By Oliver C Mullins; et al
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Extra info for Asphaltenes, heavy oils, and petroleomics
Chemical intuition would be utilized to define the chemical families, while the mathematical machinery of standard chemometric methods would be utilized to generate the structure-function matricies. Petroleomics proceeds in the same way that analysis of the genome can identify likely health problems. With a new oil sample, one could obtain the petroleome and predict likely “health” problems of this oil. The health of the crude oil includes all aspects in the production, transportation, refining, and sale of the end products.
5) 0 G(θ0 , ϕ0 |θ, ϕ, t) can be interpreted as the time evolution of the probability → W (θ, φ, t) with − μ oriented in (θ0 , φ0 ) at t = 0. 6) [1 + 2P2 (cos θ0 )], 4π where P2 is the Legendre polynomial of second order. It is therefore convenient to expand the Green’s function in terms of Legendre functions28 W (θ0 , φ0 , t) = G(θ0 , φ0 |θ, φ, t) = ∞ l ∗ e−l(l+1)Dt Yl,m (θ0 , φ0 )Yl,m (θ, φ). 7) l=0 m=−l Applying boundary conditions and the normalization conditions together with the starting condition one derives that only one expansion coefficient c2,0 (t) is non zero28 c2,0 (t) = e−6Dt .
3), yield in the most general case a five-exponential decay for the anisotropy r (t)32 5 r (t) = αi e − τt i . 28 In such a case, the diagonalized diffusion tensor will have only two elements which we will label as D|| and D⊥ . These two elements govern the molecular relaxation due to Brownian motion parallel and perpendicular to the symmetry axis respectively. The correlation times of the anisotropy decay can be expressed as28 τ1−1 = 6D⊥ τ2−1 = 5D⊥ + D|| τ3−1 = 2D⊥ + 4D|| . 21 a,b) where D is again D= kT , 6V η the diffusion coefficient calculated for a sphere under the same conditions of volume, temperature and viscosity as the ellipsoid, ρ is the ratio of the longitudinal 32 Henning Groenzin and Oliver C.