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ISA Saint Louis Short Course Dec 9-10, 2010

Advanced pH Measurementand Control - Day 1

pH Challenges and Opportunities

Welcome

• Gregory K. McMillan – Greg is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow.

Presently, Greg contracts as a consultant in DeltaV R&D via CDI Process & Industrial. Greg received the ISA “Kermit Fischer Environmental” Award for pH control in 1991, the Control Magazine “Engineer of the Year” Award for the Process Industry in 1994, was inducted into the Control “Process Automation Hall of Fame” in 2001, was honored by InTech Magazine in 2003 as one of the most influential innovators in automation, and received the ISA Life Achievement Award in 2010. Greg is the author of numerous books on process control, his most recent being Essentials of Modern Measurements and Final Elements for the Process Industry. Greg has been the monthly “Control Talk” columnist for Control magazine since 2002. Greg’s expertise is available on the web site: http://www.modelingandcontrol.com/

Top Ten Signs of a Rough pH Startup

Food is burning in the operators’ kitchen The only loop mode configured is manual An operator puts his fist through the screen You trip over a pile of used pH electrodes The technicians ask: “what is a positioner?” The technicians stick electrodes up your nose The environmental engineer is wearing a mask The plant manager leaves the country Lawyers pull the plugs on the consoles The president is on the phone holding for you

Extraordinary Sensitivity and Rangeability

pH Hydrogen Ion Concentration Hydroxyl Ion Concentration0 1.0 0.000000000000011 ` 0.1 0.00000000000012 0.01 0.0000000000013 0.001 0.000000000014 0.0001 0.00000000015 0.00001 0.0000000016 0.000001 0.000000017 0.0000001 0.00000018 0.00000001 0.0000019 0.000000001 0.0000110 0.0000000001 0.000111 0.00000000001 0.00112 0.000000000001 0.0113 0.0000000000001 0.114 0.00000000000001 1.0

aH = 10pH

pH = - log (aH)

aH = cH

cH cOH = 10pKw

Where:aH =hydrogen ion activity (gm-moles per liter)

cH =hydrogen ion concentration (gm-moles per liter)

cOH =hydroxyl ion concentration (gm-moles per liter)

= activity coefficient (1 for dilute solutions)pH = negative base 10 power of hydrogen ion activitypKw = negative base 10 power of the water dissociation constant (14.0 at 25oC)

Hydrogen and Hydroxyl Ion Concentrations in a Water Solution at 25oC

0.00000000

2.00000000

4.00000000

6.00000000

8.00000000

10.00000000

12.00000000

14.00000000

0.00000000 0.00050000 0.00100000 0.00150000 0.00200000

3.00000000

4.00000000

5.00000000

6.00000000

7.00000000

8.00000000

9.00000000

10.00000000

11.00000000

0.00099995 0.00099996 0.00099997 0.00099998 0.00099999 0.00100000 0.00100001 0.00100002 0.00100003 0.00100004 0.00100005

14

12

10

8

6

4

2

0

pH

Reagent Influent Ratio

11

10

9

8

7

6

5

4

3

pH

Reagent Influent Ratio

Despite appearances there are no straight lines in a titration curve (zoom in reveals another curve if there are enough data points - a big “IF” in neutral region)

For a strong acid and base the pKa are off-scale and the slope continually changes by a factor of ten for each pH unit deviationfrom neutrality (7 pH at 25 oC)

As the pH approaches the neutral point the response accelerates (looks like a runaway). Operators often ask what can be done to slow down the pH response around 7 pH.

Yet titration curves are essential for every aspect of pH systemdesign but you must get numerical values and avoid mistakessuch as insufficient data points in the area around the set point

Nonlinearity - Graphical Deception

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.000 0.500 1.000 1.500 2.000

Reagent / Influent

pH Calculated pH

Weak Acid and Strong Base

pka = 4

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.000 0.500 1.000 1.500 2.000

Reagent / Influent

pH

Strong Acid and Weak Base

pka = 10

Figure 3-1e: Weak 2-Ion Acid Titrated with a Weak 2-Ion Base

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.000 0.500 1.000 1.500 2.000

Reagent / Influent

pH

Multiple Weak Acids and Weak Bases

pka = 3

pka = 5

pka = 9

Nonlinearity - Graphical Deception

Slope moderatednear each pKa

pKa and curve changes with temperature!

Figure 3-1d: Weak Acid Titrated with a Weak Base

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.000 0.500 1.000 1.500 2.000

Reagent / Influent

pH

Weak Acid and Weak Base

pka = 4

pka = 10

Double Junction Combination pH Electrode

W W

W

W

W

WW

W

W

W

Em

R10R9 R8R7

R6

R5

R4

R3

R2

R1

Er

E5

E4

E3

E2

E1

outer gellayer

inner gellayer

secondjunction

primary junction

solution ground

Process Fluid

silver-silver chlorideinternal electrode

silver-silver chlorideinternal electrode

potassium chloride (KCl) electrolyte in salt bridge between junctions

7 pH buffer

Ii

High acid or base concentrations can affect glass gel layer and reference junction potentialIncrease in noise or decrease in span or efficiency is indicative of glass electrode problemShift or drift in pH measurement is normally associated with reference electrode problem

Process ions try to migrate into porous reference junctionwhile electrolyte ionstry to migrate out

Nernst Equationassumes insideand outside gellayers identical

Measurementbecomes slow from a loss ofactive sites ora thin coatingof outer gel

Life Depends Upon Process Conditions

25 C 50 C 75 C 100 CProcess Temperature

Months

>100% increase in life from new glass designsfor high temperatures

High acid or base concentrations (operation at the extremes of the titration curve) decrease life for a given temperature. A deterioration in measurement accuracy and response time often accompanies a reduction in life. Consequently pH feedforward control is unreliable and the feedforward effect and timing is way off for such cases.

New High Temperature Glass Stays Fast

0

50

100

150

200

0 50 100 150 200

minutes

mV

New Glass

Other

Glass electrodes get slow as they age. High temperatures cause premature aging

New Design Eliminates Drift after Sterilization

New Old #1 Old #2

Solid Large Surface Reference Junction

High Temperature Glass with Removable Reference Junction

Low Flow Assembly for Low Conductivity Streams

Air Bleed Screw

Mounting Plate203.2 x 457.2 mm

( 8” x 18”)

Cal Cup HolderDiffuser (inside low flow cell)

Reservoir Filter

500 mlElectrolyte Reservoir

VP Connector

Low Flow Cell

Sample OUT

Sample IN

Reference Tubing

Combination Electrode

Vent TubeReservoir Clip

Air Bleed Screw

Mounting Plate203.2 x 457.2 mm

( 8” x 18”)

Cal Cup HolderDiffuser (inside low flow cell)

Reservoir Filter

500 mlElectrolyte Reservoir

VP Connector

Low Flow Cell

Sample OUT

Sample IN

Reference Tubing

Combination Electrode

Vent TubeReservoir Clip

Horizontal Piping Arrangements

AE

AE

AE

AEAEAE

5 to 9 fps to minimize coatings0.1 to 1 fps to minimize abrasion

20 to 80 degreesThe bubble inside the glass bulbcan be lodged in tip of a probe that is horizontal or pointed up or caught at the internal electrodeof a probe that is vertically down

pressure drop foreach branch mustbe equal to to keep the velocities equal

Series arrangement preferred to minimize differences in solids, velocity, concentration, and temperature at each electrode!

10 OD10 OD

20 pipe diameters

20 pipe diameters

static mixer or pump

flush

drain

flush

drain

throttle valve toadjust velocity

throttle valve toadjust velocity

Vertical Piping ArrangementsA

E AE

AE

AE

AE

AE

5 to 9 fpscoating abrasion

10 O

D1

0 O

D

0.1 to 1 fps

holeorslot

Orientation of slot in shroud

throttle valve toadjust velocity

throttle valve toadjust velocity

Series arrangement preferred to minimize differences in solids, velocity, concentration, and temperature at each electrode!

What is High Today may be Low Tomorrow

AB A

B A

BpH

time

Most calibration adjustments chase the short term errors shownbelow that arise from concentration gradients from imperfectmixing, ion migration into reference junction, temperature shifts, different glass surface conditions, and fluid streaming potentials.With just two electrodes, there are more questions than answers.

• Inherently ignores single measurement failure of any type including the most insidious PV failure at set point

• Inherently ignores slowest electrode• Reduces noise and spikes particularly for steep curves• Offers online diagnostics on electrode problems

– Slow response indicates coated measurement electrode

– Decreased span (efficiency) indicates aged or dehydrated glass electrode

– Drift or bias indicates coated, plugged, or contaminated reference electrode or high liquid junction potential

– Noise indicates dehydrated measurement electrode, streaming potentials, velocity effects, ground potentials, or EMI

• Facilitates online calibration of a measurement

Middle Signal Selection Advantages Middle Signal Selection Advantages

For more Information on Middle Signal Selection see Feb 5, 2010 post http://www.modelingandcontrol.com/2010/02/exceptional_opportunities_in_p_11.html

Options for Maximum Accuracy

• A spherical or hemi-spherical glass measurement and flowing junction reference offers maximum accuracy, but in practice maintenance prefers:– A refillable double junction reference to reduce the complexity of installation and

the need to adjust reference electrolyte flow rate – This electrode is often the best compromise between accuracy and maintainability.

– A solid reference to resist penetration and contamination by the process and eliminate the need to refill or replace reference particularly for high and nasty concentrations and pressure fluctuations – This electrode takes the longest time to equilibrate and is more prone to junction effects but could be right choice in applications where accuracy requirements are low and maintenance is high.

• Select best glass and reference electrolyte for process • Use smart digital transmitters with built-in diagnostics• Use middle signal selection of three pH measurements

– Inherent auto protection against failure, drift, coating, loss in efficiency, and noise • Allocate time for equilibration of the reference electrode• Use “in place” standardization based on a sample with the same

temperature and composition as the process. If this is not practical, the middle value of three measurements can be used as a reference. The fraction and frequency of the correction should be chosen to avoid chasing previous calibrations

• Insure a constant process fluid velocity at the highest practical value to help keep the electrodes clean and responsive

Online Diagnostics for Cracked Glass

Reference Electrode Glass

ElectrodeSolution Ground

3K 0-5 M

Cracked Glass!

Reference - Joseph, Dave, “What’s the Real pH of the Stream”, Emerson Exchange 2008

• Cracked Glass Fault– pH Glass electrode normally has high impedance of 50-150 Meg-ohm

– Glass can be cracked at the tip or further back inside the sensor

– Recommended setting of 10 Megohm will detect even small cracks

Online Diagnostics for Coated Sensor

Coated Sensor!

Reference Electrode

Glass ElectrodeSolution

Ground

40k 150 M

• Coated Sensor Detection Can– activate sensor removal and

cleaning cycle– place output on hold while

sensor is cleaned

Reference - Joseph, Dave, “What’s the Real pH of the Stream”, Emerson Exchange 2008

Temperature Comp Parameters

Solution pH Temperature Correction

Isopotential Point Changeable for Special pH Electrodes

pH / ORP Selection

Preamplifier Location

Type of Reference Used

Ranging

AMS pH Range and Compensation Configuration

Impedance Diagnostics On/Off

Reference Impedance

Warning and Fault Levels

Reference Zero Offset

Calibration Error Limit

Glass Electrode Impedance

Warning and Fault Levels

Glass Impedance Temp Comp

(Prevents spurious errors due to Impedance decrease with Temperature)

AMS pH Diagnostics Configuration

Live Measurements and Status

Calibration Constants from Last Calibrations

Buffer Calibration Type & Buffer Standard Used

Sensor Stabilization Criteria Zero Offset Beyond this Limit will create a Calibration Error

If you want to know more about Buffer Calibration, hit this button…

AMS pH Calibration Setup

Tips on doing Buffer Calibration

Temperature Range and Values of Selectable Buffers in the Xmtr

Explanation Buffer Calibration Parameters

AMS pH Buffer Calibration Tips

AMS pH Standardization Steps

AMS Temperature Standardization Steps

AMS pH Overview Dashboard

AMS pH Auxiliary Variables Dashboard

AMS pH Diagnostics Dashboard

AMS pH Diagnostics Descriptions

History Time Stamp Calibration Method

Slope mV/pH

Offset (mV)

Glass Impedance, (mOhm)

Reference Impedance, (kOhm)

Temperature (oC)

1-Latest 120days Auto-cal 56.0 11 820 13 25

2 90days Auto-cal 57.5 10 760 10 28

3 60days Auto-cal 57.1 9 670 15 26

4 30days Manual 58.4 10 550 10 27

5-Oldest 2days Manual 59.0 3 480 3 30

Factory Calibration

0.0 Auto-cal 59.3 2 500 2 25

Calibration Record in Electrode

Wireless pH Transmitters Have Latest Advances

Better resolution and diagnostics than smart wired transmitters

Wireless pH Transmitters Eliminate Ground Spikes

Wired pH ground noise spike

Temperature compensated wireless pH controlling at 6.9 pH set point

Incredibly tight pH control via 0.001 pH wireless resolution

setting still reduced the number of communications by 60%

UT Separations Research Program - Wireless Conductivity and pH Lab Setup

• In the UT lab that supports the pilot plant, solvent concentration and loading were varied and the conductivity and pH were wirelessly communicated to the DCS in the control room

Inferential Measurements - Effect of Solvent on pH

• pH measures the activity of the hydrogen ion, which is the ion concentration multiplied by an activity coefficient. An increase in solvent concentration increases the pH by a decrease in the activity coefficient and a decrease in the ion concentration from a decrease per the water dissociation constant.

• pH is also affected by CO2 weight percent since pH changes with the concentration of carbonic acid.

• Density measurements by Micromotion meters provide an accurate inference of CO2 weight percent.

Inferential Measurements - Effect of MEA Solvent on pH

Correlation of pH to CO2 Weight Percent in Methyl Ethyl Amine (MEA)

MEA2% =( 0.2573)(pH) - 2.4727R² = 0.9641

MEA6.5% = (0.2047)(pH) - 1.75R² = 0.9445

MEA11% = (0.0598)(pH) - 0.1864R² = 0.9785

0.300

0.320

0.340

0.360

0.380

0.400

0.420

8.00 8.50 9.00 9.50 10.00 10.50 11.00 11.50

pH

MEA

(CO

2 fre

e w

iegh

t %)

2%

6.50%

11%

Inferential Measurements - Effect of PZ Solvent on pH

Correlation of pH to CO2 Weight % in Piperazine (PZ)

PZ10%= (0.1573)(pH) - 1.1783R² = 0.9407

PZ12.5% = (0.118)(pH) - 0.7192R² = 0.9969

PZ15% = (0.0776)(pH) - 0.2664R² = 0.9897

0.35

0.37

0.39

0.41

0.43

0.45

0.47

8 8.5 9 9.5 10 10.5

pH

PZ w

iegh

t % (C

O2 f

ree)

10% CO2

12.5% CO2

15% CO2

Effect of Process Temperature on Solution pH

• The standard temperature compensation in pH measurement corrects for the change in milliVolts per pH unit generated by the glass electrode as defined by the Nernst equation.

• The solution pH changes with temperature and this error is not corrected by the automatic standard temperature compensation.

• The change in solution pH with temperature is the result of changes in the dissociation constants with temperature.

• Smart wireless pH transmitters allow the user to develop, document, and integrate the solution temperature compensation.

• For strong acid and base solutions at moderate temperatures, the effect of the water dissociation constant in the basic region is often approximated as -0.033 pH/oC.

5

5.5

6

6.5

7

7.5

8

8.5

9

0 10 20 30 40 50 60 70 80 90 100

Solution Temperature (oC)

pH 6.0

pH 6.5

pH 7.0

pH 7.5

pH 8.0

ReferenceTemperature

So

luti

on

pH

Effect of Process Temperature on Solution pH

The Essential Titration Curve

• The titration curve is the essential tool for every aspect of pH system design and analysis.

– Model fidelity

– Valve sizing and resolution requirements

– Feedforward control

– Reagent demand control

– Controller Tuning

– Performance analysis

– Disturbance analysis

• The first step in the design of a pH system is to generate a titration curve at the process temperature with enough data points to cover the range of operation and show the curvature within the control band (absolute magnitude of the difference between the maximum and minimum allowable pH).

• For a set point on the steepest part of the titration curve, one stage of neutralization is needed for every two pH units away from set point. Advanced control and precise valves can eliminate one stage.

Control Valve Rangeability and Resolution

pH

Reagent FlowInfluent Flow

6

8

Influent pHB

A

Control BandSet point

BEr = 100% Fimax Frmax

Frmax = A Fimax

BEr = A

Ss = 0.5 Er

Where:A = distance to center of reagent error band on abscissa from influent pHB = width of allowable reagent error band on abscissa for control band Er = allowable reagent error (%)

Frmax = maximum reagent valve capacity (kg per minute)

Fimax = maximum influent flow (kg per minute)

Ss = allowable stick-slip (resolution limit) (%)

Port A

Port B

Supply

ZZ

ZZ

ZZ

Z

Control Signal

Digital Valve Controller

Must be functionally testedbefore commissioning!

SV

Terminal Box

Diaphragm Actuator with Solenoid Valves

Size of Step Determines What you See

Time (seconds)

0 50 100 150 200 250 300 350 400 450

(%)

35

40

45

50

55

60

65

0.5% Steps 1% Steps 2% Steps 5% Steps 10% Steps

(%)

40

45

50

55

60

65

70

1% Steps 2% Steps0.5% Steps 5% Steps 10% Steps

4" Segmented Ball Valves with Metal Seals,Diaphragm Actuators and Standard Positioners

Fisher V150HD/1052(33)/3610J

Neles R21/QP3C/NP723

Input Signal

Actuator PositionFlow Rate (Filtered)

Maintenance test of 25% or 50% steps will not detect dead band - all valves look good for 10% or larger steps

Effect of Step Size Due to Sensitivity Limit

Limit Cycle in Flow Loop from Valve Stick-Slip

Controller Output (%)Saw Tooth Oscillation

Process Variable (kpph)Square Wave Oscillation

Real Rangeability Real Rangeability

Minimum fractional flow coefficient for a linear trim and stick-slip:

Minimum fractional flow coefficient for an equal percentage trim and stick-slip:

Minimum controllable fractional flow for installed characteristic and stick-slip:

Cxmin minimum flow coefficient expressed as a fraction of maximum (dimensionless)Pr valve pressure drop ratio (dimensionless) Qxmin minimum flow expressed as a fraction of the maximum (dimensionless)Rv rangeability of control valve (dimensionless) R range of the equal percentage characteristic (e.g. 50)Xvmin maximum valve stroke (%)Sv stick-slip near closed position (%)

maxmin

v

vx X

SC

]1[

minmax

v

vv

X

S

x RC

2min

minmin

)1( xRR

xx

CPP

CQ

min

1

xv QR

Best Practices to Improve Valve Performance

Actuator, valve, and positioner package from a control valve manufacturer Digital positioner tuned for valve package and application Diaphragm actuators where application permits (large valves and high

pressure drops may require piston actuators) Sliding stem (globe) valves where size and fluid permit (large flows and

slurries may require rotary valves) Next best is Vee-ball or contoured butterfly with rotary digital positioner

Low stem packing friction Low sealing and seating friction of the closure components Booster(s) on positioner output(s) for large valves on fast loops (e.g.,

compressor anti-surge control) Valve sizing for a throttle range that provides good linearity [4]:

o 5% to 75% (sliding stem globe), o 10o to 60o (Vee-ball)o 25o to 45o (conventional butterfly)o 5o to 65o (contoured and toothed butterfly)

Online diagnostics and step response tests for small changes in signal Dynamic reset limiting using digital positioner feedback [2]

Reagent Savings is Huge for Flat Part of Curve

pH

Reagent to Feed Flow Ratio

Reagent Savings Original

set point

Optimum set point

4

10

Oscillations could be due to non-ideal mixing, control valve stick-slip. or pressure fluctuations

Effect of Sensor Drift on Reagent Calculations

pH

Reagent to Feed Flow Ratio

4

10

6

8

FeedforwardReagent Error

FeedforwardpH Error

Sensor Drift

pH Set PointInfluent pH

The error in a pH feedforward calculationincreases for a given sensor error as theslope of the curve decreases. This resultCombined with an increased likelihood ofErrors at low and high pH means feedforwardCould do more harm than good when goingfrom the curve’s extremes to the neutral region.

Flow feedforward (ratio controlof reagent to influent flow) workswell for vessel pH control if there are reliable flow measurements with sufficient rangeability

Feedforward control always requires pH feedback correction unless the set point is on the flat part of the curve, use Coriolis mass flow meters and have constant influent and reagent concentrations

Common Problems with Titration Curves

• Insufficient number of data points were generated near the equivalence point • Starting pH (influent pH) data were not plotted for all operating conditions• Curve doesn’t cover the whole operating range and control system overshoot• No separate curve that zooms in to show the curvature in the control region• No separate curve for each different split ranged reagent• Sequence of the different split ranged reagents was not analyzed• Back mixing of different split ranged reagents was not considered• Overshoot and oscillation at the split ranged point was not included• Sample or reagent solids dissolution time effect was not quantified• Sample or reagent gaseous dissolution time and escape was not quantified• Sample volume was not specified • Sample time was not specified• Reagent concentration was not specified • Sample temperature during titration was different than the process temperature • Sample was contaminated by absorption of carbon dioxide from the air • Sample was contaminated by absorption of ions from the glass beaker• Sample composition was altered by evaporation, reaction, or dissolution • Laboratory and field measurement electrodes had different types of electrodes • Composite sample instead of individual samples was titrated • Laboratory and field used different reagents

Dynamic First Principal Modeling

Integration of component mass balances

in vessel volume

Calculation of component normalities

Interval halving search for pH that satisfiesthe charge balance

all component mass flows* ( Fi )

Calculation of mixture’s density mixture’s

liquid density

( m )

signed ionic charges ( Zi )

component mass fractions ( Xi )

molecular weights

component normalities ( Ni )

acid and base negativelogarithmic base 10 acid dissociation constants ( pKai )

water pKw

pH

component fractionalmolar densities

( wi )

For inline systems, mass flow ratios are used instead of integrators to compute mass and mole fractions

m (wi i)

Componentliquid

densities

(i)

*Note that all component mass flows in all streams (not just acids and bases) must be included in the component mass balances

The titration curves are obtained byincrementing the reagent mass flow

Calculation of Normality

z * d * xN = ------------- (2-1e)

M

N c = ------- (2-1f) z

Where: c = molar concentration of diluted acid or base (gm-moles per liter)d = density of 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 basex = weight fraction of pure acid or base in solutionz = number of replaceable hydrogen or hydroxyl ions per molecule of acid or

baseN = grams-ions of replaceable hydrogen or hydroxyl groups per liter

Charge Balance Normalities from Dissociation

1N1 s N (2-4a)

1 + P1

(1 + 0.5P2)

N2 s N (2-4b)

(1+ P2 (1+P1))

(1+0.33*P3*(2+P2))

N3 s N (2-4c)

(1+P3 (1+P2(1+P1)))

P1 = 10(s*(pH - pK1

)) (2-4d)

P2 = 10(s*(pH - pK2

)) (2-4e)

P3 = 10(s*(pH – pK3

)) (2-4f)

Charge Balance Equations

For strong acids and bases, the acids and bases are completely dissociated everywhere on the pH scale, which gives the following charge balance:

Nbi Nai 10pH 10(pH – pKw) = 0 (2-4g)

i i

For weak acids and bases with a single dissociation, the concentration of ions depend upon pH and are computed via equation 2-4a, which gives the following charge balance:

1 1 Nbi ] Nai ] + 10pH – 10(pHpKw) (2-4h)

i (1 + Pbi) i (1 + Pai)

Charge Balance Nomenclature

Where:N = concentration of an acid or base (normality)N1 = concentration of ions from a single dissociation (normality)

N2 = concentration of ions from a double dissociation (normality)

N3 = concentration of ions from a triple dissociation (normality)

Nai = concentration of an acid i (normality)

Nbi = concentration of a base i (normality)

pK1 = negative base 10 logarithmic first acid dissociation constant

pK2 = negative base 10 logarithmic second acid dissociation constant

pK3 = negative base 10 logarithmic third acid dissociation constant

pKw = negative base 10 logarithmic water dissociation constant

P1 = parameter for an acid or base with one dissociation

P2 = parameter for an acid or base with two dissociations

P3 = parameter for an acid or base with three dissociations

Pai = parameter for dissociation of an acid i with a single dissociation

Pbi = parameter for dissociation of a base i with a single dissociation

s = ion sign (s 1 for acids and s 1 for bases)

Virtual Plant Knowledge Synergy

Dynamic Process Model

OnlineData Analytics

Model PredictiveControl

Loop MonitoringAnd Tuning

DCS batch and loopconfiguration, displays,

and historian

Virtual PlantLaptop or DesktopPersonal Computer

OrDCS Application

Station or Controller

Embedded Advanced Control Tools

EmbeddedModeling Tools

Process Knowledge

Virtual Plant Setup

Advanced Control Modules

Process Module for Bioreactor or Neutralizer

Virtual PlantLaptop or Desktop

or Control System Station

Configuration and Graphics

Signal characterizers linearize loop via reagent demand control

AY 1-4

AC 1-1

AY 1-3

splitter

AT 1-3

AT 1-2

AT 1-1

AY 1-1

AY 1-2

middlesignal

selector

signalcharacterizer

signalcharacterizer

pH set point

Eductors

FT 1-1

FT 1-2

NaOH Acid

LT 1-5

Tank

Static Mixer

Feed

To other Tank

Downstream system

LC 1-5

From other Tank

To other Tank

Modeled pH Control System

Titration Curve Slope is Key to Fidelity

slope

pH

5/15/2008 Titration Curve Slope

0

5

10

15

20

2 3 4 5 6 7 8 9 10 11 12

pH

Slo

pe

Slope

Acid Flow Ramp

Field Generation of Titration Curve

Static Mixer

Feed

AT 1-1

FT 1-1

FT 1-2

Reagent

10 to 20pipe

diameters

FilterDelay

Div

Curve

Reagent to Feed Ratio

Measured pH

X,Y pair

FC 1-1

Div

Transportation Time Delay

Feed Flow

Ramp inROut mode

Filter

Y Axis(filtered pH)

Synchronized X Axis (Reagent/Feed Ratio)

Coriolis MassFlow Meter

Coriolis MassFlow Meter

AC 1-1

Mass Hold Up =Density Volume

Axial Agitation Recommended for pH Control

The agitation in a vessel should be a vertical axial pattern without rotation and be intense enough to break the surface but not cause froth

baffles

Vertical well mixed tankliquid height should be0.5 to 1.5x tank diameter

Radial Agitation Detrimental for pH Control

Stagnant Zone

Stagnant Zone

The stagnant zones introduce a large and variable dead time. The use of an external recirculation stream and an eductor ring can reduce stagnation

Horizontal Tanks and Sumps are Bad News

MFeed

Reagent

AT 1-3

Short Circuiting

Stagnant Zone

PlugFlow

Multiple recirculation streams can help but this type of geometry is best usedfor attenuation of oscillations upstream or downstream of a pH control system.The insertion of an inline pH control system in the recirculation line could makethis a viable system by putting a fast system in series with a large volume

Vessel Time Constant and Dead TimeFor a vertical well mixed vessel:

Vdp (5-3a)

Fi Fr Fc Fa

Fa Nq Ns Di 3 (5-3b)

0.4Nq (5-3c)

(Di Dt ) 0.55

dp LU) (5-3d)

V

p dp (5-3e)

Fi Fr

For a vessel with proper geometry, baffles, and axial patterns, the equipment dead time from mixing is approximately the turnover time

For a vessel with proper geometry, baffles, and axial patterns, the continuous equipment time constant is the residence time minus the dead time

Equipment Dynamics Nomenclature

Where:

Di impeller diameter (meter)

Dt tank inside diameter (meter)

Fi influent mass flow (kg per minute)

Fr reagent mass flow (kg per minute)

Fc recirculation mass flow (kg per minute)

Fa agitation mass flow (kg per minute)

L distance between inlet and outlet nozzles (meter)

Nq agitator discharge coefficient (0.4 to 1.4)

Ns agitator speed (revolutions per minute)

average fluid density (kg per cubic meter)dp process dead time from mixing (minutes)

p process time constant from mixing (minutes)

U average bulk velocity (meters per minute)

V vessel liquid volume (cubic meters)

Reagent Injection Delay

For reagent dilution or after closing of a control valve to a dip tube or injection tube:

Vdp Fr

Where:

Fr reagent mass flow (kg per minute)

average fluid density (kg per cubic meter)dp process dead time from mixing (minutes)

V injection volume (cubic meters)

The delivery delay from an empty or back filled reagent pipe, injection tube, and dip tube is the largest source of dead time in a pH loop

Use isolation valves close coupled to the injection point coordinated with the action ofthe control valve to reduce reagent holdup between process and reagent control valve

Static Mixer - Good Radial but Poor Axial Mixing

Oscillations and noise will pass through a static mixer un-attenuated and the poor dead time to time constant ratio leads to more oscillations

The extremely small residence time of a static mixer greatly reduces the magnitude of the dead time and the volume of off-spec material

“The Future is Inline” due to a much lower cost, smaller footprint, and faster response if you can address oscillation and noise issues

Attenuation of Oscillations by a Volume

For a single vessel volume:

To

Ao Ai (5-3j)

p

Where:Ai amplitude of input oscillation into volume (reagent to influent ratio)

Ao amplitude of output oscillation from volume (reagent to influent ratio)

To period of oscillation (minutes)

p process time constant from mixing (minutes)

Back mixed volumes attenuate oscillations in concentration that must be translated to pH via a titration curve to see the effect on the pH trend

The average pH measurement upstream and downstream will differ dueTo the nonlinearity. The upstream pH fluctuations must be translated toconcentration fluctuations (changes in reagent to influent ratio) and then attenuated per Equation 5-3j and translated back to pH via titration curve

Translation of Oscillations via Titration Curve

pH

Reagent FlowInfluent Flow

6

8

The effect of fluctuations in influent concentration or mixing uniformity on measurement error and the effect of pressure fluctuations and control valve resolution on the ratio of reagent to influent is less on flat portions of the titration curve but high acid or base concentrations at the curve extremes may attack glass and wetted materials of construction and increase reference junction potentials

Everyday Mistakes in pH System Design

M

Mistake 7 (gravity flow)

AT 1-1

AT 1-3

AT 1-2

Mistake 4 (horizontal tank)

reagentfeed tank

Mistakes 5 and 6(backfilled dip tube &injection short circuit)

Mistake 11 (electrode in pump suction)

Mistake 8 (valve too far away)

Mistake 9 (ball valve with no positioner)

Mistake 10 (electrodesubmerged in vessel)

Mistake 12 (electrode too far downstream)

Mistake 3 (single stage for set point at 7 pH)

Influent (1 pH)

Mistake 1: Missing, inaccurate, or erroneous titration curveMistake 2: Absence of a plan to handle failures, startups, or shutdowns

Inline and Tank Control System Performance

The Inline system has the fastest recovery time and lowest cost but due to thelack of back mixing, the signal will wildly fluctuate for set points on the steeppart of the titration curve. A signal filter (e.g. 12 sec) or reagent demand controlattenuate the oscillations but an offset from the set point is seen downstream

The tank responses shown above assumes a negligible reagent delivery delay and arethus faster than typical. In most systems the reagent injection delay is so large due to a dip tube, the period of oscillation is 10x slower than what is seen in an inline system

Methods to Reduce Capital and Operating Costs

• Use inline systems to replace vessels• Use online models to provide inferential measurements of influent

concentrations, 3rd voting pH measurement for tough applications, and online titration curves for reagent demand control and adaptive control

• Use high resolution valves and advanced process control to:– Reduce vessel size

– Eliminate a stage of neutralization

– Reduce reagent costs

– Eliminate out-of-spec effluent

Review of Key Points

• pH electrodes offer by far the greatest sensitivity and rangeability of any measurement. To make the most of this capability requires an incredible precision of mixing, reagent manipulation, and nonlinear control. pH measurement and control can be an extreme sport

• Solution pH changes despite a constant hydrogen ion concentration because of changes in water dissociation constant (pKw) with temperature, and activity coefficients with ionic strength and water content

• Solution pH changes despite a constant acid or base concentration because of changes in the weak acid or base dissociation constants (pKa) with temperature

• Titration curves have no straight lines A zoom in on any supposed line should reveal another curve if there are sufficient data points

• Slope of titration curve at the set point has the greatest effect on the tightness of pH control as seen in control valve resolution requirement. The next most important effect is the distance between the influent pH and the set point that determines the control valve rangeability requirement

• Titration curves are essential for every aspect of pH system design and analysis• First step in the design of a pH system is to generate a titration curve at the

process temperature with enough data points to cover the range of operation and show the curvature within the control band (absolute magnitude of the difference between the maximum and minimum allowable pH)

Review of Key Points

• Accuracy and speed of response of pH measurements stated in the literature assume the thin fragile gel layer of a glass electrode and the porous process junction of the reference electrode have had no penetration or adhesion of the process and are in perfect condition at laboratory conditions

• Time that glass electrodes are left dry or exposed to high and low pH solutions must be minimized to maximize the life of the hydrated gel layer

• Long term error of pH measurements installed in the process is an order of magnitude greater than the error normally stated in the literature

• pH measurement error may look smaller on the flatter portion of a titration curve but the associated reagent delivery error is larger

• Cost of pH measurement maintenance can be reduced by a factor of ten by more realistic expectations and calibration policies

• The onset of a coating of the glass measurement electrode shows up as a large increase in its time constant and response time

• The onset of a non conductive coating of the reference electrode shows up as a large increase in its electrical resistance

• Non-aqueous and pure water streams require extra attention to shielding and process path length and velocity to minimize pH measurement noise

• Slow references may be more stable for short term fluctuations from imperfect mixing and short exposure times from automated retraction

• The fastest and most accurate reference has a flowing junction but it requires regulated pressurization to maintain a small positive electrolyte flow

Review of Key Points

• For non abrasive solids, installation in a recirculation line with a velocity of 5 to 9 fps downstream of a strainer and pump may delay onset of coatings

• For abrasive solids and viscous fluids, a thick flat glass electrode can minimize coatings, stagnant areas, and glass breakage

• For high process temperatures, high ion concentrations, and severe fouling, consider automatic retractable assemblies to reduce process exposure

• When the fluid velocity is insufficient to sweep electrodes clean, use an integral jet washer or a cleaning cycle in a retractable assembly

• The control system should schedule automated maintenance based on the severity of the problem and production and process requirements

• pH measurements can fail anywhere on or off the pH scale but middle signal selection will inherently ride out a single electrode failure of any type

• Equipment and piping should have the connections for three probes but a plant should not go to the expense of installing three measurements until the life expectancy has been proven to be acceptable for the process conditions

• The more an electrode is manually handled, the more it will need to be removed

• A series installation of multiple probes insures the electrodes will see the same velocity and mixture that is important for consistent performance

• Use properly sized sliding stem (globe) reagent valves with diaphragm actuators, tuned digital positioners, and properly tightened low friction packing

• The extremely small reagent valves used in pH control are prone to improper sizing, irregular flow characteristics, greater stick-slip, and plugging

• The extremely small reagent valves used in pH control may be operating in laminar flow where the flow is proportional to pressure drop or even worse in the transition region where the flow response is erratic

• To prevent plugging and a transition to laminar flow for pH control on a well mixed volume, use pulse width modulation

• Most statements in the literature as to valve rangeability are erroneous because they ignore the installed valve gain and stick-slip

• The reagent flow required for neutralization is usually so small that the installed valve characteristic is the inherent trim characteristic

• A small plug flow volume may have a smaller integrated error than a large back mixed volume because the dead time magnitude is smaller

• For large volumes, maximize back mixing and minimize plug flow to minimize the error from load upsets and the effects of the pH nonlinearity

• For a vessel with proper geometry, baffles, and axial patterns, the equipment dead time from mixing is approximately the turnover time

• The actual equipment dead time is often larger than the turnover time because of non ideal mixing patterns and fluid entry and exit locations

Review of Key Points

Review of Key Points

• A system considered to be well mixed may be poorly mixed for pH control

• To be “well mixed” for pH control, the deviation in the reagent to influent flow from non ideal mixing multiplied by the process gain must be well within the control band

• Back mixing (axial mixing) creates a beneficial process time constant and plug flow or radial mixing creates a detrimental process dead time for pH control

• The agitation in a vessel should be vertical axial pattern without rotation and be intense enough to break the surface but not cause froth

• The actual equipment dead time is often larger than the turnover time because of non ideal mixing patterns and fluid entry and exit locations

• Horizontal tanks are notorious for short circuiting, stagnation, and plug flow that cause excessive dead time and an erratic pH response

• The dead time from back filled reagent dip tubes or injection piping is huge

• To provide isolation, use a separate on-off valve and avoid the specification of tight shutoff and high performance valves for throttling reagent

• Set points on the steep portion of a titration curve necessitate a reagent control valve precision that goes well beyond the norm and offers the best test to determine a valve’s actual stick-slip in installed conditions

• Reagent valve stick-slip may determine the number of stages of neutralization required, which has a huge impact on a project’s capital cost

• For a vessel with proper geometry, baffles, and axial patterns, the continuous equipment time constant is the residence time minus the dead time

• For batch operations without acid-base reactions, there is no steady state and the concentration ramp is described by an integrator gain rather than a time constant

• Horizontal tanks are notorious for short circuiting, stagnation, and plug flow that cause excessive dead time and an erratic pH response

• Back mixed volumes attenuate oscillations in concentration that must be translated to pH via a titration curve to see the effect on the pH trend

• An un-agitated vessel with a pH control loop can be turned from a terrible loser into a big time winner by moving the loop upstream or downstream

• Use volumes upstream to reduce reagent use and smooth out disturbances and volumes downstream to reduce pH constraint violations

• Oscillations and noise will pass through a static mixer un-attenuated and the poor dead time to time constant ratio leads to more oscillations but the extremely small residence time of a static mixer greatly reduces the magnitude of the dead time and the volume of off-spec material. pH measurements or online estimators on a downstream volume can reveal that a static mixer loop is doing a great job

• pH control loops should not be installed on sumps, ponds, and lagoons but on a static mixer or vertical well mixed vessel upstream or downstream

Review of Key Points

• A split range gap adds dead time and a split range overlap increases the severity of a limit cycle from slip stick and increases reagent use

• Use a split range gap that is about twice the stick-slip or the potential error in the positioner calibration, whichever is largest

• Split ranging and signal reversing is better implemented in a Fieldbus function block than via a special calibration of an I/P or positioner

• Split ranging and signal reversing is better implemented in a Fieldbus function block than via a special calibration of an I/P or positioner

• Gaseous and solid reagents often have huge hidden costs from additional reagent consumption, emission, solids disposal, and maintenance costs

• The delivery delay from an empty or back filled reagent pipe, injection tube, and dip tube is the largest source of dead time in a pH loop

• The best method of reducing reagent delivery delay and mixing dead time is to inject the reagent into a high feed or recirculation flow

• While the shape of the titration curve doesn’t change much by dilution, dilution can dramatically decrease reagent delivery delays, improve reagent addition reproducibility by eliminating transitions to laminar flow, increase valve reliability by reducing plugging, and enhance mixing by increasing the reagent injection velocity and reducing the differences in viscosity and density between the reagent and the influent, which is a normally a dilute water stream

Review of Key Points