Darcy flows

At 10 MPa and 35 °C, C02 has a density of approximately 700kg/m3. Under these conditions, a cubic meter of sandstone with 10% porosity contains approximately 70 kg of C02 if the pore space is completely filled by C02. However, saturation of C02 is not complete, and some brine remains in the invaded pore spaces (Saripalli McGrail 2002 Pruess et al. 2003). In addition, non-uniform flow of C02 bypasses parts of the aquifer entirely. Darcy-flow based analytical and numerical solutions are used to evaluate some of these effects by simulating the advance of the C02 front over time-scales of decades to hundreds of years and over lateral distances of tens to hundreds of kilometers. To account for the extreme changes in density and viscosity of C02 with pressure and temperature, these models must incorporate experimentally constrained equations of state (Adams Bachu 2002). 

In practice we measure changes in pressure and salt concentration, rather than chemical potential, and it can be helpful to think of transport coefficients in terms of Darcy flow and diffusion. We define xs = ns/(nw + ns), where nw, ns are the number of moles of water and salt, and write the change in chemical potential of salt across the membrane as... 

Pressure applied to the external solution would also increase the pressure inside the capsule, and in the absence of fluid compressibility there would be no change in the capsule volume. Without access to the inside of the capsule we cannot apply a pressure difference to investigate Darcy flow through the membrane. One possiblity, yet to be tested experimentally, is to add to the external solution an uncharged polymer which cannot pass through the membrane. The external chemical potential of water is thereby reduced [9], and the resulting flow out of the capsule can be shown to depend upon the permeability k of the membrane. 

Masud, A. and Hughes, T.J.R. (2002) A stabilized finite element method for darcy flow. Comput. Methods Appl. Mech. Eng. 191, 4341-4370... 

Therefore, the equations governing the velocity components in Darcy flow are ... 

This is the equation that has traditionally been used to obtain solutions for two-dimensional potential flows. The methods used to obtain such solutions can therefore be used to find the velocity distributions in Darcy flows. 

The above equations for the pressure variation in Darcy flow involve the permeability, K. This quantity is mainly dependent on the porosity of the material, , i.e., the ratio of the pore volume. Vp, to the total volume, V, of the porous material, and on the mean diameter of the particles. The relation between these quantities depends on the shape of the particles and how they are arranged. If, for example, the particles... 

Using the Darcy flow model and the Boussinesq approximation, the governing equations are ... 

In addition to the modifications to the Darcy flow model, it is also sometimes necessary to note that the apparent thermal conductivity. ka, as used above arose from conduction through the fluid and solid media. This was the basis for Eq. (10.36). However, in fact, as tfie fluid flows through the tortuous paths between the solid... 

Numerical models for electrochemical process performance assessment or dimensioning generally assume uniform properties or one-dimensional property variations. For example, plug flow with axial dispersion is usually assumed within fdter-press electrolysers [1], whereas a Darcy flow model is commonly used within the gas diffusion layer of PEM electrolysers and fuel cells [2],... 

If a fault is hydrocarbon-wet or the pressure difference across it exceeds the capillary entry pressure, it will leak and become a permeability barrier to flow. The probability that a hydro carbon column will be retained by a permeability barrier over geological time is a function of the rate of flow through the fault. In the case of Darcy flow, the rate of flow (Q) per unit area is proportional to the pressure gradient (AF/Ax) across the fault, the fault permeability (/c), and inversely proportional to the fluid viscosity (a) ... 

Simple one-dimensional reservoir models (two phase Darcy flow) indicate that, in general, the flow rates across permeable fault seds will be too high to sustain high pressure gradients or corresponding differences in hydrocarbon column lengths over geo-... 

To illustrate these top seal leakage dynamics, model calculations of simple Darcy flow were per-... 

We used the data of nine gas fields located over the North German part of the European Upper Carboniferous Basin (see Fig. 1, black dots named A-G and M and N) to simulate the vertical flow of methane over the last 1(X) myr, using a diffusion model and a Darcy flow model. From the results obtained we determined the physical process driving gas through rocks. 

Results of modeling case histories with Darcy flow... 

Table 3 Results from the history matches cases A-G and M and N using diffusion and Darcy flow of methane gas balances, diffusion constants and rock salt permeabilities ...

Fig. 6. History match of cases A-G and M and N over the last 100 myr with Darcy flow gas balances obtained for vertical flow of methane.

Calibration of the Darcy flow model the resulting rock salt seal permeabilities and their significance... 

With the published laboratory data, strong support is obtained for Darcy flow to be the mechanism driving gas through rocks. Additionally the boundary condition put on the migration process by the evidence in Fig. 2 is fulfilled Darcy flow requires a strict dependency of methane quantities stored in reservoirs on those generated over the same area and on the thickness of seals. 

Impact of Darcy flow of gases on physics, exploration for gas and atmospheric research... 

If the flux of pore water relative to the sediments can be determined, one can calculate the effective permeability of pressure seals for different potenti-ometric gradients, assuming Darcy flow (see Appendix A). 

The Brinkman equation (1) transitions properly from Stokes flow (in the absence of inertia) to Darcy flow in a porous medium ... 

This approach was also found to correlate power law fluid flow through granular beds of column to particle diameter ratio 5.8 < D/ds < 20 in the creeping (Darcy) flow regime (99). 

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