Kassem Ghorayeb

Double diffusive convection in a vertical rectangular cavity

In the present work, we study the onset of double diffusive convection in vertical enclosures with equal and opposing buoyancy forces due to horizontal thermal and concentration gradients (in the case GrS/GrT=−1, where GrS and GrT are, respectively, the solutal and thermal Grashof numbers). We demonstrate that the equilibrium solution is linearly stable until the parameter RaT|Le−1| reaches a critical value, which depends on the aspect ratio of the cell, A. For the square cavity we find a critical value of Rac|Le−1|=17 174 while previous numerical results give a value close to 6000. When A increases, the stability parameter decreases regularly to reach the value 6509, and the wave number reaches a value kc=2.53, for A→∞. These theoretical results are in good agreement with our direct simulation. We numerically verify that the onset of double diffusive convection corresponds to a transcritical bifurcation point. The subcritical solutions are strong attractors, which explains that authors who have worked pr...

Modeling Multicomponent Diffusion and Convection in Porous Media

Summary Numerical investigations of diffusion and convection in multicomponent hydrocarbon mixtures in two-dimensional ~2D! crosssectional ( x,z) porous media are performed using the finitevolume method. Spatial discretization is performed by a secondorder centered scheme. It is shown that methane, unlike in binary hydrocarbons where it often segregates towards the bottom-hot side of the porous media, may be at higher concentration at the cold-top side in ternary mixtures and in multicomponent reservoir fluids. This behavior, which is consistent with oilfield data, is due to competing diffusion mechanisms which have not been properly accounted for in the past. It is also demonstrated that convection may significantly affect the compositional variation in some hydrocarbon reservoirs. Depending on fluid mixtures, a weak convection may drastically change compositional variation.

Interpretation of the Unusual Fluid Distribution in the Yufutsu Gas-Condensate Field

It is generally believed that at steady state, a heavy fluid mixture cannot float, without motion, at the top of a light fluid mixture in a cavity. The expectation is that because of pressure diffusion, segregation occurs with the light fluid at the top and the heavy fluid at the bottom. We present, for the first time, an extensive set of measurements in 5-km vertical wells in a large hydrocarbon formation of 1-km thickness with horizontal dimensions on the order of several kilometers that show a high-density fluid mixture at the top of a light-density fluid mixture at steady state. The data in the 5-km wells show liquid in the middle, and vapor at the top and bottom. In the hydrocarbon formation, there is a gradual decrease of density with depth. A theoretical model based on the thermodynamics of irreversible processes is used to provide an interpretation of the unusual density variation vs. depth both in the hydrocarbon formation and in the long wells, as well as the unusual species distribution in the hydrocarbon formation. The results reveal that thermal diffusion (caused by geothermal temperature gradient) causes the segregation of heavy components in the subsurface fluid mixture to the cold side in the Earth (that is, the top), overriding pressure and molecular diffusion (Fickian diffusion). As a consequence of the competition of these three diffusion effects, a heavy fluid mixture can float at the top with a light fluid mixture underneath. In the past, thermal diffusion has been thought of as a second-order effect. For the fluid mixture in our work, thermal diffusion is the main phenomenon affecting the spatial density and species distribution.

Onset of oscillatory flows in double-diffusive convection

A numerical study is presented of unsteady double-diffusive convection in a square cavity with equal but opposing horizontal temperature and concentration gradients. The boundary conditions along the vertical side-walls are imposed in such a way that the buoyancy ratio N = GrS⧹GrT is equal to −1, where GrS and GrT are the solutal and thermal Grashof numbers, respectively. In this situation, steady-state convective flow is stable up to a threshold value Grc1 of the thermal Grashof number which depends on the Lewis number Le. Beyond Grc1, oscillatory convective flows occur. Here we study the transition, steady-state flow–oscillatory flow, as a function of the Lewis number. The Lewis number varies between 2 and 45. Depending on the values of the Lewis number, the oscillatory flow occurring for GrT slightly larger than Grc1 is either centro-symmetric ( for Le ⩾ 17) or asymmetric single frequency flow ( for Le ⩽ 17) . For larger values of the thermal Grashof number, the two regimes occur for fixed values of GrT and Le. Furthermore, computations show that Grc1 reaches a minimum equal to 4.75×104 for Le ≈ 7

Double diffusive instability in an inclined cavity

Double diffusive convection in a rectangular two-dimensional cavity with imposed temperatures and concentrations along two opposite sidewalls is considered. The study is performed for two-dimensional cavities in which the thermal and solutal buoyancy forces have the same magnitude, but are of opposite sign. The influence on the convective instability of the aspect ratio A (height/length) of the cavity and the cavity inclination α with respect to gravity is discussed. The onset of convection is computed for an infinite layer and compared to that for bounded boxes. The study is completed by the continuation of bifurcating solutions. It is found that, due to centrosymmetry, steady bifurcations are either pitchfork or transcritical depending on A and α. However, a primary pitchfork bifurcation is found to create unstable steady solutions, even if it is the first bifurcation. For the aspect ratios we studied, and close to the onset of convection, the stable solutions are mainly one-roll structures that can be ...

Two-Phase Multicomponent Diffusion and Convection for Reservoir Initialization

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.

Uncertainty Management in Field Development Planning

An field optimal development concept is selected and supported using the following approach: - Exploring possible subsurface realizations based on static and dynamic uncertainties - Building alternative development concepts based on development decisions to be made and the corresponding available options - Testing the robustness of these concepts to different subsurface realizations. - Selecting the optimal development concept and articulating its credentials using value drivers.