-15
• Publisher: Springer Verlag

Summary

This concise professional reference provides a fundamental framework for the design and operation of solid-state fermentation bioreactors, enabling researchers currently working at laboratory scale to scale-up their processes. After surveying the main bioreactor types currently used in solid-state fermentation, it focuses on the mathematical modeling of bioreactors, which is covered in three parts. Firstly, the book shows how to plan a research program in order to characterize the growth kinetics in a manner appropriate for incorporation into bioreactor models. Secondly, it addresses the heat and mass transfer phenomena that occur in solid-state fermentation bioreactors and the mathematical expressions that are used to describe them. Thirdly it demonstrates, through a number of case studies, how mathematical models can be used in the optimization of bioreactor performance. The final part of the book addresses several issues closely related with bioreactor operation, namely process monitoring equipment, process control strategies and the selection of an appropriate air preparation system.

Table of Contents

1 Solid-State Fermentation Bioreactor Fundamentals: Introduction and Overview	1	(12)
David A. Mitchell, Marin Berovic, and Nadia Krieger
1.1 What Is "Solid-state Fermentation"?	1	(2)
1.2 Why Should We Be Interested in SSF?	3	(2)
1.3 What Are the Current and Potential Applications of SSF?	5	(1)
1.4 Why Do We Need a Book on the Fundamentals of SSF Bioreactors?	6	(2)
1.5 How Is this Book Organized?	8	(4)
1.5.1 Introduction to Solid-State Fermentation and Bioreactors	9	(1)
1.5.2 Introduction to the Various Classes of SSF Bioreactors	9	(1)
1.5.3 Fundamentals of Modeling of SSF Bioreactors	10	(1)
1.5.4 Modeling Case Studies of SSF Bioreactors	11	(1)
1.5.5 Key Issues Associated with SSF Bioreactors	11	(1)
1.5.6 A Final Word	12	(1)
Further Reading	12	(1)
2 The Bioreactor Step of SSF: A Complex Interaction of Phenomena	13	(20)
David A. Mitchell, Marin Berovic, Montira Nopharatana, and Nadia Krieger
2.1 The Need for a Qualitative Understanding of SSF	13	(1)
2.2 The General Steps of an SSF Process	14	(2)
2.3 The Bioreactor Step of an SSF Process	16	(1)
2.4 The Physical Structure of SSF Bioreactor Systems	17	(5)
2.4.1 A Macroscale View of the Phases in an SSF Bioreactor	17	(3)
2.4.2 A Microscale Snapshot of the Substrate Bed	20	(2)
2.5 A Dynamic View of the Processes Occurring	22	(9)
2.5.1 A Dynamic View with a Time Scale of Seconds to Minutes	22	(2)
2.5.2 A Dynamic View with a Time Scale of Hours to Days	24	(7)
2.6 Where Has this Description Led Us?	31	(1)
Further Reading	32	(1)
3 Introduction to Solid-State Fermentation Bioreactors	33	(12)
David A. Mitchell, Marin Berovic, and Nadia Krieger
3.1 Introduction	33	(1)
3.2 Bioreactor Selection and Design: General Questions	34	(4)
3.2.1 The Crucial Questions	35	(1)
3.2.2 Other Questions to Consider	36	(2)
3.3 Overview of Bioreactor Types	38	(3)
3.3.1 Basic Design Features of the Various Bioreactor Types	38	(2)
3.3.2 Overview of Operating Variables	40	(1)
3.4 A Guide for Bioreactor Selection	41	(2)
Further Reading	43	(2)
4 Heat and Mass Transfer in Solid-State Fermentation Bioreactors: Basic Principles	45	(12)
David A. Mitchell, Marin Berovic, Oscar F. von Meien, and Luiz F.L. Luz Jr
4.1 Introduction	45	(1)
4.2 An Overall Balance Over the Bioreactor	45	(2)
4.3 Looking Within the Bioreactor in More Detail	47	(9)
4.3.1 Phenomena Within Subsystems Within the Bioreactor	47	(3)
4.3.2 Transfer Between Subsystems When the Substrate Bed Is Treated as a Single Pseudo-Homogeneous Phase	50	(1)
4.3.3 Transfer Between Subsystems When the Substrate Bed Is Treated as Two Separate Phases	51	(2)
4.3.4 Bulk Gas Flow Patterns and Pressure Drops	53	(3)
4.3.5 Mixing Patterns in Agitated Beds of Solids	56	(1)
Further Reading	56	(1)
5 The Scale-up Challenge for SSF Bioreactors	57	(8)
David A. Mitchell, Oscar F. von Meien, Luiz F.L. Luz Jr, and Marin Berovic
5.1 Introduction	57	(1)
5.2 The Challenges Faced at Large Scale in SLF and SSF	57	(1)
5.3 The Reason Why Scale-up Is not Simple	58	(5)
5.4 Approaches to Scale-up of SSF Bioreactors	63	(1)
Further Reading	64	(1)
6 Group Bioreactors: Unaerated and Unmixed	65	(12)
David A. Mitchell, Nadia Krieger, and Marin Berovic
6.1 Basic Features, Design, and Operating Variable for Tray-type Bioreactors	65	(1)
6.2 Use of Bag Systems in Modern Processes	66	(1)
6.3 Heat and Mass Transfer in Tray Bioreactors	67	(8)
6.3.1 Oxygen Profiles Within Trays	67	(2)
6.3.2 Temperature Profiles Within Trays	69	(2)
6.3.3 Insights from Dynamic Modeling of Trays	71	(4)
6.4 Conclusions	75	(2)
Further Reading
7 Group II Bioreactors: Forcefully-Aerated Bioreactors Without Mixing	77	(18)
David A. Mitchell, Penjit Srinophakun, Nadia Krieger, and Oscar F. von Meien
7.1 Introduction	77	(1)
7.2 Basic Features, Design, and Operating Variables for Packed-Bed Bioreactors	77	(16)
7.3 Experimental Insights into Packed-Bed Operation	81	(1)
7.3.1 Large-Scale Packed-Beds	82	(1)
7.3.2 Pilot-Scale Packed-Beds	83	(1)
7.3.3 Laboratory-scale Packed-beds	84	(9)
7.4 Conclusions on Packed-Bed Bioreactors	93	(1)
Further Reading	94	(1)
8 Group III: Rotating-Drum and Stirred-Drum Bioreactors	95	(20)
David A. Mitchell, Deidre M. Stuart, Matthew T. Hardin, and Nadia Krieger
8.1 Introduction	95	(1)
8.2 Basic Features, Design, and Operating Variables for Group III Bioreactors	95	(3)
8.3 Experimental Insights into the Operation of Group III Bioreactors	98	(6)
8.3.1 Large-Scale Applications	98	(2)
8.3.2 Pilot-Scale Applications	100	(1)
8.3.3 Small-Scale Applications	101	(3)
8.4 Insights into Mixing and Transport Phenomena in Group III Bioreactors	104	(8)
8.4.1 Solids Flow Regimes in Rotating Drums	105	(5)
8.4.2 Gas Flow Regimes in the Headspaces of Rotating Drums	110	(2)
8.5 Conclusions on Rotating-Drum and Stirred-Drum Bioreactors	112	(2)
Further Reading	114	(1)
9 Group IVa: Continuously-Mixed, Forcefully-Aerated Bioreactors	115	(14)
David A. Mitchell, Nadia Krieger, Marin Berovic, and Luiz F.L. Luz Jr
9.1 Introduction	115	(1)
9.2 Basic Features, Design, and Operating Variables of Group IVa Bioreactors	115	(2)
9.3 Where Continuously-Agitated, Forcefully-Aerated Bioreactors Have Been Used	117	(8)
9.3.1 Stirred Beds with Mechanical Agitators	117	(4)
9.3.2 Gas-Solid Fluidized Beds	121	(2)
9.3.3 Bioreactors Mixed by the Motion of the Bioreactor Body	123	(2)
9.4 Insights into Mixing and Transport Phenomena in Group IVa Bioreactors	125	(3)
9.5 Conclusions on Group IVa Bioreactors	128	(1)
Further Reading	128	(1)
10 Group IVb: Intermittently-Mixed Forcefully-Aerated Bioreactors	129	(12)
David A. Mitchell, Oscar F. von Meien, Luiz F.L. Luz Jr, Nadia Krieger, J. Ricardo Pérez-Correa, and Eduardo Agosin
10.1 Introduction	129	(1)
10.2 Basic Features of Group IVb Bioreactors	129	(2)
10.3 Experimental Insights into the Performance of Group IVb Bioreactors	131	(7)
10.3.1 Large-Scale Intermittently-Mixed Bioreactors	131	(4)
10.3.2 Pilot-Scale Intermittently-Mixed Bioreactors	135	(3)
10.3.3 Laboratory-Scale Intermittently-Mixed Bioreactors	138	(1)
10.4 Insights into Mixing and Transport Phenomena in Group IVb Bioreactors	138	(2)
10.5 Conclusions on Group IVb Bioreactors	140	(1)
Further Reading	140	(1)
11 Continuous Solid-State Fermentation Bioreactors	141	(18)
Luis B. R. Sánchez, Morteza Khanahmadi, and David A. Mitchell
11.1 Introduction	141	(1)
11.2 Basic Features of Continuous SSF Bioreactors	141	(7)
11.2.1 Equipment	141	(5)
11.2.2 Flow Patterns: Real-Flow Models	146	(2)
11.3 Continuous Versus Batch Mode of Operation	148	(4)
11.3.1 Reduction of Upstream and Downstream Investment	148	(1)
11.3.2 Uniformity of the Product from Batch and Continuous Bioreactors	149	(1)
11.3.3 Enhanced Production Rates	150	(1)
11.3.4 Contamination	150	(2)
11.4 Comparison by Simulation of the Three CSSFBs	152	(6)
11.4.1 Continuous Tubular Flow Bioreactors (CTFBs) with Recycling	152	(2)
11.4.2 Continuous Rotating Drum Bioreactor (CRDB)	154	(1)
11.4.3 Continuous Stirred Tank Bioreactor (CSTB)	155	(1)
11.4.4 Evaluation of the Various CSSFB Configurations	156	(2)
11.5 Scientific and Technical Challenges for CSSFBs	158	(1)
Further Reading	158	(1)
12 Approaches to Modeling SSF Bioreactors	159	(20)
David A. Mitchell, Luiz F.L. Luz Jr, Marin Berovic, and Nadia Krieger
12.1 What Are Models and Why Model SSF Bioreactors?	159	(2)
12.2 Using Models to Design and Optimize an SSF Bioreactor	161	(3)
12.2.1 Initial Studies in the Laboratory	161	(2)
12.2.2 Current Bioreactor Models as Tools in Scale-up	163	(1)
12.2.3 Use of the Model in Control Schemes	164	(1)
12.3 The Anatomy of a Model	164	(3)
12.4 The Seven Steps of Developing a Bioreactor Model	167	(10)
12.4.1 Step 1: Know What You Want to Achieve and the Effort You Are Willing to Put into Achieving It	170	(1)
12.4.2 Step 2: Draw the System at the Appropriate Level of Detail and Explicitly State Assumptions	170	(1)
12.4.3 Step 3: Write the Equations	171	(2)
12.4.4 Step 4: Estimate the Parameters and Decide on Values for the Operating Variables	173	(1)
12.4.5 Step 5: Solve the Model	174	(1)
12.4.6 Step 6: Validate the Model	175	(2)
12.4.7 Step 7: Use the Model	177	(1)
Further Reading	177	(2)
13 Appropriate Levels of Complexity for Modeling SSF Bioreactors	179	(12)
David A. Mitchell, Luiz F.L. Luz Jr, Marin Berovic, and Nadia Krieger
13.1 What Level of Complexity Should We Aim for in an SSF Bioreactor Model?	179	(1)
13.2 What Level of Detail Should Be Used to Describe the Growth Kinetics?	179	(4)
13.2.1 Growth Should Be Treated as Depending on Which Factors?	180	(2)
13.2.2 Is It Worthwhile to Describe the Spatial Distribution of the Biomass at the Microscale?	182	(1)
13.2.3 Typical Features of the Kinetic Sub-models	183	(1)
13.3 What Level of Detail Should Be Used to Describe Transport Processes?	183	(2)
13.4 At the Moment Fast-Solving Models Are Useful	185	(3)
13.5 Having Decided on Fast-Solving Models, How to Solve Them?	188	(1)
13.6 Conclusions	188	(1)
Further Reading	189	(2)
14 The Kinetic Sub-model of SSF Bioreactor Models: General Considerations	191	(16)
David A. Mitchell and Nadia Krieger
14.1 What Is the Aim of the Kinetic Analysis?	191	(3)
14.2 How Will Growth Be Measured Experimentally?	194	(3)
14.2.1. The Problem of Measuring Biomass in SSF	194	(2)
14.2.2 Indirect Approaches to Monitoring Growth	196	(1)
14.3 What Units Should Be Used for the Biomass?	197	(4)
14.3.1 Grams of Biomass per Gram of Fresh Sample	199	(1)
14.3.2 Grams of Biomass per Gram of Dry Sample	199	(1)
14.3.3 Grams of Biomass per Gram of Initial Fresh or Dry Sample	200	(1)
14.3.4 Which Set of Units Is Best to Use for Expressing the Biomass?	201	(1)
14.4 Kinetic Profiles and Appropriate Equations	201	(3)
14.5 Conclusions	204	(1)
Further Reading	205	(2)
15 Growth Kinetics in SSF Systems: Experimental Approaches	207	(12)
David A. Mitchell and Nadia Krieger
15.1 Experimental Systems for Studying Kinetics	207	(4)
15.1.1. Flasks in an Incubator	208	(2)
15.1.2. Columns in a Waterbath	210	(1)
15.1.3. Comparison of the Two Systems	211	(1)
15.2 Experimental Planning	211	(3)
15.3 Estimation of Biomass from Measurements of Biomass Components	214	(3)
15.3.1 Suitable Systems for Undertaking Calibration Studies	214	(2)
15.3.2 Conversion of Measurements of Components of the Biomass	216	(1)
15.3.3 Limitations of these Calibration Methods	217	(1)
15.4 Conclusion	217	(1)
Further Reading	217	(2)
16 Basic Features of the Kinetic Sub-model	219	(16)
David A. Mitchell, Graciele Viccini, Lilik Ikasari, and Nadia Krieger
16.1 The Kinetic Sub-model Is Based on a Differential Growth Equation	219	(1)
16.2 The Basic Kinetic Expression	220	(2)
16.3 Incorporating the Effect of the Environment on Growth	222	(9)
16.3.1 Incorporating the Effect of Temperature on Growth	225	(3)
16.3.2 Incorporating the Effect of Water Activity on Growth	228	(2)
16.3.3 Combining the Effects of Several Variables	230	(1)
16.4 Modeling Death Kinetics	231	(3)
16.4.1 General Considerations in Modeling of Death Kinetics	231	(1)
16.4.2 Approaches to Modeling Death Kinetics that Have Been Used	232	(2)
16.5 Conclusion	234	(1)
Further Reading	234	(1)
17 Modeling of the Effects of Growth on the Local Environment	235	(14)
David A. Mitchell and Nadia Krieger
17.1 Introduction	235	(2)
17.2 Terms for Heat, Water, Nutrients, and Gases	237	(7)
17.2.1 Metabolic Heat Production	237	(1)
17.2.2 Water Production	238	(1)
17.2.3 Substrate and Nutrient Consumption	238	(1)
17.2.4 Oxygen Consumption and Carbon Dioxide Production	239	(4)
17.2.5 General Considerations with Respect to Equations for the Effects of Growth on the Environment	243	(1)
17.3 Modeling Particle Size Changes	244	(2)
17.3.1 An Empirical Equation for Particle Size Reduction	244	(1)
17.3.2 How to Model Particle Size Changes in Bioreactor Models?	245	(1)
17.4 Product Formation – Empirical Approaches	246	(1)
17.5 Conclusions	247	(1)
Further Reading	247	(2)
18 Modeling of Heat and Mass Transfer in SSF Bioreactors	249	(16)
David A. Mitchell, Oscar F. von Meien, Luiz F.L. Luz Jr, and Marin Berovic
18.1 Introduction	249	(1)
18.2 General Forms of Balance Equations	249	(3)
18.3 Conduction	252	(3)
18.3.1 Conduction Across the Bioreactor Wall	252	(1)
18.3.2 Conduction Within a Phase	253	(2)
18.4 Convection	255	(4)
18.4.1 Convection at the Bioreactor Wall	255	(1)
18.4.2 Convective Heat Removal from Solids to Air	256	(2)
18.4.3 Convective Heat Removal Due to Air Flow Through the Bed	258	(1)
18.5 Evaporation	259	(4)
18.5.1 Evaporation from the Solids to the Air Phase	260	(1)
18.5.2 Water Removal Due to Air Flow Through the Bed	261	(2)
18.6 Conclusions	263	(1)
Further Reading	263	(2)
19 Substrate, Air, and Thermodynamic Parameters for SSF Bioreactor Models	265	(14)
David A. Mitchell, Oscar F. von Meien, Luiz F.L. Luz Jr, and Marin Berovic
19.1 Introduction	265	(1)
19.2 Substrate Properties	265	(8)
19.2.1 Particle Size and Shape	266	(1)
19.2.2 Particle Density	267	(1)
19.2.3 Bed Packing Density	268	(2)
19.2.4 Porosity (Void Fraction)	270	(1)
19.2.5 Water Activity of the Solids	271	(2)
19.3 Air Density	273	(1)
19.4 Thermodynamic Properties	274	(4)
19.4.1 Saturation Humidity	275	(1)
19.4.2 Heat Capacity of the Substrate Bed	276	(1)
19.4.3 Enthalpy of Vaporization of Water	277	(1)
Further Reading	278	(1)
20 Estimation of Transfer Coefficients for SSF Bioreactors	279	(12)
David A. Mitchell, Oscar F. von Meien, Luiz F.L. Luz Jr, and Marin Berovic
20.1 Introduction	279	(1)
20.2 Thermal Conductivities of Substrate Beds	279	(1)
20.3 Heat Transfer Coefficients Involving the Wall	280	(3)
20.3.1. Bed-to-Wall Heat Transfer Coefficients	281	(1)
20.3.2 Wall-to-Headspace Heat Transfer Coefficients	281	(1)
20.3.3 Wall-to-Surroundings Heat Transfer Coefficients	282	(1)
20.3.4 Overall Heat Transfer Coefficients	282	(1)
20.4 Solids-to-Air Heat and Mass Transfer Coefficients Within Beds	283	(1)
20.5 Bed-to-Headspace Transfer Coefficients	284	(5)
20.6 Conclusions	289	(1)
Further Reading	289	(2)
21 Bioreactor Modeling Case Studies: Overview	291	(4)
David A. Mitchell
21.1 What Can the Models Be Used to Do?	291	(1)
21.2 Limitations of the Models	292	(1)
21.3 The Amount of Detail Provided about Model Development	293	(1)
21.4 The Order of the Case Studies	294	(1)
22 A Model of a Well-mixed SSF Bioreactor	295	(20)
David A Mitchell and Nadia Krieger
22.1 Introduction	295	(1)
22.2 Synopsis of the Model	295	(8)
22.2.1 The System, Equations, and Assumptions	295	(6)
22.2.2 Values of Parameters and Variables	301	(2)
22.3 Insights the Model Gives into the Operation of Well-Mixed Bioreactors	303	(9)
22.3.1 Insights into Operation at Laboratory Scale	303	(4)
22.3.2 Insights into Operation at Large Scale	307	(3)
22.3.3 Effect of Scale and Operation on Contributions to Cooling of the Solids	310	(2)
22.4 Conclusions on the Operation of Well-Mixed Bioreactors	312	(2)
Further Reading	314	(1)
23 A Model of a Rotating-Drum Bioreactor	315	(16)
David A. Mitchell, Deidre M. Stuart. and Nadia Krieger
23.1 Introduction	315	(1)
23.2 A Model of a Well-Mixed Rotating-Drum Bioreactor	315	(13)
23.2.1 Synopsis of the Mathematical Model and its Solution	315	(5)
23.2.2 Predictions about Operation at Laboratory Scale	320	(5)
23.2.3 Scale-up of Well-Mixed Rotating-Drum Bioreactors	325	(3)
23.3 What Modeling Work Says about Rotating-Drum Bioreactors Without Axial Mixing	328	(1)
23.4 Conclusions on the Design and Operation of Rotating-Drum Bioreactors	329	(1)
Further reading	330	(1)
24 Models of Packed-Bed Bioreactors	331	(18)
David A. Mitchell, Penjit Srinophakun, Oscar F. von Meien, Luiz F.L. Luz Jr, and Nadia Krieger
24.1 Introduction	331	(1)
24.2 A Model of a Traditional Packed-Bed Bioreactor	331	(10)
24.2.1 Synopsis of the Mathematical Model and its Solution	333	(1)
24.2.2 Base-Case Predictions	334	(2)
24.2.3 Insights that Modeling Has Given into Optimal Design and Operation of Traditional Packed-Beds	336	(5)
24.3 A model of the Zymotis Packed-Bed Bioreactor	341	(6)
24.3.1 The Model	341	(1)
24.3.2 Insights into Optimal Design and Operation of Zymotis Packed-Beds	342	(5)
24.4 Conclusions on Packed-Bed Bioreactors	347	(1)
Further Reading	347	(2)
25 A Model of an Intermittently-Mixed Forcefully-Aerated Bioreactor	349	(14)
David A. Mitchell, Oscar F. von Meien, Luiz F.L. Luz Jr, and Nadia Krieger
25.1 Introduction	349	(1)
25.2 Synopsis of the Model	349	(4)
25.3 Insights the Model Gives into Operation of Intermittently-Mixed Bioreactors	353	(7)
25.3.1 Predictions about Operation at Laboratory Scale	353	(4)
25.3.2 Investigation of the Design and Operation of Intermittently-Mixed Forcefully-Aerated Bioreactors at Large Scale	357	(3)
25.4 Conclusions on Intermittently-Mixed Forcefully-Aerated Bioreactors	360	(2)
Further Reading	362	(1)
26 Instrumentation for Monitoring SSF Bioreactors	363	(12)
Mario Fernández and J. Ricardo Pérez-Correa
26.1 Why Is It Important to Monitor SSF Bioreactors?	363	(1)
26.2 Which Variables Would We Like to Measure?	363	(2)
26.3 Available Instrumentation for On-line Measurements	365	(4)
26.4 Data Filtering	369	(2)
26.5 How to Measure the Other Variables?	371	(3)
Further Reading	374	(1)
27 Fundamentals of Process Control	375	(12)
J Ricardo Pérez-Correa and Mario Fernández
27.1 Main Ideas Underlying Process Control	375	(2)
27.1.1 Feedback	375	(1)
27.1.2 Control Loop	376	(1)
27.1.3 Computer Control Loop	376	(1)
27.2 Conventional Control Algorithms	377	(9)
27.2.1 On/Off Control	377	(3)
27.2.2 PID Control	380	(5)
27.2.3 Model Predictive Control	385	(1)
Further Reading	386	(1)
28 Application of Automatic Control Strategies to SSF Bioreactors	387	(16)
J. Ricardo Pérez-Correa, Mario Fernández, Oscar F. von Meien, Luiz F.L. Luz Jr, and David A. Mitchell
28.1 Why Do We Need Automatic Control in SSF Bioreactors?	387	(1)
28.2 How to Control SSF Bioreactors?	388	(2)
28.3 Case Studies of Control in SSF Bioreactors	390	(10)
28.3.1 Control of the Bioreactors at PUC Chile	390	(5)
28.3.2 Model-Based Evaluation of Control Strategies	395	(5)
28.4 Future Challenges in the Control of SSF Bioreactors	400	(1)
Further Reading	401	(2)
29 Design of the Air Preparation System for SSF Bioreactors	403	(10)
Oscar F. von Meien, Luiz F.L. Luz Jr, J. Ricardo Pérez-Correa, and David A. Mitchell
29.1 Introduction	403	(1)
29.2 An Overview of the Options Available	404	(3)
29.3 Blower/Compressor Selection and Flow Rate Control	407	(1)
29.4 Piping and Connections	408	(1)
29.5 Air Sterilization	408	(1)
29.6 Humidification Columns	409	(1)
29.7 Case Study: An Air Preparation System for a Pilot-Scale Bioreactor	410	(2)
Further Reading	412	(1)
30 Future Prospects for SSF Bioreactors	413	(16)
David A. Mitchell, Marin Berovic, and Nadia Krieger
30.1 The Increasing Importance of SSF	413	(1)
30.2 Present State and Future Prospects	414	(3)
References	417	(12)
Appendix: Guide to the Bioreactor Programs.	429	(14)
A.1 Disclaimer	429	(1)
A.2 General Information and Advice	429	(2)
A.3 Use of the Well-Mixed Bioreactor Model	431	(1)
A.4 Use of the Rotating-Drum Bioreactor Model	431	(4)
A.5 Use of the Traditional Packed-Bed Bioreactor Model	435	(1)
A.6 Use of the Zymotis Packed-Bed Bioreactor Model	436	(3)
A.7 Use of the Model of an Intermittently-Mixed Forcefully-Aerated Bioreactor	439	(4)
Index	443