Supercritical Vapor Research Articles

Performance of a supercritical carbon dioxide compressor using a streamline curvature based throughflow method

Supercritical carbon dioxide (sCO2) has emerged as a promising working fluid for the Brayton power cycle, offering enhanced efficiency due to its high density and low viscosity near the critical point. A critical component of the sCO2 Brayton cycle is the turbomachinery, namely the compressor. The pronounced sensitivity of the thermophysical properties of sCO2 in the vicinity of the critical point where the compressor operates can significantly impact the performance characteristics of sCO2 compressors. This study presents a two-dimensional (2D) streamline curvature-based throughflow method, considering real gas thermophysical properties, to analyze a centrifugal compressor operating with sCO2 at near-critical inlet conditions. The method’s validity is established through comparisons of the predicted performance characteristics with those of the Sandia National Laboratories compressor and by comparing the predicted flow field with the pitch-averaged flow field obtained from computational fluid dynamic (CFD) analysis. Moreover, various compressor intake conditions including subcritical vapor, supercritical vapor, supercritical liquid, and near-critical conditions are investigated to explore their impact on compressor performance. The streamline curvature-based throughflow method demonstrates its effectiveness by achieving significant agreement between the flow field and performance characteristics, both at design and off-design conditions where efficiency predictions were within 5.84% near the best efficiency point compared to CFD simulations. At near critical conditions, a maximum of 3201% increase the computational run-time required for CFD based computation was observed compared to superheated conditions while only a maximum of 164% increase in run-time was observed in the throughflow based computations as a result of the numerical under-relaxation required.

Classification and wall heat transfer of non-ideal CO2 isothermal laminar boundary layers

The heat transfer properties of non-ideal fluids are crucial in engineering applications. In order to investigate the wall heat transfer characteristics, the self-similar method has been employed to solve supercritical carbon dioxide (SCO2) isothermal laminar boundary layers. The temperature profile regimes are classified into 14 different categories based on their monotonicity and position relative to the pseudo-critical temperature, Tpc. For no trans-Tpc, the boundary layer exhibits subcritical liquid or supercritical vapor, being liquid-like or gas-like region. When free-stream temperature and wall temperature are both lower than Tpc at a large Mach number (Ma), the temperature profile intersects the Tpc twice. In this scenario, the boundary layer is composed of liquid layer, supercritical vapor layer and liquid layer adjacent to the wall, and the wall heat transfer is determined by the thickness of the two bottom layers. At once trans-Tpc, it is seen that the formation of supercritical vapor or liquid film due to pseudo-boiling/condensation plays a key role in the heat transfer deterioration or enhancement. Mainly related to the film thickness and the pseudo-boiling/condensation intensity, the influence of wall temperature and free-stream pressure on the wall heat transfer has been explored by introducing a new dimensionless number Nu*.

Transcritical Behavior of Methane in the Cooling Jacket of a Liquid-Oxygen/Liquid-Methane Rocket-Engine Demonstrator

The successful design of a liquid rocket engine is strictly linked to the development of efficient cooling systems, able to dissipate huge thermal loads coming from the combustion in the thrust chamber. Generally, cooling architectures are based on regenerative strategies, adopting fuels as coolants; and on cooling jackets, including several narrow axial channels allocated around the thrust chambers. Moreover, since cryogenic fuels are used, as in the case of oxygen/methane-based liquid rocket engines, the refrigerant is injected in liquid phase at supercritical pressure conditions and heated by the thermal load coming from the combustion chamber, which tends to experience transcritical conditions until behaving as a supercritical vapor before exiting the cooling jacket. The comprehension of fluid behavior inside the cooling jackets of liquid-oxygen/methane rocket engines as a function of different operative conditions represents not only a current topic but a critical issue for the development of future propulsion systems. Hence, the current manuscript discusses the results concerning the cooling jacket equipping the liquid-oxygen/liquid-methane demonstrator, designed and manufactured within the scope of HYPROB-NEW Italian Project. In particular, numerical results considering the nominal operating conditions and the influence of variables, such as the inlet temperature and pressure values of refrigerant as well as mass-flow rate, are shown to discuss the fluid transcritical behavior inside the cooling channels and give indications on the numerical methodologies, supporting the design of liquid-oxygen/liquid-methane rocket-engine cooling systems. Validation has been accomplished by means of experimental results obtained through a specific test article, provided with a cooling channel, characterized by dimensions representative of HYPROB DEMO-0A regenerative combustion chamber.

CFD and exergy analysis of subcritical/supercritical CO2 based naturally circulated solar thermal collector

Solar water heating system is inefficient during winter due to the chances of water freezing and higher viscosity at low temperatures. Several investigations are being done to increase the efficiency of the solar water heater using various secondary fluids for different climatic conditions. This paper emphasises on the study of heat transfer and fluid flow behavior of CO2 based naturally circulated indirect solar water heating system. Subcritical (liquid and vapour) and supercritical CO2 are considered as loop fluid, and the results are compared with water based system. Three-dimensional computational fluid dynamics simulations are carried out for two different weather conditions i.e., winter (278 K) and summer (305 K). Results are obtained for 33° collector inclination angle from horizontal at various operating pressures 50–70 bar for subcritical and 80–100 bar for supercritical CO2. The CO2 based system yields very high Reynolds number (subcritical liquid: ∼160 times; subcritical vapour: ∼204 times; supercritical vapour: ∼260 times) and very high Nusselt number (subcritical liquid: ∼14 times; subcritical vapour: ∼19.5 times; supercritical vapour: ∼48 times) compared to water based system. Supercritical CO2 based system exhibits 12% higher energy efficiency compared to water. Whereas, subcritical vapour based system exhibits 140% higher exergy efficiency relative to water based system.

Bayesian Calibration of a Natural State Geothermal Reservoir Model, Krafla, North Iceland

AbstractThe Krafla area in north Iceland hosts a high‐temperature geothermal system within a volcanic caldera. Temperature measurements from boreholes drilled for power generation reveal enigmatic contrasts throughout the drilled area. While wells in the western part of the production field indicate a 0.5–1 km thick near‐isothermal (∼210°C) liquid‐dominated reservoir underlain by a deeper boiling reservoir, wells in the east indicate boiling conditions extending from the surface to the maximum depth of drilled wells (∼2 km). Understanding these systematic temperature contrasts in terms of the subsurface permeability structure has remained challenging. Here, we present a new numerical model of the natural, pre‐exploitation state of the Krafla system, incorporating a new geologic/conceptual model and a version of TOUGH2 extending to supercritical conditions. The model shows how the characteristic temperature distribution results from structural partitioning of the system by a rift‐parallel eruptive fissure and an aquitard at the transition between deeper basement intrusions and high‐permeability extrusive volcanic rocks. As model calibration is performed using a Bayesian framework, the posterior results reveal significant uncertainty in the inferred permeability values for the different rock types, often exceeding two orders of magnitude. While the model shows how zones of single‐phase supercritical vapor develop above the deep intrusive heat source, more data from deep wells is needed to better constrain the extent and temperature of the deep supercritical zones. However, the model suggests the presence of a significant untapped resource at Krafla.

Experimental Investigation of Near- and Supercritical Heat Transfer to R125 Flowing in a Horizontal Tube

Knowledge about supercritical heat transfer to refrigerants with horizontal flow is scarce and experimental data is mostly lacking. This makes an accurate sizing of heat exchangers impossible. In addition, the majority of the tested geometries in literature are limited to an inner diameter of only 16 mm. In order to close the gap and increase the knowledge about supercritical heat transfer, a novel experimental setup was used to investigate supercritical heat transfer phenomena on larger tube diameters. The test section consists of a horizontal counter current tube-in-tube heat exchanger. R125 flows in the inner tube having an inner diameter of 24.77 mm. The influence of mass flux (226 - 585 kg/m2s), heat flux (7.7 - 21.9 kW/m2) and supercritical pressure (3.7 - 4.1 MPa, corresponding to 1.03 - 1.12 times the critical pressure) on local forced convective heat transfer was investigated. No visible influence of pressure on the convective heat transfer coefficient is noticed, indicating that buoyancy is present and influential in the performed measurements. The applied heat flux does have an effect, with a decrease in the heat transfer coefficient for an increase in heat flux. This effect is more pronounced at higher mass fluxes. At high mass flux, increasing the heat flux with 42% results in a drop in heat transfer coefficient of 46%, while this is only 40% and 26% at medium and low mass flux, respectively. However, there appears to be a limit to this detrimental effect at higher mass fluxes. Finally, heat transfer increases for an increase in mass flux. Increasing the mass flux with 76% results on average in a rise in heat transfer coefficient of 88%, for measurements at medium heat flux. At high heat fluxes, an increase of 71% is observed for a rise in mass flux of 59%. Nine heat transfer correlations are evaluated. The majority underestimates the heat transfer significantly, however, two correlations operate adequately and are proposed as a basis for future correlation development. The unique dataset and insights presented in this work enable a better understanding of the heat transfer in supercritical vapor generators. Future work includes incorporating top and bottom wall temperature measurements, adjusting control and application of the heat flux and investigating refrigerants with a low Global Warming Potential.

Formation of amorphous silica nanoparticles and its impact on permeability of fractured granite in superhot geothermal environments

Superhot geothermal environments in granitic crusts of approximately 400–500 °C are a frontier of geothermal energy. In the development of such environments, there is a concern of a reduction of permeability of fractured granite due to the formation of fine particles of amorphous silica induced by the phase change from subcritical water to supercritical water or superheated steam. However, the formation of silica particles and a resultant reduction in permeability have not been demonstrated to date. Therefore, experiments were conducted on the formation of amorphous silica particles with various combinations of temperature (430–500 °C) and pressure (20–30 MPa), in which the phase change of Si-containing water from liquid to either supercritical fluid or vapor was induced. Amorphous silica nanoparticles occurred under all conditions with smaller particles for higher temperature. The permeability of fractured granite was also observed to decrease significantly within several hours during injection of the particles into rock at 450 °C and 30 MPa under a confining stress of 40 MPa, with slower permeability reduction at a smaller number of particles or in the presence of larger aperture fractures. The present study suggests that the nanoparticles are likely to form and destroy the permeability in superhot geothermal environments, against which countermeasures should be investigated.

Investigation of the quantum vacuum as an energy sink for subcritical and supercritical vaporization lasers

In this paper, it is shown that the quantum electrodynamic vacuum particle production rate by a vaporization laser is negligible and is not a significant energy sink at electric field strengths beyond the Schwinger Limit.

The spray vaporization characteristics of gasoline/diethyl ether blends at sub-and super-critical conditions

The multi-hole spray vaporization characteristics of gasoline, diethyl ether (DEE) and their blends were investigated at two pressures and elevated temperatures by using high speed schlieren photography and laser sheet patternation. Results show that the effects of DEE addition on spray behaviors depend on the ambient conditions that may lead to sub- and supercritical vapor generation mechanisms: (a) for 0.5 MPa ambient pressure at sub-critical state, spray plumes from different nozzle holes are separated. DEE addition results in higher vapor tip penetration, higher spray angle and decreased liquid cross-sectional area, indicating that DEE addition enhances vaporization. However, this effect becomes weaker at higher temperature due to accelerated gasoline vaporization. (b) for 3.8 MPa ambient pressure, spray plumes coalesce as a single plume-like structure due to stronger aerodynamic resistance to the axial penetration of each plume. In addition, opposite from the 0.5 MPa ambient pressure case, DEE addition results in an inhibited vaporization because the fuel blends are more easily heated to supercritical state with the addition of DEE. The thickened interface and reduced mean free path at supercritical state lead to restricted vapor phase generation. This phenomenon is also evidenced by the absence of large liquid blob on the patternation images.

The equation of state, composition and conductivity of supercritical iron vapor in the framework of the model plasma fluid

The equation of state, composition and conductivity of supercritical iron vapor in the framework of the model plasma fluid

Widom line, dynamical crossover, and percolation transition of supercritical oxygen via molecular dynamics simulations.

Supercritical oxygen, a cryogenic fluid, is widely used as an oxidizer in jet propulsion systems and is therefore of paramount importance in gaining physical insights into processes such as transcritical and supercritical vaporization. It is well established in the scientific literature that the supercritical state is not homogeneous but, in fact, can be demarcated into regions with liquid-like and vapor-like properties, separated by the "Widom line." In this study, we identified the Widom line for oxygen, constituted by the loci of the extrema of thermodynamic response functions (heat capacity, volumetric thermal expansion coefficient, and isothermal compressibility) in the supercritical region, via atomistic molecular dynamics simulations. We found that the Widom lines derived from these response functions all coincide near the critical point until about 25 bars and 15-20 K, beyond which the isothermal compressibility line begins to deviate. We also obtained the crossover from liquid-like to vapor-like behavior of the translational diffusion coefficient, shear viscosity, and rotational relaxation time of supercritical oxygen. While the crossover of the translational diffusion coefficient and shear viscosity coincided with the Widom lines, the rotational relaxation time showed a crossover that was largely independent of the Widom line. Further, we characterized the clustering behavior and percolation transition of supercritical oxygen molecules, identified the percolation threshold based on the fractal dimension of the largest cluster and the probability of finding a cluster that spans the system in all three dimensions, and found that the locus of the percolation threshold also coincided with the isothermal compressibility Widom line. It is therefore clear that supercritical oxygen is far more complex than originally perceived and that the Widom line, dynamical crossovers, and percolation transitions serve as useful routes to better our understanding of the supercritical state.

PERFORMANCE ANALYSIS OF RANKINE CYCLE USING SUPERCRITICAL STEAM FOR ENERGY CONVERSION SYSTEM OF RDE

PERFORMANCE ANALYSIS OF RANKINE CYCLE USING SUPERCRITICAL STEAM FOR ENERGY CONVERSION SYSTEM OF RDE. The energy conversion system in the experi- mental power reactor (RDE) is designed using a steam turbine or in a cogeneration configuration with a Rankine cycle. This energy conversion system also functions as a reactor coolant system that implements an indirect cycle. Between the primary cooling system and the secondary cooling system is mediated by a heat exchanger that acts as a steam generator (SG). The temperature of the reactor outlet is 700 o C and the temperature of the steam generator outlet is 530 o C with the pressure of 60 bar. One of the performance parameters for energy conversion systems is thermal efficiency. This research aims to study the possibility of increasing thermal efficiency by conditioning the supercriti- cal vapor in the turbine inlet. The analysis and calculation of cooling thermodynamic parameters and coolant system performance parameters are performed using ChemCAD computer software. A simu- lation using ChemCAD for the RDE energy conversion system by conditioning the supercritical va- por at various pressure variations obtained that the highest thermal efficiency of 29.41 % occurred at supercritical vapor conditions with a pressure of 270 bar. This thermal efficiency is about 2.5 % higher than thermal efficiency at a pressure of 60 bar. Therefore a pressure of 270 bar can be consi - dered as an operating parameter for the Rankine cycle on RDE. Keywords : experimental power reactor, cooling system, ChemCAD, thermal efficiency

The design of CO2-based working fluids for high-temperature heat source power cycles

The application of CO2 power cycles is advantageous to exploit high-temperature sources (500-800°C) in the case of available low-temperature heat sinks (15-25°C). However, their efficiency is strongly reduced for higher heat sink temperatures. At these temperatures, due to the low-critical temperature of CO2 (about 31°C), CO2 is in fact compressed in the supercritical vapor phase rather than in the liquid phase, thus increasing energetic demand for compression. One of the solutions envisaged to overcome this problem is the addition of one or more chemicals that allow having a mixture with a higher critical temperature than the one of pure CO2. This preserve the working fluid compression in its liquid phase, even in the case of heat sinks with temperatures greater than 25°C.This research shows that the addition to CO2 of a properly selected chemical component enables to increase the critical temperature up to 45°C with relevant improvements of cycle efficiency with respect to pure-CO2 power cycles. In particular, it summarizes the most relevant criteria to be accounted for when selecting CO2-additives. Moreover, the paper warns of the thermodynamic effects deriving from adding to CO2 a second characterized by a much more high critical temperature, such as the occurrence of infinite-pressure critical points and multiple-phase liquid-liquid and vapor-liquid critical points. Finally, the paper analyses the thermodynamic properties of a high-critical temperature CO2-based mixture, suitable for these applications, that presents multiple phase critical points. In this regard, it is specified that the paper also aims at filling a knowledge gap in the study of thermodynamic properties of mixtures presenting how do enthalpy and specific volume change in response to pressure variations in the event of liquid-liquid and vapour-liquid critical points. Finally, we present the comparison between performances of power cycles which use, as working fluid, either pure CO2 or the novel designed higher temperature CO2-based mixture.

Pathways to dewetting in hydrophobic confinement

Liquid water can become metastable with respect to its vapor in hydrophobic confinement. The resulting dewetting transitions are often impeded by large kinetic barriers. According to macroscopic theory, such barriers arise from the free energy required to nucleate a critical vapor tube that spans the region between two hydrophobic surfaces--tubes with smaller radii collapse, whereas larger ones grow to dry the entire confined region. Using extensive molecular simulations of water between two nanoscopic hydrophobic surfaces, in conjunction with advanced sampling techniques, here we show that for intersurface separations that thermodynamically favor dewetting, the barrier to dewetting does not correspond to the formation of a (classical) critical vapor tube. Instead, it corresponds to an abrupt transition from an isolated cavity adjacent to one of the confining surfaces to a gap-spanning vapor tube that is already larger than the critical vapor tube anticipated by macroscopic theory. Correspondingly, the barrier to dewetting is also smaller than the classical expectation. We show that the peculiar nature of water density fluctuations adjacent to extended hydrophobic surfaces--namely, the enhanced likelihood of observing low-density fluctuations relative to Gaussian statistics--facilitates this nonclassical behavior. By stabilizing isolated cavities relative to vapor tubes, enhanced water density fluctuations thus stabilize novel pathways, which circumvent the classical barriers and offer diminished resistance to dewetting. Our results thus suggest a key role for fluctuations in speeding up the kinetics of numerous phenomena ranging from Cassie-Wenzel transitions on superhydrophobic surfaces, to hydrophobically driven biomolecular folding and assembly.

Feed pump for supercritical power block—SIGMA KNE 5.1

The power blocks with supercritical vapour parameters demand development of new pumps. This paper deals with a process of developing such a feed pump with the aid of numerical flow and mechanical simulations. Some results and figures are presented.

Buried Hydrothermal Systems: The Potential Role of Supercritical Water,“ScriW”, in Various Geological Processes and Occurrences in the Sub-Surface

It is well known that seawater that migrates deep into the Earth’s crust will pass into its supercritical domain at temperatures above 407°C and pressures above 298 bars. In the oceanic crust, these pressures are attained at depths of 3 km below sea surface, and sufficiently high temperatures are found near intruding magmas, which have temperatures in the range of 800°C to 1200°C. The physico-chemical behaviour of seawater changes dramatically when passing into the supercritical domain. A supercritical water vapour (ScriW) is formed with a density of 0.3 g/cc and a strongly reduced dipolar character. This change in polarity is causing the ScriW to lose its solubility of the common sea salts (chlorides and sulphates) and a spontaneous precipitation of sea salts takes place in the pore system. However, this is only one of many cases where the very special properties of ScriW affect its surroundings. The objective of this paper is to increase awareness of the many geological processes that are initiated and governed by ScriW. This includes interactions between ScriW and its geological surroundings to initiate and drive processes that are of major importance to the dynamics and livelihood of our planet. ScriW is the driver of volcanism associated with subduction zones, as ScriW deriving from the subduction slab is interacting with the mantle rocks and reducing their melting point. ScriW is also initiating serpentinization processes where olivines in the mantle rocks (e.g. peridotite) are transformed to serpentine minerals upon the uptake of OH-groups from hydrolysed water. The simultaneous oxidation of Fe2+ dissolved from iron-bearing pyroxenes and olivines leads to the formation of magnetite and hydrogen, and consequently, to a very reducing environment. ScriW may also be the potential starter and driver of the poorly understood mud and asphalt volcanism; both submarine and terrestrial. Furthermore, the lack of polarity of the water molecules in ScriW gives the ScriW vapour the potential to dissolve organic matter and petroleum. The same applies to supercritical brines confined in subduction slabs. If these supercritical water vapours migrate upwards to reach the critical point, the supercritical vapour is condensed into steam and dissolved petroleum is partitioned from the water phase to become a separate fluid phase. This opens up the possibility of transporting petroleum long distances when mixed with ScriW. Therefore, we may, popularly, say that ScriW drives a gigantic underground refinery system and also a salt factory. It is suggested that the result of these processes is that ScriW is rejuvenating the world’s ocean waters, as all of the ocean water circulates into the porous oceanic crust and out again in cycles of less than a million years. In summary, we suggest that ScriW participates in and is partly responsible for: 1) Ocean water rejuvenation and formation; 2) Fundamental geological processes, such as volcanism, earthquakes, and meta-morphism (including serpentinization); 3) Solid salt production, accumulation, transportation, and (salt) dome formation; 4) The initiation and driving of mud, serpentine, and asphalt volcanoes; 5) Dissolution of organic matter and petroleum, including transportation and phase separation (fractionation), when passing into the subcritical domain of (liquid) water.

Ring schlieren: Description and interpretation of field relations in the Halifax Pluton, South Mountain Batholith, Nova Scotia

A ∼35 km coastal transect of the Halifax Pluton in South Mountain Batholith (SMB) reveals 96 m-scale ring schlieren, clustered in four locations. Ring schlieren are alternating melanocratic gradational to leucocratic bands in granites forming open to closed, nested, circular to elliptical, concentric to eccentric structures with centres aligned along the major axis or minor axis of the outer ellipse, with a cylindrical form in three dimensions, and in which cross-cutting relations suggest a younging direction towards the centre. We use detailed geometric measurements of these ring schlieren to interpret the process(es) of their formation, and to indicate the relative timing of emplacement of the SMB. The dimensions and orientations of the rings are highly variable: major-axis lengths (1.39 ± 1.43 m), minor-axis lengths (1.01 ± 0.79 m), ellipticities (1.34 ± 0.25), and major-axis orientations (008°±54°). Ring schlieren appear to be the youngest structures in this part of the batholith. Modal-abundance and grain-size variation in the rings suggests that they result from shear flow. In three dimensions, the rings are nested vertical cylinders, and probably represent vertical fossil pathways, either of descending xenoliths or of ascending supercritical vapour bubbles. Such processes can produce, and preserve, a track in a crystal-melt mush having a degree of crystallinity between 55 and 75%. Two miarolitic cavities within one multi-ring structure suggest that a rising bubble train may have produced the rings.

Experimental Research on Band-emissivities of 12%Cr Steel Oxidized in Supercritical Water Vapor

The surface temperature of large rotating machinery is an indispensable parameter for the strength design and life assessment.The infrared radiation(IR) pyrometry is a type of non-contacting measurement technique which can be used to detect the surface temperature of rotating machinery directly.The oxidation film of steam turbine rotors,due to being operated in high parameters steam for long terms,is one of the most important factors for IR pyrometry.To study on the influence of oxidization on IR pyrometry,the 12%Cr steel samples were oxidized in supercritical water vapor(up to 24 MPa/400 ℃) in the presented device,then the emissivity of the oxidized samples were measured with a monochromatic pyrometer.The results show that growth rate of the emissivity measurements varying with temperature and their dispersion were decreased with the development of being oxidized gradually.It suggests that the monochromatic pyrometer can be used to detect the temperature variation of objects with setting fitted emissivity(such as 0.88).It is demonstrated that IR pyrometry could be applied to monitor the surface temperature of steam turbine rotors.

Structure and properties of high-temperature austenitic low-carbon 01Kh15N22AG2V4TYu and 02Kh18N12AG11MFB steels

Principles of multicomponent alloying of high-temperature steels are formulated on the basis of reported and obtained experimental data. The short- and long-term strength, the structure, and the phase composition of high-temperature austenitic low-carbon steels 01Kh15N22AG2V4TYu and 02Kh18N12AG11MFB are studied in the structural states that form upon forging and aging and ensure the maximum hardening. These steels are found to have a high short-term strength and high-temperature strength. The tests of these steels performed for 8 × 103 h without failure of specimens at a temperature of 680°C and stresses of 100–120 MPa show that they are promising materials that can operate at 620–680°C for 2 × 105 h at a stress of 70 MPa in power units intended for operation at supercritical vapor parameters. The specific features of the fine structures of the steels in the forged and aged states that provide their high high-temperature strength are revealed. The evolution of structural constituents during long-term strength tests is studied, and the role of these constituents in fracture is determined.

Thermodynamic modeling of post-entrapment crystallization in igneous phases

Inclusions of quenched silicate liquid in igneous phenocryst phases represent important windows into the pre-eruption chemistry of volcanic rocks. Melt inclusions are subject to a variety of potential modifications after entrapment, which obscure the connection between final inclusion composition, and entrapment conditions. We concentrate on the effects of post-entrapment crystallization (PEC) in the cooling inclusion. PEC is neither an isobaric nor an isochoric process. Pressure decreases between 2 and 27 bars per degree of cooling, depending on the chemistry of melt and host and on the degree of PEC. In the equilibrium case, between about 50% and 65% of this pressure effect is due to thermal expansivity of the liquid, 10–35% from thermal expansivity of the host, and 5–40% from mass transfer between the inclusion and host. This complicates the application of simple element-partitioning schemes for back-calculating the effects of post-entrapment crystallization except in the simplest cases. We present a thermodynamic algorithm for PEC correction. This method is based on the self-consistent thermodynamic model set used in the MELTS software package. The algorithm moves backward through the PEC process, incrementally adding equilibrium crystal composition to the liquid while accounting for consequent variations in pressure and oxygen fugacity. Entrapment conditions are assumed to have been reached when the instantaneous liquidus solid composition most closely matches that of the bulk host crystal. Besides giving information on the degree of PEC and initial inclusion composition, the proposed algorithm can provide constraints on the pressure, temperature and oxygen fugacity at the time of entrapment. Olivine- and orthopyroxene-hosted inclusions from Popocatépetl, Mexico help constrain pre-eruption conditions for mixed magmas from recent eruptive products. Feldspar-hosted inclusions from Satsuma-Iwojima, Japan suggest that these magmas were substantially undersaturated with respect to supercritical vapor phase at the time of entrapment and underwent on the order of 29% post-entrapment crystallization. Quartz-hosted inclusions can potentially be employed in more silicic compositions, but this will require refinement of existing thermodynamic models.