3. Basic transport equations

samples for estimating the dissociation rate of synthesized CO2 hydrate (CO2H) reported by [1]. To decrease the CO2 concentration in the air, carbon dioxide capture and storage (CCS) is regarded to be an effective way. One concept of CCS is to store CO2 in gas hydrate in subseabed geological formation, as was illustrated by [6]. Besides, many studies about the formation and dissociation of CO2 hydrate (CO2H) while stored in the deep ocean or geologic sediment have been introduced. In particular, flow and transport in sediment is multidisciplinary science including the recovery of oil, groundwater hydrology and CO2 sequestration. It reported the measurements of the dissociation rate of well-characterized, laboratory-synthesized carbon dioxide hydrates in an open-ocean seafloor [5]. The pore effect in the phase equilibrium mainly due to the water activity change was discussed in [7]. The reactive transport at the pore-scale to estimate realistic reaction rates in natural sediments was discussed in [3]. This result can be used to inform continuum scale models and analyze the processes that lead to rate discrepancies in field applications. Pore-scale model is applied to examine engineered fluids [4]. Unstructured mesh is well suited to pore-scale modeling because of adaptive sizing of target unit with high mesh resolution and the ability to handle complicated geometries [17, 18]. Particularly, it can easily be coupled with computational fluid dynamics (CFD) methods, such as finite volume method (FVM) or finite element method (FEM). Unstructured tetrahedral mesh used to define the pore structure is discussed in [19]. Another case includes a numerical simulation of laminar flow based on FVM with unstructured meshes was used to solve the incompressible, steady Navier-

28 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

The objective of this work is to develop a new pore-scale model for estimating the dissociation rate of CO2H in homogeneous porous media. To cooperate with molecular simulation and field-scale simulators, we aim at establishing pore-scale modeling to analyze the simultaneous kinetic process of CO2H dissociation due to non-equilibrium states. Major assumptions in this

1. Only dissociation occurred at the surface, no any formation occurred immediately with

2. CO2 dissociated at the surface is assumed to be dissolved into liquid water totally without

3. The surface structure does not collapse with the dissociation of CO2H at the surface of pellets.

In this study, the dissociation flux (F1) is assumed to be proportional to the driving force, the

<sup>F</sup><sup>1</sup> <sup>¼</sup> <sup>k</sup>blRTln CHsol

CI 

(1)

Stokes equations through a cluster of metal idealized pores by [20].

4. Homogeneous face-centered packing of multi-CO2H pellets.

5. Single phase flow coupled with mass, heat, and momentum transfers.

study are listed as below:

considering the gas nucleated.

2. Dissociation modeling at the surface

free energy difference (Δμ) introduced by [6], presented as

dissociation.

Flow in the porous media around CO2H is governed by the continuity and the Navier-Stoke's equations. The advection-diffusion equations of non-conservative type for mass concentration C and temperature T are also considered.

$$\nabla \cdot \mathbf{u} = 0 \tag{3}$$

$$\frac{\partial \mathbf{u}}{\partial t} + \nabla \cdot (\mathbf{u} \mathbf{u}) = -\nabla P + \frac{1}{\text{Re}} \nabla \cdot \left[ \nabla \mathbf{u} + (\nabla \mathbf{u})^T \right] + \frac{\rho\_w}{\text{F} \mathbf{n}^2} \mathbf{g} \tag{4}$$


Table 1. Parameters used in this study.

$$\frac{\partial \mathbb{C}}{\partial t} + \mathbf{u} \cdot \nabla \mathbb{C} = \frac{1}{\text{Re} \mathbb{S} \mathbf{c}} \nabla^2 \mathbb{C} \tag{5}$$

where Q\_

conductivity equation.

rHC<sup>0</sup> p

p) of 2080:0 JK�<sup>1</sup>

6. Computational conditions

density of CO2H (rH) is given as 1116:8 kgm�3.

where <sup>α</sup><sup>H</sup> <sup>¼</sup> <sup>λ</sup><sup>H</sup>

layer is listed below:

hydrate (C<sup>0</sup>

of hydrate, HL, is interpolated from [2] as

where TI is the surface temperature. Then, we have

<sup>H</sup> (¼ HLF1, where HL is the latent heat of hydrate dissociation) is the dissociation heat

Direct Numerical Simulation of Hydrate Dissociation in Homogeneous Porous Media by Applying CFD Method…

HL ¼ 207; 917 � 530:97 � TI (9)

<sup>∂</sup>x<sup>2</sup> (11)

http://dx.doi.org/10.5772/intechopen.74874

ms�2, the heat capacity of

m�1. The

(10)

31

transferred to the CO2H, λ<sup>H</sup> is the thermal conductivity of hydrate. Dissociation heat per mole

TI <sup>¼</sup> <sup>λ</sup>LhHTL <sup>þ</sup> <sup>λ</sup>HhLTH � <sup>207</sup>; <sup>917</sup>∙FcalhLhH λLhH þ λHhL � 530:97∙FcalhLhH

where TL and TH are the temperatures defined at the centroids cell in the aqueous phase and solid hydrate, respectively; hL and hH are half widths of centroid in the aqueous phase and solid hydrate, respectively. Besides, the temperature in the pellet is calculated by using the heat

Two types of cells, tetrahedrons and triangular prisms, are applied in the present unstructured grid system, as introduced in Figure 2. In detailed, the surface of hydrate uses prism. Both the flow field and inside the pellet are tetrahedral meshes. Upward is the inflow where initially the uniform velocity profile is adopted. Prism mesh and no-slip condition are imposed at the surface of the pellet. To analyze more detailed mass and heat transfer simulatneously, one cell-layer of the prisms that attached to the CO2H surface is divided into at least five very thin layers as referred in [8] for high Prandtl or Schmidt number. The basic parameters of computation are denoted in Table 1. The initial values of dimensionless parameters are listed in Table 2 at the temperatures from 276.15 to 283.15 K. Reynolds number, Schmidt number, and Prandtl number function of the temperature or pressure are listed in Table 2. The minimum grid size of this computational model is listed in Table 3. Lm, Lc, and LT are the applied mesh thicknesses. δm, δc, and δT are the thickness of momentum, concentration, and thermal boundary layers, respectively. The relationship between δm, δc, and δT quoted from the theory of flat plate boundary

∂2 T

is the thermal diffusivity of CO2H. These relative properties of CO2H are quoted

, and the thermal conductivity (λH) of 0:324 WK�<sup>1</sup>

∂T <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>α</sup><sup>H</sup>

from [9], the thermal diffusivity of aqueous phase (αH) of 1:<sup>38</sup> � <sup>10</sup>�<sup>7</sup>

kg�<sup>1</sup>

$$\frac{\partial T}{\partial t} + \mathbf{u} \cdot \nabla T = \frac{1}{\text{Re}\text{Pr}} \nabla^2 T \tag{6}$$

where the viscosity, diffusivity, and thermal conductivity of pure water are included in dimensionless parameters such as the Reynolds number, the Schmit number, and the Prandtl number, which are interpolated as functions of temperature and are updated at every computational time step as summarized in Table 1. U and d (=0.001 m) are the velocity of inflow and diameter of hydrate pellet.
