Are Turboexpanders Complicated?

The short answer to this question is a "No"! Not all turboexpander applications are equal and not all of them are complicated.

This article is discussing a design characteristic that MIGHT cause turboexpanders to be (regarded) a more complicated machine compared to other rotating machinery. On a deeper level, it is addressing how power generation by a turboexpander is different from other type of turbines and why turboexpanders FALSELY have not been extensively utilized for power generation in gas pressure reduction stations.

1. Turboexpander Power Generation Capacity

Complication in design and application of a turboexpander arises when a low flow rate and/or a high-pressure ratio is involved. For a low flow rate, picture values in the order of 1 Sm³/s and for a high pressure-ratio, imagine values around 8 to 10.

A detailed discussion of the reason for that complication is complicated itself! Here a simple explanation is presented.

Power generated by a turboexpander comes from energy (or more precisely enthalpy) difference between its inlet and outlet, which depends on inlet and discharge pressure and temperature.

From another perspective, power generation is proportional to flow rate (Q) and pressure difference across turboexpander (ΔP). A proof of this is presented in the next section by a Dimensional Analysis.

Power ∝ Q × ΔP

Pressure difference is the available potential. It is determined by the process and acts as a driving force, waiting to happen! It can be wasted, or can be recovered in the form of power. The means to recover it, is flow rate.

Flow is the means to take advantage of the driving force, pressure. It contains the energy associated with the pressure difference. By harnessing that energy, power can be generated. A low flow rate does not provide enough means to utilize the potential energy. It is not sufficient for turning potential energy to kinetic energy.

From rotating machinery engineering point of view, low flow rate means lower momentum available on each pressure reduction stage. Then to be able to absorb the available energy efficiently, the machinery needs to work at an increased speed, hence increasing the momentum with the help of speed factor rather than the mass factor. In other words, power is proportional to flow rate and (square of) speed. This is shown in the next section by Dimensional Analysis.

Power ∝ ṁ × V²

The higher the rotational speed, the more efficient is the turboexpander in generating power from available potential energy. By operating at a low speed, for example 3000 rpm associated with a 50 Hz generator, efficiency will be very low, resulting in poor or impossible financial viability of the plant.

Complicated turboexpanders are then limited to high speed, low flow, high pressure-ratio turboexpanders. Careful considerations are required when designing rotating machinery at high speeds, the most important one being aerodynamic stability during transient operation, such as start-up and shutdown, while the machinery is passing its critical speeds.

With the current technologies though, high speed operation is not a big deal. Numerous turboexpanders are successfully under very high speed operations all around the world. However, these come at higher costs. The question then is the classic one; are the capital (and operational) costs worth the revenue by power generation?

Having said that, there are many high flow rate applications suitable for utilizing turboexpanders, resulting in low or moderate rotational speed, high power generation capacity, and no complexity. Examples are industries requiring gas for their processes or furnaces, such as Steel and Aluminium, and city gate stations of relatively populated cities.

2. Dimensional Analysis:

3. Case Study

A case study verifies the qualitative discussion presented above. With reference to Table 1, it is shown that for the same pressure ratio (3:1), a low flow turboexpander needs to operate at above 35,000 rpm to have a satisfactory efficiency (of over 80%), while moderate flow and high flow turboexpanders give an even better performance at 20,000 rpm and 10,000 rpm respectively.

While operating a low flow turboexpander without a gearbox, i.e. at 3000 rpm or generator speed, generates nearly zero power, power generation capacity of a high flow turboexpander directly coupled to a generator is only 8% less than its highest efficiency condition.

This case study is made possible by effective utilization of TePS, Turboexpander Performance Simulator.

Turboexpander Performance (2)

A Note on Turboexpander Aerodynamic Design

Turboexpander polytropic efficiency can be expressed as a function of its specific speed (as defined below):

In which N is turboexpander rotational shaft speed, Q₂ is turboexpander discharge flow and Δh is the ideal enthalpy reduction through the turboexpander.

Turboexpander polytropic efficiency is increased with the increase of its specific speed up to an optimum value. This trend suggests two methods to increase turboexpander efficiency (and hence its power generation):

1. Increasing turboexpander shaft speed (N);
2. Increasing turboexpander number of stages (or decreasing Δh).

Turboexpander shaft speed is limited by the capability of its hydrodynamic bearing. To increase the speed to values higher than this limit, magnetic bearings (with higher capital cost) have to be utilized. On the other hand, increasing the number of stages also means a higher capital cost. These costs need to be justified and balanced by the increase in turboexpander power generation capacity.

Following table shows simulation results for three different proposed turboexpander designs with the same process conditions. Results show that how turboexpander power generation is increased via either increasing number of stages or utilizing magnetic bearings (and therefore designing the turboexpander for higher shaft speeds).
 

Preliminary turboexpander aerodynamic design

 

Following points should be considered when optimizing turboexpander design using such an approach:

• Maximum allowable shaft speed (limited by hydrodynamic bearing) for the specific turboexpander process design conditions;
• Optimum specific speed value for the selected turboexpander design.

PS Contact me for more details on turboexpander design conditions, simulation and preliminary aerodynamic and mechanical designs.

Turboexpander Performance (1)

Turboexpander Design and Off-Design Performance

Turboexpanders are being widely applied in cryogenic and power recovery cycles. In both cases there exists a fluid that has to be expanded to meet the process requirements. This is based on high chilling effect of expansion process in a cryogenic cycle. An example of such an application is medium-sized natural gas liquefaction (or LNG) plants. In a power recovery cycle, there is an end user with a specific fluid pressure requirement and turboexpander duty is to reduce the pressure to match the demand. Gas pressure reduction stations at the inlet of cities or power plants are examples of such an application.

For both cycles, power generated by turboexpander shaft (either driving a compressor or generating electrical power through a generator) is considered as a by-product intending to increase the overall efficiency.

In most turboexpanders applications, inlet gas conditions (flow, temperature, pressure and molecular weight) are varying. This variation can be intense for gas pressure reduction stations supplying gas to household sector as natural gas demands is much higher in cold seasons of the year. As turboexpander efficiency (same as any other turbomachinery) is highly affected negatively when operating in off-design conditions it won't operate efficiently throughout a year if the process designer fails to select the optimum design conditions for turboexpander operation. This can be done only if the process designer is familiar enough with turboexpander off-design performance.

Turboexpander off-design performance can be predicted using efficiency correction factors:

In which C_Q, C_P, C_T and C_MW are correction factors due to deviation of flow, pressure, temperature and molecular weight with reference to design values respectively. Typical turboexpander efficiency correction factors are given in the below diagrams for constant speed operation of turboexpander (such as electrical power generation application). Similar curves exist for turboexpander variable speed operation (like compressor drive application). This factors and how they affect determining turboexpander design point are briefly discussed below.

 

Turboexpander efficiency correction curves

 [Source: Bloch, Soares, 2001, "Turboexpanders and Process Applications", Butterworth-Heinemann]

Flow:

Although flow correction curve is nearly symmetrical and either lower or higher flow causes the same reduction in turboexpander efficiency but lower flow means that lower power can be produced at turboexpander shaft. So turboexpander design flow should be determined such that as much as possible flow can be passed through it during the year.

If flow variation is too high that causes the turboexpander to operate at very low flows (and hence very low efficiency) in some months of the year, then it might be economically feasible to select two turboexpanders and operate only one (and keep one stand-by) in low-flow situation.

Pressure:

It can be seen from the diagram that the reduction in turboexpander efficiency is negligible with increase of pressure relative to design pressure. This leads to the conclusion that if lowest inlet gas pressure is selected as design pressure, then turboexpander will operate with maximum efficiency (from inlet pressure point of view) throughout the year.

Temperature:

Unlike flow and pressure, temperature is an inlet gas parameter that can be controlled. That is done via a pre-heater normally considered upstream of the turboexpander. The need for pre-heating arises from the above-mentioned chilling effect of gas expansion process in a turboexpander; this can cause gas to be chilled to lower than its allowable temperature and may result in droplet formation. So turboexpander inlet gas temperature is determined (by calculation) considering its discharge temperature to be minimum allowable gas temperature. This temperature then should be maintained by controlling gas pre-heater.

Molecular Weight:

Molecular weight is a function of gas composition and its design value should be based on average gas components mole percent.

It should be noted that the exact design conditions can be determined based on these guidelines with the help of an economic analysis considering turboexpander power generation and pre-heater required energy for a 1-year operation. This requires the simulation of turboexpander performance with inlet gas parameters variations taken into consideration.