Feed Substrate Concentration Research Articles

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis-Menten kinetics using the disjoint policy.

The optimal temperature policy that maximizes the time-averaged productivity of a continuous immobilized enzyme packed bed reactor is determined. This optimization study takes into consideration the enzyme thermal deactivation with substrate protection during the reactor operation. The general case of reversible Michaelis-Menten kinetics under constant reactor feed flow rate is assumed. The corresponding nonlinear optimization problem is solved using the calculus of variations by applying the disjoint policy. This policy reduces the optimization problem into a differential-algebraic system, DAE. This DAE system defines completely the optimal temperature-time profiles. These profiles depend on the kinetic parameters, feed substrate concentration, operating period, and the residence time and are characterized by increasing form with time. Also, general analytical expressions for the slopes of the temperature and residual enzyme activity profiles are derived. An efficient solution algorithm is developed to solve the DAE system, which results into a one-dimensional optimization problem with simple bounds on the initial feed temperature. The enzymatic isomerization of glucose into fructose is selected as a case study. The computed productivities are very close to that obtained by numerical nonlinear optimization with simpler problem to solve. Moreover, the computed conversion profiles are almost constant over 90% of the operating periods, thus producing a homogeneous product.

Air stripping effect in a chemostat

AbstractThe effect of air stripping on a chemostat is Investigated. An operating diagram is constructed to illustrate the relationship between the volatile substrate and the dilution rate subjected to different amounts of air stripping. Air stripping provides another degree of freedom to operate a chemostat in addition to manipulating feed concentration and dilution rate. Thus, a high dose of feed substrate can be tolerated while still maintaining the process in a stable‐operating mode. A stable operation of a chemostat is guaranteed when a proper combination of feed substrate concentration, initial start‐up conditions and aeration rates is implemented.

Nonlinear feedforward control of bioreactors with input multiplicities

A steady-state nonlinear feedforward controller (FFC) for measurable disturbances is designed for a continuous bioreactor, which is represented by Hammerstein type nonlinear model wherein the nonlinearity is a polynomial with input multiplicities. The manipulated variable is the feed substrate concentration (Sf) and the disturbance variable is the dilution rate (D). The productivity (Q=DP) is considered as the controlled variable. The desired value of Q=3.73 gives two values of feed substrate concentration. The nonlinearity in the gain is considered for relating output to the manipulated variable and separately for the relation between output to disturbance variable. The FFC is also designed for the overall linearized system. The performance of the FFC is evaluated on the nonlinear differential equation model. The FFC is also designed for the model based on a single nonlinear steady-state equation containing both D and Sf. This nonlinear FFC gives the best performance. The nonlinear FFC is also designed by using only linear gain for the disturbance and nonlinear gain for the manipulated variable. Similarly, nonlinear FFC is also designed by using linear gain for the manipulated variable and the nonlinear gain for the disturbance variable. The performances of these FFC schemes are compared.

A biochemically structured model for Saccharomyces cerevisiae

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S f, as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations.

Salt accumulation resulting from base added for pH control, and not ethanol, limits growth of Thermoanaerobacteriumthermosaccharolyticum HG-8 at elevated feed xylose concentrations in continuous culture.

Thermoanaerobacter thermosaccharolyticum HG-8 was grown in continuous culture to characterize growth limitation at high feed substrate and product concentrations. Continuous fermentation of 50 and 73 g/L xylose at a dilution rate based on the feed flow, D(f), of 0.053 h(-)(1) and with the pH controlled at 7.0 by addition of KOH resulted in steady state utilization of >99% of the xylose fed and production of ethanol and acetic acid at a mass ratio of about 2:1. Continuous cultures of T. thermosaccharolyticum growing at D(f) = 0.053 h(-)(1) achieved complete utilization of 75 g/L xylose in the presence of 19.1 g/L K(+) (0.49 M) and an ethanol concentration of 22.4 g/L ethanol. When the feed to a culture initially at steady state with a 75 g/L xylose feed and D(f) = 0.053 h(-)(1) was increased to 87.5 g/L xylose, limitation of growth and xylose utilization was observed. This limitation was not relieved by repeating this feed upshift experiment in the presence of increased nutrient levels and was not reproduced by addition of ethanol to a steady-state culture fed with 75 g/L xylose. By contrast, addition of KCl to a steady-state culture fed with 75 g/L xylose reproduced the K(+) concentration, limitation of growth and xylose utilization, and product concentration profiles observed in the feed upshift experiment. The maximum concentration at which growth of batch cultures was observed was 0.43 M for KCl, NaCl, and equimolar mixtures of these salts, suggesting that the observed limitation is not ion-specific. These data support the interpretation that inhibition salt accumulation resulting from addition of KOH for pH control is the limiting factor manifested in the feed upshift experiment and that both nutrient limitation and ethanol inhibition played little or no role as limiting factors. More generally, salt inhibition would appear to be a possible explanation for the discrepancy between the tolerance to added ethanol and the maximum concentration of produced ethanol reported in the literature for fermentation studies involving thermophilic bacteria.

Effect of process configuration and substrate complexity on the performance of anaerobic processes

The roles of substrate complexity (molecular size of the substrate) and process configuration in anaerobic wastewater treatment were investigated to determine optimal methanogenic technology parameters. Five substrates (glucose, propionate, butyrate, ethanol, and lactate) plus a mixed waste (60% carbohydrate, 34% protein, and 6% lipids) were studied under five reactor configurations: batch-fed single-stage continuous stirred tank reactor (CSTR), continuously fed single-stage CSTR, two-phase CSTR, two-stage CSTR, and single-stage upflow anaerobic sludge blanket (UASB). The substrate feed concentration was 20,000 mg/L as COD. The solids retention time (SRT) and hydraulic retention time (HRT) in the CSTR reactors were 20 d, while HRT in the UASB was 2 d. All reactors were operated for at least 60 d (equal to 3SRT). Substrate complexity was observed to be less significant under two-phase, two-stage and UASB reactor configurations. Two-phase CSTR, two-stage CSTR, and single-stage UASB configurations yielded the lowest effluent chemical oxygen demands (130–550, 60–700, and 50–250 mg/L, respectively). The highest effluent chemical oxygen demands were detected when feeding glucose, propionate, and lactate to continuously fed single-stage CSTRs (10, 400, 9900, and 4700 mg/L COD, respectively) and to batch-fed single-stage CSTRs (11, 200, 2500, and 2700 mg/L COD, respectively). Ironically, the one stage CSTR — most commonly utilized in the field — was the worst possible reactor configuration.

Model predictive control of continuous yeast bioreactors using cell population balance models

Continuous cultures of budding yeast are known to exhibit autonomous oscillations that adversely affect bioreactor stability and productivity. We demonstrate that this phenomenon can be modeled by coupling the population balance equation (PBE) for the cell mass distribution to the mass balance of the rate limiting substrate. An efficient and robust numerical solution procedure using orthogonal collocation on finite elements is developed to approximate the PBE model by a coupled set of nonlinear ordinary differential equations (ODEs). A controller design model is obtained by linearizing and temporally discretizing the ODEs derived from spatial discretization of the PBE model. The resulting linear state-space model is used to develop model predictive control (MPC) strategies that regulate the discretized cell number distribution by manipulating the dilution rate and the feed substrate concentration. Two choices of the controlled output vector are considered: (i) the entire discretized distribution; and (ii) a subset of the discretized distribution. The ability of the MPC controllers to stabilize steady-state and periodic solutions is evaluated via simulation. We show that superior closed-loop performance is obtained when a subset of the distribution is employed as controlled outputs.

Identification of Hammerstein model for bioreactors with input multiplicities

A closed loop identification method of Hammerstein model for continuous bioreactor with input multiplicity is proposed. Hammerstein model consists of nonlinear steady-state gain followed by a unity gain linear system. The method consists of first getting local first order plus time delay (FOPTD) models around the two input multiplicity values of the substrate feed concentration. The model parameters of the FOPTD is identified by a least square optimization method. The initial guess for the model parameters are obtained from the settling time, the initial delay in the closed loop servo response and using a simple proportional controller formula. From the local process gain values obtained for the several step changes around the two operating conditions, the nonlinear gain portion of the Hammerstein is then obtained. The actual nonlinear gain and the identified nonlinear gain is compared.

A Model Predictive Control Strategy for Stabilization of Oscillating Yeast Cultures

Continuous cultures of budding yeast are known to exhibit autonomous oscillations that adversely affect bioreactor stability and productivity. This phenomenon is modeled by coupling the population balance equation (PBE) for the cell mass distribution to the mass balance for the rate limiting substrate. An efficient and robust numerical solution technique is developed using orthogonal collocation on finite elements. The controller design model is obtained by linearizing and temporally discretizing the ordinary differential equations resulting from spatial discretization of the PBE model. The resulting linear state-space model is used to design model predictive controllers that regulate the cell number distribution by manipulating the dilution rate and the feed substrate concentration. The ability of the controllers to stabilize steady-state and periodic solutions is evaluated via simulation.

Modelling of a continuous two-phase partitioning bioreactor for the degradation of xenobiotics

The possibility of operating a two-phase partitioning bioreactor for phenol degradation in continuous mode has been explored in this paper, using a mechanistic model for the bioreactor. Characteristics of continuous culture fermentations with substrate inhibition were investigated using steady-state and dynamic simulations. The simulations confirmed that over certain ranges of aqueous dilution rates, up to three steady states for the cell and substrate concentrations could be obtained. These corresponded to stable and unstable steady states, as well as washout conditions. The unstable nature of the steady states was examined for two different operating regions representing extremes of solvent dilution rate and feed substrate concentration. Step decreases in feed substrate concentration, when operating at the unstable steady state, resulted in the system reaching a stable steady state, while step increases in feed substrate concentration eventually resulted in the system washing out. Dynamic simulations also revealed variations in the sensitivity of the continuous model to substrate concentrations, depending on the operating point. This variation indicates non-linearity in dynamic behaviour.

Analysis of forced periodic operations of continuous bioprocesses: multiple input variations

Continuous bioprocesses subject to time-invariant feed conditions are attractive due to ease of operation and control. Nonlinearities in kinetics of bioprocesses provide an opportunity to possibly improve the time-average performance of these by periodic forcing of feed conditions. This possibility is investigated in this article for cycling of dilution rate and feed concentration of the limiting substrate using the generalized π-criterion. A unified analysis of optimality of forced periodic operation of continuous cultures producing a wide range of products and subject to periodic variation in either dilution rate or feed concentration of the limiting substrate has recently been reported (Parulekar, 1998, Chemical Engineering Science, 53, 2481–2502). The analysis is extended in this article, with the particular focus being the interaction effect due to simultaneous variations of the two input variables. Without placing any restrictions on the kinetics of the bioprocesses, it is established that subjecting a bioprocess to simultaneous periodic variations in dilution rate and substrate feed concentration does always lead to improved performance, at least at high frequencies. Where appropriate, analytical expressions are obtained for optimum phase difference (between periodic variations in the two inputs) and optimum amplitude ratio that lead to the maximum fractional improvement in the bioprocess performance (vis-à-vis operation at a steady state). Numerical illustrations pertain to bioprocesses generating many important metabolites. In each example, the two-dimensional control variable space is divided into appropriate regions based on differences in the effects of periodic variations in either or both inputs on the bioprocess. The π-criterion is also employed to investigate if forced periodic operation may enable cell retention in continuous cultures under conditions where cell washout is the only admissible steady state.

A diffusion-reaction model for ?-chymotrypsin carrying uniform thermosensitive gel beads

In this study, the kinetic behavior of α-chymotrypsin-immobilized, uniform poly(isopropylacrylamide) gel beads was investigated. The kinetic study was performed by using a continuous reactor operated at steady-state conditions. In the experiments, substrate feed concentration, residence time, and reactor temperature were changed. The results were explained by a diffusion-reaction model developed for steady-state conditions. The effectiveness factor and Thiele modulus values of the thermosensitive enzyme-gel system were estimated at different temperatures by using an iterative procedure based on fourth order Runge-Kutta algorithm. The results indicated that the overall hydrolysis rate was controlled by the substrate diffusion through the gel matrix. A bending point was detected for the Thiele modulus at the lower critical solution temperature (LCST) of the thermosensitive gel. The effective diffusion coefficient of substrate and effectiveness factor decreased suddenly at LCST. The mass transfer process within the thermosensitive carrier could be described in detail by the proposed model. The results of our numerical procedure were also compared with an analytical approximate solution available in the literature. The consistency between two different model was reasonably good.

The incidence of oscillatory behavior in the continuous fermentation of zymomonas mobilis

The incidence of oscillatory behavior in the continuous culture of Zymomonas mobilis has been examined using a combination of experimental investigations and a predictive model. The tendency to oscillatory behavior was assessed by perturbing the feed substrate concentration and dilution rate in a continuous fermentation starting from a number of distinct initial conditions. The entire range of qualitative dynamic behavior was observed: overdamped, underdamped, and sustained oscillatory responses. The predictive capabilities of a model previously proposed by our research group were confirmed over this range of operation. A key component of this model is the inclusion of a dynamic specific growth rate term which accounts for the inhibition associated with historical ethanol concentration change rate. Parameters and relationships estimated for the model were used to identify key characteristics leading to oscillatory behavior. In particular, differences in the sensitivities of ethanol production rate versus specific growth rate to ethanol concentration and its rate of change dictate whether sustained oscillations will occur. Experimental evidence indicates that a change in morphology is associated with oscillatory behavior. The change in morphology to a more filamentous form may explain the change in specific growth and product formation characteristics.

Robust [formula omitted]∞ control of a class of continuous fermentation processes

This paper deals with the H ∞ control of a class of fermentation processes that are described by an unstructured fermentation process model. For a given dilution rate, an optimal controller has been developed which guarantees the so-called L 2-gain from the disturbance to the error between the substrate concentration and the desired optimal substrate concentration to be no larger than a prescribed value in lieu of the system's uncertainties. The disturbance affecting the system's dynamics comes from the residue of the feed substrate concentration, external noise, and unmodelled dynamics. It is stressed that this optimal controller requires only the substrate concentration to be measurable.

Model predictive control algorithms and their application to a continuous fermenter

In many continuous fermentation processes, the control objective is to maximize productivity per unit time. The optimum operational point in the steady state can be obtained by maximizing the productivity rate using feed substrate concentration as the independent variable with the equations of the static model as constraints. In the present study, three model-based control schemes have been developed and implemented for a continuous fermenter. The first method modifies the well-known dynamic matrix control (DMC) algorithm by making it adaptive. The other two use nonlinear model predictive control algorithms (NMPC, nonlinear model predictive control) for calculation of control actions. The NMPC1 algorithm, which uses orthogonal collocation in finite elements, acted similar to NMPC2, which uses equidistant collocation. These algorithms are compared with DMC. The results obtained show the good performance of nonlinear algorithms.

Modeling and simulation of competition between two microorganisms for a single inhibitory substrate in a biofilm reactor

A simple biofilm model was developed to simulate the competition between two microorganisms for a common inhibitory substrate. The following assumptions were made for the simulations: (1) the biofilm has a uniform thickness and is composed of 5 segments, (2) growth of two microorganisms A and B which utilize the common substrate is expressed by the Haldane kinetics with a spatial limitation term and is independent of the other microorganism in the biofilm reactor, and (3) diffusion of the substrate, movement of the microorganisms, and continuous loss of the biomass by shearing are expressed by Fick's Law-type equations. The qualitative behavior of the biofilm reactor is characterized by five regions, I-V, depending on the operation conditions, the substrate concentration in feed, and the dilution rate. In region I, both microorganisms are washed out of the biofilm reactor. In region II, microorganism B is washed out, and in region III, microorganism A is washed out of the biofilm. In region IV, both microorganisms coexist with one another. In region V, both microorganisms coexist with a sustained oscillatory behavior. Convergence to regions I-V depends on the initial conditions. In regions II-V, washout of either or both microorganisms is also observed with initial conditions too far away.

Periodic operation of bioreactors for autocatalytic reactions with Michaelis-Menten kinetics

The performance of an isothermal tubular bioreactor carrying out autocatalytic reactions obeying Michaelis-Menten Kinetics is analyzed for improvement in the average yield of product B. Under steady-state condition, the reactor is shown to exhibit input multiplicities in the yield of B with the mean residence time. Simulation results show that a significant improvement in the average yield of B is obtained under feed substrate concentration cycling. The two values of mean residence time giving identical yield under conventional steady-state operation is shown to give distinctly different behaviour under periodic operation. The lower value of the residence time gives improved average yield of B. The performances of the reactor with power law kinetics and that with the Michaelis-Menten kinetics show distinct average yield under periodic operation even though steady-state operation gives identical yield.

High frequency multi-input periodic operation of continuous fermentation process

This paper examines the problem of high frequency multi-input periodic operation of continuous fermentation process. Based on π-criterion published prevously, it is shown theoretically that a continuous fermentation process under the operation of simultaneous high frequency periodic change of feed substrate concentration and dilution rate is always superior over the steady state operation except at the optimal feed substrate concentration. This, however, is yet to be confirmed experimentally. Finally, via computer simulations, a good correlation between the simulation and theoretical calculation of the percentage of improvements on the process productivity is revealed.

Recursive least squares scheme for operating a class of continuous fermentation processes at optimal steady state productivity

This paper has developed a recursive least squares scheme for operating a class of continuous fermentation processes at the optimal steady state productivity. More precisely, the class of continuous fermentation processes under investigation is described by a widely accepted non-segregated fermentation process model. Based on a recursive least squares algorithm, an on-line estimation scheme for estimating the optimal set points for feed substrate concentration and dilution rate is developed. Finally, via simulation, it is shown that this on-line estimation scheme is robust against measurement time (sampling time). © 1998 Society of Chemical Industry

Control of Oscillating Microbial Cultures Described by Population Balance Models

Nonlinear feedback control laws are derived which attenuate undesired oscillations or induce synchrony in microbial cultures described by population balance models. The population balance model is solved using a finite difference method. A model suitable for controller design is obtained by expressing the population balance equations in terms of moments of the cell age distribution. Oscillations are damped, and the culture is forced to a desired equilibrium point by designing a feedback linearizing controller which manipulates dilution rate and feed substrate concentration and regulates cell number concentration and substrate concentration. An approximate equilibrium solution to the population balance equations is used to determine setpoint values for the two controlled variables. Cell synchrony is induced by designing a feedback linearizing controller which manipulates feed substrate concentration and regulates substrate concentration to an oscillatory trajectory of a predetermined period. The performance of the nonlinear controllers is evaluated through closed-loop simulations.