CMG是怎么根据油水和油气相渗数据计算出三相相渗曲线的？且计算的三相相渗曲线是只包括油的相渗，还是也包括气和水的相渗？涉及到那些方法？有没有考虑Stone模型？

CMG是根据Stone模型进行三相相渗曲线计算的。对于水湿油藏来说，油相为中间相，根据油水和油气相渗计算的三相相渗为油的相渗，而水的相渗直接从油水相渗表获得，气的相渗直接从油气相渗表获得。

在计算过程中，Stone模型是常用的相渗模型之一，它考虑了油、气和水在油藏中的分布和移动。 

采用的Stone 2和Stone 1模型有关介绍如下：

Stone’s Second Model

In Stone’s second model for K_ro as modified by Aziz and Settari, the oil relative permeability is computed as

K_rw and K_rg are always looked up as functions of S_w and S_g, respectively. K_row and K_rog are read from water-oil and gas-liquid relative permeability tables, respectively. In IMEX, K_row is tabulated as a function of S_w and K_rog is tabulated as a function of S_g. If *KROIL *STONE2*SWSG is in effect and values of S_w, S_o and S_g are given, K_row is looked up in the table as K_row(S_w) and K_rog is looked up as K_rog(S_g). When *KROIL *STONE2 *SO is in effect, K_row is looked up from the table as K_row(1 – S_o) and K_rog is looked up as K_rog(1 – S_wcon – S_o). *SO corresponds to having K_row and K_rog looked up directly as functions of S_o.

In some situations, the user may know K_row and K_rog as functions of S_o rather than of S_w and S_g. IMEX requires that the K_row and K_rog curves be entered as functions of S_wand S_g, respectively, but the user may enter K_row(S_w = 1 – S_o) as K_row(S_o) and K_rog(S_g = 1-S_wcon – S_o) as K_rog(S_o) and specify *KROIL *STONE2 *SO. The effect is exactly the same as having K_rog and K_row tabulated directly as functions of S_o.

Stone’s First Model

In Stone’s First Model as modified by Aziz and Settari, K_ro is computed as

where

So*= (S_o – S_om) / (1 – S_wcon – S_om)  

Sw*= (S_w – S_wcon) / (1 – S_wcon – S_om)

 Sg*= S_g / (1 – S_wcon – S_om)

for the “minimal” value S_om of the oil saturation, IMEX uses the linear function of S_g proposed by Fayers and Matthews (1984):

S_om(S_g) = ( 1 – a(S_g) ) S_orw + a(S_g) S_org,

Where

a(S_g) = S_g / (1 – S_wcon – S_org)

As in Stone’s second model, when the subkeyword *SO is specified, K_row(1 – S_o) and K_rog(1 – S_wcon– S_o) are used in the formula; otherwise, K_row(S_w) and K_rog(S_g) are used.

The LINEAR ISOPERM model was proposed by Baker (1988). In this method,K_ro(S_g, S_w) is defined in the region S_wcon < S_w < 1 – S_orw, 0 < S_g < (1 – S_orw – S_w)(1 – S_org – S_wcon) / (1 – S_orw – S_wcon), by specifying curves (isoperms) along which K_ro assumes a constant value. In particular, the isoperms are assumed to be straight line segments. For example, if

K_ro(S_g=0, S_w) = K_row(S_w) = 0.2 for S_w = S_w2

and

K_ro(S_g, S_wcon) = K_rog(S_g) = 0.2 for S_g =S_g2

then all points (S_g, S_w) on the line segment joining (0, S_w2) to (S_g2, S_wc),

(S_g, S_w) = (0, S_w2) + b (S_g2, S_wcon – S_w2), 0 < b < 1,

also have K_ro(S_g, S_w) = 0.2 .

The *SEGREGATED model corresponds to a model which uses a segregated assumption for the gas and water. S_o is assumed to be constant throughout the block and the water in the gas zone is assumed to be equal to the connate water saturation. Using volume fraction arguments and some algebraic manipulation

where K_rog is the oil relative permeability for a system with oil, gas and connate water (created as in *SWSG but looked up as in *SO), and K_row is the oil relative permeability for a system with oil and water only (created as in *SWSG but looked up as in *SO). This model gives similar results as STONE2 on the IMEX templates. However, on a large field problem, significant differences were noted both in results and in CPU times.

With pseudo-miscible option, *KROIL only determines the immiscible K_ro calculation. The miscible K_ro is calculated separately in pseudo-miscible model (Appendix E).