(329c) Modeling and State Estimation of Wax Deposition in a Subsea Pipeline Segment

Wax deposition presents an ongoing and costly challenge in offshore oil transportation, particularly in subsea pipelines where low ambient temperatures can greatly lower the temperature of the oil being transported. It can accumulate progressively along the inner walls of the pipeline, resulting in a decrease in flow area, increased pumping pressure needed to maintain a particular production rate, and potentially complete obstruction. In severe situations, the wax deposit can become excessively thick, making it impossible to remove through standard pigging methods. This scenario may necessitate the replacement of the pipeline and the cutting-off of the clogged section, potentially costing millions of dollars [1]. In addition, too frequent or excessive pigging operations can lead to significant economic costs. Thus, accurately forecasting wax growth rates and deposition thickness is essential for effectively timing pigging operations [2].

Many current models fail to accurately depict the internal temperature and wax concentration profiles within the deposited layer, and they also do not account for their transient evolution. These limitations highlight the necessity for a model that can illustrate the spatiotemporal dynamics of temperature and wax concentration within the deposit. In this research, we modify the previously developed model designed for predicting wax deposition in a cold-finger experimental setup to a more applicable and realistic geometry: a radial slice of a subsea pipeline [3]. We extend the governing equations for a laboratory-scale cylindrical apparatus to propose a transient heat and mass transfer model for wax deposition in a radial slice of a submerged pipeline focusing on the inward growth of wax deposits due to the surrounding cold seawater. The wax layer is presumed to consist of a single representative component. This modification allows us to investigate the spatial and temporal evolution of temperature and the concentration in the deposit under moving boundary conditions and conditions that reflect real-world operations.

Challenges in implementing spatially distributed sensors have led to significant research efforts in the field of chemical engineering to address the estimation of spatiotemporal states in distributed parameter systems [4, 5]. In this research, the governing equations represent a nonlinear distributed parameter system (DPS) because of their PDE nature, and the resulting model captures spatially varying states such as temperature and concentration within the wax layer. However, these internal parameters are unmeasurable in practice, particularly in deep-water settings where implementing sensors is challenging or impossible. To estimate these states, we propose designing a nonlinear state observer that relies solely on the measured bulk oil temperature as the system output. The continuous PDE system is discretized in the radial direction through the finite difference method. Subsequently, an observer is developed to reconstruct the full state vector, which includes concentration and temperature profiles as well as the moving interface location between oil and wax. This allows for real-time monitoring of the wax deposit growth, providing a foundation for system monitoring. This approach is generalizable and can be extended to accommodate multi-component wax systems and the axial direction of the pipeline.

References

[1] Lee HS. Computational and Rheological Study of Wax Deposition and Gelation in Subsea Pipelines. PhD Thesis, University of Michigan, Ann Arbor, MI, 2007.

[2] Zheng S, Fogler HS, Haji‐Akbari A. A fundamental wax deposition model for water‐in‐oil dispersed flows in subsea pipelines. AIChE Journal. 2017 Sep;63(9):4201-13.

[3] Mahir, Luqman Hakim Ahmad, et al. "An experimentally validated heat and mass transfer model for wax deposition from flowing oil onto a cold surface." AIChE Journal 67.2 (2021): e17063.

[4] Xie J, Xu Q, Ni D, Dubljevic S. Observer and filter design for linear transport-reaction systems. European Journal of Control. 2019; 49:26-43.

[5] Zhang L, Xie J, Dubljevic S. Tracking model predictive control and moving horizon estimation design of distributed parameter pipeline systems. Computers & Chemical Engineering. 2023; 178:108381.