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CO2 Sequestration through Deep Saline Injection and ...

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Light Intensity (W/m^2) a<br />

50<br />

45<br />

40<br />

35<br />

30<br />

25<br />

20<br />

15<br />

10<br />

5<br />

0<br />

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1<br />

Distance (cm)<br />

Figure 7<br />

Light Intensity Distribution between Plates with Reflection Considered<br />

Equation 8 can be used to iteratively calculate the apparent light intensity at x=0. Here, x is the<br />

position between plates, d is the distance between the parallel plates, <strong>and</strong> Iapp denotes the<br />

apparent light intensity. The remaining parameters are the same as those in Eqs. (3) <strong>and</strong> (4).<br />

The light not utilized in photosynthesis can be calculated by keeping track of Iapp with pct set to<br />

unity <strong>and</strong> subtracting Iapp with the desired pct once the iteration is complete.<br />

2 ⎛ −2ε<br />

mCd<br />

⎞<br />

Iappnew = I0+ pct ⋅Iapp exp ⎜<br />

⎝( Kc + C)( Kx + d)<br />

⎠<br />

⎟<br />

The apparent light intensity calculated in the iteration is then used to calculate the light intensity<br />

at the boundary with illumination from both boundaries (x=0 <strong>and</strong> x=d). This can be calculated<br />

by adding the apparent light intensity to the transmitted light intensity using Eqs. (3) <strong>and</strong> (4) with<br />

x set to the spacing between the plates <strong>and</strong> Io set to the apparent light intensity found using<br />

Eq.(8). This is shown in Eq. (9). The input light intensity can then be adjusted until the light<br />

intensity at the boundaries is at the saturation light intensity.<br />

( )<br />

( )<br />

⎛ ⎛ −ε<br />

mCx<br />

⎞ ⎛ −εmC d −x<br />

⎞⎞<br />

I = Iapp<br />

⎜exp + exp<br />

⎟<br />

⎜ ⎜ ⎟ ⎜<br />

( Kc + C)( Kx + x) ⎜(<br />

Kc + C)( Kx + d −x<br />

) ⎟<br />

⎝ ⎠<br />

⎟<br />

⎝ ⎝ ⎠⎠<br />

18<br />

(8)<br />

(9)

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