Supercritical Systems Research Articles

Modeling of coupled wellbore-reservoir flow in steam-like supercritical geothermal systems

The capabilities to efficiently model the transport of mass and heat in geothermal reservoirs at supercritical conditions are necessary to support the efforts to explore and utilize supercritical hydrothermal systems, as well as to extend the utilization of existing geothermal fields at greater depths, where supercritical temperatures might be encountered. Similar capabilities are needed to model the flow in wells producing supercritical fluids, possibly in a coupled way with the reservoir flow. As a step in this direction, the new EOS2H module for sub-critical and steam-like super-critical H2O-CO2 mixtures has been linked to T2Well, the extension of the TOUGH2 numerical reservoir simulator developed for the transient modeling of fully coupled wellbore-reservoir flow. The resulting code is verified against simulations performed with other supercritical reservoir simulators and steady-state subcritical and supercritical wellbore flow simulations. It is then used to perform coupled wellbore-reservoir flow simulations at the well-sector scale relevant to the conditions found in well IDDP-1, Krafla, Iceland.

A Rayleigh quotient method for criticality eigenvalue problems in neutron transport

The alpha- and k-effective eigenproblems describe the criticality and fundamental neutron flux mode of a nuclear system. Traditionally, the alpha-eigenvalue problem has been solved using methods that focus on supercritical systems with large, positive eigenvalues. These methods, however, struggle for very subcritical problems where the negative eigenvalue can lead to negative absorption, potentially causing the methods to diverge. We present Rayleigh quotient methods that are applied to demonstrably primitive discretizations of the one-dimensional slab, multigroup in energy, neutron transport equation. These methods are capable of solving subcritical and supercritical alpha- and k-effective eigenvalue problems. The derived eigenvalue updates are optimal in the least squares sense and positive eigenvector updates are guaranteed from the Perron-Frobenius Theorem for primitive matrices.

Direct tests of fluid-to-fluid scaling expressions for supercritical heat transfer in tubes

This article describes the first in the literature direct tests of the accuracy of fluid-to-fluid scaling expressions for supercritical heat transfer in tubes. The fluid-to-fluid scaling expressions of Zahlan, Groeneveld and Tavoularis (ZGT) for the convective heat transfer coefficients (HTC) of water and CO2 at supercritical pressures were tested against new measurements in Refrigerant R134a flowing vertically upwards in an electrically heated tube with 8 mm ID at pressures, mass fluxes, heat fluxes and bulk temperatures that were ZGT-equivalent to those in previous measurements in CO2. The ZGT expressions for scaling the HTC in water and R134a were also tested after determining the HTC at equivalent conditions in water from transcritical look-up tables. For normal heat transfer (NHT) in all fluids considered, the error in the Nusselt number ratio did not appear to have a statistically significant correlation with the Nusselt number value, the mass flux or the heat flux. This error could be accounted for statistically with the use of a correction coefficient, the value of which depended on the pair of fluids considered and the direction of scaling, thus pointing to the non-universality of these expressions. For deteriorated heat transfer (DHT) in CO2, this error appeared to increase with increasing Nusselt number within the narrow range of available results. It was also found that the ZGT scaling expressions do not scale accurately the onset of DHT in different fluids. An important finding of this work is that scaling errors became particularly large as the bulk temperature Tb approached the pseudocritical temperature Tpc. For both NHT and mild DHT, the ZGT scaling expressions appear to be fairly accurate for the three pairs of fluids considered in the liquid–like region with Tb/Tpc⩽0.94 and possibly in the gas–like region with Tb/Tpc⩾1.02, whereas outside this range scaling errors could be significant. These findings have important implications for the design of supercritical heat transfer systems and components.

Enantioselective potential of teicoplanin- and vancomycin-based superficially porous particles-packed columns for supercritical fluid chromatography

Application of the superficially porous particles (SPPs) grafted with chiral selectors can substantially improve resolution in chromatographic techniques. In this work, we carried out a deeper study on supercritical fluid chromatography systems with 2.7 µm SPPs bonded with teicoplanin and vancomycin. Fast separations of the majority of enantiomers of phytoalexins, substituted tryptophans, and ketamine derivatives, as representatives of important biologically active and structurally diverse chiral compounds have been achieved. The chromatographic behavior of the structurally different analytes served to characterize these separation systems. The influence of separation conditions, namely mobile phase composition, i.e. type of co-solvent and additive on retention, enantioselective resolution and enantioselectivity was examined. The success rate of baseline and partial separations in individual groups of compounds differed with the chiral stationary phase and also with mobile phase composition. The best, baseline separations for the phytoalexins were achieved on the TeicoShell column using methanol as a co-solvent and trifluoroacetic acid as an additive if used. Mostly partial separations were achieved on the vancomycin-based column for all groups of analytes. Complementary separation behavior of these CSPs was confirmed for the majority of the chiral compounds examined in this work.

Point defect model for the corrosion of steels in supercritical water: Part I, film growth kinetics

A Point Defect Model has been developed to describe theoretically the corrosion of metals and alloys in supercritical aqueous systems. The model, SCW_PDM, accounts for the kinetics of growth of the barrier layer and the total scale thickness and for the oft-reported growth of the barrier layer with the barrier/outer layer interface remaining at the location of the original metal surface. The barrier layer grows into the metal via the production of oxygen vacancies at the metal/barrier layer interface and their annihilation at the barrier layer/outer layer interface. The proposed atomic-level rate laws for the scale growth and oxidation weight gains, not only can act as deterministic equations for extracting values of some fundamental parameters in SCW_PDM, but also can be employed to describe the oxidation kinetics of steels directly and successfully.

Investigation of hydrogen oxidation in supercritical H2O/CO2 mixtures using ReaxFF molecular dynamics simulation

Hydrogen oxidation kinetics in supercritical H2O/CO2 mixtures is a fundamental topic in supercritical water oxidation (SCWO) technology. A series of reactive molecular dynamics (ReaxFF-MD) simulations were performed to investigate hydrogen oxidation process in supercritical mixtures. The results showed that HO2 and H2O2 radicals played key roles in the reaction kinetics. High concentration H2O suppressed the production of OH radical and increased steric hindrance for effective collisions, exerting negative influence on hydrogen oxidation. The presence of CO2 advanced the oxidation rate of hydrogen mainly through the elementary reaction CO2 + H → CO + OH. It was found that high O2 concentration promoted the oxidation of hydrogen and also affected the reaction induction time. The hydrogen reaction mechanisms under supercritical conditions were illustrated, showing different characteristics from those at atmospheric condition. The results will facilitate the development of continuum-scale kinetic models for accurate prediction of hydrogen oxidation behavior in supercritical systems.

The risks of long-term re-injection in supercritical geothermal systems

Supercritical geothermal systems are appealing sources of sustainable and carbon-free energy located in volcanic areas. Recent successes in drilling and exploration have opened new possibilities and spiked interest in this technology. Experimental and numerical studies have also confirmed the feasibility of creating fluid conducting fractures in sedimentary and crystalline rocks at high temperature, paving the road towards Enhanced Supercritical Geothermal Systems. Despite their attractiveness, several important questions regarding safe exploitation remain open. We dedicate this manuscript to the first thermo-hydro-mechanical numerical study of a doublet geothermal system in supercritical conditions. Here we show that thermally-induced stress and strain effects dominate the geomechanical response of supercritical systems compared to pore pressure-related instabilities, and greatly enhance seismicity during cold water re-injection. This finding has important consequences in the design of Supercritical Geothermal Systems.

Control of Supercritical Organic Rankine Cycle based Waste Heat Recovery System Using Conventional and Fuzzy Self-tuned PID Controllers

This research develops a supercritical organic Rankine cycle (ORC) based waste heat recovery (WHR) system for control system simulation. In supercritical ORC-WHR systems, the evaporator is a main contributor to the thermal inertia of the system, which is greatly affected by transient heat sources during operation. In order to capture the thermal inertia of the system and reduce the computation time in the simulation process, a fuzzy-based dynamic evaporator model was developed and integrated with other component models to provide a complete dynamic ORC-WHR model. This paper presents two control strategies for the ORC-WHR system: evaporator temperature control and expander output control, and two control algorithms: a conventional PID controller and a fuzzy-based self-tuning PID controller. The performances of the proposed controllers are tested for set point tracking and disturbance rejection ability in the presence of steady and transient thermal input conditions. The robustness of the proposed controllers is investigated with respect to various operating conditions. The results show that the fuzzy self-tuning PID controller outperformed the conventional PID controller in terms of set point tracking and disturbance rejection ability at all conditions encountered in the paper.

Rigorous modelling and deterministic multi-objective optimization of a super-critical CO2 power system based on equation of state and non-linear programming

CO2 power cycle is one of the promising sustainable technologies that generate power from fossil fuel, nuclear, solar, and various waste heat energy. The heat transfer process plays a key role in influencing the thermodynamic or thermo-economic performance of CO2 power cycle. The drastic variation of CO2 thermo-physical properties results in great difficulty in modeling and optimizing the heat exchangers and CO2 cycle configurations. In the present study, a mathematical programming method is proposed for the simulation and optimization of simple, regenerative, and recompression super-critical CO2 power systems. An accurate equation of state is applied to calculate CO2 properties, thereby enabling the performance indicator a continuous function of system parameters. A multi-objective non-linear programming model is formulated in GAMS for the automatic heat exchange pinch locating and system optimization. The simulation and optimization models are validated by comparison with REFPROP-based method. The maximum and average simulation errors are 0.064% and 0.015%. The thermal efficiency values achieved using the developed optimization method are improved by 6.14–10.85% compared with previous solutions. Then, a case study of a 573.15 K waste heat driven super-critical CO2 power system optimization is elaborated. Results show that pinch locating of all heat exchangers and system optimization can be simultaneously conducted within a short time. The solution optimality is validated by comparing the traditional pinch assignment concept and optimization method. Sensitivity analyses of heat source inlet temperature and heat sink temperature rise are also conducted. For both objectives of maximizing thermal efficiency and net power output, the recompression super-critical CO2 cycle features highest in thermal efficiency and the regenerative super-critical CO2 cycle features highest in net power output. Finally, a multi-objective optimization is conducted to achieve the Pareto Front for the studied three super-critical CO2 power systems.

Exergoeconomic analysis applied to supercritical CO2 power systems

Different sCO2 cycle concepts together with a newly proposed cycle configuration were simulated and a comparison was conducted to show the advantages and disadvantages of each cycle considered here. The cycles were compared using a wide range of the turbine inlet temperature, while alternating the used cooling system (air vs. wet cooling systems). The thermodynamic and cost inefficiencies within the simulated cycles were identified using exergoeconomic evaluation methods. The high exergy destruction costs in coolers indicate that the investment cost should be reduced by using different material than titanium due to its high cost. Also, the calculated product cost demonstrates a potential advantage of the proposed cycle. The analysis showed, in general, that sCO2-based cycles are promising for various applications, resulting in system efficiencies and costs that could compete with conventional power generation technologies soon. The sCO2 recompression concept and the novel sCO2 cycle showed the best results among all investigated sCO2 cycles.

Review of Experimental Research on Supercritical and Transcritical Thermodynamic Cycles Designed for Heat Recovery Application

Supercritical operation is considered a main technique to achieve higher cycle efficiency in various thermodynamic systems. The present paper is a review of experimental investigations on supercritical operation considering both heat-to-upgraded heat and heat-to-power systems. Experimental works are reported and subsequently analyzed. Main findings can be summarized as: steam Rankine cycles does not show much studies in the literature, transcritical organic Rankine cycles are intensely investigated and few plants are already online, carbon dioxide is considered as a promising fluid for closed Brayton and Rankine cycles but its unique properties call for a new thinking in designing cycle components. Transcritical heat pumps are extensively used in domestic and industrial applications, but supercritical heat pumps with a working fluid other than CO2 are scarce. To increase the adoption rate of supercritical thermodynamic systems further research is needed on the heat transfer behavior and the optimal design of compressors and expanders with special attention to the mechanical integrity.

Modeling interfacial tension of normal alkane-supercritical CO2 systems: Application to gas injection processes

To study the gas injection scenario for successful implementation of enhanced oil recovery (EOR) processes, the prediction of interfacial tension (IFT) between injected gas and the crude oil is of paramount significance. In the present study, some intelligent methods were developed for determining IFT values between supercritical CO2 and normal alkanes. IFT was considered as a function of temperature, pressure, and molecular weight of normal alkanes. The developed methods were Multilayer perceptron (MLP), Genetic Algorithm Radial Basis Function (GA-RBF), and Conjugate Hybrid-PSO ANFIS (CHPSO-ANFIS). The average absolute percent relative errors (AAREs) for the stated techniques were found to be 2.59%, 1.39%, and 1.81%, respectively, showing that GA-RBF is the most efficient technique. This model was then compared to the other previously developed models in literature. It was also found that the current GA-RBF model with AARE of 1.39% surpasses the previously developed models. Finally, the results of the Leverage approach showed that GA-RBF model could be trusted to predict the IFT of the normal alkane- supercritical CO2 systems in the used range of pressure, temperature, and n-alkanes. This study represents the most reliable technique in predicting the IFT value between supercritical CO2 and normal alkanes to be applied in studies on gas injection processes.

The flow transition characteristics of supercritical CO2 based closed natural circulation loop (NCL) system

Supercritical fluid based natural circulation loop (NCL) systems have been proposed and used in many energy conversion systems in recent years. Supercritical fluid systems can contribute to new generation system design as well as thermo-hydraulic theories of functional fluids. In this study, the flow transition characteristics of supercritical CO2 based NCL system are discussed both numerically and experimentally. Numerical models with variable heat input conditions are simulated, which are focused on the flow transitions during the input changes. It is found that the supercritical NCL flow is very sensitive to heat influx changes. The numerical results are also discussed together with experimental results on the general trends in this study. Experimental results show that besides several kinds of transition flows, the heating control and cooling control can be both effective during the continuous operations of a supercritical loop system. The heater/cooler effect and parameter analysis are also conducted, which contributes to the design of active control of supercritical NCL system.

The heat transfer of supercritical CO2 in helically coiled tube: Trade-off between curvature and buoyancy effect

Supercritical CO2 Rankine cycle has great development potential as a power cycle for converting low-grade thermal energy into electricity. Better understanding of supercritical CO2 heat transfer in helically coiled tubes (HCTs) is required for design and operation of supercritical CO2 Rankine cycle power systems. In this work, the SST k∼ω model is employed. A new dimensionless buoyancy parameter Ψ is proposed which denotes the ratio of gravitational buoyancy force to overall curvature effect. Furthermore, a flow regimes map is proposed based on the inclination angle of the dividing streamline between the two vortexes and buoyancy parameter Ψ. The mixed convection region in HCT is decomposed into a gravitational buoyancy force dominated heat transfer region (B Region α>45°) and a curvature effect dominated heat transfer region (C Region α<45°). Subsequently, the effects of HCT geometry on heat transfer mechanisms are respectively investigated in B and C Region, which help us better understanding the relationship of the buoyancy criterion and flow characteristics. The results indicate that the effects of coiled pitch and coiled diameter on heat transfer can be neglected in B Region. In C Region, the heat transfer is suppressed as coiled pitch increases and it will appear oscillation when torsion effect is strong enough. In addition, the heat transfer is enhanced with curvature increases but except for near the pseudo-critical region.

A numerical prediction on heat transfer characteristics from a circular tube in supercritical fluid crossflow

Studies on fluids at supercritical pressure have been developed in a rapid-growth manner so that geometries are not restricted to circular tube. This paper is devoted to conduct a brief review of the recent main experiments on supercritical fluids such as CO2, water, R134a and n-decane, and to comment the findings. In addition, this paper discusses the probability of supercritical fluids flowing across tube bundles for the frequent use in shell-and-tube heat exchangers in supercritical power cycle systems. A numerical prediction of flow patterns and heat transfer characteristics of a circular tube in supercritical water crossflow is carried out to make a fundamental investigation of the application of supercritical fluids on external flows. Results indicate that the influence of heat flux on heat transfer in crossflow is similar with that for in-tube flows. The thermal physical properties significantly affect the heat transfer and the flow patterns also show unique characteristics with the change of boundary conditions.

Diffuser performance of centrifugal compressor in supercritical CO2 power systems

The paper focuses on understanding the performance of a vaned diffuser in a supercritical CO2 compressor using real gas assumptions. The rapidly changing properties of CO2 in the non-ideal thermodynamic region can have a significant impact on the performance of the diffuser. To account for this, the relationship between the flow properties (i.e. fundamental derivative) and the local geometry (i.e. cross-sectional area of the nozzle) has been discussed theoretically. To examine it analytically, the study has considered the influence of real gas properties on the performance of a vaned diffuser using computational fluid dynamics (CFD) modelling. The selected compressor stage geometry is similar to the compressor impeller tested in the Sandia sCO2 compression loop facility. The effect of changes in the number of blades and the corresponding changes in the cross throat area on the flow properties such as density and speed of sound were investigated and discussed. The results illustrate that a diffuser with a higher number of blades (smaller throat area) compared to a diffuser with a wider throat area has a higher probability of creating flow instability in the passage stage.

Assessing the corrosion product scale formation characteristics of X80 steel in supercritical CO2-H2O binary systems with flue gas and NaCl impurities relevant to CCUS technology

The corrosion product scale formation mechanism of X80 steel in the supercritical (SC) CO2-H2O binary phase containing flue gases and NaCl impurities at 8 MPa and 60 °C was investigated. The formation process of corrosion product scale was significantly different in the SC CO2-saturated aqueous and water-saturated SC CO2 phases. In the SC CO2-saturated aqueous phase, an amorphous product scale was formed initially, then a crystalline product scale was precipitated. The formation process of the corrosion product scale in the saturated-water SC CO2 phase proceeded in just the opposite way. In the water-saturated SC CO2 phase, the inner scale had better protectiveness to the substrate than the outer scale, but it was just the opposite in the SC CO2-saturated aqueous phase. The severity of pitting in the SC CO2-saturated aqueous phase was much greater than the pitting corrosion in the water-saturated SC CO2 phase.

Multiple solutions to weakly coupled supercritical elliptic systems

We study a weakly coupled supercritical elliptic system of the form $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u = |x_2|^\gamma \left( \mu _{1}|u|^{p-2}u+\lambda \alpha |u|^{\alpha -2}|v|^{\beta }u \right) &{}\quad \text {in }\Omega -\Delta v = |x_2|^\gamma \left( \mu _{2}|v|^{p-2}v+\lambda \beta |u|^{\alpha }|v|^{\beta -2}v \right) &{}\quad \text {in }\Omega u=v=0 &{}\quad \text {on }\partial \Omega , \end{array}\right. } \end{aligned}$$ where $$\Omega $$ is a bounded smooth domain in $${\mathbb {R}}^{N}$$ , $$N\ge 3$$ , $$\gamma \ge 0$$ , $$\mu _{1},\mu _{2}>0$$ , $$\lambda \in {\mathbb {R}}$$ , $$\alpha , \beta >1$$ , $$\alpha +\beta = p$$ , and $$p\ge 2^{*}:=\frac{2N}{N-2}$$ . We assume that $$\Omega $$ is invariant under the action of a group G of linear isometries, $${\mathbb {R}}^{N}$$ is the sum $$F\oplus F^\perp $$ of G-invariant linear subspaces, and $$x_2$$ is the projection onto $$F^\perp $$ of the point $$x\in \Omega $$ . Then, under some assumptions on $$\Omega $$ and F, we establish the existence of infinitely many fully nontrivial G-invariant solutions to this system for $$p\ge 2^*$$ up to some value which depends on the symmetries and on $$\gamma $$ . Our results apply, in particular, to the system with pure power nonlinearity ( $$\gamma =0$$ ) and yield new existence and multiplicity results for the supercritical Henon-type equation $$\begin{aligned} -\Delta w = |x_2|^\gamma \,|w|^{p-2}w \quad \text {in }\Omega , \qquad w=0 \quad \text {on }\partial \Omega . \end{aligned}$$

Existence of solutions to the supercritical Hardy-Littlewood-Sobolev system with fractional Laplacians

It is known that the supercritical Hardy-Littlewood-Sobolev (HLS) systems with an integer power of Laplacian admit classic solutions. In this paper, we prove that the supercritical HLS systems with fractional Laplacians \begin{document}$ (-Δ)^s $\end{document} , \begin{document}$ s∈(0,1) $\end{document} , also admit classic solutions.

Hydrogen gas-free processes for single-step preparation of transition-metal bifunctional catalysts and one-pot γ-valerolactone synthesis in supercritical CO2-ionic liquid systems

Hydrothermal carbonization of glucose (180 °C, 4 h) with 5-sulfosalicylic acid and nickel or copper sulfate afforded transition-metal (Ni/NiO, Cu/CuO) functional carbon (FC) catalysts in a single-step without hydrogen gas. Hydrogenation of levulinic acid to γ-valerolactone (GVL) in supercritical carbon dioxide (scCO2)-ionic liquid ([BMIM]Cl) systems with formic acid as H-donor source and Ni/NiO-FC catalysts gave 97% GVL yields (170 °C, 3 h). The Ni/NiO-FC catalysts (d = 50 to 200 nm) had well-dispersed Ni/NiO particles (<5 nm) with –SO3H, COOH and phenolic −OH functional groups; Ni/NiO-FC catalysts were more effective than Cu/CuO-FC catalysts. Ni/NiO-FC catalysts were active for conversion of substrates (ethyl levulinate, fructose, cellobiose or cellulose) to respective products (GVL, 5-HMF, sugars). The role of scCO2 in the reaction system is one of improving mass transport and suppressing side-reactions via GVL product removal. Proposed methods for catalyst synthesis and substrate hydrogenation do not require hydrogen gas and are widely applicable to processing biomass.