A fundamental wax deposition model for water‐in‐oil dispersed flows in subsea pipelines

Water‐in‐oil dispersions frequently form in subsea oil pipeline transportation and their presence affects the wax deposition rate in subsea pipelines. A fundamental model for wax deposition on the wall of water‐in‐oil dispersed phase flow pipelines has not been developed. Dispersed water droplets can affect the heat and mass transfer characteristics of wax deposition and alter the deposit growth rate. In this study, wax deposition from water‐in‐oil dispersed flows is comprehensively modeled using first principles of heat and mass transfer. The role of the dispersed water phase on the heat and mass transfer aspects of wax deposition is analyzed. The developed model predicts different effects of the water volume fraction and droplet size on the wax deposition rates in laboratory flow loop experiments and in field scale wax deposition processes. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4201–4213, 2017     

An experimentally validated heat and mass transfer model for wax deposition from flowing oil onto a cold surface

A transport model is proposed for wax deposition onto a cold finger from flowing wax-containing oils. The model solves transient energy and mass balances simultaneously for a reversible first-order kinetic rate for precipitation of pseudo-single-component wax, and the effects of yield stress using a critical solid wax concentration to withstand flow-induced stress at the deposit-fluid interface. The model can predict the time evolution of the deposit thickness, and the spatial and temporal evolution of temperature and wax concentration as validated using cold finger experiments. It was found that for high wax content oils, deposit thickness growth is dominated by heat transfer. For low wax content oils that are unable to gel, the thickness growth is slow and accompanied by occasional sloughing. Regardless of the mechanism controlling the growth, mass transfer cannot be neglected as wax diffusion into the deposit continues to take place after the deposit has stopped growing.     

原油管道蜡沉积物径向性质研究进展

蜡沉积物性质对原油管道清管方案的制定有重要影响,是原油流动保障领域的研究热点之一。本文回顾了近年来关于管道蜡沉积物径向特性的研究成果,对当前实验研究手段和方法进行了系统的对比分析;从蜡沉积物组成、析蜡特性、宏观形态与微观结构、力学特性四个方面深入阐述了对管道蜡沉积物径向性质的认识与结论,分析了其内在影响因素和作用机理;评述了蜡分子扩散系数及径向含蜡量分布预测模型的理论基础和存在缺陷;提出了未来的研究方向：加快研发更加精确的机械取样装置,深入研究沉积物微观结构特性对宏观流变性的影响机理并建立二者之间的定量关系,建立考虑多孔网状结构中蜡分子扩散动力学的蜡沉积物径向性质预测模型。     

原油组成对原油管道结蜡规律的影响

利用旋转式动态结蜡装置,对不同组成的人工油样(胶质和沥青质含量不同或蜡含量不同)进行了不同条件下的实验研究.通过对管壁沉积物取样并利用差式扫描量热法(DSC)和四组分法进行分析,探究了不同原油组成对结蜡的影响规律.结合胶质和沥青质在结蜡过程中的作用机理,发现胶质和沥青质的存在虽然总会削弱蜡分子的迁移动力,阻碍蜡分子的沉积,但在含量较小时会协同蜡分子的沉积作用,而当含量较大时会以粘壁的形式附着于管壁.对蜡含量不同原油的结蜡规律研究发现:原油所含蜡分子的碳数越高,结蜡层中的蜡含量就越少.但由于碳数较高的蜡分子具有相对较长的碳链,更容易与原油中的胶质和沥青质发生共晶作用,故更易与胶质和沥青质一起沉积于壁面.     

Wax deposition modeling of oil/gas stratified smooth pipe flow

Wax deposition modeling is complicated under oil/gas two‐phase pipe flow and therefore remains poorly understood. One‐dimensional empirical heat and mass transfer correlations are unreliably for deposition modeling in stratified flow, due to non‐uniform deposit across the pipe circumference. A mathematical model has been developed to predict the deposit thickness and the wax fraction of deposit in oil/gas stratified pipe flow using a unidirectional flow analysis of non‐isothermal hydrodynamics and heat/mass transfer. The predictions for wax deposition are found to compare satisfactorily with experimental data with three different oils for single phase and oil/gas stratified pipe flow. In particular, the reason that the deposit forming a crescent shape at the cross section of pipe observed in different experiments is revealed, based on the non‐uniform circumferential distributions of two most important parameters for the wax deposition, diffusivity at oil–deposit interface, and the solubility gradient at the oil–deposit interface at different time. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2550–2562, 2016     

甲醇合成结蜡原因和处理方法

甲醇合成生产普遍以铜基催化剂为主,此催化剂下生产甲醇的同时伴有高碳链的碳氢化合物和石蜡生产。当正常生产过程中石蜡过多时会造成甲醇气液分离器、水冷器、阀门管道、甚至合成塔出口的堵塞,严重时会造成停车清蜡。因此研究石蜡产生的机理以及如何避免和减少石蜡的产生是很有必要的。     

A Numerical model of exchange chromatography through 3‐D lattice structures

Rapid progress in the development of additive manufacturing technologies is opening new opportunities to fabricate structures that control mass transport in three dimensions across a broad range of length scales. We describe a structure that can be fabricated by newly available commercial 3‐D printers. It contains an array of regular three‐dimensional flow paths that are in intimate contact with a solid phase, and thoroughly shuffle material among the paths. We implement a chemically reacting flow model to study its behavior as an exchange chromatography column, and compare it to an array of 1‐D flow paths that resemble more traditional honeycomb monoliths. A reaction front moves through the columns and then elutes. The front is sharper at all flow rates for the structure with three‐dimensional flow paths, and this structure is more robust to channel width defects than the 1‐D array. © 2018 American Institute of Chemical Engineers AIChE J, 64: 1874–1884, 2018     

Nonbuoyancy density‐driven convective mass and heat transfer: Scaling analysis and solution methodology

Density change during mass or heat transfer can cause convection in the absence of buoyancy forces. Prior studies have shown that this convection can be significant in the determination of diffusion coefficients and in the casting of polymeric membranes. Including this effect is challenging even for advanced numerical codes. A general methodology for obtaining the mass‐average velocity for unsteady‐state, one‐dimensional, multicomponent mass and/or heat transfer circumvents the problem of numerically solving the coupled continuity equation. Scaling analysis permits assessing the importance of this convection for a generic equation‐of‐state. Numerical predictions for evaporation from a liquid layer for components having density ratios of 1:1 and 0.7:1 indicate that ignoring convection results in errors of 34% and 24% in the evaporation time and final thickness, respectively. This convection also influences the evaporation in the percutaneous application of cosmetics, medications, and insecticides, curing of paints, varnishes, and lacquers, and formation of thin films. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

油水两相流蜡沉积研究进展

蜡沉积研究中,油水两相蜡沉积的研究已成为研究重点,但对此领域的研究还处于起步阶段。本文系统阐述了国内外蜡沉积研究的发展现况,对近些年蜡沉积机理研究的新进展--剪切剥离以及老化机理作了分析。介绍了冷板、冷指实验装置和环道实验装置,对国内外学者进行的蜡沉积实验情况作了概述。介绍了国内外单相原油与油水两相蜡沉积动力学模型的研究现状,在单相模型基础上对Couto油水两相模型和Bruno改进模型进行了描述。今后的研究应以蜡沉积机理与预测模型为重点,分析油水两相流蜡沉积的影响因素,这对于缓解输油管道蜡沉积问题,增强管道输送能力具有现实意义。     

Effect of polyethylene pipe on wax deposition under different temperature and flow rate conditions

Wax deposition is an important but troublesome boulder in petroleum industry that has always plagued pipeline engineering operators. In this study, wax deposition in the polyethylene pipes has different behaviors comparing wax deposition in stainless steel pipes such as smaller weight of wax deposits and lower wax content. After wax deposition experiments, some important parameters, including diffusivity and temperature gradient, were measured and calculated to explore the differences between two material pipes. Moreover, those factors can make a significant impact on radial mass flux. A series of results in polyethylene pipes suggests that higher diffusivity enhances diffusion flux of wax in the radial direction. But it was found that radial concentration gradient accounted for a larger proportion. These factors are the relationship of competition and cooperation and the combination of them results in different performances of wax deposition between polyethylene and stainless steel pipes.     

沥青质引发的蜡油体系结蜡层分层现象及分层规律

利用自主研发的Couette结蜡装置,对蜡含量相同的油样1(不含沥青质)和油样2[含0.75%(质量分数)沥青质]进行结蜡实验,并研究其结蜡层的分层现象和分层规律。通过对油样1和油样2结蜡表层和底层的宏观形貌、DSC放热、析蜡量、蜡晶微观形貌的分析发现:油样1结蜡层无明显分层现象,而油样2结蜡层分层现象明显,沥青质的加入导致了结蜡层的分层。与结蜡表层相比,油样2结蜡底层的析蜡点、蜡含量与沥青质含量显著升高,蜡晶形貌发展为致密的类球状大蜡晶。油样2结蜡表层沉积量随壁温的升高、油壁温差和转速的增大而减小;结蜡底层沉积量随壁温升高而减小,随油壁温差和转速的增大而增大;总的蜡沉积量随壁温的升高和转速的增大而减小,随油壁温差的增大先增大后减小。     

An aging theory-based mathematic model for estimating the wax content of wax deposits using the Fick's second law

In this study, a mathematic model is proposed for estimating the wax content of wax deposits. The proposed model was built based on the diffusion of wax molecules and counter-diffusion of oil molecules and described using the Fick's second law, allowing for the stacking fraction and orientational order of precipitated wax crystals and the tortuosity of diffusion path of de-waxed oil molecules during the counter-diffusion. The calculated results were verified by comparing with the flow-loop wax deposition experimental results. Dependence of radial position, deposition duration, bulk temperature, and wall temperature were investigated. These factors significantly affected the wax content during wax deposition. Good agreements were observed between the predictions and experimental results. The variation trends of wax content affected by various aspects are consistent with the existing studies.     

Modelling wax deposition of diesel in sequential transportation of product oil pipeline using optimized back propagation neural network

Contamination of gasoline by wax deposit of diesel is a severe problem in sequential transportation of product oil pipelines in cold areas. However, most works on wax deposition are focused on crude oil. In response, this paper aims to investigate wax deposition from a unique perspective of diesel oil in sequential transportation. To this end, a cold finger apparatus was designed and constructed. It is found that the wax deposition rate of diesel oil increases with oil temperature and wax content, and decreases with cold finger temperature. A non-monotonic variation trend is observed against shear stress. To predict diesel wax deposition rate, a back propagation (BP) neural network optimized by bald eagle search (BES) algorithm is proposed. Grey relational analysis (GRA) is employed to get the highly relevant factors as input parameters of the developed model. Prediction accuracy and generalization ability of the BES-BP model is experimentally verified. This work will be helpful to schedule the transportation program of product oil to avoid contamination of gasoline by diesel wax deposit.     

Wax deposition modeling of oil/water stratified channel flow

Wax deposition modeling becomes complicated when multiphase flow is involved. Empirical heat and mass transfer correlations are unreliable for multiphase deposition modeling and full scale computational fluid dynamics calculations require expensive computational intensity. In this work, numerical methods are used to study wax deposition in oil/water stratified flow through a channel. A unidirectional flow analysis is used to calculate the nonisothermal hydrodynamics and mass transfer. It was found that the change in the position of the oil/water interface throughout the channel must be taken into accounted for the mass balance to be valid. Unfortunately, this change has not been accounted for in all previous studies. In addition, the growth of the wax deposit as a function of time along with the effect of oil/water flow rate ratio is discussed. The presence of water significantly reduces the severity of wax deposition by altering the heat and mass transfer characteristics. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Transport and deposition patterns in drying sessile droplets

The literature on drying sessile droplets and deposition of suspended material is reviewed including the simple explanation of the “coffee ring” deposit given by Deegan et al.¹ Analytical and numerical solutions for the flow are given, including the effect of Marangoni stresses, pinning or movement of the contact line, and viscous, thermal, gravitational, and other effects. The solution space is explored using dimensionless groups governing mass, momentum, and heat transfer effects in the droplet, external gas, and substrate. The most common types of deposition patterns are summarized, including those produced by pinned contact lines, sticking‐and‐slipping contact lines, and Marangoni effects. The influence of contact‐line deposits is also reviewed, and the effects of colloidal, polymeric, and other depositing materials. Advanced applications from ink‐jet printing to disease diagnosis are discussed as well. The review helps readers take stock of what has been learned and what remains incompletely explained. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1538–1571, 2014     

Investigation of inhibitors efficacy in wax deposition mitigation using a laboratory scale flow loop

Statistically reliable wax inhibition experimental data was obtained by utilizing the newly built laboratory scale flow loop. The comb‐shaped inhibitors are found more effective in decreasing the thickness compared to the linear inhibitor under the same conditions. Moreover, this becomes more predominant as the chain length of inhibitors increases. Interestingly, even though all the inhibitors decreased the deposit thickness, the wax content increased significantly. Besides, the longer chain length (PI‐B) of the inhibitor results in a higher wax content. Since the combination of growth and aging influenced by the presence of inhibitor significantly, paraffin inhibition efficiency (PIE) based on the wax mass was proposed to quantitatively assess the inhibitors. Based on the PIE, PI‐B, and PI‐C have more inhibition efficiency than PI‐A. Therefore, when selecting wax inhibitor, one should be aware about the strength of the deposit gel in addition to the reduction of the deposit mass. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4131–4139, 2016     

A Reynolds mass flux model for gas separation process simulation:I. Modeling and validation

Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The aniso-tropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux (RMF) model. With the RMF model, the concentration and temperature as well as the velocity distributions can be simulated numerical y. The modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation, while the modeled Reynolds heat flux and Reynolds stress equations are used to close the turbulent heat and mo-mentum transfer equations, so that the Boussinesq postulate and the isotropic assumption are abandoned. To val-idate the presented RMF model, simulation is carried out for CO2 absorption into aqueous NaOH solutions in a packed column (0.1 m id, packed with 12.7 mm Berl saddles up to a height of 6.55 m). The simulated results are compared with the experimental data and satisfactory agreement is found both in concentration and temper-ature distributions. The sequel Part II extends the model application to the simulation of an unsteady state ad-sorption process in a packed column.     

Investigation of thickness and wax content of wax deposits in polyethylene pipe using a flow loop

In this study, the thickness and wax content of wax deposits were found to be thinner and lower in the polyethylene (PE) pipe than in the stainless steel (SS) pipe using a flow loop apparatus. The diffusivity of wax, radial thermal gradient, and wax precipitation rate in the PE and SS pipes were calculated and compared. It was found the diffusivity of wax in the PE pipe was higher and tended to enhance the wax deposition in the PE pipe, while the radial thermal gradient and wax precipitation rate were lower in the PE pipe and had the opposite effects. These factors are shown to be comparable with each other and the effect of the thermal gradient dominates the mass flux of wax from bulk to the oil-deposit interface and into the deposits finally, thus causing differences in thickness and wax content of deposits between the PE and SS pipes.     

Model predictive control of a second-order hyperbolic transport-reaction process

The model predictive controller (MPC) design is developed for a tubular chemical reactor, considering a second-order hyperbolic partial differential equation as the model of the transport-reaction process with boundary actuation. Without loss of generality, closed–closed boundary conditions and relaxed total flux are assumed. At the same time, the model is discretized in time by the Cayley–Tustin method, and, under the assumption that only the reactor's output is measurable, the observer design for the state reconstruction is addressed and integrated with the MPC design. The Luenberger observer gain is obtained by solving the operator Ricatti equation in the discrete-time setting, while the MPC accounts for constrained and optimal control. The simulations show that the output-based MPC design stabilizes the system under the input and output constraints satisfaction. In addition, to address the models' disparities, the results for both parabolic and hyperbolic equations are presented and discussed.