Our client was looking to repurpose a liquid transport and storage system for a different fuel. The new fuel blend has a larger viscosity and density. Heat tracing is applied to the pipe line to reduce the liquid viscosity during transport. The new fuel is pumped into a storage tank, which mixes the new fuel with another fuel that has a smaller density.
The objective of this study is to determine whether the existing system can be used for the new fuel. This requires careful consideration of the following key aspects of the system:
- A static stress analysis of the transport pipeline to evaluate the stresses due to thermal expansion resulting from heat tracing.
- A steady-state flow calculation quantifying the pressure drop in the transport pipeline.
- A dynamic stress and surge analysis to study the transient pressures and unbalanced loads in the system for several scenarios, i.e., a pump trip or an emergency shutdown.
- A CFD analysis of the storage tank to evaluate the mixing for various nozzle configurations.
Methodology: Analyzing Transport and Mixing Subsystems
The system can be subdivided into a transport and a mixing part. This allows for analyzing the two subsystems in parallel, which are coupled via boundary conditions.
Transport Subsystem: Stress and Surge Analysis for Pipeline Safety
The transport subsystem requires both a stress analysis and a surge analysis.
- First, the static stress analysis is performed to assess whether the increased stresses due to additional thermal loading are within the allowable limit as per the ASME B31.3 code. If any modifications in the piping or supporting arrangement are necessary, they are applied to the model.
- The modified model is then imported into our in-house software BOSfluids for the surge analysis. A steady-state flow calculation is used to determine the pressure drop over the pipe line due to frictional and minor losses and also shows at which condition the pumps are operating. The steady-state flow is used as an initial condition for the surge analysis. This quantifies the transient pressures and unbalanced forces in the pipe line resulting from a pump trip or an emergency shutdown.
- The unbalanced loads are used in the dynamic stress analysis, which computes the stresses of the combined static and dynamic loads. In case of the stresses exceeding the allowable values, changes to the model are made to reduce the combined stresses.
- Any changes to the model require reassessing the static stresses and, potentially, the steady-state flow calculation. It is therefore an iterative process.
Surge analysis: Evaluating Pump Trips and Emergency Shutdowns
The transient surge analysis is performed for two scenarios: a pump trip and an emergency shutdown. In both cases, the unbalanced loads are affected greatly by the modeled transient behavior.
- For the pump trip, the pump characteristics and its failure model are critical. BOSfluids includes two options for converting the pump map to Suter curves, which govern the transient behavior of the pump.
- For the emergency shutdown, the valve characteristics and its closure time determine to a large extend the magnitude of the transient pressure peaks. BOSfluids has predefined valve characteristics for common valve types.
An important aspect of a surge analysis is the possibility of vapor cavity implosions. Vapor cavities (gas bubbles) can form when the pressure locally drops below the vapor pressure. Through flow reversal, such cavities can implode, which results in large transient pressure peaks. Whether or not there is a significant reverse flow that implodes the cavity, depends on the transient behavior of the pumps or valves.
Figure 1 | Part of the Surge Model
Surge Analysis Results: Mitigation Cavitation Implosions
The surge analysis revealed that cavitation implosions yielded relatively large unbalanced loads in the emergency shutdown scenario. Further analysis showed that these loads can be reduced by including one or a combination of the following mitigation measures:
- Replacement of the current valve with another valve type
- Addition of a check valve to prevent backflow
- Addition of a surge vessel that counteracts the vacuum pressure
Stress Analysis Results: Ensuring System Integrity under Thermal Expansion
Inclusion of the previously mentioned measures results in stresses that are within the allowable limit as per ASME B31.3. Thus, the system can withstand the additional stresses resulting from thermal expansion. Even so, it was found that the original support is no longer optimal and it is recommended to change its configuration to reduce the stresses.
Mixing tank - CFD analysis: CFD Simulation for Optimal Fuel Blending
Within the tank, the two fuels are being mixed to obtain a homogenized blend. The mixing is affected by three mechanisms:
- Gravity; the heavier fuel tends to settle at the bottom of the tank, while the lighter fuel floats above it.
- Diffusion; because of Fick’s law, concentration gradients lead to a transport of molecules from high to low concentration. Over time, this tends towards a homogenized mixture.
- Advection; bulk fluid flow results in stronger concentration gradients and possibly turbulence, which increases the interface area. This can drastically enhance the diffusion process. However, turbulent flow also results in more energy dissipation.
In the absence of significant fluid flow, gravity is expected to dominate over the diffusion process and fuel separation is anticipated. In order to obtain a homogenized mixture, the fluid flow needs to enhance the mixing through the advection process. The strength of this process is dependent on the magnitude of the flow velocity. As the nozzle configuration determines the fluid flow, it directly influences the advection process.
CFD Analysis: Evaluating Nozzle Configurations for Efficient Mixing
The mixing in the tank is analyzed using CFD simulations for various nozzle configurations. CFD splits the domain into small volumes, for which several equations are solved. This approach is capable of simulating the flow in three dimensions over time and is therefore an excellent method for evaluating complex flow problems, such as the mixing of the fuels.
The mass fraction over time shows the local fuel mixing, and the velocity field highlights any potential dead zones: areas where the flow velocity is nearly zero over a longer period of time. As the highest flow velocity is expected near the nozzle, a fine mesh resolution is required in this region to accurately capture the mixing.Â
Evaluation and Conclusion: Single Nozzle Configuration for Stable Mixing
It was found that a single nozzle was able to generate a stable vortex, while the configuration with three nozzles resulted in chaotic behavior. The single nozzle configuration is favorable, as the stable vortex promotes efficient mixing. The chaotic behavior results in lower flow velocities and, hence, inefficient mixing.
Figure 2 | Stable vortex with higher flow velocities
Figure 3 | Chaotic flow behaviour with lower flow velocities
