3 foroozesh barzegari ayatollahi

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Unformatted text preview: ( *) # $ $ $ 1 +$ % 3 3 ) $ * * 6 $ + ) ) - ) *( 9( : %% ' ( 3( * * - # % ( $ 6 % + # % $# )+ &% 8 + $# 8 ( -' %( % ' * .2 * * 3 # ) ) % $ $ " 4 5 +. 7/ +. " / * ) * $ %$ ' ) % $) 3 $ ( )% ( ! " %% ) %( *) $ + , -. $ # * $ %* 5$ $ +3 - + - ( ). ( ! 3 * % ) ) ( $ $) %() % ( % Foroozesh, Barzegari, Ayatollahi, Jahanmiri method, the fully implicit method utilizes the pressure and saturation implicitly in new time(n+1). Therefore, more running time is required and mathematical complexity is greater. ⎡ΔT n + 1Δφ n + 1 ⎤ = o ⎥ ik ⎢o ⎣ ⎦ ⎡ΔT n + 1Δφ n + 1 ⎤ = w ⎥ ik ⎢w ⎣ ⎦ Vp ik Δt Vp ik Δt n ⎛S ⎞ Δ t ⎜ o ⎟ + q oik ⎜B ⎟ ⎝ o ⎠ik ⎛S Δt ⎜ w ⎜B ⎝w n ⎞ ⎟ +q wik ⎟ ⎠ik These equations have been developed in residual format and the iterative method or approximate direct method were used in an attempt to solve them. Moreover, two factors have been considered: (1) the outlet effect, which requires that capillary pressure to approach zero at the sand face, and (2) the compatibility condition, as the vertical pressure gradeint in the well must be the same as the pressure gradient at the reservoir/wellbore boundary...
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