## Eii Tii

Where k is the number of segments with different process levels and Hi is the number of observations in each sample. 3. Estimation of S by moving-ranges of a successive data points. Use differences of successive observations as if they were ranges of n observations. A plot of S for group size a versus a will indicate if there is between-sample variation. If the plot is flat, the between-sample variation is insignificant. This approach should not be used if there is a trend in data. If there are...

## P11p22

If p22 0, an improvement in performance of steady-state operation is feasible only in the range 0 < r) < 772 Figure 7.3(a) . If p22 < 0, a positive SJ occurs in the range rji < 77 < r 2 t) fj rt, Figure 7.3(a) , with (-P11) provided 2 > pwpn-Fixed ri, variable r2. The necessary and sufficient condition for occurrence of a local maximum in SJ and its value are SJ - (pn - ) at C - - if P22 < 0. (7.92) 2 V P22J ri p22 The upper bound on 8J in Eq. 7.92 corresponds to p2i (defined in...

## R

The control limits of the R chart are > 3 1-3 and DA 1 + 3 (6.8) which are tabulated for various values of n and are available in many SPC references and in the Table of Control Chart Constants in the Appendix. The estimator for the mean process level (centerline) is x. Since the estimate of the standard deviation of the mean process level a is y n d2y n The control limits for an x chart based on R are UCL, LCL x A2R, A2 . (6.11) Example Consider the following data set where three...

## Info

Phase space dimension d, information coefficient i, and correlation coefficient p, corresponding to each data pair, and the result of the heuristic classification scheme. Classifications I, C and R stand for Independent, Coupled and Redundant, respectively. Table 5.3. Phase space dimension d, information coefficient i, and correlation coefficient p, corresponding to each data pair, and the result of the heuristic classification scheme. Classifications I, C and R stand for...

## Multivariable Batch Processes

Batch processes often exhibit some batch-to-batch variation. Variations in charging the production recipe, differences in types and levels of impurities in raw materials, shift changes of operators, and disturbances during the progress of the batch are some of the reasons for this behavior. Monitoring the trajectories of the process variables provides four different types of monitoring and detection activities End of batch quality control. This is similar to the traditional quality control...

## Data Length Equalization and Determination of Phase Landmarks in Batch Fermentation

Most batch processes, including many fermentation processes, pass through several phases based on complex physiological phenomena during the progress of the batch (Figure 6.13). In this book, we used the term stage to refer to different process operations such as fermentation and separation, and the term phase to refer to distinct episodes in time during the progress of the batch where qualitatively different activities take place. Since batch fermentation time varies from batch to batch due to...

## Cs

The last term in Eqs. 2.72, 2.74 and 2.76 is due to volume correction that is applied to glucose, penicillin and oxygen concentrations since these are based on liquid volume (Vabiotic)- Biomass concentration, X ( me , e number of elements per culture volume, and m average mass per element) is on the other hand based on culture volume (V). In Eq. 2.73, ms and ep are the maintenance on glucose and the specific rate of product formation, respectively and aa and as are the stoichiometric biomass...

## Experimental Data Collection and Pretreatment

Data collection during the progress of a batch is necessary for monitoring and controlling process operation for optimal cultivation and production. An essential element of effective monitoring and control is high quality data obtained during the progress of the batch via appropriate instrumentation sensors. The information collected may also be used for modeling the process or improving the process design and production policies. This chapter focuses on a number of important topics about...

## Contributions of MFA and MCA to Modeling

Metabolic flux analysis (MFA) and metabolic control analysis (MCA) are mathematical tools that have become widely applicable in metabolic engineering. Both tools are interrelated and widely used in metabolic engineering research 331, 426, 565 . They are useful in developing models of metabolic activity in a biochemical system. They would be instrumental in developing detailed first principles models of fermentation processes. The flux is a fundamental determinant of cell physiology and a...

## ANN Applications in Fermentation Industry

Application of ANN models in biochemical and fermentation industries concentrate mostly on soft sensor development for estimating infrequently measured quality variables such as biomass concentration using process variables that are frequently measured. Developing such empirical models is almost similar to developing statistical regression models. There are numerous applications for different types of fermentations in the literature. Applications include use of ANN models to estimate biomass...

## Role of Metabolic Engineering in Process Improvement

For several decades, various industrial strains have been successfully developed by traditional mutagenesis and selection to improve the yield and productivity of native products synthesized by these strains. The development of molecular biological techniques for DNA recombination introduced a new dimension to metabolic pathway modification. Genetic engineering allowed precise modification of specific enzymatic reactions in metabolic pathways, leading to the construction of well-defined genetic...

## Batch Fermentation Process

Linear time alignment of two trajectories with different durar tions 484 . Note that the dissimilarity measure d(ti, rj) between T and R is denoted as d(i,j) for simplicity of notation in Eq. 6.49. Hence, the distortion measure assessment will take place along the diagonal straight line of the rectangular (tj, rj) plane shown in Figure 6.18. Linear time normalization implicitly assumes that the temporal trajectory variations are proportional to the duration of the batch (or the...

## Realtime Knowledge Based Systems RTKBS

Chemical process industries (CPI) require a high level of supervision in realtime. Supervision tasks may include scheduling processing stages, supervising data acquisition, distributed control systems, and alarm management. This means low level process operations such as adjustment of PID control settings and high level qualitative decisions such as implementing different operational policies and fault handling are to be dealt with together. All these activities are realized with accumulated...

## Artificial Neural Networks

Although this chapter is devoted to empirical modeling techniques for modeling linear systems, artificial neural networks ANNs which can be used to model both linear and nonlinear systems are discussed here as well because of their popularity. Following a short historical perspective, summarizing foundations of ANNs. Due to availability of numerous ANN software on different platforms, there is no need to construct ANN models from scratch unless a very special, custom application is aimed. The...

## Myq

Figure 7.4. a Operating diagram for Example 1 with the cell growth following Monod kinetics fim 1.0 h l, K 0.05 gL-1, and Kj gt oo in Table 3, D in h l and SF in gL-1 . p SF D on the curve ABCDE. Forced periodic operation with variations in D and SF is superior to steady-state operation i at all frequencies in region I SFq,Dq lying below the curve ABFG , ii for 0 lt u lt wi and U2 lt u gt lt oo u gt 2 gt u gt i in region II 5Vo, D0 lying between the curves BFG and BCDE , and iii for all uj...

## Dynamic Optimization of Batch Process Operations

Discussion on optimal operation of fermentation processes in Chapter 7 focused on the search for open-loop optimal trajectories Section 7.2 and regulation of process operation to track reference trajectories while rejecting disturbances by using optimal feedback control Section 7.5 and model predictive control MPC Section 7.6 . These techniques rely on the availability of reliable dynamic models for the process and disturbances. Industrial practice involves following recipes developed in the...

## Contribution Plots

Multivariate quality control techniques use data from measurements of process variables, taking into account the correlation between process variables, to detect special causes affecting the process. Multivariate control charts such as SPE and T2 charts indicate when the process goes out of control, but they do not provide information on the source causes of abnormal process operation. The engineers and plant operators need to determine the actual problem once an out-of-control situation is...

## Bioreactor Operation Modes

The three popular modes of operation of mechanically agitated reactors for cell cultivation are batch, fed-batch and continuous operations. The mechanically agitated reactors are equipped with capabilities for on-line and off-line sensing of a variety of culture characteristics, such as pH, temperature, concentrations of dissolved gases such as CO2 and O2 , biomass concentration, cell morphology, concentrations of various components of the nutrient medium, total protein content of cells,...

## Y MR 634

Compute the control limits with the centerline at MR Recall that or d R d gt and d- gt and d3 depend on a. 6.1.4 Exponentially Weighted Moving-Average Chart The exponentially weighted moving-average EWMA Zi is defined as Zi wxi 1 w zi-i 6.36 where 0 lt w lt 1 is a constant weight, x. is the mean of sample i of size n, and the starting value at i 1 is zq i. EWMA attaches a higher weight to more recent data and has a fading memory where old data are discarded from the average. Since the EWMA...

## Conservation Equations for the Gas Phase

For the three bioreactor operation modes batch, fed-batch and continuous , the continuously flowing gas phase is ubiquitous. The conservation equation for a specie i in the gas phase e.g., i O2, CO2 can then be expressed as d ClGVG dt QgfQgf - QcCic - N.aV, VG VT-V 2.3 with cig denoting concentration of specie 1 in the gas phase, Qg the volumetric gas phase flow rate, Vq the gas phase holdup in the bioreactor volume of gas phase in bubbles and head space , the subscript F the gas feed, Ni the...

## Statistical Design of Experiments

Experiments are frequently performed to assess the effects of inputs, operating conditions, and changes in the process on the outputs. For example, the effects of variations in fermentation temperature, air flow rate, or strain type used on the attributes of a product would provide valuable information for optimizing productivity. Experiments are costly since they consume time and raw materials. Properly planned experiments minimize unnecessary duplications, generate more information with fewer...

## Xv255

Where rQl is assumed to be constant and might be treated as a yield coefficient 426 . During the product synthesis phase, when the rate of biomass formation is rather low, there is still significant heat generation associated with metabolic maintenance activities. Therefore, we have included the second term on the right hand side of Eq. 2.55 to account for the heat production during maintenance. Because the heat generation and C02 evolution show similar profiles, their production rate due to...

## Chemically Structured Models

The effects of key chemicals on the key rate processes are accounted for in the chemically structured models. All viable cells in the cell population are considered to be functionally similar, with conservation equations in the abiotic and biotic phases being considered for those species that are present in both phases. For such species, generation in the abiotic and biotic phases and transport across the interface between the abiotic and biotic phases must be fully accounted for. Synthesis of...

## Exhaust Condenser

Experimental setup of the fermentation system. Figure 5.18. Experimental setup of the fermentation system. measurement do not have an explicit mutual dependence in model equations. When the classification scheme indicates a Coupled measurements, we will write those measurements in each other's model equations. If the scheme indicates Redundant measurements, we will claim that making a set of measurements for one coordinate yields a remarkable amount of information about the other,...

## Conservation Equations for a Single Bioreactor

Irrespective of the type of operation, a description of the behavior of a suspension culture requires applying the principle of conservation for each of the three distinct phases gas, liquid and solid phases and constituents of each phase. When the nutrients are in the liquid phase, as is the case with submerged cultures and which are the primary focus here, the solid phase is comprised essentially entirely of cell mass. In cases involving nutrients such as cellulose which are insoluble in the...

## X2 X3 X4

2.665e-01 2.188e-01 1.507e-01 7.433e-02 4.312e-01 3.819e-01 3.240e-01 2.612e-01 2.614e-01 2.013e-01 4.533e-01 4.568e-01 4.098e-01 2.905e-01 4.802e-01 3.664e-01 2.679e-01 2.190e-01 1.508e-01 5.043e-01 5.770e-01 5.125e-01 4.315e-01 3.829e-01 2.616e-01 5.979e-01 5.800e-01 6.041e-01 4.535e-01 6.268e-01 2.493e-01 3.651e-01 2.675e-01 2.186e-01 4.183e-01 4.283e-01 4.398e-01 5.029e-01 5.751e-01 4.302e-01 5.318e-01 6.052e-01 5.422e-01 5.959e-01 6.257e-01 1.250e-01 2.476e-01 3.627e-01 2.665e-01 3.214e-01...

## Continuous Operation

In a continuous culture operation, nutrients essential for growth are continuously fed and a portion of the culture is continuously withdrawn. The culture volume is controlled using a level controller. A continuous culture is usually preceded by a batch or fed-batch culture. If the mass flow rates of the bioreactor feed and bioreactor effluent are identical and timeinvariant, a time-invariant steady state operation can be realized after sufficient time since the start of continuous culture...

## Structured Model for Penicillin Production

The model proposed in this case is a derivative of the morphologically structured model by Nielsen 424 and accounts for effects of dissolved oxygen on cell growth and penicillin production and variations in volume fractions of abiotic and biotic phases due to biomass formation 63 . Penicillin production is considered to occur in the subapical hyphal cell compartment and to be affected by glucose and oxygen. The morphological structure of the model is described in detail elsewhere 423, 424 ....

## SPM of Continuous Processes with Multivariate Statistical Techniques

In traditional quality control of multivariable processes, a number of quality variables are monitored using Shewhart charts 542 . But because of inter- Figure 6.7. EWMA chart of observations. Figure 6.7. EWMA chart of observations. actions among the variables that cause crosscorrelation, autocorrelation and colinearity, monitoring one variable at a time approach may become misleading and time consuming if the number of variables to be monitored is high. The potential for erroneous...

## C

Figure 5.5. a Trajectories of two realizations of the periodically driven pendulum for two nearby initial conditions e0,w0, t gt 0 0.36564,-7.4964,100 solid curve and 6 0, u gt 0, lt J gt 0 0.36564,-7.4964,100.1 dotted curve , b How a rectangular block of initial points get deformed in a simulation interval of 4 units, stretching in one direction and squeezing in the other, c Same initial rectangular block after a simulation time of 10 units. Using the length of the ith ellipsoidal principal...

## I

Downstream processes in industrial scale penicillin production. culture volume, sequential growth is followed in this manner. Inoculum size is typically around 10 of the total culture volume. Since formation of secondary metabolites in this case, penicillin is usually not associated with cell growth, it is a common practice to grow the cells in a batch culture followed by a fed-batch operation to promote synthesis of the antibiotic. When inoculum at the desired concentration is...

## Process Control

Automatic control of batch fermentation processes provides the opportunity to regulate the operation when variations in input conditions such as changes in impurity compositions in feedstock or disturbances during the run such as equipment malfunctions may cause departure from optimal reference trajectories. A simple temperature control loop or stirrer speed controller can save a 80,000 liter batch from getting ruined. Control of batch fermentation processes can be defined as a sequence of...

## L ilse

Where 6h x denotes the threshold value of x. Soft thresholding shrinks the wavelet coefficients which are greater than the threshold value towards zero by subtracting the threshold value from the wavelet coefficients as well x A , x gt A 0 , x lt A 3.35 Different methods for selecting the threshold value have been suggested in the literature by Donoho and co-workers 132 . These methods are grouped Figure 3.13. Wavelet decomposition of a process signal CO2 evolution rate . Figure 3.13. Wavelet...

## Sensors

Sensors may be categorized as on-line and off-line sensors. On-line sensors are preferred since they provide process information quickly without any disruption in the process and any sampling and cultivating delays, and fewer human errors, and allow for arbitrary frequencies of measurement. Off-line analysis techniques are used because of the difficulty and expense of developing sterilizable probes or constructing a sampling system for some process variables and product properties. Sensors must...

## Kinetics and Process Models

Growth of living viable cells requires intimate contact of a small quantity of living cells with a liquid solution medium containing appropriate levels of nutrients at a suitable pH and temperature. Depending on the morphology of cells under consideration, one needs to consider two different manifestations of cell growth. For unicellular organisms which divide as they grow, an increase in biomass mass of viable cells is accompanied by an increase in the number of cells present in the culture...

## Fault Diagnosis

8.2 Statistical Techniques for Fault Diagnosis 8.2.1 Statistical Discrimination and Classification 8.2.2 FDD with Fisher's Discriminant Analysis 8.2.4 Statistical Techniques for Sensor Fault Detection 8.3 Model-based Fault Diagnosis Techniques 8.3.1 Residuals-Based FDD Methods 8.3.2 FDD Based on Model Parameter Estimation 8.3.3 FDD with Hidden Markov Models 8.4 Model-free Fault Diagnosis Techniques 8.4.1 Real-time Knowledge-Based Systems RTKBS 8.4.2 Real-time Supervisory KBS for Process...

## Process Monitoring

Batch processes convert raw materials to products during a finite period of time by following prescribed processing recipes. A high degree of reproducibility is necessary to obtain successful batches. Monitoring and control of batch processes are crucial for detecting deviations from reference trajectories and interfering with undesirable trends to bring the operation to conditions that assure acceptable product quality. The goal of statistical process monitoring SPM is to detect the existence,...

## Structured Kinetic Models

Structured kinetic representations are warranted in situations involving significant changes in composition of the biotic phase and the kinetics of eel- lular rate processes is significantly sensitive to changes in cell composition. Since it is not practical to account for variations in every component of the biotic phase, the structured kinetic model for a particular bioprocess must focus on carefully selected key components and rate processes of major interest for that bioprocess. Depending...

## Batch Fermentation Introduction

Batch processes have been around for many millennia, probably since the beginning of human civilization. Cooking, bread making, tanning, and wine making are some of the batch processes that humans relied upon for survival and pleasure. The term batch process is often used to refer generically to both batch and fed-batch operations. In the former case, all ingredients used in the operation are fed to the processing vessel at the beginning of the operation and no addition or withdrawal of...

## Extensions of Linear Modeling Techniques to Nonlinear Model Development

Several paradigms are available for developing nonlinear dynamic input-output models of processes. These models have the capability to describe pathological dynamic behavior and to provide accurate predictions over a wider range of operating conditions compared to linear models. ANNs were introduced in the previous section. Chapter 5 presents system science methods for nonlinear model development. Various other nonlinear model development paradigms such as time series models, Volterra kernels,...

## State Space Reconstruction

If the source of the signal were an autonomous linear system, looking at the frequency spectrum of the signal would be utmost informative, thus the Fourier domain would be an appropriate space to examine the signal. If the linear system had an explicit time component hosting some burst of high frequency events localized in time domain, then a linear transform, such as wavelet transform, would be useful. Much of the contemporary signal processing toolkits e.g. Matlab 373 are based on the ability...

## Penicillin Fermentation

In September 1928, Alexander Fleming, a professor of bacteriology at St. Mary's Medical School in London, observed that mould had developed accidentally on a Staphylococcus aureus culture plate that was left on the laboratory bench and that the mould had created a bacteria-free circle around itself. He was inspired to further experiment and he found that a mould culture prevented growth of Staphylococcus, even when diluted 800 times. He named the active substance penicillin 154 , In December...

## J l J Ysxkitxkdt 4146

The integrals are evaluated numerically by using traditional tools such as the trapezoidal rule. An alternative computation of w can be made by attaching a penalty term toEq. 4.139 PSSE L - 2 Lxk 2 t Wj t 2dt 4.147 where 6j controls the roughness of the estimated weight functions. The solution can be found by using the pointwise approach which results in w T t TT t JftT0 -1rTA i 4.148 where 0 diag 9o, , 9m-i . Alternatively, the basis function approach can be used to compute w. The FDA...

## Multiblock PLS and PCA Methods for Modeling Complex Processes

Multiblock data analysis has its origins in path analysis and path modeling in sociology and econometrics. In situations where the number of variables is very large or the process that is analyzed is large and consists of many different stages, it is logical to group variables in a meaningful way, either based on their similarity, or their origin in the system or process, and then summarize each group that is called block. Each block may be divided into sub-blocks according to process phases...

## Fractional Factorial Design

The number of experiments required in a full 2fc factorial design increases geometrically with k. For a process with 7 factors, for example 27 128 experiments are needed to estimate the 7 main effects, and 120 interactions. There are 21 two-factor, 35 three-factor, 35 four-factor, 21 five-factor, 7 six-factor and 1 seven-factor interactions 78 . Fortunately, not all of these interactions are important. Furthermore, the main effects tend to be larger in absolute magnitude than the two-factor...

## Ax

Typical values of Ykcai range between 0.096 and 0.126 g kcal for many microorganisms. When significant amount of product is present, based on the stoichiometric description of cell growth Eq. 3.36 , total heat evolved Eq. 3.48 AQ AHs AS -AHn -AN - 3.51 -AHx -AX - -AffPJ -AP 3.52 where AHpt and APi represent the heats of combustion of products Pi and the amount of those products respectively. In this example, stoichiometric balances and calculation of yield coefficients will be illustrated for...

## An Unstructured Model for Penicillin Production

In this case study, the mechanistic model of Bajpai and Reuss 36 was used as starting point for model development. The original model has been extended by including additional input variables such as agitation power, and aeration rate. Functional relationships among the process variables are summarized in Table 2.3 and all inputs and outputs are listed in Figure 2.1. A variety of mathematical representations have been suggested for describing certain biological behaviors by researchers...

## Data Pretreatment Outliers and Data Reconciliation

Data pretreatment is necessary to assure that data used in modeling, monitoring and control activities provide an accurate representation of what is happening in a process. Data corruption may be caused by failures in sensors or transmission lines, process equipment malfunctions, erroneous recording of measurement and analysis results, or external disturbances. These faults would cause data to have spikes, jumps, or excessive oscillations. For example, sensor faults cause bias change, drift or...

## Preface

This book deals with batch process modeling, monitoring, fault diagnosis, and control, focusing on batch fermentation processes. Fermentation is one of the main bioprocesses used in pharmaceutical, food, and chemical industries. Most fermentation processes are carried out as batch or fed-batch operations. Batch processes have been around for many millennia, and received increasing attention in the second half of the twentieth century. Although batch processes are simple to set up and operate,...

## Chemical Industries

A Series of Reference Books and Textbooks 1. Fluid Catalytic Cracking with Zeolite Catalysts, Paul B. Venuto and E. Thomas Habib, Jr. 2. Ethylene Keystone to the Petrochemical Industry, Ludwig Kniel, Olaf Winter, and Karl Stork 3. The Chemistry and Technology of Petroleum, James G. Speight 4. The Desulfurization of Heavy Oils and Residua, James G. Speight 5. Catalysis of Organic Reactions, edited by William R. Moser 6. Acetylene-Based Chemicals from Coal and Other Natural Resources, Robert J....