September 2016, Vol. 243, No. 9
Features
Transient Modeling of Natural Gas Transmission Systems
Transient flow regularly occurs in the gas pipeline during normal operation due to variations in demand, inlet and outlet flow changes, and compressor start and stop. Transients can also occur in natural gas pipelines during filling and line pressurization, emergency shutdown, gas blowdown, line depressurization processes, and pipe leaks or rupture (Mokhatab et al., 2015).
There are several reasons for applying transient analysis during the design phase of gas transmission pipelines. First, the designed system must be able to operate under different scenarios. Otherwise, the transmission company could face penalties for not delivering the contracted gas volumes and incur unpredicted capital investment on the system, dramatically affecting its cash flow.
The second reason is related to the operational behavior of some end users, such as gas-fired power plants with different demand profiles that may interrupt gas consumption completely for periods up to a week in duration. These scenarios must be considered because they directly affect pipeline capacity management and transmission costs as well as the operation schedule of compression stations and individual compressor units.
Transient analysis is used to help select turbo compressors that best fit system requirements arranged in a series (few units and bigger machines) or parallel (more units and smaller machines). It is also necessary to run failure analysis for a single compressor unit or even for a complete station and predict system response in terms of remaining capacity vs. time. Transient analysis is important to establish maintenance strategy and define whether a standby unit will be installed to enhance system availability.
Transient analysis is useful during negotiation of ship-or-pay contracts that normally starts well before the design phase. Additional uses are related to the operation of the pipeline in control rooms, training operation personnel and commercial planning (Santos, 1997, Santos and Mokhatab, 2008).
Case Study
The following descriptions pertain to compressor stations where centrifugal gas compressors, driven by two shaft gas turbines, are used.
Many gas-fired power plants are part of an energy generation portfolio and are used to cover load swings in the electricity demand. They may start to operate early in the morning to cover the increased electricity demand after having been shut down during the night. There is currently no effective storage concept for electricity, so the grid flexibility rests on the flexibility of the gas supply. Pipeline operators may anticipate the load by “packing the pipeline.” They use the storage capacity of the pipeline to prepare for the large demand. For the compressor station, this means that operators will increase the station throughput.
This can be done by directly increasing the power of the gas turbines (by increasing the gas producer speed of the turbine), or by lowering the suction pressure setpoint, increasing either the discharge pressure setpoint or the flow setpoint for the station, depending on which control scheme is deemed advantageous (Kurz et al., 2014).
If a change in operating conditions at a certain time (t0) is desired, with the goal to reach certain new conditions at a time (te), key operational factors include the time Δt = te-t0 it takes to accomplish said change, as well as the fuel consumed during that change.
A gas turbine-driven compressor adapts to changes in process conditions by the power produced by the turbine, which primarily is set by the fuel flow into the combustor. A surrogate for the power produced by the turbine is the speed of its gas generator. The speed of the power turbine, and the gas compressor connected to it, are not controlled (as long as they stay within allowable ranges), but are established as the speed where the power produced by the power turbine is balanced by the power absorbed by the driven gas compressor (Figure 1).
Figure 1: Available power, compressor characteristic and pipeline characteristic (Kurz and Brun, 2012).
For the gas compressor, the process dictates suction, discharge pressure and, for a given amount of power available, the compressor will react with a certain throughput.
The control commands can (i) directly increase the power of the gas turbines (usually, by increasing the gas producer speed of the turbine), or by (ii) lowering the suction pressure setpoint, (iii) increasing the discharge pressure setpoint, or (iv) increasing the flow setpoint for the station.
Changing the pressure set points (ii, iii) or the flow setpoint (iv) will cause the control system to modify the fuel flow into the engine, and thus change the gas producer speed, until the actual process conditions match the setpoint. The pressure in the pipeline system reacts slowly, while the flow in the pipeline system reacts quickly to changes in the gas turbine power settings. Therefore, changing the pressure set points (ii, iii) will lead to a rapid increase of the gas turbine power. Changing the flow setpoint, on the other hand, will lead to slower increases in gas turbine power because the system reacts instantly to changes in compressor flow.
Simple Transient Model
In this section, we use a transient model of a pipeline that is as simple as possible. The pipeline simulation uses a bulk representation of the two key physical behaviors of a pipeline: the capability to store gas and the pressure loss as a function of gas velocity in the pipe.
No effort was made to determine these parameters from first principles (as is done in typical pipeline simulation codes). Rather, they are selected so the model duplicates the behavior of a typical pipeline. The compressor behavior is defined by its flow-head-efficiency-speed (Figure 1), based on steady state data.
The engine behavior is modeled by parameters as a function of its gas producer speed, which is controlled by the selected control algorithm. In this study, we evaluate the impact of the ramp rate for the gas producer speed, that is, the maximum rate at which the control system allows the gas producer speed to change.
For each time step, as a function of the gas producer speed, the engine model yields the power output as well as the fuel consumption. The compressor operating points are determined based on the available power adjusted by the effect of off-optimum power turbine speed, the suction and discharge pressure (the isentropic head) imposed by the pipeline condition. Compressor speed and flow are results of the calculation. For each time step, the resulting gas turbine fuel consumption is recorded.
This model simulates the system interaction of a compressor, its driver and the piping system. The driver and the piping interact with the compressor as follows: A driver module provides power to the compressor module; a compressor module responds with a corresponding operating speed.
The driver module then recalculates the off optimum losses and calculates a new power. This loop runs continuously, attempting to achieve equilibrium. The compressor module defines the flow into the piping system module.
The piping system module responds with corresponding inlet and outlet pressures. The compressor module then recalculates its operating point and calculates a new flow. This loop runs continuously, attempting to achieve equilibrium.
The response of the compressor to a change in power from the driver is virtually instantaneous. The response of the piping system to a change in the flow from the compressor is extremely slow. One hundred miles (160 km) of 36-inch (900-mm) pipe at an average pressure of 800 psia (55 bara) contains about 200,000,000 scf of gas. Typical time scales can be estimated by calculating how long it takes to bring the pipeline from 40 bar to 55 bar at a constant in-flow surplus of 600 MMscf/d. This takes about an hour.
The speed lines are intersected by a line of constant surge margin. Values for head, power, flow and discharge temperature at the intersections are collected in an array to develop a second set of polynomial coefficients with power as the common independent variable. The surge margin of this line is manipulated to cause the convergence of the prevailing head across the compressor from the piping system and calculated head at power and surge margin. Iteration of the convergence is achieved by a proportional plus integral algorithm. This achieves faster convergence and subsequently ensures that it does not interfere with other routines within the simulation.
The compressor map was developed at constant suction conditions. In order for the compressor model to predict the operating point (speed), the input power (P’) must be adjusted for the difference between the operating suction density and the design suction density.
The pipeline model is a closed loop comprised of two volumes of half the total pipeline volume connected to the compressor and a flow resistance Δp characterized by the Darcy-Weisbach equation:
Pressures in each half pipe are a function of the pressure, temperature and compressibility of the gas within. When the flow through the compressor and the resistance are equal, the loop is at equilibrium or steady state.
Simulation Results
Figures 2a through 2d show the operating points on a compressor map when the gas turbine is controlled by different ramp rates for the gas producer. In each example, the calculation starts at a steady state operating point at 85% NGP (gas producer speed), followed by an acceleration to maximum (100%) gas producer speed. Start and end points are the same for all examples. They constitute the steady state operating points at 85% gas producer speed and 100% gas producer speed (full load), respectively (Kurz et al., 2014).
The individual graphs show the path of the compressor operating points in the compressor head vs. flow map. Additionally head, flow, power turbine speed (NPT), compressor discharge temperature, suction and discharge pressure, standard flow, gas producer speed (NGP), fuel consumption, gas turbine produced power, and gas turbine heat rate are shown as a function of time. These charts in particular show the time the gas turbines spend at low efficiency points, and also allow the determination of the time at which the compressor operates in its choke region.
Figure 2a: Ramp rate 0.5% NGP per second.
For the fastest ramp rate (Figure 2a), the compressor flow briefly increases dramatically at a rate that initially does not allow the pipeline to react with a significant increase in head requirement. The rapid flow increase ends once the packing of the pipe leads to an increase in required head. At that point, the engine has already reached maximum power. Therefore, it operates on a line of constant power (not precisely, because the power turbine speed gets closer to optimum toward the end of the process), and the increase in head leads to a reduction in flow. The fast acceleration leads to a fast increase in gas turbine efficiency.
Figure 2b: Ramp rate 0.05% NGP per second.
Figure 2c: Ramp rate 0.01% NGP per second.
Figure 2d: Ramp rate 0.0032 % NGP per second.
On the other hand, the efficiency of the compressor is low in the high-flow, low-head region. It improves significantly once the operating points move back to the center of the map. The time spent in the low-head region is, due to the rapid increase in engine power, relatively short.
The medium (Figure 2b), and slow (Figures 2c and 2d) ramp rates show cases where, just as in the previous case, flow initially increases, but due to the slower ramp rate, the engine does not reach full gas producer speed until it also reaches maximum flow (Figure 2b). At maximum flow, the pipeline has already reacted with a significant increase in the required head. After the maximum power is reached, the compressor reacts to the increase with a flow reduction, approximately along a line of constant power. This branch then is identical to the behavior in Figure 2a.
The slowest case barely reaches the 100% equilibrium point within the two-hour timeframe set for the calculations. At this slow ramp rate (Figures 2c and 2d), the engine does not reach full power until the pipeline requires a reasonably high head. Therefore, the compressor will, for the entire simulation, operate at or near its best efficiency. For the fast acceleration rates, on the other hand, as in the case of Figure 2a, the compressor operates quite inefficiently for some period. However, this period is relatively short.
Comparing the cases (Figure 3), we see that the fastest ramp rate, which also leads to the shortest time to reach the 100% equilibrium point, also has the lowest relative fuel consumption, that is, the lowest fuel consumption relative to the total amount of gas transported within the two-hour time frame. While the cases with slower ramp rates avoid the regions of lower compressor efficiency, as well as the high off-optimum power turbine speed at high load, the higher average engine efficiency for the faster ramp rates is better than for the slower ramp rates (Figure 4).
The study nevertheless emphasizes the need for gas compressors with a wide operating range and good efficiency since the deviations from the best efficiency point of the compressor are significant for all but the cases with very slow acceleration.
Figure 3: Moved gas, fuel consumed, and relative fuel consumption for cases in Figures 2, “a” to “d.”
Figure 4: Typical part load efficiency for different gas turbine models. The relative thermal efficiency is the thermal efficiency of the engine at the given load, normalized by its thermal efficiency at full load.
Conclusion
With a simple, yet realistic simulation model, the question for the most appropriate control schemes to affect changes in pipeline operation conditions has been answered. The numerical calculation provides results that are applicable to a large class of pipeline operating scenarios in which the task is to increase the station throughput as fast and efficiently as possible.
This study shows the fastest acceleration of the gas turbine provides the most efficient control scheme for such applications. It clearly shows the disadvantage of operating the compressor in choke (albeit very briefly) is far outweighed by the advantage of operating the gas turbine at full load, and thus at high efficiency. We also see that beyond a certain acceleration rate, the gains can be neglected.
References
- Kurz, R., and Brun, K., “Upstream and Midstream Compression Applications- Part 2: Implications on Operation and Control of the Compression Equipment,” ASME Paper GT2012-68006 (2012).
- Kurz, R., White, R.C., and Brun, K., “Transient Operation in Pipeline Compressor Stations,” ASME Paper GT2014-25016 (2014).
- Mokhatab, S., Poe, W.A., and Mak, J.Y., “Handbook of Natural Gas Transmission & Processing,” 3rd Edition, Gulf Professional Publishing, Burlington, MA, USA (2015).
- Santos, S.P., “Transient Analysis – A Must in Gas Pipeline Design,” paper presented at 29th PSIG Annual Meeting, Tucson, AZ, USA (Oct. 15–17, 1997).
- Santos, S.P., and Mokhatab, S., “Transient Simulation During Gas Pipeline Design Saves on Later Costs,” Pipeline & Gas Journal, 235, 1, 28-32 (2008).
Authors
Rainer Kurz is manager of Systems Analysis at Solar Turbines Inc., San Diego, CA. He has authored numerous publications about turbomachinery related topics with an emphasis on compressor applications, dynamic behavior, and gas turbine operation and degradation. He was elected ASME Fellow in 2003 and has received several ‘Best Paper’ and ‘Best Tutorial’ Awards at the ASME TurboExpo Conferences as well as the 2013 Industrial Gas Turbine Technology award.
Robert C. White is a principal engineer in the Project Application Engineering Department at Solar Turbines Inc., San Diego, CA.He has over 40 years of experience in the industry, with particular emphasis on control systems.
Klaus Brun is program director of the Machinery Program at Southwest Research Institute, San Antonio, TX. His experience iincludes engineering, project management, and management at Solar Turbines, GE and Alstom. He holds seven patents, authored over 250 papers, and published two textbooks on gas turbines. He won an R&D 100 award in 2007 for his Semi-Active Valve invention and has received several ASME Oil & Gas Committee Best Paper/Tutorial awards. He is executive correspondent of Turbomachinery International Magazine and an associate editor of the ASME Journal of Gas Turbines for Power.
Saeid Mokhatab is an internationally recognized gas-engineering consultant actively involved in several large-scale gas field development projects, concentrating on design, pre-commissioning and startup of processing plants and downstream transmission pipelines. He has authored or coauthored nearly 250 technical publications on the relevant subjects and has received several international awards in recognition of his outstanding work in the natural gas industry. He is a frequent contributor to P&GJ.
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