Patent ID: 7505882

Claim:
A method for modeling with a reservoir simulator by solving a non-linear S-shaped function F=ƒ(S) which is representative of a property S in a physical subterranean reservoir system having fluid flow therein, the S-shaped function having an inflection point S c and a predetermined value of F to which ƒ(S) converges, the method comprising the steps of: a) by a computer, selecting an initial value S v+1 as a potential solution to the function ƒ(S); b) performing a Newton iteration (T) on the function ƒ(S) at S v to determine a next iterative value S v+1 ; c) determining whether S v+1 is located on the opposite side of the inflection point S c from S v ; d) setting S v+1 =S l , a modified new estimate, if S v+1 is located on the opposite side of the inflection point of ƒ(S) from S v ; e) determining whether S v+1 is within a predetermined convergence criteria; f) setting S v =S v+1 if S v+1 is not within a predetermined convergence criteria; g) repeating steps (b)-(f) until S v+1 is within the predetermined convergence criteria; h) selecting S v+1 as a satisfactory solution S to the S-shaped function F=ƒ(S); and i) utilizing the satisfactory solution S to the S-shaped function ƒ(S) for modeling the fluid flow within the subterranean reservoir with the reservoir simulator.