RELAP5 Analysis of Two-Phase Decompression and Rarefaction Wave Propagation Under a Temperature Gradient

2010 ◽  
Vol 169 (1) ◽  
pp. 34-49 ◽  
Author(s):  
Nathan Lafferty ◽  
Victor Ransom ◽  
Martin Lopez De Bertodano
Keyword(s):  
Wave Propagation ◽  
Temperature Gradient ◽  
Rarefaction Wave ◽  
Two Phase

Two-Phase Multicomponent Diffusion and Convection for Reservoir Initialization

2006 ◽  
Vol 9 (05) ◽  
pp. 530-542 ◽  
Author(s):  
Hadi Nasrabadi ◽  
Kassem Ghorayeb ◽  
Abbas Firoozabadi
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Thermal Diffusion ◽  
Multicomponent Diffusion ◽  
Compositional Variation ◽  
Horizontal Temperature Gradient ◽  
Two Phase ◽  
Thermogravitational Column

Summary We present formulation and numerical solution of two-phase multicomponent diffusion and natural convection in porous media. Thermal diffusion, pressure diffusion, and molecular diffusion are included in the diffusion expression from thermodynamics of irreversible processes. The formulation and the numerical solution are used to perform initialization in a 2D cross section. We use both homogeneous and layered media without and with anisotropy in our calculations. Numerical examples for a binary mixture of C1/C3 and a multicomponent reservoir fluid are presented. Results show a strong effect of natural convection in species distribution. Results also show that there are at least two main rotating cells at steady state: one in the gas cap, and one in the oil column. Introduction Proper initialization is an important aspect of reliable reservoir simulations. The use of the Gibbs segregation condition generally cannot provide reliable initialization in hydrocarbon reservoirs. This is caused, in part, by the effect of thermal diffusion (caused by the geothermal temperature gradient), which cannot be neglected in some cases; thermal diffusion might be the main phenomenon affecting compositional variation in hydrocarbon reservoirs, especially for near-critical gas/condensate reservoirs (Ghorayeb et al. 2003). Generally, temperature increases with increasing burial depth because heat flows from the Earth's interior toward the surface. The temperature profile, or geothermal gradient, is related to the thermal conductivity of a body of rock and the heat flux. Thermal conductivity is not necessarily uniform because it depends on the mineralogical composition of the rock, the porosity, and the presence of water or gas. Therefore, differences in thermal conductivity between adjacent lithologies can result in a horizontal temperature gradient. Horizontal temperature gradients in some offshore fields can be observed because of a constant water temperature (approximately 4°C) in different depths in the seabed floor. The horizontal temperature gradient causes natural convection that might have a significant effect on species distribution (Firoozabadi 1999). The combined effects of diffusion (pressure, thermal, and molecular) and natural convection on compositional variation in multicomponent mixtures in porous media have been investigated for single-phase systems (Riley and Firoozabadi 1998; Ghorayeb and Firoozabadi 2000a).The results from these references show the importance of natural convection, which, in some cases, overrides diffusion and results in a uniform composition. Natural convection also can result in increased horizontal compositional variation, an effect similar to that in a thermogravitational column (Ghorayeb and Firoozabadi 2001; Nasrabadi et al. 2006). The combined effect of convection and diffusion on species separation has been the subject of many experimental studies. Separation in a thermogravitational column with both effects has been measured widely (Schott 1973; Costeseque 1982; El Mataaoui 1986). The thermogravitational column consists of two isothermal vertical plates with different temperatures separated by a narrow space. The space can be either without a porous medium or filled with a porous medium. The thermal diffusion, in a binary mixture, causes one component to segregate to the hot plate and the other to the cold plate. Because of the density gradient caused by temperature and concentration gradients, convection flow occurs and creates a concentration difference between the top and bottom of the column. Analytical and numerical models have been presented to analyze the experimental results (Lorenz and Emery 1959; Jamet et al. 1992; Nasrabadi et al. 2006). The experimental and theoretical studies show that the composition difference between the top and bottom of the column increases with permeability until an optimum permeability is reached. Then, the composition difference declines as permeability increases. The process in a thermogravitational column shows the significance of the convection from a horizontal temperature gradient.

scholarly journals Acoustic wave propagation in two-phase heterogeneous porous media

2013 ◽  
Vol 21 (3) ◽  
pp. 238-244
Author(s):  
J. I. Osypik ◽  
N. I. Pushkina ◽  
Ya. M. Zhileikin
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Acoustic Wave ◽  
Heterogeneous Porous Media ◽  
Acoustic Wave Propagation ◽  
Two Phase

Qualitative phenomenological investigation of the transient temperature gradient during gas turbine's hot section component cooling

2019 ◽  
Vol 234 (3) ◽  
pp. 709-715
Author(s):  
AM Tahsini
Keyword(s):  
Temperature Gradient ◽  
Life Expectancy ◽  
Transient Behavior ◽  
Temperature Gradients ◽  
Transient Temperature ◽  
Qualitative Model ◽  
Time Rate ◽  
Two Phase ◽  
Qualitative Phenomenological ◽  
Different Time Scales

In this study, the temporal variation of temperature gradient in the gas turbine hot section components in the transient process is raised, and according to its impact on life expectancy computations, the accuracy of the usual methods is investigated qualitatively. It is worth noting that in such two-phase problems, existing different time-scales prevent some common simplifications that are usually used for unsteady investigations like a quasi-steady assumption, and so there is no choice but to conduct coupled transient studies despite their high time-consuming manner. Hence, the phenomenological and qualitative model is introduced to analyze the cooling problem and show the transient behavior. The results show that during unsteady operations, if the time rate of changes is high, some considerable overshoots (more than 30%) of temperature gradients in hot sections may be ignored in common quasi-steady predictions, which must be predicted only by using the unsteady and coupled simulations.

Stability of planar rarefaction wave to the 3D bipolar Vlasov–Poisson–Boltzmann system

2019 ◽  
Vol 30 (01) ◽  
pp. 23-104 ◽  
Author(s):  
Shu Wang ◽  
Teng Wang
Keyword(s):  
Wave Propagation ◽  
Boltzmann Equation ◽  
Asymptotic Stability ◽  
Rarefaction Wave ◽  
Stability Result ◽  
Three Dimensions ◽  
Wave Patterns ◽  
Shock Profiles ◽  
Poisson Boltzmann ◽  
Math Phys

We investigate the time-asymptotic stability of planar rarefaction wave for the 3D bipolar Vlasov–Poisson Boltzmann (VPB) system, based on the micro–macro decompositions introduced in [T. P. Liu and S. H. Yu, Boltzmann equation: Micro–macro decompositions and positivity of shock profiles, Comm. Math. Phys. 246 (2004) 133–179; Energy method for the Boltzmann equation, Physica D 188 (2004) 178–192] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of basic wave patterns for bipolar VPB system in three dimensions.

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