Case Study of an Automatic pH Control Strategy for a Strong

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PROCESS DESIGN AND CONTROL Case Study of an Automatic pH Control Strategy for a Strong Acid-Strong Base System B. Todd Brandes* Albemarle Corporation, 451 Florida Street, Baton Rouge, Louisiana 70801-1765

The control of pH has been studied extensively for its distinct, nonlinear, and unstable character as well as its wide application in the process industries. Of particular importance is the strong acid-strong base system for its steep titration curve and difficulty in reaching steady state. In this study, the development and design of a simple yet robust single-tank industrial neutralization process is presented. The technical keys are the proper choice of holdup volume, the understanding of pH sensor time lag and maintenance procedures for them, the proper tank mixing design, the choice of set point, and the incorporation of the difference between the actual and indicated pH. Introduction There are innumerable applications of conventional automatic controls in the chemical process industries, with the objective of controlling quantities such as flow, temperature, pressure, level, speed, etc. Much work has been undertaken to both develop the fundamental principles of these strategies and implement them industrially in a practical, robust, and cost-effective manner. In general, these quantities are well-suited for a conventional feedback control system using the proportional-integral-derivative (PID) algorithm since they often vary with process conditions in approximately linear manners (i.e., the fundamental differential equation describing the process is a linear ordinary differential equation1). The PID algorithm performs well in controlling such processes because a single set of tuning parameters is suitable over a wide range of process conditions. However, some process variables are particularly nonlinear and present specific challenges to the PID algorithm. One such variable is the pH of an aqueous acid-base mixture, particularly for a strong acid-strong base pair. In this paper, an industrial application of pH control is discussed for the treatment of an aqueous H2SO4 waste stream with a 25 wt % NaOH solution. Despite the well-documented control difficulties of this system, a very simple, straightforward process seemingly contradictory to literature was designed, constructed, and started-up that met the controls objectives in a robust and stable manner. The work introduced a novel, broad characterization of the neutralization process dynamics that provided a very useful insight to define, incorporate, and characterize the adverse issues with pH control that have normally been collectively generalized as poor process controllability. Included below is the development of a theoretical model used for the study of the dynamics and design of the process. Also, results * Tel.: (803) 539-5136. Fax: [email protected].

(803) 536-0981. E-mail:

of the installed process after startup are provided to complete the case study. Overview of pH Control There has been much work conducted by other researchers to evaluate neutralization process dynamics and design robust control strategies. Sung and Lee2 and Wright and Kravaris3 provide good general overviews of pH control. Overall, most of the work in the literature suggests a series of tanks or advanced control is required to achieve stable pH control, because a single tank system is so adversely influenced by dead time and secondary time lag effects. For an overview, some of the major issues of pH control discussed in the literature are summarized below. Multi-Tank Systems. References in the literature discuss the effectiveness of a neutralization process for strong acid-strong base systems in a single tank,4 two tanks in series,4-7 and even three or more tanks in series.3,7,8 Tanks with fast, efficient mixing and residence times in the range of 10-30 min are recommended. Nearly all agree that stable control is achieved with two or more tanks. Dead Time. Davalloo and Nowroozi4 advised that dead time is the critical feature that determines controllability. Secondary Lag Effects. The time lag between the indicated and actual pH is an important characteristic that can significantly destabilize a pH control loop.3,5,6,9 The discrepancy can easily be g2 pH units and be caused by either the probe dynamics or a fouling outer film on the probe. Similarly, the time required to mix a neutralization drum to homogeneity is another such secondary effect.5,10 Process Disturbances. Adverse effects external to a pH control loop often can make the system unstable.5,10 Of the two most common disturbances, feed rate and composition, it is the composition that normally causes the most control stability problems by changing the process gain orders of magnitude.

10.1021/ie049057a CCC: $30.25 © 2005 American Chemical Society Published on Web 06/03/2005

Ind. Eng. Chem. Res., Vol. 44, No. 15, 2005 5623

Advanced Control. Due to the traditional shortcomings of pH control using conventional PID methods, much work has been conducted to improve its stability using advanced control methods.2,3,5,6,10,11 Since the heart of many of these methods is based upon a process model, several have been developed including first principles, on-line identification, neural networks, fuzzy logic, and the “strong acid equivalent”. NaOH Buffering. Walker and Liu4 suggested NaOH solutions can, with significant exposure time to the atmosphere (about 3 weeks), absorb enough CO2 to have some buffering character and, therefore, stabilize a single-tank pH control system. Nonlinearity and Controllability. Finally, by nature, the dynamics of neutralization processes tends to be highly nonlinear6,12,13 and can vary 3 orders of magnitude over the range of pH. For this reason, these references explained that single-tank neutralization processes normally cycle between pH 4 and 10 and do not converge. Skogestad7 used controllability analysis based upon frequency response to analyze the system theoretically. He found that a very fast response time is required for good control by a strategy that simply manipulates the titrant flow into a single tank, which is typically faster than possible.

Figure 1. Titration curve for a typical strong acid water with NaOH (starting with initially 3.292 wt % NaOH in water).

Process Case Application The feature application of this study was a continuous mixed neutralization vessel designed, constructed, and operated on the industrial scale. The objective of the process was to continuously treat an acidic wastewater stream (here called “acid water”) that had a typical pH ∼2 to neutralize it before a subsequent processing step was performed. The objective of the control system was to provide stable pH control with a set point between 7 and 10. The success of the neutralization process was important for two key reasons: (1) after processing, the stream ultimately arrived at the on-site wastewater treatment system and was required by environmental regulation to have a pH between 2.0 and 12.5, and (2) the processing equipment downstream of the neutralization vessel was constructed of materials that were not resistant to acidic species. Description of the Proposed Process. The acid water featured in this study was composed of, on average, 2.7 wt % H2SO4, 12.5 wt % Na2SO4, about 200 ppm equivalent NH3, and the balance water. There is a natural variation of H2SO4 concentration due to the batch nature of the production process, ranging from 1 to 4 wt %. Because of the convenience of availability, the logical material selected as the titrant was 25 wt % NaOH in water. Since H2SO4 is a strong acid and NaOH is a strong base, the resulting salt is neutral and there is very little buffer capacity in the mixture. Even though there has been reference to the potential buffering capability of CO2 that might exist in industrial NaOH solution supplies and to the potential that the acid water contains trace quantities of equivalent NH3, the titration curve is very steep near the neutral region as shown in Figure 1 and exhibits essentially nonbuffered character. This aspect of the system presents a very distinct challenge for conventional PID control. The process characteristic is very nonlinear, with response behavior on the basic end much slower than that with pH < 12, which generally leads to instability and poor ability of the control system to converge to set point quickly with a rapid decay ratio. It was, therefore, proposed to

Figure 2. Continuous neutralization drum flow diagram.

dampen the effect of the system nonlinearity by designing a mixing process with a relatively large holdup volume (which has linear characteristics), thereby allowing mixing dynamics to significantly affect the overall process dynamics and also dilute the impact of process dead time. Figure 2 shows a flow diagram of this unit operation. At this point, the design seems to contradict many key findings presented in the literature. However, several important features were studied at length in this work to properly address these concerns and ultimately incorporate them to achieve a robust design. The heart of the process is a tank made of carbon steel with a large corrosion allowance. This material was selected for cost and compatibility with neutral to slightly basic Na2SO4 solutions based upon available corrosion data.14 Agitation is provided by a centrifugal pump and a circulation loop with a tank mixing eductor. The outlet of the eductor is directed toward an acid water injection leg installed in the side of the drum to promote good mixing and neutralization in the bulk of the liquid, far from the drum wall. The acid water injection leg is made of alloy 20 for compatibility with H2SO4 solutions.14 The NaOH solution is introduced at the top of the drum and is directed into the bulk of the liquid. A pH probe, designated by “AT,” is installed in the pipe between the drum and pump suction. Finally, control valves are provided to control the acid water feed rate with a flow controller, the NaOH solution feed rate with a pH controller, and the level with a level controller. An important characteristic of the pH probe is its measurement time lag. The TBI Bailey type TBX557 probe was selected for this application. The vendor provided information that their probe would achieve ∼90% response in 30 s. That means, if the probe were

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Figure 3. Dynamic response of pH probe to a step change in the pH of the surrounding fluid (diamonds are indicated readings from the probe, the triangle is the vendor advertisement of “90% response in 30 s,” and the curve is the best-fit first-order response for measured indications, with τ ) 21 s).

immersed in a solution of a certain pH at steady state and it was instantly moved to a solution of a different pH, after 30 s the pH indicated by the probe would have changed by 90% of the difference between the pHs of the two solutions. Treating this feature as a first-order dynamic process, the indicated pH is therefore related to the solution pH according to

pHInd ) pH1 + ∆pH(1 - e-t/τ)

(1)

where pHInd denotes the instantaneous indication after the probe has been moved from one solution to the other, pH1 denotes the original solution, ∆pH is the difference in pH between the two solutions, t is time, and τ is the time constant. Rearranging,

0.9 )

pHInd - pH1 ) 1 - e-(30sec)/τ ∆pH

(2)

gives τ ) 13 s. After the purchase of this probe, it was tested by immersing it in a standard solution of pH ) 4, allowing the indication to reach steady state, and then quickly moving it to a solution with pH ) 10. The indicated pH was recorded at various times to characterize the dynamic response. The results are shown in Figure 3, along with the “90% response in 30 s” reference point and the best-fit first-order curve with τ ) 21 s. Although the probe does not exactly match the advertisement, its time constant is reasonably close and is, indeed, approximately first-order. Closed-Loop Process Model Development. To accurately determine the holdup volume in the neutralization drum shown in Figure 2 that is required to stabilize the performance of the pH control system, a detailed dynamic model of the process was developed. The model included three main parts: the vessel composition dynamics, the titration curve, and the controller algorithm. For simplification, the material “acid water” is considered to be a single, pure component. As such, the information provided in Figure 1 can be readily employed by simply providing an unsteadystate material balance for three components: pure NaOH from the 25% NaOH stream, pure water from the 25% NaOH stream, and pure acid water. The vessel composition is easily characterized by performing an unsteady-state material balance around the drum. For simplification, it is assumed that the level controller shown in Figure 2 is sufficient to keep the holdup volume constant. Further, it is assumed that the

Figure 4. Linearization of the titration curve for a typical strong acid water with NaOH (with pH0 ) 13.8).

specific gravity is constant so that the total system mass is constant. These two assumptions are not strictly accurate but are reasonable for studying the pH control system behavior, and they introduce very little error into the model. Therefore, the total material balance can be expressed as

A˙ + B˙ - P˙ ) F

dV dt

(3)

where A˙ , B˙ , and P˙ are the mass flow rates of acid water, 25% NaOH solution, and neutralized product, respectively, F is the density of the liquid in the vessel, V is the holdup volume, and t is time. Since it was assumed that the volume is constant, the derivative is zero and eq 3 becomes

A˙ + B˙ - P˙ ) 0

(4)

Similarly, the mass balance for neat NaOH can be written as

0.25B˙ - P˙ xB )

dxB d (VFxB) ) VF dt dt

(5)

where xB is the mass fraction of NaOH in the liquid in the vessel, and the mass balance for acid water (as a pure component) can be written as

A˙ - P˙ xA )

dxA d (VFxA) ) VF dt dt

(6)

where xA is the mass fraction of acid water in the liquid in the vessel. Naturally, the component mass fractions sum to unity:

xA + xB + xW ) 1

(7)

Much work has been performed to characterize the pH of mixtures of acids and bases and is readily available in many general and inorganic chemistry textbooks (e.g., refs 15 and 16), but for this work the relationship was simplified and treated empirically. The data given in Figure 1 are linearized and well-correlated by an equation with the following form

B 1 )R +β pH0 - pH A

()

(8)

where B/A is the ratio of NaOH/(acid water) and pH0, R, and β are constants. Since acid-base reactions are generally very fast, it is assumed that there is no time lag in reaching the equilibrium described by eq 8. Figure 4 shows the data in Figure 1 plotted in the form of eq


8, with pH0 ) 13.8, R ) 231.55, and β ) -3.0857. Note, eq 8 ignores the effect of total electrolyte concentration and ionic strength. Nonetheless, it is reasonably accurate and sufficient for this study. Also, the equation does not characterize the tail at the concentrated acid range with pH < 3, but this study focuses on a process that is attempting to control pH g 7. Additionally, the acid water is supplied with a pH generally ∼2.0, so this process typically would not encounter a bulk pH < 3. Finally, the general equations for the controllers are required to complete the closed-loop simulation. It is assumed that the acid water flow controller and the drum level controller work perfectly to keep those quantities always at their set points. Only the behavior of the pH controller is included here. The author generally has had the most success with PI-only (proportional and integral) control, so, for the purposes of this study, the derivative portion is not included and the behavior of the pH controller is taken to be described by the PI portion of the PID algorithm, which is readily available from standard automation and controls textbooks. Therefore, the position of the 25% NaOH control valve is given by17

m ) m0 + Kce +

Kc τI

∫0t e dt

(9)

where m is the valve position (0-100%), m0 is the controller bias, Kc is the controller gain, τI is the integral reset time, and e is the controller error given by

e ) pHSP - pHInd

(10)

with pHSP ) pH set point and pHInd ) pH indicated by the probe. To prevent reset windup, the integration in eq 9 is performed only when 0 < m < 100%. The firstorder time lag of the pH probe is characterized by eq 1 as explained above. Finally, the flow of the 25% NaOH solution, as determined by its control valve position, is given by the following, which assumes a linear valve characteristic with the majority of the pressure drop in the delivery system provided by the valve itself,

B˙ )

m B˙ 100 max

Table 1. Process Constants for Simulation Demonstration quantity acid water feed rate “fully opened” 25% NaOH solution flow mixture liquid density pH probe time constant

variable value A˙ B˙ max F τ

4000 1000 64 13

units lb/hr lb/hr lb/ft3 s

the process constants defined in Table 1 and with the process initially at steady state. Figure 5 shows the response to a unit set point change with minimum integrated absolute error (IAE) tuning parameters, starting with an initial pH of 7. Design Study. As set forth above, one objective of this study was to determine a holdup volume that provides robust pH control stability for set point changes and process disturbances. To evaluate this volume, an adjustment was made to the IAE17 tuning method such that the error is based upon the actual pH and not the indicated pH. Then, the model could be evaluated for various selected volumes, optimally tuning for each volume as described above and obtaining the IAEactual. For a sensitivity study, the calculation was performed with the probe time constant of 13 and 45 s with the nominal conditions given above and for set point changes from 7 to 8. Figure 6 shows that, at a holdup volume of approximately 10-20 ft3 (approximately 9-18 min residence time), the IAEactual is close to a minimum, indicating the proper design volume. Note that this value is satisfactory for a new pH probe and for one that experiences a significantly higher time constant. Larger volumes provide only slightly improved IAEactual and are considered diminished return. Equally as critical as the residence time, proper mixing design is required to maintain the integrity of the pH indication and prevent secondary effects from

(11)

where B˙ max is the flow rate of 25% NaOH when the control valve is fully opened (m ) 100%). This is an important idealization of the performance of a control valve that is further explored later in this paper. Closed Loop Simulation

Figure 5. Closed-loop dynamic response with a pH set point change from 7 to 8 (10 ft3 holdup volume, with minimum IAE parameters Kc ) 43%/pH and τI ) 53 min).

Equations 1 and 4-11 comprise the model of the closed loop process to characterize all three parts of the system: composition, strong acid/strong base titration, and PI control. The equations can be solved simultaneously using many different platforms, such as code software (e.g., FORTRAN, BASIC, Pascal, etc.), math software (e.g., MathCAD and Maple), or even a spreadsheet (e.g., Excel and Lotus 123). The solution platform selected for this study was an Excel spreadsheet employing discrete numerical methods, where the rows correspond to time steps and the columns feature the logical sequence of solutions at a given time step. To demonstrate the solution of the closed-loop pH control process model, the dynamic response was determined for a set point change at time 5 min, given

Figure 6. Effect of holdup volume on the actual IAE for set point changes from pH 7 to 8.

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Table 2. Process Constants for Tuning and Stability Study quantity acid water feed rate “fully opened” 25% NaOH solution flow holdup volume mixture liquid density pH probe time constant

variable value A˙ B˙ max V F τ

4000 1000 20 64 13

units lb/hr lb/hr ft3 lb/ft3 s

adversely affecting the process dynamics. Uhl and Gray18 provided a discussion of vessel mixing time resulting from jet mixers. They offered a graphical correlation with a grouping of mixing time, jet geometry and velocity, and holdup volume on the ordinate and jet Reynolds number on the abscissa. Using a design basis that the mixing time should be ∼1/10th of the residence time, it was determined that ∼140 gpm through a 11/2 in. pipe would achieve ∼1 min mixing time. By using a tank mixing eductor, which can entrain at least three times the motive flow, a circulation rate of ∼140/(3 + 1) ) 35 gpm would meet the design basis. Tuning and Stability Study. Generally, this process is to be operated with constant set points, so the most likely upsets would be due to startup, acid water feed rate disturbance, and 25% NaOH solution supply pressure disturbance. In reality, startup is a large disturbance where the acid water feed rate rapidly steps from no flow to the normal flow set point. It is, therefore, the ability of the pH control system to handle this case that is considered the most strict test. Utilizing the model developed above, with the process constants defined in Table 2, the process was tuned and evaluated for this case in which it is initially at steady state and the acid water flow rate steps from zero to the set point at the 5 min mark. For a pH set point of 9, Figure 7 illustrates the closed-loop response with tuning that minimizes the IAEindicated, showing that the indicated pH is stable, oscillates with a small amplitude, but has a decay ratio below unity though well above 1/4. As explained above, minimizing the IAEindicated does not provide all of the information regarding the success of a controller. In this case, shown in Figure 8, reducing the gain 50% allows the process to converge more quickly and the actual/indicated pH amplitude ratio is also reduced. Naturally, as shown in Figures 9 and 10, operating at a lower pH set point causes the process to accept disturbances with less stability, and operating at a higher pH set point tends to make the process more stable.

Figure 7. Closed-loop dynamic response with an acid water flow rate disturbance from 0 to 4000 lb/hr at time 5 min (Kc ) 300%/ pH and τI ) 1.21 min).




Results of Plant Implementation The neutralization process described above was constructed, started-up, and operated full time at Albemarle Corporation. The drum was 415 gallons, carbon steel, and constructed with a 50 psig pressure rating to allow operation under a slight pressure. The pump provided about 50 gpm of circulation flow rate plus an additional ∼15 gpm for product flow rate. Three pH probes (described above) were installed to allow voting logic to improve the service factor. The control system was a “DeltaV” vs 7.2 digital distributed control system (DCS),19 which featured pre-built, standard PID blocks (although PI-only was used) with on-line auto tune capability and foundation fieldbus I/O. All of the performance objectives were met with, ultimately, only minor adjustments. For a brief representation of the constructed process’s performance,


Figure 11. Typical observed closed-loop response of constructed process for pH unit set point change.

Figure 12. Measured performance of control valve for 25% NaOH solution.

Figure 11 illustrates the stable closed-loop response when the pH set point is changed from 10 to 9. Key observations during startup uncovered the following important issues: the 25% NaOH solution control valve behavior differed from that in eq 11; the pH probe tended to become coated with a thin film of dirt that significantly increased its time constant; the pH set point could be adjusted to improve stability; and the process was able to handle disturbances (25% NaOH flow supply pressure and acid water feed rate). Valve Behavior for the 25% NaOH Solution. Typically, four main problems can be experienced with control valve performance that could adversely affect the stability of PID control: improper selection of the valve coefficient (Cv), valve hysteresis, improper choice of linear or equal percentage characteristic, and “zeroshift”. The first three potential problems did not occur with this application, primarily due to the small valve size, ample supply pressure for the 25% NaOH solution, and correct choice of linear characteristic. The fourth problem, zero-shift, was experienced and is characterized by a control device that offers no impact upon the process until the output of the controller reaches a relatively high value, which effectively adds dead time to the process. In this case, no 25% NaOH solution began to flow until the valve was opened approximately 11%, as shown in Figure 12. This situation is particularly a problem for startup, during which the controller output is continuing to increase due to process error but with no improvement being realized from the action. Often, a controller is tuned to respond more quickly to overcome this period of no control action but is too fast for the region in which the valve begins to affect the

Figure 13. Closed-loop dynamic response with an acid water flow rate disturbance from 0 to 4000 lb/hr at time 5 min (Kc ) 37.5%/ pH and τI ) 1.21 min, with “real” valve behavior).

process. A controller bias can be used to minimize the problem by, for example, causing the valve to start at 10% opened when the controller is put into automatic. As a comparison to Figure 8, the valve performance given in Figure 12 was included in the model as a replacement for eq 11 and simulated with the same conditions given in Table 2. The same tuning parameters used in Figure 8 did not give stable, converging results. Reducing the gain by 75% provided the stable closed-loop response shown in Figure 13, with similar time to convergence and with about twice the amplitude as shown in Figure 8. Note that this gain is 12.5% of the original value featured in Figure 7 that was derived from the minimum IAEindicated and with the ideal valve performance given by eq 11. pH Probe Fouling. It was observed during startup that the stability of the pH controller tended to decay within a few weeks. Attempts were made to dampen process disturbances, alter the set point to find a region of lower process gain, and retune the PID controller. None of these seemed to have the ability to return the performance back to the success observed initially during startup. Finally, the last troubleshooting activity was to inspect the pH probes and evaluate if they needed to be replaced. Upon removal it was very apparent that the pH control stability problem was due to an opaque, brown scale that had formed all over the glass tip of the probe, significantly reducing the diffusion rate of ions into the probe and thereby increasing the probe’s time constant, τ. The scale was very easily removed with a soft cloth and a dilute acid solvent. The probes were reinstalled and the process was restarted with the original tuning parameters. Fortunately, the same excellent pH control stability that was obtained during the early period of startup was restored. To avoid the same problem again, a preventive maintenance plan was implemented in which the probes were routinely cleaned, which has allowed the process to remain robust. To explore the effect of increasing probe time constant, Figure 14 shows the simulated process response to an acid water flow rate disturbance with a “dirty” probe time constant. Comparing to Figure 13 (with a “clean” probe), the deviation between the indicated and actual pH has increased significantly with a dirty probe, and the controller stability has reduced to essentially critically damped. The controller can be retuned by significantly decreasing the gain and increasing the reset to make it much “slower” to improve its performance, but the amplitude and time to convergence would each be larger than that shown in Figure 13. Ultimately, there is a balance between acceptably slow

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Figure 14. Closed-loop dynamic response with acid water flow rate disturbance from 0 to 4000 lb/hr at time 5 min (Kc ) 37.5%/ pH, τI ) 1.21 min, with “real” valve behavior and dirty pH probe with τ ) 60 s).

Figure 16. Closed-loop simulation of 25% NaOH solution header pressure disturbance plant test.

Figure 15. Results of 25% NaOH solution header pressure disturbance plant test. Table 3. Process Constants for Simulation of 25% NaOH Solution Header Pressure Disturbance Plant Test quantity

variable

value

units

acid water feed rate holdup volume mixture liquid density pH probe time constant Gain Reset

A˙ V F τ Kc τI

6500 40 64 13 6 5

lb/hr ft3 lb/ft3 s %/pH minutes

controller response rate, controller stability, and preventive maintenance period, all with a common set of controller tuning parameters. Albemarle has selected a bimonthly preventive maintenance schedule and tuning that delivers about 15 min convergence time when the acid water flow is initially started. pH Set Point Strategy. As explained above, the choice of pH set point is strategic in that higher values tend to make the controller more stable. The pitfall is that the controller could be tuned more slowly because of the lower process gain, but if a disturbance occurs that brings the pH near or even below 7, that “slow” controller would not be fast enough to return the process to steady state in a stable manner. After operating experience with all of the realistic disturbances, a set point between 9 and 10 has provided robust performance. Stability During Disturbances. The final evaluation of the pH control system implemented in the plant

Figure 17. Results of acid water feed rate disturbance plant test.

was to prove its ability to remain stable during process disturbances. Two simple tests were conducted for this purpose. For the first test, the supply pressure in the 25% NaOH solution header system was suddenly reduced from the normal 60 to 46.5 psig by quickly partially closing a valve at the supply pump, allowing the process to respond and return to steady state, and then quickly fully reopening the valve at the pump. This disturbance corresponded to a sudden 15% reduction in the 25% NaOH solution flow rate. Figure 15 shows the recorded results where the pH slightly reduced upon header pressure reduction but stably returned to the set point. Likewise, upon return of the header pressure to normal, the pH slightly increased and again stably returned to the set point. As a comparison, this test was simulated with the closed-loop model (with the corrected valve performance) using the conditions given in Table 3. Figure 16 shows the simulation results with a response that is very similar to that recorded from the plant. For the second test, the acid water feed rate was similarly quickly reduced 15% and the process response was recorded. As shown in Figure 17, the indicated pH increased by 0.05 pH units within about two minutes;


the acid water flow controller regained control and returned the acid water flow rate to its set point, and the pH controller, likewise, returned the pH to its set point within just a few more minutes.

F ) liquid density τ ) pH probe time constant τI ) controller integral reset time

Literature Cited Conclusions Based upon the study of the neutralization of a strongly acidic wastewater with a strong base, a simple yet robust process was developed, designed, and successfully implemented industrially. By carefully considering the effects of several key features of the process, the proper design was achieved to account for all of the complexities. Technical keys included the understanding of pH sensor time lag and maintenance procedures for them, the proper tank mixing design, the choice of set point, and the understanding of the difference between the actual and indicated pH. All of these were incorporated to design a single holdup tank with the proper volume and tank mixing method. The design bases included a residence time of ∼10 min, a mixing time of ∼1 min, and a pH set point of 9-10. Other important findings included the introduction of dead time from valve performance that has zero-shift, the need for proper preventive maintenance procedures to clean pH probes and keep their time constants low, and the overall improved performance with lower controller gains and higher resets than typically determined from conventional tuning formulas. Notation A˙ ) mass flow rate of acid water B˙ ) mass flow rate of 25% NaOH solution B/A ) ratio of NaOH/(acid water) B˙ max ) flow rate of 25% NaOH when the control valve is fully opened (m ) 100%) e ) controller error Kc ) controller gain m ) valve position (0-100%) m0 ) controller bias P˙ ) mass flow rate of neutralized product pH0 ) constant pH1 ) pH of original solution pHInd ) instantaneous pH indicated by the probe pHSP ) pH controller set point t ) time V ) holdup volume xA ) mass fraction of acid water in the liquid (as a pure component) xB ) mass fraction of NaOH in the liquid xW ) mass fraction of water in the liquid (from the 25% NaOH solution only) R ) constant β ) constant ∆pH ) difference in pH between two solutions

(1) Deshpande, P. B.; Ash, R. H. Computer Process Control: with Advanced Applications; Instrument Society of America: Research Triangle Park, NC, 1988. (2) Sung, S. W.; Lee, I.-B. pH Control Using a Simple Set Point Change. Ind. Eng. Chem. Res. 1995, 34, 1730-1734. (3) Wright, R. A.; Kravaris, C. On-Line Identification and Nonlinear Control of an Industrial pH Process. J. Process Control 2001, 11, 361-374. (4) Davalloo, P.; Nowroozi, M.. Neutralizing Industrial Wastes with Conventional Controllers: a Pilot Plant Study. In INTECH; Instrument Society of America: Research Triangle Park, NC, 1979; Vol. 26 (9), pp 75-78. (5) Waller, K. V.; Gustafsson, T. K. Fundamental Properties of Continuous pH Control. ISA Trans. 1983, 22 (1), 25-34. (6) Walker, W. A.; Liu, Y. Design Criteria for pH Control Systems. In Chemical Engineering: InitiativessAttitudessCycles, Proceedings of the Fourteenth Australasian Chemical Engineering Conference, CHEMECA 86; Adelaide, Australia, August 19-22, 1986; Institution of Chemical Engineers, Institution of Engineers Australia, and Royal Australian Chemical, 1986; pp 217-220. (7) Skogestad, S. A Procedure for SISO Controllability Analysiss With Application to Design of pH Neutralization Processes. Comput. Chem. Eng. 1996, 20 (4), 373-386. (8) McMillan, G. K. pH Control; Instrument Society of America: Research Triangle Park, NC, 1984. (9) Herschkovitch, H. Z.; McAvoy, T. J.; Liapis, A. I. Dynamic Modeling of pH Electrodes. Can. J. Chem. Eng. 1978, 56, 346353. (10) Nichols, N.; Sinha, R. In-Line pH Control: Is it Right for Your Application? Control Eng. 1995, 42 (3), 73-74. (11) Smith, B. E.; Kravaris, C. Robust Nonlinear Control of pH Processes. In Proceedings of the 1996 IEEE International Conference on Control Applications; Institute of Electrical and Electronics Engineers: Piscataway, NJ, 1996; pp 528-533. (12) Shinskey, F. G. Process Control Systems; McGraw-Hill Book Co.: New York, 1967; pp 275-282. (13) Shinskey, F. G. pH and pIon Control in Process and Waste Streams; John Wiley & Sons: New York, 1973. (14) Schweitzer, P. A. Corrosion Resistance Tables, 4th ed.; Marcel Dekker Inc.: New York, 1995. (15) Brescia, F.; Arents, J.; Meislich, H.; Turk, A. Fundamentals of Chemistry, 4th ed.; Academic Press: New York, 1980. (16) Brady, J. E.; Holum, J. R. Fundamentals of Chemistry; John Wiley & Sons: New York, 1984. (17) Smith, C. A.; Corripio, A. B. Principles and Practice of Automatic Process Control; John Wiley & Sons: New York, 1985. (18) Uhl, V. W.; Gray, J. B. Mixing Theory and Practice; Academic Press: New York, 1966; Vol. I, pp 243-245. (19) DeltaV® software; Fisher-Rosemount Systems, Inc.: Austin, TX, 2003.

Received for review September 27, 2004 Revised manuscript received May 5, 2005 Accepted May 6, 2005 IE049057A

Case Study of an Automatic pH Control Strategy for a Strong

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