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Chap5(MB)Lec - Chapter 5Material Balances Microscopic...

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Chapter 5…Material Balances Microscopic balances (pde) Balances over slice in time and space Macroscopic balances (ode or equation) Over entire reservoir and time slice Over entire reservoir and entire time
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Microscopic Balances... 1D radial flow + flow in - r-direction material balance on components (j=oil, gas, water) Δ r r Flow in Flow out h Fig. 5-1 Control volume Drainage area or volume
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Microscopic Balances... Δ r r Flow in Flow out h present-initial=in- out Amount of j in CV at t+ Δ t Amount of j in CV at t Amount of j into CV during Δ t Amount of j from CV during Δ t Present Initial In Out
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Microscopic Balances... Δ r r Flow in Flow out h present-initial=in- out Amount of j in CV at t+ Δ t Present = φ hC j ( ) t + Δ t π r + Δ r ( ) 2 r 2 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ = φ hC j ( ) t + Δ t π r 2 + 2 r Δ r + Δ r ( ) 2 r 2 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ 2 π r Δ r φ hC j ( ) t + Δ t
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Microscopic Balances... Δ r r Flow in Flow out h present-initial=in- out Amount of j in CV at t+ Δ t Initial = φ hC j ( ) t π r + Δ r ( ) 2 r 2 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ = φ hC j ( ) t π r 2 + 2 r Δ r + Δ r ( ) 2 r 2 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ 2 π r Δ r φ hC j ( ) t
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Microscopic Balances... Δ r r Flow in Flow out h present-initial=in- out In = 2 π r + Δ r ( ) hN j ( ) r + Δ r Δ t = 2 π h rN j ( ) r + Δ r Δ t Amount of j into CV during Δ t Amount of j from CV during Δ t From = 2 π h rN j ( ) r Δ t
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Microscopic Balances... Δ r r Flow in Flow out h present-initial=in- out 2 π r Δ r φ hC j ( ) t + Δ t 2 π r Δ r φ hC j ( ) t = 2 π h rN j ( ) r + Δ r Δ t 2 π rN j ( ) r Δ t
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Microscopic Balances... Δ r r Flow in Flow out h present-initial=in- out 2 π r Δ r φ hC j ( ) t + Δ t 2 π r Δ r φ hC j ( ) t = 2 π h rN j ( ) r + Δ r Δ t 2 π h rN j ( ) r Δ t φ C j ( ) t + Δ t − φ C j ( ) t Δ t = rN j ( ) r + Δ r rN j ( ) r Δ r
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Microscopic Balances...
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