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chemical engineering

Questions and Answers of Chemical Engineering

What is the differential equation model of the series PID controller? Qualitatively describe its response to a step change in e(t).
Several linear transmitters have been installed and calibrated as follows:(a) Develop an expression for the output of each transmitter as a function of its input. Be sure to include appropriate
A process instrumentation diagram of a flash drum is shown in Figure. Steam is condensed in a steam coil to vaporize a portion of the liquid feed, and the liquid product is removed by a pump. There
Adapted from Luyben and Luyben (1997).(a) Calculate the gain of an orifice plate and differential pressure transmitter for flow rates of 10, 50, 75 and 90% of full scale,(b) Calculate the gains of
Chilled ethylene glycol (sp gr = 1.11) is pumped through the shell side of a condenser and a control valve at a nominal flow rate of 200 gal/min. The total pressure drop over the entire system is
A pneumatic control valve is used to adjust the flow rate of a petroleum fraction (sp gr = 0.9) that is used as fuel in a cracking furnace. A centrifugal pump is used to supply the fuel, and an
I. M. Appelpolscher has acquired considerable knowledge of pneumatic control valves over the years. In particular, he knows that the flow characteristic of a “quick-opening” valve is f = √ℓ
A theoretical force balance for the control valve shown in Figure can be expressed asAssuming the second-order differential equation is linear, find values of the coefficients of the equation (in
Steady-state tests have been run on a neutralization tank, where pH is the controlled variable and w is the acid flow rate. The data follow the relationship shown in figure: You are asked to evaluate
A thermocouple Located in a thermowell and connected to a temperature transmitter is used to measure the liquid temperature in a bioreactor. A steady-state calibration of this instrument (transducer)
An engineer sets the pressure in a supply tank using a very accurate manometer as a guide and then reads the output of a 20-psig pressure gauge attached to the tank as 10.2 psig. Sometime later she
A process temperature sensor/transmitter in a fermentation reactor exhibits second-order dynamics with time constants of 1 s and 0.1 s. If the quantity being measured changes at a constant rate of
Consider the distillation column shown in Figure. It would be reasonable to control the liquid level in the reflux drum, hD, by manipulating either reflux flow rate, R, or distillate flow rate, D.
A stirred-tank blending system with a bypass stream is shown in Figure. The control objective is o control the composition of a key component in the exit stream, x4. The chief disturbance variables
Suppose that the distillation column shown in figure has been designed to separate a methanol-water mixture that is .50% methanol (MeOH). This high purity column has a large number of trays and a
It has been suggested that the capital cost for the distillation column in figure can be reduced by using a ?flooded condenser.? In the proposed design, the reflux drum would be eliminated, and the
The exit stream from a chemical reactor is sent to a storage tank, as shown in Figure. The exit stream from the storage tank serves as the feed stream to a separation process. The function of the
Consider the liquid storage system shown in figure. Only volumetric flow rates, q and q, can be manipulated. Determine the model degrees of freedom, NF, and the control degrees of freedom,NFC.
A double-pipe heat exchanger with a partial bypass for the cold stream is shown in Figure. The mass flow rate of the hot stream wh, and the bypass fraction, f, can be manipulated. Heat losses can be
Consider the blending system of Exercise 102. Inlet how rate, w2, and the bypass fraction, f, can be manipulated. Determine the model degrees of freedom, NF, and the control degrees of freedom, NFC.
Nitrogen gas is used to purge a mixture of air and small amounts of a flammable vapor from a process vessel. The nitrogen is introduced continuously through an opening in the vessel, and the
The probability of a particular type of sensor functioning properly is 0.99. Consequently, a triply redundant sensor system has been proposed for a critical measurement. Thus, three independent
Air samples from a process area are continuously drawn through a 1/4-in, diameter tube to an analytical instrument that is located 40 meters away. The tubing has an outside diameter of 6.35 mm and a
The liquid feed stream for the gas-liquid separator (or flush drum) shown in Figure consists of a hydrocarbon mixture. Because the pressure in the vessel is significantly lower than the feed
The loss of the coolant to a process vessel can produce an unacceptably high pressure in the vessel. As a result, a pressure relief valve is used to reduce the pressure by releasing the vapor mixture
A temperature control system for a distillation column is shown in figure. The temperature T of a tray near the top of the column is controlled by adjusting the reflux flow rate R. Draw a block
Consider the liquid-level PI control system shown in Figure with the following parameter values: A = 3 ft2, R = 1.0 min/ft2, Kv = 0.2 cfm/psi, Km = 4 mA/ft, Kc 4, and τ1 = 3 min. Suppose that
Consider proportional-only control of the stirred-tank heater control system in Figure. The temperature transmitter has a span of 50°F and a zero of 55 °F. The nominal design conditions are T = 80
It is desired to control the exit concentration of c3 of the liquid blending system shown in Figure. Using the information given below, do the following:(a) Draw a block diagram for the composition
A proportional-only feedback controller is implemented as shown in figure. We ordinarily think of the process and controller gains as being positive.(a) Give an example of a process whose gain
For a Liquid-level control system similar to that in figure, Appelpolscher has argued that integral control action is not required because the process acts as an Integrator (cf, Eq. 11-77). To
A block diagram for internal model control, a control technique that is considered in Chapter, is shown in Figure. Transfer function Gp denotes the process model, while Gp,denotes the actual process
An electrically heated, stirred-tank system is shown in figure. Using the given information do the following: (a) Draw a block diagram for the case where T3 is the controlled variable and voltage
The block diagram of a special feedback control system is shown in Figure. Derive art expression for the closed-loop transfer function, Y(s)/D(s).
A block diagram of a closed-loop system is shown in figure.(a) Derive a closed-loop transfer function for disturbance changes, Y(s)/Ds).(b) For the following transfer functions, what values of Kc
A mixing process consists of a single stirred-tank instrumented as shown in figure. The concentration of a single species A in the feed stream varies. The controller attempts to compensate for this
A PI controller is to be used in a temperature control system for a bioreactor. For nominal conditions, it has been determined that the closed-loop system is stable when τ1 = 10 min and – 10 <
A process is described by the transfer function Find the range of controller settings that yield stable closed-loop systems for (a) A proportional-only controller. (b) A proportional-integral
The block diagram of a feedback control system is shown in figure. Determine the values of Kc that result in a stable closed-loop system.
The question has been raised whether an open-loop unstable process can be stabilized with a proportional-only controller.(a) For the process and controller shown in figure a, find the range of Kc
For the liquid-level control system in Figure determine the numerical values of Kc and τ1; that result in a stable closed—loop system. The level transmitter has negligible dynamics, while the
As a newly hired engineer of the Ideal Gas Company, you are trying to make a reputation in the Process Control Group. However, this objective turns out to be a real challenge with I. M. Appelpolscher
It is desired to control the exit temperature T2 of the beat exchanger shown In Figure by adjusting the steam flow rate w3, unmeasured disturbances occur in inlet temperature T1. The dynamic behavior
A process is described by the transfer functionwhich includes actuator and measurement dynamics. The process engineering group has the option of redesigning the process to eliminate the right-half
A feedback control system has the open-loop transfer function, GOL(s) = 0.5Kce–3s / (10s + 1). Determine the values of Kc for which the closed-loop system is stable using two approaches:(a) An
A process control system contains the following(a) Show how GOL(s) can be approximated by a FOPTD model;Find K, τ, and θ for the open-loop process transfer function(b) Use Routh stability methods
A process has the transfer function, where K has a nominal-value of K = 1. PID controller settings are to be calculated using the Direct Synthesis approach with ?c = 5 min.Suppose that these
The liquid level in a reboiler of a steam-heated distillation column is to be controlled by adjusting the control valve on the steam line, as shown in figure. The process transfer function has been
A process has the transfer function, G(s) 2e–0.2t/ (s + 1). Compare the PI controller settings for the following design approaches: (a) Direct Synthesis method (τc = 0.2) (b) Direct
A process including sensor and control valve can be modeled by:Show that the Direct Synthesis method can be used to derive Controller M in Table 12.1, by utilizing the time-delay approximation in
A process stream is heated using a shell and tube heat exchanger. The exit temperature is controlled by adjusting the steam control valve shown in figure. During an open-loop experimental test, the
Suggest a modification of the Direct Synthesis approach that will allow it to be applied to open-loop unstable processes.
A process including sensor and control valve can be modeled by a fourth-order transfer function:(a) Design PID controllers using two design methods:(i) A sccond-order-plus4ime-delay model using the
Consider the level control problem in Example 12.3. Attempt to reduce the set-point overshoot of the PI controller (?c = 15) by using set-point weighting (cf. Eq. 12-39). Which value of b gives the
Consider the PID controller of Example 12.3 for τc = 8. (a) Suppose that the PID controller is implemented as the series form in Table 12.2, rather than as the parallel form that was employed
Consider the blending system shown in Figure. A feedback control system is used to reduce the effect of disturbances in feed composition, x1, n the controlled variable, product composition, x. Inlet
A PID controller is used to control the temperature of a jacketed batch reactor by adjusting the flow rate of coolant to the jacket. The temperature controller has been tuned to provide satisfactory
Suppose that a process can be adequately modeled by the first-order-plus-time-delay model in Eq. 12-10. (a) Calculate PI controller settings using the Hagglund-Astrom tuning relations in Table
Consider the experimental step response data for the heat exchanger of Exercise 12.5. Determine the PI controller settings using the step response method and two controller tuning relations: (a)
Consider the transfer function model in Eq. 12-10 with K = 2, τ = 5 and θ = 1. Compare the PID controller settings obtained from the Ziegler-Nichols and Tyreus-Luyben tuning relations in
IGC’s operations area personnel are experiencing problems with a particular feedback control loop on an interstage cooler. Appelpolscher has asked you to assess the situation and report back what
A problem has arisen in the level control loop for the flash separation unit shown in Figure. The level control loop had functioned in a satisfactory manner for a long period of time. However, the
A heat transfer process has the following transfer function between a temperature T and an inlet flow rate q where the time constants have units of minutes:If the flow rate varies sinusoidally with
Using frequency response arguments, discuss how well e-Gs can be approximated by a two-term Taylor series expansion, that is, by 1 – θs. Compare your results with those given in the text for a UI
A data acquisition system for environmental monitoring is used to record the temperature of an air stream as measured by a thermocouple. It shows an essentially sinusoidal variation after about 15 s.
A perfectly stirred tank is used to heat a flowing liquid. The dynamics of the system have been determined to be approximately as shown in figure. Where: P is the power applied to the heater Q is
For each of the following transfer functions, develop both the amplitude and phase angle of the Bode plot. Find AR and ? for each transfer function at of values of w = 0.1,1, and 10.
A second-order process transfer function is given by(a) Find |G| and (b) Plot |G (jw)| vs. wτ and Note that you can obtain the wt plots by setting τ = 1 and reparameterizing τ0/τ accordingly.
Plot the Bode diagram (0.1 w 100) of the third- order transfer function, Find both the value of w that yields a ? 180o phase angle and the value of AR at that frequency.
Using MATLAB, plot the Bode diagram of the following transfer function:Repeat for the situation where the time-delay term is replaced by a 1/1 Padéapproximation.
Two thermocouples, one of them a known standard, are placed in an air stream whose temperature is varying sinusoidally. The temperature responses of the two thermocouples are recorded at a number of
Exercise 5.19 considered whether a two-Lank liquid surge system provided better damping of step disturbances than a single-tank system with the same total volume. Reconsider this situation, this time
For the process described in Exercise 6.5, plot the composite amplitude ratio and phase angle curves on a single Boric plot for each of the four cases of numerator dynamics. What can you conclude
Develop expressions for the amplitude ratio of each of the two forms of the PW controller:(a) The parallel controller transfer function of Eq.8-14.(b) The series controller transfer function of
A process has the transfer function,With K = 10, ? = 2min, ? = 1min, Obtain the Bode plot for this transfer function. Do you need to approximate the denominator exponential term, or can your computer
Appelpolscher has just left IGC’s Monday morning status meeting with Smarly, Quirk, and the operations personnel. Over the weekend, a major unit in the hydrogen production process, a centrifugal
Plot a Nyquist diagram for the transfer function in Exercise 13.8. Repeat with the exponential term replaced by a 1/1 Padé approximation. Why are these two plots so different in appearance for large
Plot the Bode diagram for a composite transfer function consisting of the one in Exercise 13.8 multiplied by that of a parallel-form PID controller with Kc = 0.21, τ1 = 5, and to τ1 = 0.42. Repent
For the process described by the transfer function (a) Find two second-order-plus-time-delay models that approximate G(s) and are of the form One of the approximate models can be found by using the
Obtain Bode plots for both the transfer function given as follows and a FOPTD approximation obtained using the method discussed in Section 6.3. What do you conclude about the accuracy of the
In Chapter we considered a stability analysis based on substituting s = jw into the characteristic equation Demonstrate that this approach is (or is not) identical to the Bode stability criterion oil.
A process that can be modeled as a time delay is controlled using a proportional feedback controller. The control valve and measurement device have negligible dynamics and steady-state gains of Kv =
A Bode diagram for a process, valve, and sensor is shown in figure.(a) Determine an approximate transfer function for this system.(b) Suppose that a proportional controller is used and that a value
Consider the storage tank with sight glass in Figure. The parameter values are R1 = 05 min/ft2, R2 = 2min/ft2, A1 = 10 ft2, Kv = 2.5cfm/mA, A2 = 0.8ft2, Km = 1.5mA/ft, and ?m = 0.5 min.(a) Suppose
A process (including valve and transmitter) has the approximate transfer function. G(s) = 2e–0.2s/(s + 1) with time constant and time delay in minutes. Determine Pt controller settings and the
Consider the feedback control system in figure, and the following transfer functions: (a) Plot a Bode diagram for the open-loop transfer function. (b) Calculate the value of K that provides a phase
Frequency response data for a process are tabulated below. These results were obtained by introducing a sinusoidal change in the controller output (under manual control) and recording the measured
For the process in Exercise 14.5, the measurement is to be filtered using a noise filter with transfer function GF(s). Would you expect this change to result in better or worse control system
The block diagram of a conventional feedback control system contains the following transfer functions: (a) Plot the Bode diagram for the open-loop transfer function. (b) For what values of K is the
The dynamic behavior of the heat exchanger shown in figure can be described by the following transfer functionsThe valve lift x is measured in inches. Other symbols are defined in Figure.(a) Find the
Consider a standard feedback control system with the following transfer functions: (a) Plot the Bode diagram for the transfer function, G = GvGpGm. (b) Design a PI controller for this process and
Hot and cold liquids are mixed at the junction of two pipes. The temperature of the resulting mixture is to be controlled using a control valve on the hot stream. The dynamics of the mixing process,
Consider the control problem of Exercise 14.10 and a PI controller with Kc = 5 and τ1 = 0.3mm. (a) Plot the Nyquist diagram for the open-loop system. (b) Determine the gain margin from the
Consider a process model,and a PI controller with the Hagglund-Astrom settings of Table 12.4. Use the robust stability limit of Eq. 14-35 to determine how robust this control system is to the assumed
For the process in Exercise 14.5, a PI controller is tie- signed so that the peak value of the complementary sensitivity function Is MT = 1.25, Use the robust stability limit of Eq. 14-35 to estimate
In ratio control, would the control loop gain for Method I (Fig) be Less variable if the ratio were defined as R = d/u instead of R = u/d? Justify youranswer.
Consider the ratio control scheme shown in Fig. Each flow rate is measured using an orifice plate and a differential pressure (D/P) transmitter. The electrical output signals horn the D/P
It is desired to control liquid level h2 in the storage tank system shown in Fig by manipulating flow rate q3 Disturbance variable q1 can be measured. Use the information available to do the
For the liquid storage system shown in Fig the control objective is to regulate liquid level h2 despite disturbances in flow rates, q1 and q4. Flow rate q2 can be manipulated. The two hand valves
The closed-loop system in Fig has the following transfer functions: (a) Design a feedforward controller based on a steady-state analysis. (b) Design a feedforward controller based on a dynamic

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