scholarly journals Equal eigenvalues in multicomponent diffusion: the extraction of diffusion coefficients from experimental data in ternary systems

Author(s):  
D.G. Miller
SPE Journal ◽  
2016 ◽  
Vol 22 (02) ◽  
pp. 505-520 ◽  
Author(s):  
M.. Ghasemi ◽  
W.. Astutik ◽  
S. A. Alavian ◽  
C. H. Whitson ◽  
L.. Sigalas ◽  
...  

Summary This paper presents a novel technique to determine multicomponent diffusion coefficients for carbon dioxide (CO2) injection in a North Sea chalk field (NSCF) in Norway at reservoir conditions. The constant-volume-diffusion (CVD) method is used, consisting of an oil-saturated-chalk core in contact with an overlying free space, which is filled with the CO2. The experimental data are matched with an equation-of-state (EOS) -based compositional model. Transport by diffusion controls the dynamics of the constant-volume system and, together with phase equilibria, allows a consistent estimation of diffusion coefficients needed to describe the observed changes in system pressure. We conduct two experiments at reservoir conditions: One uses a core plug saturated with live oil and the other with stock-tank oil (STO). Once the experiments are completed, EOS-based compositional simulation is performed to match the experimental data by use of the oil- and gas-diffusion coefficients as history-matching parameters. The modeling work is conducted with a commercial reservoir simulator by use of a 2D radial-grid model to describe the experimental setup. The experiment uses an outcrop chalk core mounted in a vertically oriented core holder. The chalk is shorter than the core holder, thus resulting in an overlying void space. The system is initially saturated with oil at reservoir conditions. CO2 is then injected from the top, forming an overlying CO2 chamber and displacing oil toward the bottom of the core holder. Once CO2 fills the overlying bulk space, the system is isolated with no further injection or production. The CO2 and oil reach and remain in equilibrium locally at the gas/oil interface throughout the test, beginning and maintaining the diffusion mechanism. Diffusion of CO2 into the oil results in a decreasing pressure, which is the main history-matching parameter. The multicomponent diffusion coefficients are found to match the model pressure/time prediction to the experimental data. This suggests the modeling work flow incorporates a representative EOS model and the main transport dynamics controlled by diffusion are being treated properly. Proper simulation of CO2 injection in fractured-chalk reservoirs requires the ability to model multicomponent diffusion accurately. The proposed CVD method provides such modeling capabilities. Our modeling and experimental work indicate the novelty of the CVD method to determine the diffusion coefficients of a system where diffusion is the dominant displacement mechanism. The fact that the oil is contained within a low-permeability-chalk sample reduces density-driven convection that could result because of nonmonotonic oil-density changes as CO2 dissolves into the oil.


2007 ◽  
Vol 14 (04) ◽  
pp. 681-685
Author(s):  
W. D. ROOS ◽  
J. K. O. ASANTE

Profiles of surface concentrations as a function of temperature, where the temperature is increased at a constant rate, contain the necessary information to extract segregation parameters. A model using rate equations can be used to simulate these profiles. Even on a high-speed computer, solving these equations can take hours. For ternary and higher component alloys the fit parameters are at least nine and finding the best fit manually can extend the search to days. Theoretical segregation and diffusion models show two temperature regions of interest. In the low-temperature region, representing the kinetics of segregation, the diffusion coefficients of the species dominate the flux of atoms to the surface, and in the high-temperature region the surface concentrations are independent of the diffusion coefficients. In the high-temperature equilibrium region the surface concentrations are determined only by the segregation energies and interaction coefficients. A procedure is presented that can find a good set of segregation parameters within seconds. The sensitivity of selecting the kinetics, as well as the equilibrium temperature regions will be demonstrated. The procedure is used to extract the segregation parameters for a Cu (111) 0.13 at% Sn 0.18 at% Sb system.


2012 ◽  
Vol 727-728 ◽  
pp. 163-168 ◽  
Author(s):  
Marcos Flavio de Campos

In the case of the modeling of sintering and heat treatments, the diffusion coefficients are an essential input. However, experimental data in the literature about diffusion coefficients for rare-earth transition metal intermetallics is scarce. In this study, the available data concerning diffusion coefficients relevant for rare-earth transition metal magnets are reviewed and commented. Some empirical rules are discussed, for example the activation energy is affected by the size of the diffusing impurity atom. Diffusion coefficients for Dy, Nd and Fe into Nd2Fe14B are given according an Arrhenius equation D=D0exp (-Q/RT). For Dy diffusion into Nd2Fe14B, Q 315 kJ/mol and D08 . 10-4m2/s.


1973 ◽  
Vol 26 (4) ◽  
pp. 469 ◽  
Author(s):  
JJ Lowke

The relationship between current ratios and electron diffusion coefficients for the Townsend-Huxley experiment is reanalysed with the assumption that diffusion can be represented by two coefficients DT and DL for diffusion transverse and parallel respectively to the applied electric field. When the new formula is used to interpret previous experimental data obtained with a diffusion tube of length 2 cm, the derived values of DT/fl become independent of pressure (fl being the electron mobility). For longer diffusion tubes (~ 6 cm), current ratios are insensitive to DL and the results differ insignificantly from those obtained using the formula previously derived on the assumption that diffusion is isotropic.


2019 ◽  
Vol 26 ◽  
pp. 20-29
Author(s):  
Henryk Leszczyński ◽  
Karolina Lademan ◽  
Katarzyna Tkacz-Śmiech ◽  
Bogusław Bożek ◽  
Marek Zajusz ◽  
...  

Even though several methods of diffusion analysis avoid a necessity for the Matano plane determination, the Matano plane locations are of interest in the multicomponent couples and when tracer experiments are performed. The positions of the Matano plane calculated from the concentration profiles should be exactly the same. However, due to experimental errors, the results can differ significantly. In the paper we consider Matano plane for multi-component couples of conserved and non-conserved overall volumes. We use Darken method and Sauer-Freise scheme, respectively and show that looking for the Matano plane as an inverse problem leads to a system of linear algebraic equations which are over-determined. The relations for the Matano plane position are derived by virtue of the least-squares methodology. The exemplary computations shows that the method is particularly useful in analysis of experimental data and allows decreasing computing errors.


2002 ◽  
Vol 16 (25) ◽  
pp. 3837-3846 ◽  
Author(s):  
A. Z. ZIAUDDIN AHMED ◽  
G. M. BHUIYAN

The embedded atom method (EAM) potentials, originally proposed for solid state calculations, have been applied to investigate the atomic transport property namely the diffusion coefficients of liquid Ni, Cu, Ag and Au. Two different liquid state theories, specifically the linearized Weeks–Chandler–Andersen (LWCA) theory and the Gibbs–Boguliubov variational method (GB) are used to evaluate the packing fraction near melting temperature. Calculated values for the diffusion coefficients are compared with the available experimental data. Results of variational calculations are found to be better in agreement. Results of calculations also allow us to conclude that the concerning EAM potentials are transferable to the study of atomic transport properties of liquid transition and noble metals.


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