Mole Fraction Of Component Research Articles

Estimation of CO2–brine interfacial tension using an artificial neural network

Experimental determination of CO2–brine interfacial tension (IFT) usually requires expensive apparatus and sophisticated interpretation procedure and is time-consuming. Hence, it is of practical importance to develop an accurate and reliable model for determining the CO2–brine IFT. This paper presents the use of feed forward artificial neural network (ANN) to accurately estimate CO2–brine IFT based on a database acquired from previous literature. The database consists of a total of 1716 CO2–brine IFT datasets that cover relatively large ranges of pressure (0.1–60.05MPa), temperature (5.25–175°C), total salinity (0–5molkg−1) and mole fractions (0–80%) of impure components. Six independent variables were considered to develop the IFT estimation model: pressure, temperature, monovalent cation (Na+ and K+) molality, bivalent cation (Ca2+ and Mg2+) molality in brine, and mole fractions of N2 and CH4 in injected CO2 streams. The ANN topology was optimized by trial-and-error in order to enhance its capability of generalization and the optimal one was determined to be 6-10-20-1 (10 and 20 neurons in the first and second hidden layers, respectively). The accuracy of the proposed ANN model was highlighted by four evaluation matrices, namely mean absolute error (MAE), mean absolute relative error (MARE), mean squared error (MSE), and determination coefficient (R2) between the measured and estimated IFT. The ANN model was further compared against four empirical IFT correlations developed in previous studies. It was observed that the ANN model outperforms significantly the empirical correlations and provides the most accurate IFT reproduction with respect to pure CO2–pure water, pure CO2–brine and impure CO2 systems.

Prediction of the binary surface tension of mixtures containing ionic liquids using Support Vector Machine algorithms

The surface tension of pure ionic liquids (ILs) and their mixtures with other compounds play a key role in the design and development of many industrial processes. Therefore, its modeling is extremely important from an industrial point of view. This study examined the capability and feasibility of three intelligence algorithms for predicting the surface tension of binary systems containing ILs. To construct and test the models, 748 data points corresponding to the experimental surface tension values of binary mixtures containing ILs were extracted from the literature. The surface tension was between 0.0157 and 0.07185N·m−1. The absolute temperature (T), mole fraction and molecular weight of the IL components (xIL and MwIL) and the density of the IL components (ρIL) together with the boiling point (Tbnon-IL) and molecular weight (Mwnon-IL) of the non-IL component were considered as model input variables to differentiate between the various compounds involved in binary systems. A comparison of the experimental data and predicted values using all three methods (in terms of statistical parameters) showed good agreement; however, the CSA-LSSVM prediction was better than the other two approaches.

Calcic amphibole thermobarometry in metamorphic and igneous rocks: New calibrations based on plagioclase/amphibole Al-Si partitioning and amphibole/liquid Mg partitioning

Dependencies of plagioclase/amphibole Al-Si partitioning, DAl/Siplg/amp, and amphibole/liquid Mg partitioning, DMgamp/liq, on temperature, pressure and phase compositions are investigated employing robust regression methods based on MM-estimators. A database with 92 amphibole-plagioclase pairs – temperature range: 650–1050°C; amphibole compositional limits: >0.02 apfu (23O) Ti and >0.05 apfu Al – and 148 amphibole-glass pairs – temperature range: 800–1100°C; amphibole compositional limit: CaM4/(CaM4+NaM4) >0.75 – compiled from experiments in the literature was used for the calculations (amphibole normalization scheme: 13-CNK method).Statistical analysis reveals a significant dependence of DAl/Siplg/amp on pressure, temperature, Al fraction in amphibole T1-site, XAlT1, and albite fraction in plagioclase, XAb, leading to the barometric expression: Pkbar=8.3144TKlnDAl/Siplg/amp−8.7TK+23377XAlT1+7579XAb−11302/−274 (precision: ±1.5 to ±2.3kbar; expressed at 1s).The DMgamp/liq was found to have a significant dependence on temperature and the logarithm of XCaliq/(XCaliq+XAlliq) ratio (glass composition expressed as anhydrous mole fraction of cation components) that led to the thermometer: T℃=71975−11896lnXCaliq/XCaliq+XAlliq8.3144lnDMgamp/liq+58−273 (precision: ±35 to ±45°C).Amphibole-liquid compositional relationships revealed that the temperature dependence of DMgamp/liq was mostly controlled by a positive correlation of lnXMgliq with temperature that led to the thermometer: T(℃)=107 lnXMgliq−108ln[XCaliq/(XCaliq+XAlliq)]+1184 (precision: ±37 to ±42°C).The plagioclase-amphibole barometer is suitable for a large diversity of amphibole-plagioclase-bearing assemblages from metamorphic (amphibolites and mafic granulites) and igneous (metaluminous granitoids to gabbros) rocks, whereas the liquid-only and the amphibole-liquid thermometers are applicable to alkaline and subalkaline igneous rocks.The calibrated expressions yield P-T estimates consistent with those obtained with widely used barometers and thermometers. Plagioclase-amphibole barometry extends pressure determinations to quartz-free and/or garnet-free assemblages.

Improved Method for Calculating Minimum Miscibility Pressure for Gas Flooding

Minimum miscibility pressure (MMP) is a key parameter determining the feasibility of complete miscibility of oil and gas. Using a slim-tube model, we have experimentally established the MMP for gas and six oil samples. We propose an improved mathematical model for determining the MMP, designed using 97 groups of MMP data for hydrocarbons (18 groups for lean-gas flooding and 79 groups for rich-gas flooding). The model obtained is universal and is a function of the reservoir temperature, the average molecular weight of the C 7+ oil fraction, and the mole fraction of volatile components (CH 4 and N 2 ) and intermediate components (CO 2 , H 2 S, C 2 –C 6 ) in the crude oil and in the injected gas. We compare our proposed model with widely used empirical models, showing considerable convergence between the experimental data and the calculations; the percentage average absolute relative error (%AARE) is 7.11%.

THREE-PARAMETER MODEL OF SUBREGULAR SOLUTIONS

Excess Gibbs energy change of subregular-type binary solution can be approximated with an insignifi cant error by the equation: where xi – mole fractions of components in a solution; Q0 ‒ mixing energy; m and n – numeric constants. Fixed parameters Q0 , m and n were determined by the least square method using experimental values of ΔG E and component activities of a binary solution. The obtained calculated expressions allow working with subregular solutions the same way as with regular solutions and getting simpler expressions of component activities in a multicomponent solution

Prediction of liquid–liquid equilibrium behavior for aliphatic + aromatic + ionic liquid using two different neural network-based models

In this study, the liquid–liquid phase behavior of aromatic compound+aliphatic compound+ionic liquid (IL) ternary systems was estimated by using two artificial neural networks (ANN) developed based on back propagation (BP) and hybrid group method of data handling (GMDH). Molar ratio of aliphatic compound, aromatic compound, and IL as well as temperature, molecular weight ratio of aliphatic compound to IL, and molecular weight ratio of aromatic compound to IL were chosen as the inputs to the networks. Additionally, the mole fraction of components in final alkane-rich phase and IL-rich phase was considered as desired outputs. The best topology of the BP-ANN model was found as (6-8-4). Besides, corresponding quadratic expression for each neuron of the hybrid GMDH model was determined. The obtained results by the hybrid GMDH model provided a near to accurate prediction of phase behavior with average relative deviation (ARD%) of 7.27%. However, the BP-ANN model presented a slightly more accurate prediction with ARD% of 4.49%. Furthermore, the comparison of the results with those obtained by the famous thermodynamic models, proved the preciseness of the proposed networks.

An Improved CO2-Crude Oil Minimum Miscibility Pressure Correlation

Minimum miscibility pressure (MMP), which plays an important role in miscible flooding, is a key parameter in determining whether crude oil and gas are completely miscible. On the basis of 210 groups of CO2-crude oil system minimum miscibility pressure data, an improved CO2-crude oil system minimum miscibility pressure correlation was built by modified conjugate gradient method and global optimizing method. The new correlation is a uniform empirical correlation to calculate the MMP for both thin oil and heavy oil and is expressed as a function of reservoir temperature, C7+molecular weight of crude oil, and mole fractions of volatile components (CH4and N2) and intermediate components (CO2, H2S, and C2~C6) of crude oil. Compared to the eleven most popular and relatively high-accuracy CO2-oil system MMP correlations in the previous literature by other nine groups of CO2-oil MMP experimental data, which have not been used to develop the new correlation, it is found that the new empirical correlation provides the best reproduction of the nine groups of CO2-oil MMP experimental data with a percentage average absolute relative error (%AARE) of 8% and a percentage maximum absolute relative error (%MARE) of 21%, respectively.

Kinetic Modeling of the Transesterification Reaction of Dimethyl Carbonate and Phenol in the Reactive Distillation Reactor

The kinetic behavior of preparing diphenyl carbonate by the transesterification of dimethyl carbonate with phenol in a reactive distillation reactor has been explored experimentally and theoretically. The transesterification reaction was described to conform a pseudo-second-order kinetics, and a semi-empirical kinetic model has been derived to explain the kinetic behavior. The model parameters were fitted to experimental data by an improved genetic algorithm. The proposed model was determined to be useful in simulating the rate constant and the mole fraction of components, which agreed well with the experimental data for different operating temperatures and catalyst concentrations.

Detailed simulation of dual-reflux pressure swing adsorption process

A model for the detailed simulation of dual-reflux pressure swing adsorption process developed in the frame of the commercial software Aspen Adsim® is presented. For validation purposes, simulations were performed and model predictions were compared with published experimental results. At cyclic steady-state, model predictions were found to be in good agreement with reported experimental results in terms of (i) average ethane mole fraction in heavy product, (ii) average nitrogen mole fraction in light product, (iii) instantaneous heavy product composition profiles, and (iv) instantaneous column composition profiles. The predicted and experimental trends obtained by analyzing the effect of various operating parameters (light reflux flowrate, duration of feed/purge step, heavy product flowrate and mole fraction of heavy component in binary feed gas mixture) on process performance are also comparable. Overall, this simulation technique of dual-reflux pressure swing adsorption can serve as an effective tool for process design, cost reduction of laboratory and/or plant trails, and enhanced process understanding.

Influence of Thermal Decomposition of Ammonia Propellant in Solar Thermal Propulsion

Solar thermal propulsion is a kind of space propulsion technology with great potential applications. Due to the difficulty of hydrogen storage in orbit, ammonia becomes an ideal candidate propellant as its stability and easier storage. In solar thermal propulsion system, the working temperature is usually above 2300K, and in this condition the dissociation of ammonia will occur. Thus, using ammonia as a single component propellant to compute and analysis the performance of thruster is not precise, and the mixture components produced from ammonia dissociation must be taken into account. In this paper a novel heat exchanger configuration with platelet technology is designed, and based on finite-rate chemical reaction method and computational fluid dynamics, the dissociation process of ammonia in the heat exchanger and nozzle is simulated. Then the influence to the specific impulse of the solar thermal propulsion system is comparatively analyzed. The simulation result indicates that the main productions of the dissociation are N2and H2, and the mole fraction of other components is small value that can be neglected. The specific impulse considering dissociation reaction is higher than not considering, so that this research can estimate the performance of solar thermal propulsion with ammonia propellant more precisely.

Reduced-Order Modeling for Compositional Simulation by Use of Trajectory Piecewise Linearization

Summary Compositional simulation can be very demanding computationally as a result of the potentially large number of system unknowns and the intrinsic nonlinearity of typical problems. In this work, we develop a reduced-order modeling procedure for compositional simulation. The technique combines trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) to provide a highly efficient surrogate model. The compositional POD-TPWL method expresses new solutions in terms of linearizations around states generated (and saved) during previously simulated “training” runs. High-dimensional states are projected (optimally) into a low-dimensional subspace by use of POD. The compositional POD-TPWL model is based on a molar formulation that uses pressure and overall component mole fractions as the primary unknowns. Several new POD-TPWL treatments, including the use of a Petrov-Galerkin projection to reduce the number of equations (rather than the Galerkin projection, which was applied previously), and a new procedure for determining which saved state to use for linearization are incorporated into the method. Results are presented for heterogeneous 3D reservoir models containing oil and gas phases with up to six hydrocarbon components. Reasonably close agreement between full-order reference solutions and compositional POD-TPWL simulations is demonstrated for the cases considered. Construction of the POD-TPWL model requires preprocessing overhead computations equivalent to approximately three or four full-order runs. Runtime speedups by use of POD-TPWL are, however, very significant—up to a factor of 800 for the cases considered. The POD-TPWL model is thus well suited for use in computational optimization, in which many simulations must be performed, and we present an example demonstrating its application for such a problem.

Modeling of catalytic monolith reactor for reforming of hexadecane with exhaust gas

A numerical two-phase one-dimensional mathematical model of a single channel catalytic monolith reactor was developed in this study. The model is capable of simulating a final steady state starting from an initial distribution of temperatures and concentrations. An algorithm was written in order to solve the conservation equations. In a catalytic reactor these equations are the mass and energy balances, rate equations and physical property relationships. The new method used to solve the equations was the combination of the Euler's method and central finite difference method. The advantage of this combined method is that the percentage error produced by the program code was negligible. The program code in MATLAB environment was executed to describe the profiles of temperatures and concentrations of each individual species in the gas and solid phase along the reactor. The reforming process is complicated for heavy hydrocarbons and it is not well defined. The model was applied, as far as the authors are aware for the first time, for autothermal reforming process with n-hexadecane (C16H34) feed to depict the performance of the monolith channel for hydrogen production at specified operating conditions. In this model, it was also assumed that the reactions only occur on the surface of catalyst. The temperatures and the concentrations of each species of interests (i.e. H2, CO2, CO, and C16H34) were obtained in both the gas phase and at the wall. The results obtained using reaction kinetics data from literature were successfully validated against experimental results from a different study with respect to reactor temperatures and concentrations of products H2, CO2 and CO. The influence of thermal conductivity and effective wall thickness of the solid phase, and mass flow rate of gas on wall temperatures and mole fractions of components were also investigated and the results were in agreement with literature data.

A Neural Network Based Model for Prediction of Saturation Pressure from Molecular Components of Crude Oil

Saturation pressure is a crucial property of reservoir fluid, which is widely used in petroleum engineering calculations. In this study, a neural network model was developed for prediction of saturation pressure based on molecular components of 100 crude oils samples. Inputs of a neural network model include mole fractions of hydrocarbon and non-hydrocarbon components (C1–C6, C7+, H2S, CO2, and N2), specific gravity of C7+, molecular weight of C7+, and reservoir temperature. Molecular components of 30 crude oil samples were employed to judge the efficiency of the proposed neural network model against the Elsharkawy model and Soave–Redlich-Kwong and Peng-Robinson equations of state. Results showed that the neural network model achieved the lowest average absolute relative error and the highest correlation coefficient. Furthermore, relative contribution of network inputs on saturation pressure was obtained by sensitivity analysis, which indicated high influence of C1 and H2S mole fractions on saturation pressure.

Monte Carlo simulation of the static properties of Hg solution in (O2, N2) gassed water

Canonical Monte Carlo (CMC) simulations were carried out to investigate the influence of O2 and N2 gases on elemental mercury (Hg) solution in water. Particle–particle interactions were all modeled using Lennard–Jones potential function. To provide insight into the interaction of O2 and N2 gases with Hg atom in water, two independent mixtures Hg/(O2,H2O) and Hg/(N2,H2O) with the same bulk mole fraction of component (0.9956, 0.0023, 0.0023, 0.0021 for H2O, O2, N2 and Hg, respectively) were simulated at T=298K.The results show that Hg in water interacts favorably with O2 more than with N2. This is consistent with the hypothesis that stronger interaction of O2 gas with the mercury atom leads to a higher adsorption and lower dynamic structure compared with N2 gas. Independent simulation of Hg/(O2,H2O) and Hg/(N2,H2O) mixtures indicates that N2 gas molecules stay off the distance at which O2 interacts with Hg as the nearest neighboring distance. This procedure enables us to describe the structural properties of Hg⋯O2 and Hg⋯N2 in water at molecular scale which hints exploring techniques of the toxicity level of mercury contaminated water. Alternatively, comparison of potential of mean force indicated that Hg⋯O2 interaction exposes the free energy of −2.93kJmol−1 which is more stable pair interaction relative to Hg⋯H2O (−2.50kJmol−1) and Hg⋯N2 (−1.79kJmol−1).

Thermodynamic Study of the Liquid-Liquid Equilibrium Water-Chloroform-Acetic Acid

Experimental liquid-liquid equilibria of the water-chloroform-acetic acid system were studied at temperature of 298.15 K. Complete phase diagrams were obtained by determining solubility and tie-line data. Data for the construction of ties-lines were determined by preparing mixtures of known mole fraction of components in the region of formation of two phases. Separation factors were evaluated for the immiscibility region.

Separation of CO2–CH4 mixtures on defective single walled carbon nanohorns – tip does matter

Using realistic models of single-walled carbon nanohorns and their single-walled carbon nanotube counterparts, we study the equilibrium separation of CO2-CH4 mixtures near ambient operating conditions by using molecular simulations. We show that regardless of the studied operating conditions (i.e., total CO2-CH4 mixture pressures and mole fractions of mixture components in the bulk phase), single-walled carbon nanohorns maximize the CO2-CH4 equilibrium separation factor. Optimized samples of single-walled carbon nanohorns consisting of narrow tubular parts capped with horn-shaped tips show highly selective adsorption of CO2 over the CH4 mixture component, with the CO2-CH4 equilibrium separation factor of ~8-12. A large surface-to-volume ratio (i.e., enhanced surface forces) and unique defective morphology (i.e., packing of adsorbed molecules in quasi-one/quasi-zero dimensional nanospaces) of single-walled carbon nanohorns are their key structural properties responsible for the excellent separation performance. Our theoretical simulation results are in quantitative agreement with a recent experimental/theoretical study of the CO2-CH4 adsorption and separation on oxidized single-walled carbon nanohorns [Ohba et al., Chem. Lett., 40, 2011, 1089]. Both experiment and theory showed that the CO2-CH4 equilibrium separation factor of oxidized samples of single-walled nanohorns measured near ambient operating conditions is ~2-5. This reduction in the separation efficiency as compared to optimized samples of single-walled carbon nanohorns is theoretically justified by their lower surface-to-volume ratio (i.e., larger diameters of tubular parts and horn-shaped tips).

GC/AED를 이용한 의료용 액화혼합가스 중 산화에틸렌 및 프레온 가스류의 몰분율 측정

산화에틸렌(<TEX>$C_2H_4O$</TEX>, Ethylene oxide, EtO)은 에탄올아민 같은 공업적으로 중요한 물질이나 에틸렌 글리콜의 생산 원료 또는 살균제로 이용되는 물질이다. 산화에틸렌은 불화탄화수소를 분사제 또는 바탕가스로 하여 액화혼합가스로 제조되어 열에 약한 의료기기나 저장시설의 소독에 널리 사용되고 있다. 액화혼합가스의 생산 및 사용 시 품질관리 및 안전관리를 위해 각 성분의 몰분율을 정확히 측정할 필요가 있다. 휘발성 액체시료 중 각 기체성분들은 증기압이나 끓는점 등과 같이 물리 화학적 성질이 다르므로 몰분율 측정 시 실린더 내부의 상층에 평형을 이루고 있는 기체시료 또는 하층의 기화되지 않은 액체시료를 직접 측정기기에 주입하는 방법에 따라 측정 결과가 다를 수 있다. 본 연구에서는 액화혼합가스를 액체 또는 기체 상태로 주입할 수 있는 새로운 온라인 시료도입장치를 고안하고 GC/AED (gas chromatograph-atomic emission detector)를 사용하여 산화에틸렌과 불화탄화수소 액화혼합가스를 측정하였으며 AED의 검출특성, 기기에 주입 시 시료의 상태, 측정파장에 따른 측정결과의 정확성 및 반복성을 조사하였다. Ethylene oxide (<TEX>$C_2H_4O$</TEX>, EtO) is used as a raw material for the production of ethylene glycol and other industrially important material such as ethanolamines and also used as a disinfecting agent. It is applied for gas-phase sterilization of thermally sensitive medical equipment, and for processing of storage facilities as a mixture with fluorinated hydrocarbon. In this perspective, accurate determination of the mole fractions of components in the liquefied gas mixture is required for the quality control and safety of production and use. Each component of the liquefied gas mixture has different chemical and physical properties such as vapor pressure and boiling point. Therefore, we can suppose that analytical results can be different according to the introduction method for the gas phase of upper layer, or for the liquid phase of lower layer in gas cylinder. In this study, we designed a new on-line sample injection device for the liquefied gas mixture in liquid or gas state, and applied to the analysis of liquefied gas mixture of ethylene oxide and fluorinated hydrocarbons by GC/AED (gas chromatograph-atomic emission detector). We studied performance of AED, and effect of sample introduction and selected wavelength to the accuracy and repeatability of analytical results.

Computation of liquid-vapor critical points for multi-component mixtures

Liquid-vapor critical point for a thermodynamic mixture is an important parameter for the design of mixture transportation and processing. The classical critical points model for the multicomponent mixture is based on the tangent plane distance in terms of the Helmholtz energy. In this work, we have applied the damped Newton-Raphson scheme to solve the model using the critical temperature, critical specific volume and change in mole fraction of each component as independent variables. According to numerical experiments, the convergence criteria, initial guesses of variables and damped factor formulation were determined. The method was tested on twenty five mixtures containing two to eleven components using the SRK and PR equation of state. Comparisons between the calculated critical parameters and experimental values illustrated the overall accuracy of the solution method is satisfactory. This method can solve all the variables simultaneously using the whole iteration, which is more reliable than the nested two-singe variable loops method proposed by Heidemann and Khalil. Thus it can be used for practical purposes of locating the liquid-vapor critical points of multi-component mixtures.

Estimating the flammability of vapours above refinery wastewater laden with hydrocarbon mixtures

In this study, the likelihood of fire hazards attributed to the vapourisation of hydrocarbon components derived from refinery wastewater drainage systems was assessed. Liquid samples containing mixtures of hydrocarbon products and water were collected from a refinery drainage system and subjected to a distillation process to separate oil and water. The oil–liquid phase was analysed using gas chromatography–mass spectrometry (GC–MS) to examine the composition of the sample. Hydrocarbon compounds ranging from C9 to C16 were detected. Mole fractions of 28 selected components in the liquid phase were obtained from the GC–FID data and used to calculate mole fractions of components in the gas phase via modified Raoult’s law. Lower Flammability Limits (LFLs) and Upper Flammability Limits (UFLs) for individual components were calculated using a stoichiometric concentration method, while the LFL and UFL values for the mixture (LFL mix and UFLmix) were calculated using the Le Chatelier equation. The LFL mix and UFLmix values were used to construct a flammability diagram and subsequently used to determine the flammability of the mixture. The findings of this study may assist in minimising fire hazards associated with the presence of hydrocarbon vapours derived from refinery wastewater streams.

The effects of solid solution and diffusion on infiltration-driven metamorphism with application to metaperidotite, Val d’Efra, Central Swiss Alps

The complication introduced by solid solutions in the analysis of infiltration-driven mineral reactions is that the mole fraction of tracer component i in fluid (Xi) changes with reaction progress (ξ). The effect was incorporated into transport models for coupled fluid flow and mineral reaction by parameterizing the relation between Xi and ξ. With specific reference to carbonation and hydration during regional metamorphism of the peridotite body in Val d’Efra, whose constituent minerals are all solid solutions, infiltration of a disequilibrium fluid produces a single sharp reaction front if rock is assumed uniform in composition. The reaction front separates completely unreacted rock downstream from rock upstream with ξ at a steady-state limit (ξss ≤ ξmax) that depends on input fluid composition (ξmax is the maximum possible value). Novel phenomena develop, however, if the flow medium, like the metaperidotite body, is composed of many small domains that differ in initial mineral modes and compositions but with Xi homogenized at a spatial scale larger than the size of the domains (e.g., by diffusion). In this case, infiltration of a disequilibrium fluid produces up to as many different reaction fronts along the flow path as there are domains with 0 ≤ ξ < ξss in all domains except upstream from the slowest moving front where ξ = ξss in all domains. Measured values of ξ in the metaperidotite, (all 0 < ξ < ξmax) are best reproduced by down-temperature infiltration of a disequilibrium fluid with \( X_{{{\text{CO}}_{2} }} = \, 0. 1 9 6 \) into a multi-domain medium with uniform \( X_{{{\text{CO}}_{2} }} \) at each spatial point along the flow path (homogenized across the domains at the m-scale by diffusion), and time-integrated fluid flux ≥1,836 mol fluid/cm2 rock. Results resolve the paradox of the widespread spatial distribution of reactants and products of infiltration-driven decarbonation/dehydration reactions in regional metamorphic terrains (which in the absence of solid solution and compositional domains indicate up-temperature flow) and the prediction of hydrodynamic models that regional metamorphic fluid flow normally is directed vertically upward and down temperature.