Wellbore temperature and pressure calculation model for supercritical carbon dioxide jet fracturing

A new numerical calculation model for wellbore temperature and pressure for SC-CO₂ jet fracturing was proposed in this research. In our model, the impact of tubing, casing, and cement on heat transfer, and the heat generated by fluid friction losses are all taken into consideration. The CO₂ physical properties are calculated by the Span–Wagner and Vesovic models. Based on our calculation model, the factors that may affect the wellbore temperature and pressure are discussed. The results indicated that ignoring the influence of the cement sheath thermal resistance on heat transfer would lead to a wellbore temperature higher than the actual value. The wellbore CO₂ pressure is always higher than its critical value, but the CO₂ temperature at the jet point in some cases is lower than its critical value. The wellbore CO₂ temperature is increased with the increase in injection temperature and cement sheath thermal conductivity and the decrease in annulus injection rate and coiled tubing injection rate. However, the decrease in the coiled tubing injection rate and increase in the cement sheath thermal conductivity are the only effective ways to ensure that the CO₂ temperature at the jet point exceeds its critical value.     

Model for calculating the temperature and pressure within the fracture during supercritical carbon dioxide fracturing

Supercritical carbon dioxide fracturing not only enhances fossil hydrogen production better than hydraulic fracturing, but also alleviates water consumption and storages some carbon dioxide in reservoirs. In this study, a numerical simulation model for calculating the temperature and pressure within a fracture during supercritical carbon dioxide fracturing was established based on rock mechanics, fluid mechanics, thermodynamics, and heat transfer. Moreover, the effects of impact of in-situ stress of reservoir, reservoir temperature, carbon dioxide temperature at the bottom of the well and injection rate on temperature and pressure in the fracture are analyzed based on this new model. The results show that the temperature and pressure of carbon dioxide in the fracture are constantly changing during the fracturing, due to the propagation of the fracture, which makes the temperature and pressure in the fracture unable to reach a steady state. The effect of supercritical carbon dioxide fracturing in reservoirs with higher temperature and lower in-situ stress is better, and higher injection temperatures and smaller injection rates should be chosen in order for carbon dioxide to quickly reach the supercritical state.     

超临界二氧化碳水平管内传热的数值模拟及与实验对比

以二氧化碳为研究对象,应用k-ε方法对其在水平管内与管外水成垂直交叉冷却的换热进行了分析.用FLUENT软件模拟了超临界二氧化碳在8、10 Mpa,流量为3.4、6.8 g/s,管径6 mm,壁厚1.1 mm,长400 mm的管中流动的状况;计算了平均换热系数h、Nu和Re的变化;并将10 Mpa、3.4 g/s时数值模拟得出的换热系数与实验进行了比较和分析.得出等热流密度下壁面温度的变化情况,数值模拟的换热曲线和实验测量的结果具有相同的趋势,在准临界点处都达到最大值.     

Study on carbon dioxide gas cooler heat transfer process under supercritical pressures

In carbon dioxide transcritical air‐conditioning and heat pump systems, the high‐pressure‐side heat exchanger operating at supercritical pressures is usually called as gas cooler. The carbon dioxide gas cooler displays much difference from the traditional heat exchangers employing constant property fluids. The commonly used logarithmic mean temperature difference (LMTD) and effectiveness—heat transfer unit (ε‐NTU) fail for the gas cooler design calculation as the carbon dioxide properties change sharply near the critical or pseudo‐critical point in the heat transfer processes. The new effective heat transfer temperature difference expression for variable fluid property derived by the authors is verified by numeric simulation of the carbon dioxide gas cooler. Moreover, the available correlated models for the cooled carbon dioxide supercritical heat transfer are used to simulate the gas cooler. Detail analysis is made for the deviations among the different models, and for the distributions of local convective coefficient, heat flux, and local temperature of carbon dioxide along the flow path in the gas cooler. Copyright © 2002 John Wiley & Sons, Ltd.     

超临界CO2水平细微管内层流流动与换热的数值模拟

对超临界CO2在水平细微管内层流流动与换热进行了数值模拟.给出了冷却和加热条件下,细微管(d＜1.0 mm)内有代表性的速度、温度剖面,以及Nusselt数随流体温度的变化.研究表明超临界CO2在水平细微管内层流流动时,由于流体热物性随温度剧烈变化,浮升力的影响非常显著,加强了管内换热;且由于流体强变物性特点,只要流体和壁面存在温差,速度及无量纲温度分布就不断变化,充分发展流不可能达到.研究结果对超临界CO2高效紧凑式换热器的设计与优化有重要的意义.     

Experimental study on heat transfer characteristics of supercritical carbon dioxide in horizontal tube

The heat transfer characteristics of supercritical carbon dioxide in a horizontal tube with water in the vertical cross flow form were experimentally investigated. The results indicate that the changes of inlet pressure, mass flow rate, and cooling water flow rate have major effects on heat transfer performance. The variations of Reynolds number and Prandtl number were obtained in counter flow and vertical cross flow. The four conventional correlations for convection heat transfer of supercritical carbon dioxide were verified by the experimental data in this study and the correlation agree with this experimental condition was determined. __________ Translated from Journal of Refrigeration, 2007, 28(1): 8–11 [译自:制 冷学报]     

一种超临界二氧化碳布雷顿循环

为提高布雷顿循环热效率,在现有超临界二氧化碳布雷顿循环的基础上,提出一种基于回热技术的分级压缩与分级膨胀相结合的再压缩布雷顿循环方案,运用热力学计算软件EES对该循环参数进行热力学分析。结果表明,当分流系数约为0.47,透平入口温度为950 K,透平入口压力为29.0 MPa时,循环热效率为59%。当透平入口温度一定,分流系数在0.47～0.48时,循环热效率最高。在透平入口压力从20.0往29.0 MPa升高的过程中,最佳分流系数从0.39逐渐增加到0.47。在回热度从0.5增长到0.6的过程中,最佳分流系数从0.47增长到0.50。     

Investigation of convection‐based energy systems using supercritical carbon dioxide as a working fluid

Carbon dioxide is the best retrofit to meet the future demand on long‐term environmental friendly working fluids. The volumetric efficiency of supercritical carbon dioxide is very high, which makes it a promising working fluid in convection‐based energy systems with high efficiency and small volume. Here, the natural convection of supercritical carbon dioxide driven only by temperature difference is studied in circulation loops. The Reynolds number of the flow is about 10⁴ when the temperature difference is only 20 K, about two orders of magnitude greater than that of water. Furthermore, the heat transfer rate is about 3 times as great as that of water. These results demonstrate the potential of carbon dioxide as a working fluid in solar thermal conversion, nuclear power and waste heat utilization, etc. The influence of the tube diameter on the flow and heat transfer characteristics is discussed. Both the velocity and the Nusselt number are greater in the loop with a larger tube diameter where flow reversal occurs periodically. It is found that flow reversal degrades the system efficiency of the natural circulation loop. Therefore, the optimization about the geometric configuration of convection‐based energy systems using carbon dioxide as a working fluid does exist and is very important for their safe and effective operation. Copyright © 2010 John Wiley & Sons, Ltd.     

A preliminary experimental investigation on characteristics of natural convection based on solar thermal collection using supercritical carbon dioxide

In this paper, an experimental work is carried out to investigate the characteristics of solar thermal collection using supercritical CO₂. This solar thermal conversion is based on supercritical CO₂ natural convection, which is much easily induced because a small change in temperature can result in large change in density close to the critical point. In addition, its critical temperature is 31.1°C and low enough to be easily reached in the low‐temperature solar thermal conversion system. The obtained results show that the supercritical CO₂ flow rate is smooth curve and not affected by the sudden variation of the solar radiation. The solar thermal conversion operation process can be divided into three periods: starting‐up, transition, and stable period. When the system reaches the stable period, the CO₂ flow rate will keep at a high value even if the solar radiation stays at a low level. It is also found that the smaller local solar radiation variation is, the better ability of keeping the flow rate near the peak level the supercritical CO₂ fluid owns. It is also found that a small pressure difference can drive a supercritical CO₂ flow with high flow rate. Furthermore, high solar thermal conversion efficiency is found at a high mass flow rate and under operation pressure near the critical point. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance of a flat-plate solar thermal collector using supercritical carbon dioxide as heat transfer fluid

Energetic and exergetic performance analyses of flat-plate solar collector using supercritical CO₂ have been done in this study. To take care of the sharp change in thermophysical properties in near critical region, the discretisation technique has been used. Effects of zonal ambient temperature and solar radiation, fluid mass flow rate and collector geometry on heat transfer rate, collector efficiency, heat removal factor, irreversibility and second law efficiency are presented. The optimum operating pressure correlation has been established to yield maximum heat transfer coefficient of CO₂ for a certain operating temperature. Effect of metrological condition on heat transfer rate and collector efficiency is significant and that on heat removal factor is negligible. Improvement of heat transfer rate is more predominant than increase in irreversibility by using CO₂. For the studied ranges, the maximum performance improvement of flat-plate solar collector by using CO₂ as the heat transfer fluid was evaluated as 18%.     

A simulation for the piston effect in supercritical carbon dioxide with the non-flow model

A simulation for piston effect in supercritical carbon dioxide by employing a simple model is conducted.In the first place,the thermal properties of carbon dioxide near its liquid-vapor critical point are discussed.It is calculated that the heat capacity ratio and isobaric expansion coefficient of supercritical fluids are extremely high.Furthermore,the simulation for piston effect in supercritical carbon dioxide between two infinite vertical walls is presented.The numerical results prove that piston effect has a much faster speed of heat transfer than thermal conduction under microgravity conditions.Moreover,the piston effect turns out to be stronger when closer to the critical point.     

Hydrogenation of carbon dioxide under atmospheric pressure and low temperature

In order to realize the effective reduction and utilization of carbon dioxide (CO₂) in coal-fired flue gas, a process was developed under atmospheric pressure that uses KBH₄ as an efficient hydrogen donor. By investigating the influencing factors of CO₂ conversion, the optimal experimental conditions were determined and the average CO₂ conversion efficiency of 50.36% was obtained when the KBH₄ concentration was 0.2 mol/L, reaction temperature was 50 °C, solution pH was 8, and flow rate was 300 mL/min. The experimental results also verified that the coexisting gases such as sulfur dioxide (SO₂), nitric oxide (NO) and oxygen (O₂) in flue gas had no significant competition or inhibition effect on CO₂ conversion. Meanwhile, the conversion products were analyzed by an Ion Chromatography (IC) and Fourier Transform Infrared Spectroscopy (FT-IR), and the results proved that the main reaction product was formate. Combined with the relevant literatures, the mechanism of CO₂ reaction with KBH₄ was proposed.     

Reasons resulting in the collapsed tubing near wellhead in high pressure and high temperature deep well during well testing and measures to prevent the collapsing

Because various reasons, the tubing near wellhead was collapsed during well testing in high pressure and high temperature deep well when the outer pressure was less than collapsing strength. To find the reasons in the abnormally collapse and countermeasures, first the quality of the tubing was checked. It was founded that the collapse was not resulted from the defect of the tubing. Then, force and stress exerted in the tubing was analyzed taking XS2 well as an example. The analysis results were concluded as follows. The collapsing strength of tubing decreased due to the axial tensile, which is seriously at the upper tubing especially. During injecting, the additional axial force that was caused by the temperature effect increased the tubing near wellhead to suffer axial tensile and further reduced the collapsing strength of tubing near wellhead. Reinforcing defect, prohibiting defect tubing to trip in hole, according to the calculation to impose appropriate annular pressure, selecting size nozzle to reverse pumping and controlling the reverse pumping speed and pressure, prohibiting to be opened flow and reducing or releasing the annular pressure can prevent the well testing tubing down-hole being collapsed at the wellhead.     

Theoretical analysis of a thermodynamic cycle for power and heat production using supercritical carbon dioxide

A numerical study of a thermodynamic cycle is described: solar energy powered Rankine cycle using supercritical carbon dioxide as the working fluid for combined power and heat production. A model is developed to predict the cycle performance. Experimental data is used to verify the numerical formulation. Of interest in the present study is the thermodynamic cycle of 0.3–1.0 kW power generation and 1.0–3.0 kW heat output. The effects of the governing parameters on the performance are investigated numerically. The results show that the cycle has a power generation efficiency of somewhat above 20.0% and heat recovery efficiency of 68.0%, respectively. It is seen that the cycle performance is strongly dependent on the governing parameters and they can be optimized to provide maximum power, maximum heat recovery or a combination of both. The power generation and heat recovery are found to be increased with solar collector efficient area. The power generation is also increased with water temperature of the heat recovery system, but decreased with heat exchanging area. It is also seen that the effect of the water flow rate in the heat recovery system on the cycle performance is negligible.     

Effect of heat extraction optimization with supercritical carbon dioxide on transcritical power cycle

An experimental and thermodynamic analysis was conducted to explore the match in operating conditions for the heat extraction of supercritical CO₂ and the CO₂ transcritical organic Rankine cycle (CTORC). The results revealed that in the optimal conditions of the experiment, the difference between the pseudocritical temperature and the inlet temperature ( ΔT _{pc − in} ) was <10 K and T _b/T _pc (ratio of the bulk temperature to the pseudocritical temperature) was ≤1 (ideal scenario: T _b/T _pc = 1). Furthermore, the heat transfer and fluid flow of CO₂ as well as the CTORC system performance at the optimal T _b/T _pc could be simultaneously improved with respect to those at ΔT _{pc − in} < 10 K. The peak values of system efficiency for the inlet temperature of the expander of 100°C and 150°C were 5.1% at 12.5 MPa and 8.0% at 17 MPa, with the corresponding T _b/T _pc being 1.24 (T _pc of 55.9°C) and 1.45 (T _pc of 70°C), respectively. Consequently, to simultaneously improve the heat transfer, fluid flow and system efficiency, T _pc of the supercritical CO₂ in the CTORC should be sufficiently high to approach half the inlet temperature of the expander for obtaining an optimal T _b/T _pc at a low condensing temperature.     

Preparation of PVdF/PSSA composite membranes using supercritical carbon dioxide for direct methanol fuel cells

Composite membranes were prepared using supercritical carbon dioxide (scCO₂) impregnation and polymerization procedures and were optimized as electrolytes by controlling the amount of divinylbenzene (DVB) for polymerization. These poly(vinylidene fluoride)/polystyrene sulfonic acid (PVdF/PSSA) membranes were characterized by various methods. The cross-sectional superficial morphology and structure of the PVdF/PSSA membranes were analyzed by scanning electron microscopy (SEM), energy dispersive spectrometer (EDS), FT-IR and small-angel X-ray scattering (SAXS). The ion exchange capacity (IEC), ion conductivity, methanol permeability and cell performance of PVdF/PSSA membranes were measured and compared with Nafion 115. As the concentration of added DVB increased, the ion conductivity and methanol permeability of the PVdF/PSSA membranes decreased. The PVdF/PSSA membrane containing 7.5 wt% DVB achieved 94% of the current density with Nafion 115.     

Numerical prediction of turbulent convective heat transfer in mini/micro channels for carbon dioxide at supercritical pressure

A new approach to take into account the effects of variable physical properties on turbulence is suggested. It allows to choose freely the turbulent closure model for conventional terms due to velocity fluctuations and to describe coherently the additional terms due to density fluctuations. Numerical calculations based on the suggested approach have been performed for carbon dioxide flowing within mini/micro channels under cooling conditions. The numerical predictions show that the effects due to density fluctuations are smaller than it could have been initially supposed and that the heat transfer impairment for mini/micro channels, which some experiments seem to highlight, is not completely explained by the considered model.     

Preparation of polysiloxane/perfluorosulfonic acid nanocomposite membranes in supercritical carbon dioxide system for direct methanol fuel cell

In this work, polysiloxane-modified perfluorosulfonic acid (PFSA) membranes were prepared by a directed sol–gel synthesis method with (3-mercaptopropyl) methyldimethoxysilane (MPMDMS) as the precursor of silicon alkoxide in the supercritical carbon dioxide (Sc-CO₂) system. Contents of polysiloxane in the modified PFSA membranes were varied according to the added amount of precursor MPMDMS. The chemical and physical properties of these modified PFSA membranes were characterized by using attenuated total reflection-infrared spectra, X-ray diffraction, thermogravimetric analysis, universal testing machine, scanning electron microscopy and transmission electron microscope. The measurement results indicated that the polysiloxane particles were not restricted in the ion clusters and well dispersed in the PFSA membrane with ordered size of about 80–100 nm. In the meanwhile, the polysiloxanes have been incorporated into the hydrophobic fluorocarbon backbone regions and interacted with C–F backbones of PFSA polymers. Dimensional stability of the modified PFSA membrane was improved after the impregnation by using Sc-CO₂. The modified membranes almost can remain the same high tensile strength as the pristine membrane. Performance of these modified membranes was evaluated in terms of proton conductivity and methanol permeability. The highest selectivity value (ratio of proton conductivity to methanol permeability) of the modified membrane was about 75.6% higher than that of pristine PFSA membrane because of its higher proton conductivity and lower methanol permeability. All the results indicated that this novel synthesis method in Sc-CO₂ system is a promising method to improve the properties of PFSA membrane for direct methanol fuel cell application.     

Preparation of polysiloxane modified perfluorosulfonic acid composite membranes assisted by supercritical carbon dioxide for direct methanol fuel cell

Polysiloxane modified perfluorosulfonic acid (PFSA) composite membranes are prepared by using (3-mercaptopropyl) methyldimethoxysilane (MPMDMS) as a precursor of silicon alkoxide in supercritical carbon dioxide (Sc-CO₂) system. In the Sc-CO₂ system with the presence of water, Sc-CO₂ is not only used as a solvent and swelling agent, but also functioned as an acid catalyst for the condensation polymerization of MPMDMS. Characteristics of the modified composite membranes are investigated by using attenuated total reflection-infrared spectra, scanning electron microscopy and transmission electron microscopy. The modified membrane with 13.9 wt.% poly(MPMDMS) is the best one among all the modified membranes, whose methanol permeability is extremely lower and selectivity (ratio of proton conductivity to methanol permeability) is about 5.49 times higher than that of pristine membrane and 5.88 times than that of Nafion^® 117, respectively. This modified PFSA membrane still can maintain its higher selectivity value than that of Nafion^® 117 in the temperature range of 25-65 °C. Therefore, the modified membranes prepared in Sc-CO₂ system may be the suitable candidate electrolytes for direct methanol fuel cell applications.     

A high temperature and pressure framework for supercritical water electrolysis

Water electrolysis technologies aim to provide a significant increase in green hydrogen production efficiency. In this work, a framework was developed to explore the use of supercritical water for alkaline electrolysis. This framework was used to perform Arrhenius analysis as a function of potential, and to explore activation energies for sub- and supercritical water electrolysis. An analysis of the conductivity of solution unveiled a discontinuity in the trends between sub- and supercritical potassium hydroxide solution conductivity. Unlike prior work on supercritical water electrolysis, this work investigates trends in electrochemical parameters, the sources of these trends, and how they change between the sub- and supercritical regimes.