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Department of Energy Science and Engineering, Beijing University of Technology, Beijing 100124, China

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Received: 10 April 2024 Accepted: 17 May 2024 Published: 23 May 2024

© 2024 The authors. This is an open access article under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).

ABSTRACT:
Oil-based drilling cuttings is a pollutive nearly-solid waste produced in oil exploitation that has to be treated for meeting clean production requirement of oil and gas exploration. A two-layer screw-driving spiral heat exchanger was thus proposed for this purpose. To investigate its effectiveness and performance, a 10-component *n*-decane one-step product proportional distribution chemical model was used to describe oil-based drilling cuttings pyrolysis process, and numerical simulations were carried out of forced convection inside the heat exchanger with a full consideration of pyrolysis and evaporation effects. The influences of rotation speed, screw pitch and cross-sectional shape of spiral tube on pyrolysis, flow, and heat mass transfer characteristics were studied. The results show that the heat absorbed needed for evaporation is much less than that for pyrolysis, and the heat transfer coefficient with consideration of evaporation and pyrolysis is almost two times greater than that without. The pyrolysis rate increases first, and then decreases once the temperature is higher than 838 K due to the coupled effects of temperature and reactant concentration change. The velocity, heat transfer coefficient and conversion ratio of oil-based drilling cuttings all increase with rotation speed, but the conversion ratio increase becomes slower and slower once the rotation speed exceeds 0.2 rad·s^{−1}. The average vorticity and flow resistance of oil-based drilling cuttings both decrease with screw pitch monotonously, while heat transfer coefficient increases first and then decreases because of the opposite effects of centrifugal force and thermal entrance length. Reducing screw pitch can increase conversion ratio, but once screw pitch is smaller than 800 mm, the conversion ratio approaches to a constant. Cross-sectional shape of spiral tube also affects pyrolysis performance, and circular cross-sectional spiral tube seems to be the best.

Keywords:
Pyrolysis; Oil-based drilling cuttings; Numerical simulation; Heat and mass transfer

Oil-based drilling cuttings is a kind of solid waste produced in the process of oil exploitation. Due to containing a variety of toxic substances, it is not allowed to be directly discharged into environment. Usually, oil-based drilling cuttings is a complex heterogeneous mixture composed of water, heavy metal, oil, solid particles and all kinds of surfactant and various other impurities, and is in the form of a stable suspension with high viscosity, poor flow property, high degree of emulsification and complicated compositions [1,2,3].
For clean production of oil field, oil-based drilling cuttings has to be treated. Pyrolysis is one of the most promising resource recycle and harmless treatment technologies [4,5,6]. However, pyrolysis of oil-based drilling cuttings is a complex thermal chemical reaction that involves complicated chemical reaction kinetics. The relationship between pyrolysis conditions and products are very complex, and flow, heat and mass transfer, and pyrolysis in a pyrolysis device are highly coupled. Therefore, for the time being, researchers usually use thermogravimetric analysis (TGA) to study its pyrolysis characteristics by measuring the weight change of heated samples [7,8,9], so that the pyrolysis process can be analyzed from a macroscopic perspective.
In open literatures, reported researches about oil-based drilling cuttings are scarce and people find that oil-based drilling cuttings has the similar components, physical and chemical properties of oil sludge. Therefore, investigations on oil sludge may give a good reference for studying the pyrolysis treatment of oil-based drilling cuttings. Prame et al. [10] studied the pyrolysis kinetic model of oil sludge generated in refinery treatment of oil-bearing wastewater at various heating rates. Their results show that the pyrolysis reaction process can be classified into two stages. In the first stage, light oil volatilizes; in the second stage, heavy oil cracks and is the main weight-loss stage of oil sludge. Schmidt et al. [11] conducted an experimental study on the pyrolysis process of oil sludge, and the results showed that temperature is the main factor affecting the pyrolysis rate. From these studies one may conclude that for oil-based drilling cuttings pyrolysis process, the main weight-loss happens in the second stage and the pyrolysis rate of oil-based drilling cuttings relies on temperature and thus the heat transfer efficiency of pyrolysis unit.
Zhao et al. [12] put forward a screw-driving spiral heat exchanger using flue gas as heating fluid, combined with the flow characteristics of oil-based drilling cuttings and high heat transfer efficiency of threaded wound heat exchanger, and studied its flow and heat transfer characteristics in the screw-driving spiral heat exchanger at low temperature by numerical simulation. It was proved that the screw-driving spiral heat exchanger can not only provide higher heat transfer efficiency, but also better increase the fluidity of oil-based drilling cuttings to avoid blocking the heat exchanger flow passage. The results also showed that rotation speed, cross-sectional shape and screw pitch all have a certain influence on flow and heat transfer characteristics of oil-based drilling cuttings at low temperature, neglecting the evaporation and pyrolysis effects. It was also found in this one-layer screw-driving spiral heat exchanger that it is difficult to heat the oil-based drilling cuttings to the pyrolysis temperature. Therefore, in this paper, a two-layer screw-driving spiral heat exchanger using flue gas as heating fluid was proposed.
As one may well understand, the pyrolysis and evaporation during pyrolysis process inside the screw-driving spiral heat exchanger for the treatment of oil-based drilling cuttings should have important influences on heat, mass and momentum transfer. Considering the fact that carrying out the experimental investigation of oil-based drilling cuttings pyrolysis in the screw-driving spiral heat exchanger is both complicated and expensive, and as a natural extension of our previous work [12], in this study, the influences of rotation speed, screw pitch and cross-sectional shape on flow, heat and mass transfer characteristics of oil-based drilling cuttings in our newly proposed two-layer screw-driving spiral heat exchanger with a full consideration of pyrolysis effects at high temperature are simulated numerically, so as to provide more insight understanding and reliable basic data and optimization for application of oil-based drilling cuttings pyrolysis method suggested previously [12].

(2) Momentum conservation equation
The momentum conservation equation for the mixture is as follows,

where,

Slip velocity

where,

Mass fraction of dispersed phase

Viscous stress

where,

where,

where,

where,

where,

Mass transfer taking place in pyrolysis process is shown as follows,

where,

where, [

where,

where, Ω

In this paper, a two-layer screw-driving spiral heat exchanger is proposed for pyrolysis treatment of oil-based drilling cuttings to increase the compactness. To investigate its effectiveness, a 10-component *n*-decane one-step product proportional distribution chemical model is used to describe the pyrolysis process of oil-based drilling cuttings, and in dealing with the evaporation of the liquid oil in oil-based drilling cuttings only forced convective mass transfer is taken into consideration. The mathematical and physical model of evaporation and pyrolysis were established and validated and used to simulate flow, heat and mass transfer processes of oil-based drilling cuttings. The influence of evaporation and pyrolysis on flow and heat transfer characteristics is further explored. The main conclusions are as follows.
(1) The proposed two-layer screw-driving spiral heat exchanger can meet the pyrolysis requirements of oil-based drilling cuttings, the greatest conversion ratio obtained is nearly 100% (99.04%). It is found that in treatment process of oil-based drilling cuttings, evaporation and pyrolysis both take places and are endothermic, evaporation heat (~23 kW) is much smaller than pyrolysis heat (~376 kW). The pyrolysis is mainly activated in the lower tube and the pyrolysis rate increases first, and then decreases along the flow path. The temperature of the turn point corresponding this variation tendency is 838 K. The evaporation mainly takes place in the upper tube of the heat exchanger, while the pyrolysis mainly in the lower tube. In addition, gaseous oil is more likely to generate unsaturated hydrocarbons in the pyrolysis process of oil-based drilling cuttings.
(2) The flow, heat transfer and pyrolysis processes of oil-based drilling cuttings are mutually coupled, and temperature is the main factor affecting the pyrolysis rate. Rotation speed has a certain influence on the flow, heat transfer and pyrolysis of oil-based drilling cuttings. The velocity, heat transfer coefficient and pyrolysis rate of oil-based drilling cuttings all increase with rotation speed. The influence on conversion ratio is not linear, and becomes weaker after the rotation speed is larger than 0.2 rad·s^{−1}. On this aspect, considering the fact that at the rotation speed of 0.5 rad·s^{−1} the conversion ratio is already greater than 99%, higher than 0.5 rad·s^{−1} is not recommended for reducing energy consumption.
(3) The influences of screw pitch on flow and heat transfer characteristics of oil-based drilling cuttings are complex. The larger the screw pitch, the smaller the average vorticity and the smaller the flow resistance; The influences of screw pitch on heat transfer coefficient of oil-based drilling cuttings are weak but complicated: it increases firstly with the screw pitch and then decreases due to the opposite effects of centrifugal force and thermal entrance length effect. The evaporation heat does not change with the screw pitch, but the pyrolysis ratio and pyrolysis heat vary with the screw pitch significantly. For small screw pitch (<800 mm), the conversion ratio and the pyrolysis heat do not change much, which means it is not a the-smaller-the-better problem in designing the heat exchanger. For large screw pitch (>800 mm) increasing the screw pitch will decrease the conversion ratio and the pyrolysis heat sharply. Therefore, 800 mm may be taken as a critical design value.
(4) The influences of cross-sectional shape produced are mainly from the fact that the change in cross-sectional shape results in the corresponding variation in the equivalent diameter and curvature ratio of flow passage of oil-based drilling cuttings, which certainly will affect the flow and heat transfer characteristics. The outlet conversion ratio of the five cross-sectional shapes all are greater than 90%, and the outlet conversion ratio of the circular section is the largest and that of square section is the smallest. Considering the fact that the circular cross-sectional spiral tube is also of the smallest pressure drop and its easiness in manufacture, the circular cross-sectional spiral tube is the best choice for engineering application.

Conceptualization, Z.L. and Y.L; Methodology, Software and Validation, F.Z. and Z.L.; Formal Analysis and Investigation, F.Z. and Y.L.; Resources, Z.L. and Y.L.; Writing – Original Draft Preparation, F.Z.; Writing – Review & Editing, Z.L.; Supervision, Z.L.; Project Administration, Y.L.; Funding Acquisition, Z.L.

Not applicable for studies not involving humans or animals.

Not applicable for studies not involving humans.

This research was funded by National Natural Science Foundation of China Project No. 52076004.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Zhao F, Li Y, Liu Z. Numerical Study on Pyrolysis Characteristics of Oil-Based Drilling Cuttings in a Two-Layer Screw-Driving Spiral Heat Exchanger. *Clean Energy and Sustainability* **2024**, *2*, 10008. https://doi.org/10.35534/ces.2024.10008

Zhao F, Li Y, Liu Z. Numerical Study on Pyrolysis Characteristics of Oil-Based Drilling Cuttings in a Two-Layer Screw-Driving Spiral Heat Exchanger. *Clean Energy and Sustainability*. 2024; 2(2):10008. https://doi.org/10.35534/ces.2024.10008

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