Mastering Pump Ratio in Two-Stage Vented Single‑Screw Extruders

Two-stage, vented single-screw extruders are common for many applications and resins. Venting is common with many styrenic resins and most applications involving postconsumer recycled (PCR) resins. A properly designed extruder and screw will be able to remove upwards of 90% of the volatiles through the vent, operate stably without flow surging at the die, and not have material flowing out through the vent opening.

Several design features are necessary to meet these processing goals, including:

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• the length and depth of the vented section
• the design of the vent diverter
• second-stage metering channel length
• the pump ratio

The Figure 1 schematic shows a two-stage vented extruder.

Figure 1: Schematic for a two-stage, vented single-screw extruder. Source (all): M.A. Spalding

The pump ratio is the ratio of the pumping ability of the second-stage metering section relative to the pumping ability of the first-stage metering section. Typically, the pump ratio ranges between 1.1 and 1.5. The pump ratio for a screw with a constant lead length is the channel depth of the second-stage metering channel divided by the depth of the first-stage metering channel. Channel depths and lengths for a typical screw made for polystyrene (PS) are shown by Figure 2 for a 6-inch diameter screw.

For this design, the first-stage metering section controls the rate. The pump ratio is 1.44. For pellet-only feedstocks, the compression ratio is 3. The compression ratio for a screw with a constant lead length is the depth of the feed channel divided by the depth of the first-stage metering channel. The compression ratio must be high enough to maintain the first-stage metering channel when full of resin and pressurized.

What Axial Pressure Profile Means for Pump Ratio

Before the pump ratio is explained, it’s instructive to discuss the screw’s axial pressure profile. The axial pressure profile for the PS screw design shown in Figure 2 was determined using numerical simulation for a rate of 1,500 lb/hr and a screw speed of 55 rpm for a specific rate of 27.3 lb/(hr rpm). The specific rate is simply the rate divided by the screw speed. The axial pressure profile is shown by Figure 3. At this rate, the PS resin required a discharge pressure of 1,600 psi to run the downstream equipment. The calculated specific rate due to just the rotation of the screw without an imposed pressure gradient is 23 lb/(hr rpm) for the first-stage metering section. Because the second-stage metering channel is deeper, the rate due just to rotation is higher at 32.7 lb/(hr rpm).

Figure 2: Typical channel depths for a 6-inch diameter screw for PS resin. The compression ratio is 3, and the pump ratio is 1.44. The barrel wall is the top horizontal line of the figure.

As Figure 3 shows, pressure is a maximum at 1,800 psi at the start of the first-stage metering section, and it decreases to zero pressure before the vent. The pressure at the vent must be zero or resin will flow out of the vent opening. Thus, the first-stage metering channel has a negative pressure gradient. This negative pressure gradient causes the flow in the channel to be higher than the specific rate due to just rotation. Here the flow is at 27.3 lb/(hr rpm) and recall that the calculated specific rate due just to rotation is 23.0 lb/(hr rpm).

Figure 3: Axial pressure profile for the PS extruder in Figure 2 at a rate of 1,500 lb/hr at a screw speed of 55 rpm.

The extra 4.3 lb/(hr rpm) was caused by the negative pressure gradient. This negative pressure gradient must occur for a properly designed two-stage extruder since the pressure needs to be relatively high at the entry to the first-stage meter due to solids conveying and melting and zero pressure at the vent channel.

The pressure in the vent channel must be zero to remove volatiles and prevent flow of resin through the vent opening. Preventing vent flow also depends on a diverter that is positioned in the vent port. Vent flow was discussed in the February 2023 issue of Plastics Technology. The pressure in the vent decreases to zero by making the channel very deep. This causes the channel to be partially filled, exposing a large surface area of the molten polymer for mass transport of the volatiles to the void portion of the channel. The volatiles are then removed through the vent.

Downstream of the vent channel is a short transition section where the channel depth becomes shallower and eventually equivalent to the second-stage metering channel depth. As molten resin moves towards the second-stage meter, a location occurs where the channel flow changes from partially filled at zero pressure to completely filled. This is commonly referred to as the fill position. The fill position can occur in the transition section or in the second-stage meter. Once the channel becomes filled, pressure generation can occur. The fill position in Figure 3 is at the entry to the second-stage metering section.

The second-stage metering channel has a pressure near zero at the entry (or fill position) and the pressure increased to the maximum discharge pressure of 1,600 psi, creating a positive axial pressure gradient. The positive pressure gradient causes the specific rate to be less than the calculated specific rate due to rotation. Recall that the specific rate is 27.3 lb/(hr rpm) and the calculated specific rate due to rotation for the second-stage metering channel is 32.7 lb/(hr rpm). Thus, the rate was reduced by 5.4 lb/(hr rpm) due to the positive pressure gradient.

Always Negative

A two-stage vented extruder will always have a negative pressure gradient in the first-stage metering section and a positive gradient in the second-stage metering section. This is because the vent section of the screw must operate at zero pressure and with partially filled channels. Since the first-stage metering channel controls the rate, the second-stage metering section must be able to pump and pressurize at the rate of the first-stage metering.

Because of this operation and the pressure gradients in the metering channels, the second stage metering section must be able to pump at a higher rate than the first-stage metering. For a screw with constant lead length, the second-stage meter must be deeper than the first-stage meter. As previously stated, the ratio of the second-stage depth to the first-stage depth is the pump ratio for a lead length that is constant.

The pump ratio is not unique to a resin or process. Instead, it depends on the length of the second-stage metering section, lead length of the meters, viscosity of the resin, and the downstream pressure requirements. For example, the screw in Figure 2 has a second-stage metering section that is 6 diameters in length, a channel depth of 0.360 inch, and discharging at a pressure of 1,600 psi. If the second-stage metering section was longer at 8 diameters, the channel depth could have been set to 0.330-inch for a pump ratio of 1.32.

If a gear pump were positioned just after the extruder, the discharge pressure could be reduced to 400 psi, and the pump would generate the needed pressure to operate the downstream equipment. Here the second-stage metering channel would be 6 diameters in length and have a channel depth of 0.310-inch for a pump ratio of 1.24. A higher pump ratio and fill position downstream from the second-stage entry is also an acceptable operation.

Poor Design, Poor Solids Conveying

Poorly designed vented extruders can amplify flow surging induced by poor solids conveying. The flow surge starts with a solids conveying section that is not designed correctly or is operating with a screw or feed casing that is too hot. Flow surging was discussed in the August 2024 issue. Figure 4 shows the axial pressure profile for a flow surging two-stage vented extruder. The solid pressure line in the figure is the midpoint of the surge. The dotted lines show the pressures at the high and low points of the surge.

Figure 4: Axial pressure for a two-stage vent extruder with a high-pressure and a low-pressure portion of a surge.

If solids conveying becomes poor, the pressure at the entry of the first-stage meter decreases. This decreases the magnitude of the negative pressure gradient in the metering section, decreasing the rate. The lower flow level passes through the partially filled vent, second-stage transition, and the first part of the second-stage metering section. The fill position moves downstream, decreasing the discharge pressure and the rate at the die. 

When solids conveying is high, the pressure at the entry to the first-stage metering section is high, causing the magnitude of the negative pressure gradient to be high and increasing the rate. Here, the higher rate causes the fill position to move upstream as shown by Figure 4. The upstream fill position causes the discharge pressure and the rate to increase at the die.

Dampening Pressure Surges

The pressure surge at the discharge for Figure 4 is ±250 psi — about the average value. Poor solids conveying will always cause a surge like this, but some second-stage designs can dampen the surge. For example, a long second-stage metering channel with a lower pump ratio can dampen the surge while a short metering channel with a higher pump ratio can increase the severity of the surge. The best way to mitigate surging is to eliminate it at the source. In this case, the solids conveying process would need to be improved.

For existing extruders, the designer does not have the luxury of moving the vent or lengthening the metering sections. In this case, the main design parameters are the depth of the first-stage metering channel and the pump ratio. As previously discussed, the first-stage metering channel depth will set the specific rate for operation, and the pump ratio will provide the pressure needed to run the downstream equipment. The depth of the first-stage metering section is also a key design feature for setting the discharge temperature.

The keys to designing two-stage, vented extruders and screws are the depth of the first-stage metering channel, the length of the second-stage metering channel and the pump ratio. Extruder designers know how to optimize these parameters for new installations and existing extruders. A proper design should maximize the rate, generate the necessary discharge pressure without vent flow and provide a steady discharge pressure.

ABOUT THE AUTHOR: Mark A. Spalding is a fellow in Packaging & Specialty Plastics and Hydrocarbons R&D at Dow Inc. in Midland, Michigan. During his 40 years at Dow, he has focused on development, design and troubleshooting of polymer processes, especially in single-screw extrusion. He co-authored Analyzing and Troubleshooting Single-Screw Extruders with Gregory Campbell. Contact: 989-636-9849; maspalding@dow.com; dow.com.