Page 320 - Principles of Applied Reservoir Simulation 2E

Part V: Technical Supplements 305

no transition zones between different phases initially. The pressure and depth
at the gas-oil contact are PGOC and GOC, respectively. Similarly, for the water-
oil contact we have PWOC and WOC.
The initial pressure assigned to the gridblock in Figure 29-1 is determined
by the depth of the node (midpoint) relative to the respective contact elevations.
Let us define the depth of the block midpoint from datum as EL iJk. With
this definition, the pressure in the block is given by the following algorithm;
a. IfEL, yA <GOCthen
= PGOC + - GOC)/144
p g = p gJB gandP.. k p g (EL, /t
b. IfEL, 7fc >WOCthen
= + R /5 and
P w (P w*c ™ ' P gsc) w
P. jk = PWOC + Pw (EL,.., - GOC)/144

c. If GOC <; EL ljk < WOC then
PO = (Post + R so ' P«c)^o and
= PWOC + - GOC)/144
P ijk p 0 (EL iJk
The above algorithm should be reasonable for systems with initial transition
zones that are small relative to the total thickness of the formation.

Pressure Corrected to Datum
Pressure P(I, J, K) of gridblock I, J, K with mid-point elevation EL(I, J,
K) may be corrected to a datum depth PDATUM by specifying a pressure
gradient GRAD. The pressure at datum is given by PDAT(I, J, K) = P(I, J, K)
+ (PDATUM - EL(I, J, K))*GRAD.

29.2 Gravity-Segregated Saturation Initialization
A simple model of a gravity-segregated saturation distribution is
calculated when KSI = 1. For depths increasing downward, we calculate
elevations and thicknesses using the geometry shown in Figure 29-1 as follows:
Block BOT = EL + 0.5 *DZ
Block THICK = DZ