By Jan Martin Nordbotten
Regardless of the massive examine attempt in either public and advertisement businesses, no textbook has but been written in this topic. This booklet goals to supply an summary to the subject of Carbon seize and garage (CSS), whereas whilst concentrating on the dominant approaches and the mathematical and numerical tools that must be hired with a purpose to study the suitable structures. The booklet truly states the carbon challenge and the position of CCS and carbon garage. Thereafter, it offers an creation to unmarried section and multi-phase movement in porous media, together with essentially the most universal mathematical research and an summary of numerical tools for the equations. a substantial a part of the booklet discusses the fitting scales of modeling, and the way to formulate constant governing equations at those scales. The ebook additionally illustrates genuine global facts units and the way the tips within the ebook will be exploited via mixtures of analytical and numerical techniques.
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Additional info for Geological Storage of CO2: Modeling Approaches for Large-Scale Simulation
One particular concern arises when temperatures and pressures are near the critical point of the ﬂuid, so that density becomes a strong function of temperature as well as pressure. 2 Conservation Laws and Governing Equations 35 leads to additional equations that may need to be solved simultaneously with Darcy’s law and mass conservation. Let us denote temperature by the symbol Θ. We begin by noting that ﬂuid density is usually a function of temperature as well as pressure. 19), inclusion of the dependence of density on temperature gives an additional term when the time derivative of density is expanded, resulting in the following equation: ρcΣ ∂p ∂Θ ⎛ k ⎞ + ρ cΣ , Θ − ٌ ⋅ ⎜ ρ ( ٌ p − ρ g )⎟ = ψ , ⎝ ⎠ ∂t ∂t μ where the total thermal contribution to volume change is deﬁned analogously to the total compressibility, cΣ ,Θ ≡ φ ∂ρ ∂φ + .
The underlying idea is to identify a speciﬁc region of space and to make the simple observation that over some time period, the change of mass of a particular substance within the identiﬁed region of space is equal to the amount of mass that enters (or leaves) through the entire boundary of the region, plus (or minus) any mass that appears (or disappears) from within the region without passing through its boundaries. This simple statement forms the basis for the equation of mass conservation. 1 Mass Conservation In order to apply the concept of mass conservation, and to derive a set of equations that can be solved for variables of interest, we begin this section with deﬁnitions of the properties and functions we will need to describe ﬂow in porous media.
Note that we will use vector notation as outlined above consistently throughout the book; a concise review of this notation is provided in the Appendix. 26 Chapter 2 Single-Phase Flow in Porous Media When deriving Darcy’s law from ﬁrst principles, we get the ﬁnal extension of Darcy’s equation for single-phase ﬂow: u=− k ( ٌ p + ρg ٌ z ) . 8). 6) is written in the more general matrix notation. Then we can substitute the expanded representation for both κ and ٌh into Darcy’s equation. 9) in the case where density is constant.