9.2 Positive Displacement Pumps (Peristaltic, Diaphragm, Progressive Cavity) & Dosing Systems

Positive Displacement Pumps & Chemical Dosing Systems

While centrifugal pumps dominate high-volume bulk fluid transfer, positive displacement (PD) pumps are indispensable across water and wastewater treatment plants for precision chemical dosing, high-viscosity sludge transfer, and shear-sensitive polymer feed. Certified operators must understand the fundamental mechanical distinction between centrifugal and PD hydraulics, manage safety relief equipment, and master liquid chemical feed calibration calculations.

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1. Operating Principles: PD Pumps vs. Centrifugal Mechanics

The fundamental operational principle of a positive displacement pump is the mechanical entrapment of a fixed, discrete volume of liquid in a cavity, followed by the physical expulsion of that volume into the discharge piping system.

+-------------------------------------------------------------------------+
|                 HYDRAULIC COMPARISON: CENTRIFUGAL VS. PD                |
|                                                                         |
|  PARAMETER               CENTRIFUGAL PUMP           POSITIVE DISPL.     |
|  ─────────────────────────────────────────────────────────────────────  |
|  Flow vs. Head           Flow decreases as head     Flow remains constant|
|                          increases                  regardless of head  |
|  Discharge Deadheading   Churns liquid; pressure    Pressure builds     |
|                          caps at shutoff head       until pipe bursts   |
|  Self-Priming Ability    Poor (requires flooded     Excellent           |
|                          suction or foot valve)     (pulls deep vacuum) |
|  Viscosity Handling      Efficiency drops sharply   Handles thick sludges|
|                          above 100 cP               up to 50,000+ cP    |
+-------------------------------------------------------------------------+

The Deadhead Hazard and Pressure Relief Valves (PRVs)

Because a positive displacement pump continues pushing its fixed volume into the discharge line regardless of resistance, closing a discharge isolation valve (or encountering a downstream line blockage) creates an immediate, dangerous spike in pressure. The pump will continue building hydraulic pressure until:

1. The electric motor stalls or trips on thermal overload,
2. The drive shaft, connecting rod, or pump housing fractures, or
3. Downstream piping, hoses, or chemical tubing catastrophically rupture, spraying hazardous chemicals (e.g., 93% sulfuric acid or 50% caustic soda).

CRITICAL SAFETY MANDATE: Pressure Relief Valves (PRVs) Every positive displacement pump installation MUST have an approved, spring-loaded or diaphragm-actuated Pressure Relief Valve (PRV) installed on the discharge line upstream of the first downstream isolation valve. The PRV discharge must be piped safely back to the chemical storage tank or pump suction supply vessel.

2. Chemical Metering Pumps: Diaphragm & Peristaltic Designs

Water treatment facilities rely on precise chemical metering pumps to inject disinfectants (sodium hypochlorite), coagulants (alum, polyaluminum chloride), oxidants (potassium permanganate), and pH adjustment chemicals (sodium hydroxide, sulfuric acid).

Mechanical & Hydraulic Diaphragm Metering Pumps

Diaphragm pumps use a flexible reciprocating diaphragm (typically PTFE / Teflon facing with an EPDM elastomeric backing) to displace fluid in a specialized liquid head:

1. Suction Stroke: The drive mechanism retracts the diaphragm, expanding liquid head volume and lowering internal pressure. Atmospheric pressure forces the suction ball check valve off its seat, drawing chemical into the head while the discharge ball check valve is pulled tightly closed onto its seat.
2. Discharge Stroke: The drive mechanism pushes the diaphragm forward, compressing liquid volume. The suction check valve is forced closed onto its seat, while the discharge check valve unseats, expelling chemical into the discharge tubing.
3. Dual Control Adjustments:
   • Stroke Speed (Frequency): Regulates the number of strokes per minute (0–120 SPM) via motor speed or electronic solenoid pulses.
   • Stroke Length (Displacement): Regulates the physical distance traveled by the diaphragm per stroke (0–100%).
   • Operating Rule: For maximum volumetric dosing accuracy and repeatability, never operate a mechanical diaphragm pump with a stroke length setting below 20% (target 40% to 90% operating window).

+-------------------------------------------------------------------------+
|               DIAPHRAGM CHEMICAL METERING PUMP PIPING TRAIN             |
|                                                                         |
|  [Bulk Storage Tank]                                                    |
|         │                                                               |
|  [Calibration Column] ──┐                                               |
|         │               ▼                                               |
|  [Y-Strainer] ──► [Diaphragm Pump Head] ──► [Pulsation Dampener]        |
|                                                   │                     |
|  [PRV (Relief to Tank)] ◄─────────────────────────┤                     |
|                                                   ▼                     |
|  [Backpressure Valve (15-25 psi)] ──► [Antisiphon Quill in Main Line]   |
+-------------------------------------------------------------------------+

Peristaltic (Hose / Tubing) Pumps

Peristaltic pumps utilize rotating shoes or rollers mounted on a central rotor to progressively compress and occlude a resilient elastomeric hose (Norprene, EPDM, or polyurethane) against a circular pump housing.

• Seal-Less & Valve-Less: The chemical remains completely contained inside the flexible tube; it never touches bearings, shafts, or check valves.
• Elimination of Off-Gas Vapor Locking: Chemicals like sodium hypochlorite (NaOCl) naturally decompose, releasing trapped chlorine and oxygen gases. In diaphragm pumps, gas bubbles collect inside the check valve chamber, causing the pump to lose prime and "vapor lock." Peristaltic pumps positively displace both liquids and gases simultaneously, making them virtually immune to vapor locking.
• Dry Run Capability: Peristaltic pumps can run dry indefinitely without mechanical damage, provided the casing contains proper tube lubricant (glycerine or silicone bath).

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3. High-Solids & Sludge Pumps: Progressive Cavity & Rotary Lobe

Wastewater treatment facilities and water plant residuals processes require heavy-duty positive displacement pumps to move thickened sludge, primary sludge, and concentrated polymer emulsions.

Progressive Cavity Pumps (Moyno Pumps)

A progressive cavity pump consists of two primary internal components:

1. Rotor: A single-lead helical screw machined from high-strength chrome-plated alloy steel or stainless steel.
2. Stator: A stationary double-lead internal helix molded from a resilient synthetic elastomer (Buna-N, EPDM, or Viton) bonded inside a steel cylinder.

As the rotor revolves eccentrically within the stator, a continuous series of sealed, honeycomb-shaped cavities form and travel progressively from the suction port to the discharge flange.

• Non-Shearing Laminar Flow: Flow is exceptionally smooth, pulsation-free, and low-shear. This makes progressive cavity pumps ideal for feeding long-chain flocculant polymers (which would shear and lose effectiveness in centrifugal impellers) and dewatered sludge cake (up to 15–25% total suspended solids).
• Thermal Dry-Run Hazard: The tight mechanical interference fit between rotor and stator requires fluid film lubrication. Operating a progressive cavity pump dry for even 30 to 60 seconds creates extreme friction that melts and chars the elastomer stator, permanently destroying it. Plants install thermal stator temperature sensors or inline conductivity dry-run switches interlocked with motor starters.

Rotary Lobe Pumps

Rotary lobe pumps utilize two intermeshing, multi-lobe rotors (typically 2-wing, 3-wing, or 4-wing rubber-coated lobes) timed by external synchronizing gears to rotate in opposite directions inside a casing. They handle high-solids primary sludge, clarifier scum, and abrasive grit with compact physical footprints and reversible flow capability.

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4. Chemical Feed Dosing & Drawdown Cylinder Calculations

Operators must regularly calibrate liquid chemical feed systems using a graduated drawdown calibration cylinder installed on the pump suction line to verify actual volumetric delivery against the plant SCADA dosing setpoint.

Mathematical Formulation for Drawdown Calibration

$\text{Flow Rate (mL/min)} = \frac{\text{Volume Displaced (mL)}}{\text{Time Elapsed (seconds)}} \times 60\text{ s/min}$

$\text{Feed Rate (GPH)} = \frac{\text{Flow Rate (mL/min)} \times 1.44}{60} = \text{Flow Rate (mL/min)} \times 0.01585$

$\text{Feed Rate (GPD)} = \text{Flow Rate (mL/min)} \times 0.3805$

Step-by-Step Worked Calibration Problem

A water treatment plant operator isolates the bulk sodium hypochlorite tank and opens the valve to a 500 mL suction calibration column. The diaphragm metering pump is set at 70% stroke length and 60% stroke speed. The operator records that the pump draws down exactly 185 mL of chemical in 45.0 seconds.

Step 1: Calculate volumetric feed rate in mL/min: $\text{mL/min} = \frac{185\text{ mL}}{45.0\text{ s}} \times 60\text{ s/min} = 246.67\text{ mL/min}$

Step 2: Convert mL/min to Gallons Per Hour (GPH): $\text{GPH} = 246.67\text{ mL/min} \times \frac{1\text{ gal}}{3,785.4\text{ mL}} \times \frac{60\text{ min}}{1\text{ hr}} = 3.91\text{ GPH}$

Step 3: Convert to Gallons Per Day (GPD): $\text{GPD} = 3.91\text{ GPH} \times 24\text{ hr/day} = 93.84\text{ GPD}$

Step 4: Verify against target chemical dose: If the plant is treating 2.5 MGD with 12.5% trade strength sodium hypochlorite (containing 1.25 lb available $Cl_2$/gal), the available active chlorine delivered is: $\text{lb } Cl_2\text{/day} = 93.84\text{ GPD} \times 1.25\text{ lb } Cl_2\text{/gal} = 117.3\text{ lb } Cl_2\text{/day}$ $\text{Dosage (mg/L)} = \frac{117.3\text{ lb/day}}{2.5\text{ MGD} \times 8.34\text{ lb/gal}} = 5.63\text{ mg/L } Cl_2$