Advanced pH Measurement and Control
Description
Advanced pH Measurement and Control: Digital Twin Synergy and Advances in Technology details system design, installation, maintenance and ongoing improvement, including a special focus on how digital twins and first-principles charge balance contribute to innovation, operability, productivity, reliability and maintainability. It offers insights into key principles and advances in electrode technology and diagnostics, including a simple and largely untapped method for computing titration curves that match laboratory curves, as well as guidance on selecting and implementing the best control valves and strategies.
The extraordinary sensitivity and rangeability of pH used for measuring and controlling hydrogen concentration introduce many challenges in managing the nonlinearity in the control loop and the precision needed for the control valve. This, combined with pH's critical role in maintaining cell health in biological processes, as well as in the production of clean water, food, pharmaceuticals and chemicals, makes the best pH control system particularly important and challenging. Despite these challenges, the outcomes can lead to significant reductions in equipment costs and, more importantly, substantial improvements in system reliability and performance.
Finally, the appendices cover fundamental principles and provide guidance on using new PID features to reduce project costs and maximize process efficiency, capacity and safety.
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Persons
Gregory K. McMillan, CAP, has more than 50 years of experience in industrial process automation, with an emphasis on the synergy of dynamic modeling and process control. He retired as a Senior Fellow from Solutia and a senior principal software engineer from Emerson Process Systems and Solutions. He was also an adjunct professor in the Washington University Saint Louis Chemical Engineering department from 2001 to 2004. McMillan is the author of numerous ISA books and columns on process control, and he has been the monthly Control Talk columnist for Control magazine since 2002. He started and guided the ISA Standards and Practices committee on ISA-TR5.9-2023, PID Algorithms and Performance Technical Report, and he wrote "Annex A - Valve Response and Control Loop Performance, Sources, Consequences, Fixes, and Specifications" in ISA-TR75.25.02-2000 (R2023), Control Valve Response Measurement from Step Inputs. McMillan's achievements include the ISA Kermit Fischer Environmental Award for pH control in 1991, appointment to ISA Fellow in 1991, the Control magazine Engineer of the Year Award for the Process Industry in 1994, induction into the Control magazine Process Automation Hall of Fame in 2001, selection as one of InTech magazine's 50 Most Influential Innovators in 2003, the ISA Life Achievement Award in 2010, and the ISA Mentoring Excellence award in 2020. He has a BS in engineering physics from Kansas University and an MS in control theory from Missouri University of Science and Technology, both with emphasis on industrial processes.
Christopher Stuart is a senior software engineer in the Process Simulation Development group at Emerson Process Systems and Solutions. He holds a bachelor of science degree in chemical engineering with a biochemical emphasis from Missouri University of Science and Technology. Stuart's research interests are in efficient algorithms for thermodynamic calculations and dynamic simulations.
Dean Cook is the Mimic product manager in the Process Simulation Development group at Emerson Process Systems and Solutions. He holds a bachelor of science degree in physics from Western Illinois University, has 30 years of experience developing dynamic simulation software, and continues to drive toward improving training and process optimization for a wide range of industries.
Zachary Sample is a digital enterprise consultant in Marketing/Business Development for Emerson Process Systems and Solutions. He has over 10 years of experience delivering cross-industry simulation solutions in various roles ranging from technical implementation and engineering to project management and consulting. In these roles, he has had a passion for helping process companies better leverage simulation to improve automation and operational performance. He has a bachelor of science degree in chemical engineering from Missouri University of Science and Technology and a master of science degree in chemical engineering from North Carolina State University.
Content
Acknowledgments vii
About the Authors xv
Preface xvii
Chapter 1 The Essentials 1
1.1 The Heart of the Matter 1
1.2 Stage Fright 9
1.3 Size Does Matter 14
1.4 One Is the Loneliest Number 17
1.5 Acceleration and Stagnation 22
1.6 Life Is a Batch 25
1.7 Industrial Importance 27
1.8 The Real Deal 27
1.9 Best Practices 28
Chapter 2 The Chemistry 33
2.1 ¿Nearly Normal 33
2.2 ¿Staying Active 38
2.3 ¿Free Dissociation 40
2.4 A Question of Balance 46
2.5 Best Practices 50
Chapter 3 Titration Curves 53
3.1 ¿Slippery Slopes 53
3.2 Laboratory Generation 59
3.3 Computer Generation 64
3.4 Field Generation 66
3.5 Buffering 68
3.6 Uses 70
3.7 Best Practices 70
Chapter 4 Electrodes 73
4.1 A Dose of Reality 73
4.2 Measurement Electrodes 92
4.3 Reference Electrodes 99
4.4 Great Expectations and Practical Limitations 102
4.5 Smart Transmitters 123
4.6 Failure Protection 125
4.7 Dynamic Response of Electrodes, Holders, and Sample Systems 126
4.8 Installation Practices 130
4.9 Calibration Procedures 136
4.10 Troubleshooting Logic 141
4.11 Best Practices 149
Chapter 5 Mixing Equipment 155
5.1 What Was Good Might Be Bad 155
5.2 Mixing Dynamics 157
5.3 Agitated Vessels 159
5.4 Static Mixers 169
5.5 Sumps, Ponds, and Lagoons 170
5.6 Best Practices 171
Chapter 6 Control Valves 173
6.1 A Moving Story 173
6.2 Resolution Requirements 178
6.3 Rangeability Requirement 181
6.4 Split-Ranging 184
6.5 Best Practices 186
Chapter 7 Reagent 191
7.1 Delivery Dilemmas 191
7.2 Dilution 194
7.3 Buffering 196
7.4 Dissolution 197
7.5 Special Strategies 200
7.6 Best Practices 203
Chapter 8 Control System 205
8.1 Feedback Control 205
8.2 Feedforward Control 207
8.3 Cascade Control 210
8.4 ¿Linear Reagent Demand Control 212
8.5 ¿Adaptive Control 216
8.6 Advanced Batch Control 219
8.7 Online Dynamic pH Estimators 224
8.8 Model Predictive Control 225
8.9 Real-Time Optimization 227
8.10 Dynamics and Performance 227
8.11 PID Tuning 258
8.12 ¿External Reset Feedback 272
8.13 ¿System Selection 278
8.14 ¿Best Practices 285
Chapter 9 Digital Twin 289
9.1 ¿Introduction 289
9.2 Key Features 293
9.3 ¿Spectrum of Uses 298
9.4 ¿Implementation 306
9.5 ¿Data-Driven Dynamics 308
9.6 ¿Titration Curve Modeling 310
9.7 ¿Instrumentation Modeling 313
9.8 ¿Speedup 321
9.9 ¿Performance Monitoring 322
9.10 ¿Generating and Fitting Profiles 323
9.11 ¿Best Practices 324
References 328
Appendix A: Automation System Performance Top 10 Concepts 329
Appendix B: Questions and Answers 345
Appendix C: Control Valve Positioners 357
Appendix D: Review of Algebra with Logarithms 369
Appendix E: Enhanced PID 371
Appendix F: First-Principle Process Relationships 377
Appendix G: Gas Pressure Dynamics 395
Appendix H: Charge Balance to Model pH 397
Appendix I: Interactive to Noninteractive Time Constant Conversion 407
Appendix J: Jacket and Coil Temperature Control 411
Appendix K: PID Forms and Conversion of Tuning Settings 417
Appendix L: Liquid Mixing Dynamics 425
Appendix M: Modeling pH Systems in Digital Twin 429
Index 437
2
The Chemistry
2.1Nearly Normal
More than any other application, successful pH applications require good communication between the chemist, specialist, and plant engineer. Unfortunately, these individuals tend to speak different languages because what is normal in terms of units for one is not nearly normal for the other, and normality units, which are the most descriptive, are not typically used.
The units chemists and engineering specialists use most frequently to quantify the concentration of acids and bases in a solution are molar, molal, and normality. The concentration unit commonly used by plant engineers is weight or mass fraction. However, because process flow sheets and the specifications for control valves generally show reagent and influent flows, it is desirable to be able to convert from any of these concentration units to flow units. The remainder of the text demonstrates how valuable it will be for control valve sizing and pH system analysis to have the ratio of reagent to influent flow as the abscissa of the titration curve.
Chemists and specialists will provide data in concentration units that should be converted to influent flow conditions and reagent flow requirements.
Chemists predominately use molar units in laboratory measurements because the calculation is based on a beaker volume. Molar concentration is the number of gram-moles per liter of solution. The number of moles is calculated by dividing the weight of the pure acid or base by its molecular weight expressed in the same weight units. The weights units used should be denoted with a dash before the word moles (i.e., lb-moles and gm-moles). Equations 2-1a and 2-1b show how to calculate gm-moles and the concentration in molar units. When using these equations, remember to convert all weight units to grams and all volume units to liters.
(2.1a)
(2.1b)
where
c = molar concentration of diluted acid or base (gm-moles per liter)
d = density of the solution (gm per liter)
M = molecular weight of pure acid or base (gm per gm-mole)
n = number of gm-moles of pure acid or base
V = volume of the solution (liters)
x = weight fraction of pure acid or base in the solution
Molal units are used predominately by engineers and scientists studying electrolytes because the concentration calculation is independent of density and, therefore, temperature. Molal concentration is the number of gm-moles per 1000 gm of solvent. Equations 2-1c and 2-1d show how to convert between molal and molar concentrations. Note that the molal concentration approaches infinity as the acid or base weight fraction approaches 1 (the grams of solvent approaches 0).
(2-1c)
(2-1d)
where
c = molar concentration of diluted acid or base (gm-moles per liter)
d = density of the solution (gm per liter)
m = molal concentration of diluted acid or base (gm-moles per kg solvent)
n = number of gm-moles of pure acid or base
V = volume of the solution (liters)
x = weight fraction of pure acid or base in the solution
Normality units are generally used in pH simulations, which use charge balance equations for acid and base ions. Normality concentration is the grams-ions of replaceable hydrogen or hydroxyl groups per liter of solution. A shorter notation of gram-equivalents per liter is frequently used. Equations 2-1e and 2-1f show how to convert between normality and molar units. Table 2-1a shows the normality versus the weight percentage for some common reagents. Note that normality is not proportional to the weight percentage for a given reagent because the density of the solution also changes.
(2-1e)
(2-1f)
where
d = density of the solution (gm per liter)
M = molecular weight of pure acid or base (gm per gm-mole)
n = number of gm-moles of pure acid or base
x = weight fraction of pure acid or base in the solution
z = number of replaceable hydrogen or hydroxyl ions per molecule of acid or base
N = Normality (grams-ions of hydrogen or hydroxyl groups per liter)
Table 2-1a. The normality of a reagent is not proportional to the weight percentage.
Reagent
Wt%
Normality
Hydrochloric acid
32
10.17
(z = 1)
38
12.35
Sulfuric acid
62.2
19.5
(z = 2)
77.7
27.2
93.2
35.2
98.0
36.0
Sodium hydroxide
10
2.75
(z = 1)
20
7.93
50
19.1
Calcium hydroxide
5
1.36
(z = 2)
10
2.78
15
4.3
As previously mentioned, it is desirable to use a ratio of reagent to influent flow for the abscissa of the titration curve for pH control system design. The method followed in this text is to convert the concentration of the acid or base from the reagent or influent streams in the effluent stream in molar, molal, and normality units to weight fraction via Equations 2-1a, 2-2a, or 2-3a (solve the equations for x). It is necessary to eliminate mixing and residence time dynamics when using the titration curve because it is a steady-state plot. For this purpose, it helps to visualize the influent and reagent streams combining in a pipeline instead of a tank so that there is an immediate translation from a change in reagent or influent flow to a change in the weight factions of the effluent stream. For pure (undiluted) acid or base reagent and influent streams, the ratio of the reagent to influent flow is equal to the ratio of the weight fraction of the acid or base in the effluent stream. Normally, the concentration of the acid or base in the influent and reagent is not 100%, so the weight fraction of the acid or base in the individual influent and reagent streams is used to calculate the diluted stream flows needed for control valve sizing and feedforward calculations via Equations 2-1g and 2-1h. When using weight fractions, it is necessary to designate which stream is the source of the acid or base and which stream is the destination to form a mixture. To reduce confusion in Equations 2-1g through 2-1l, the subscript rr designates the concentration of the acid or base reagent in the reagent stream; re designates the concentration of the acid or base reagent in the effluent; ii designates the concentration of the incoming acid or base in the influent stream; and ie designates the concentration of the incoming acid or base in the effluent throughout the text. Because the influent flow is usually known before the effluent flow, Equation 2-1h is substituted for Fe in Equation 2-1g to yield Equation 2-1i for calculating the reagent flow. The desired flow ratio for the abscissa of the titration curve is the ratio of the diluted reagent to the diluted influent mass flow. Per Equation 2-1i, this is equal to the ratio of the reagent to influent weight fractions in the effluent multiplied by the inverse of the ratio of the reagent to influent weight fractions in the incoming streams. To convert from mass flow to volumetric flow, each mass flow must be divided by the diluted stream density in consistent units. Note that most reagent concentrations are given in weight percentage and must be divided by 100 to get the weight fraction of the diluted reagent. If a laboratory titration curve states the initial sample volume, the abscissa has the volume of reagent titrated to reach the pH set point specified, and the reagent concentration used in the laboratory and plant are equal, then , then Equation 2-1j can be used to calculate the...
