Empirical formulae are presented for calculating vapor-liquid equilibria (VLE) in the CO2-H2O system at 10 temperatures between 110 and 350°C. At each temperature, separate functions are used to ...represent the bubble- and dew-point boundary curves that: originate at the saturation vapor pressure of water (PH2Osat) at XCO2 = 0; diverge with increasing pressure up to ∼P (XmaxCO2) where δP/δXCO2 = +∞ along the dew-point curve; then converge with increasing pressure above P(XmaxCO2). At temperatures below 265°C and pressures >P(XmaxCO2), the compositions of coexisting liquid and vapor XL(V)CO2 and XV(L)CO2 do not converge completely with increasing pressure due to the absence of critical behavior. Thus, relatively simple functions suffice to accurately represent VLE at those temperatures. In contrast, at T>265°C, XL(V)CO2 and XV(L)CO2 converge rapidly as P approaches Pc (the critical pressure in the CO2-H2O system at a given temperature between 265 and 374°C and P≤215 MPa). For those temperatures, therefore, more complex VLE formulae are required to achieve close representation of phase relations. For dew-point equations, this includes adding an exponential "correction term" to ensure that δP/δXCO2 = 0 at the critical points indicated by corresponding bubble-point functions. Stable liquid-vapor coexistence in mixed-volatile systems requires fLi = fVI (isofugacity conditions) for all "i" (volatile components) in the two fluid phases. Thus, the equations presented in this paper specify numerous P-T-X conditions where fLH2O = fVH2O and fLCO2 in the CO2-H2O system. These results have important applications in the ongoing effort to develop a more rigorous thermodynamic model for CO2-H2O fluids at geologically relevant temperatures and pressures.
A highly precise and accurate vibrating U-tube technique was developed to determine the upper baric stabilities of liquid-vapor assemblages in the CO
-H
O system at high subcritical temperatures ...(∼275-360 °C). The first step is to create an isobaric-isothermal, physically isolated and chemically homogeneous sample of “high-pressure” CO
-H
O fluid of known composition. Fluid pressure (P) is then lowered slowly at constant temperature. Pressure readings and matching values for τ (the period of vibration of the U-tube) are recorded at 0.1 or 0.2 MPa intervals. When the fluid begins to separate into two phases (liquid + vapor), a distinct inflection is observed in the trend of P vs. τ. Performing such experiments for fluid compositions at 0.05 mole fraction CO
(X
) intervals in the range 0.05 ≤ X
≤ 0.40 at 300 °C produced a complete high-P liquid-vapor boundary curve for the CO
-H
O system at that temperature. Agreement with corresponding curves determined in previous studies ranges from poor to excellent.
The primary goal of this investigation was to derive a set of expressions that can be used to calculate the amphibole-melt partitioning behavior of the rare earth elements (REE) and the high field ...strength elements (HFSE) in natural systems. To supplement the existing data set on basaltic systems, we conducted experiments on systems where amphibole was in equilibrium with dacitic, tonalitic and low Si rhyolitic melts. These experiments, doped with La, Sm, Gd, Lu, Ta, Nb, Y, Zr, and Hf, were run at pressures of 2 and 5 kbar, temperatures between 900°C and 945°C, and oxidation conditions ranging from QFM-1 to NiNiO+1.
The partitioning data obtained in this study were combined with published data to calculate two sets of expressions describing trace element partitioning. The first set models the partitioning of trace elements into amphibole using temperature, pressure and several compositional parameters, including the compositionally-compensated partition coefficients of Ti, Al, Caand SiO
2, and the exchange of Fe and Mg between the crystal and the melt (D
Mg/D
Fe). The second set of expressions are slightly less precise, but require no specific knowledge of P, T, or f
O2 and, for application to natural systems, can be constructed solely on the basis of information available from standard electron microprobe analyses. These expressions predict amphibole-melt partition coefficients for REE and HFSE within an internal precision of 14–40% (relative) for alkali basalt to low Si rhyolite, from 850°C to 1100°C, 2–20 kbar and oxygen fugacity from QFM-1 to NiNiO+1.
Partition coefficients calculated from the expressions derived in this study were used to model the partial melting and fractional crystallization of a hypothetical amphibolite and hydrous melt, respectively. Fractionation and/or melting in amphibole-bearing systems produces a magma with a convex upward REE pattern, a characteristic common to many hornblende-bearing dacites. However, the removal or addition of an amphibole component cannot produce the strong HFSE depletion relative to the REE observed in many arc magmas.
A method for fitting multiequation models to data sets of finite precision is proposed. This is based on the Gauss–Newton algorithm devised by Britt and Luecke (1973); the inclusion of several ...equations of condition to be satisfied at each data point results in a block diagonal form for the effective weighting matrix. This method allows generalized nonlinear least-squares fitting of functions that are more easily represented in the parametric form
(x(t),y(t))
than as an explicit functional relationship of the form
y=f(x).
The Aitken (1935) formulas appropriate to multiequation weighted nonlinear least squares are recovered in the limiting case where the variances and covariances of the independent variables are zero. Practical considerations relevant to the performance of such calculations, such as the evaluation of the required partial derivatives and matrix products, are discussed in detail, and the operation of the algorithm is illustrated by applying it to the fit of complex permittivity data to the Debye equation.
Thermochemical cycles for production of hydrogen from water can be constructed by appropriate combination of hydrogen- and oxygen-producing reactions carried out at different temperatures. While ...hundreds of specific reaction schemes are possible, the individual reactions can be regarded as belonging to relatively few general types. On the basis of published thermochemical data, we describe a procedure whereby an equilibrium analysis of these reaction types can be carried out systematically for a large number of specific sets of reactants. This provides quantitative criteria for assessing the inherent thermodynamic viability of possible reaction cycles, which may be of use when coupled with the more practical considerations that have traditionally formed the basis for the design of thermochemical hydrogen-production schemes. Results of applying this thermodynamic screening process systematically to hydrogen production reactions involving a large number of metal-metal oxide and metal-metal oxide-carbon systems show that polythermal reaction schemes involving the latter systems are highly efficient in generating hydrogen from coal, in comparison with usual coal gasification processes.
Laboratory experiments were conducted to investigate the adsorption kinetic behavior of pure and mixed gases (CO2, CH4, approximately equimolar CO2 + CH4 mixtures, and He) on a coal sample obtained ...from the Black Warrior Basin at the Littleton Mine (Twin Pine Coal Company), Jefferson County, west-central Alabama. The sample was from the Mary Lee coal zone of the Pottsville Formation (Lower Pennsylvanian). Experiments with three size fractions (45-150 m, 1-2 mm, and 5-10 mm) of crushed coal were performed at 40 C and 35 C over a pressure range of 1.4 6.9 MPa to simulate coalbed methane reservoir conditions in the Black Warrior Basin and provide data relevant for enhanced coalbed methane recovery operations. The following key observations were made: (1) CO2 adsorption on both dry and water-saturated coal is much more rapid than CH4 adsorption; (2) water saturation decreases the rates of CO2 and CH4 adsorption on coal surfaces, but it appears to have minimal effects on the final magnitude of CO2 or CH4 adsorption if the coal is not previously exposed to CO2; (3) retention of adsorbed CO2 on coal surfaces is significant even with extreme pressure cycling; and (4) adsorption is significantly faster for the 45-150 m size fraction compared to the two coarser fractions.
Dry melting of high albite Anovitz, Lawrence M; Blencoe, James G
The American mineralogist,
12/1999, Letnik:
84, Številka:
11-12
Journal Article
Recenzirano
Odprti dostop
The properties of albitic melts are central to thermodynamic models for synthetic and natural granitic liquids. We have analyzed published phase-equilibrium and thermodynamic data for the dry fusion ...of high albite to develop a more accurate equation for the Gibbs free energy of this reaction to 30 kbar and 1400°C. Strict criteria for reaction reversal were used to evaluate the phase-equilibrium data, and the thermodynamic properties of solid and liquid albite were evaluated using the published uncertainties in the original measurements. Results suggest that neither available phase-equilibrium experiments nor thermodynamic data tightly constrain the location of the reaction. Experimental solidus temperatures at 1 atm range from 1100 to 1120°C. High-pressure experiments were not reversed completely and may have been affected by several sources of error, but the apparent inconsistencies among the results of the various experimentalists are eliminated when only half-reversal data are considered. Uncertainties in thermodynamic data yield large variations in permissible reaction slopes. Disparities between experimental and calculated melting curves are, therefore, largely attributable to these difficulties, and there is no fundamental disagreement between the available phase-equilibrium and thermodynamic data for the dry melting of albite. Consequently, complex speciation models for albitic melts, based on the assumption that these discrepancies represent a real characteristic of the system, are unjustified at this time.
The molar volume of mixtures of CO2 and H2O is a strong function of the fluid composition. Both CO2 and H2O participate in the metamorphism of carbonate rocks, resulting in a change in the fluid ...composition during reaction. One of the effects of the change in composition is the increase in pore-fluid pressure with only small increases in extent of reaction, xi. Pressure calculated from the volumetric properties of CO2-H2O mixtures at 400 °C increases greatly with small increases of xi but drops at greater values because of the increase in pore volume as a result of deltaV solid. The pore pressure increase at small values of xi, though, readily exceeds the reported tensile strength of carbonate rocks, and the rock cannot sustain significant reaction without fracturing. The result of a small amount of reaction is a fractured rock with increased permeability, which promotes fluid transport.
Densities ρ of pure CO
2, Ch
4, and {(1 −
x)CO
2+
xCH
4}, {(1 −
x)CO
2+
xN
2}, and {(1 −
x)CH
4+
xN
2} were measured at the pressures (9.94, 19.94, 29.94, 39.94, 59.93, 79.93, and 99.93) MPa and ...temperatures (323.15, 373.15, 473.15, and 573.15) K. For each binary system, results were obtained at intervals of 0.1·
xfrom mole fraction
x= 0 to
x= 1. The results were obtained with a custom-designed, high pressure, high-temperature vibrating-tube densimeter. Excess molar volumes
V
m
Ewere calculated from the densities for the end members and mixtures.
V
m
Eis generally positive, although negative values of
V
m
Ewere observed for some CO
2-bearing mixtures.
V
m
Eis typically less than ±4 per cent of the total volume of the mixture. A dramatic increase in
V
m
Eis observed for CO
2-containing mixtures as (ρ,
T) conditions approach those of the critical point for CO
2. The values of
V
m
Eare accurately represented by two-parameter Margules equations. Our results are in good agreement with those obtained by previous investigators.
Empirical formulas are presented for calculating vapor-liquid equilibria (VLE) in the CO2-H2O system at 10 temperatures between 110 and 350 degrees C. At each temperature, separate functions are used ...to represent the bubble- and dew-point boundary curves that: originate at the saturation vapor pressure of water (pH2O sat) at XCO2 = 0; diverge with increasing pressure up to ~P (X max/CO2) where unknown symbol P/unknown symbol XCO2 = + infinity along the dew-point curve; then converge with increasing pressure above P(X max/CO2). At temperatures below 265 degrees C and pressures > P(X max/CO2), the compositions of coexisting liquid and vapor XL(V)/CO2 and XV(L) CO2 do not converge completely with increasing pressure due to the absence of critical behavior. Thus, relatively simple functions suffice to accurately represent VLE at those temperatures. In contrast, at T > 265 degrees C, XL(V) CO2 and XV(L) CO2 converge rapidly as P approaches Pc (the critical pressure in the CO2-H2O system at a given temperature between 265 and 374 degrees C and P is less than or equal to 215 MPa). For those temperatures, therefore, more complex VLE formulae are required to achieve close representation of phase relations. For dew-point equations, this includes adding an exponential "correction term" to ensure that unknown symbol P/unknown symbol XCO2 = 0 at the critical points indicated by corresponding bubble-point functions. Stable liquid-vapor coexistence in mixed-volatile systems requires fL/i = fV/I (isofugacity conditions) for all "i" (volatile components) in the two fluid phases. Thus, the equations presented in this paper specify numerous P-T-X conditions where fL/H2O = fV/H2) and fL/CO2 = fV/CO2 in the CO2-H2O system. These results have important applications in the ongoing effort to develop a more rigorous thermodynamic model for C02-H20 fluids at geologically relevant temperatures and pressures. PUBLICATION ABSTRACT
