In addition, besides physical constraints, the sets of permeability and porosity must also satisfy constraints given by the geological model and by other information known about the reservoir. In This Work Parameters of the Inverse Problem in this work is a set of independent quantities that completely define the reservoir properties and skin factors of wells. In another word, we can compute reservoir properties and skin factors from a given set of such parameters. The reservoir model is three dimensional and described in an cartesian coordinate system and can have any irregular shape. The reservoir's boundary can be closed, constant pressure, or any combination of these boundaries.
Fluid properties can be strong, weak, or independent function of pressure.
Relative permeability is well-defined by Stone's Model. The number of wells, well pattern, well completion and direction of penetration are arbitrary. Neumann boundary condition is specified at wells. Specified flow rates are time dependence and can be single phase fluid or total of two phase fluid. This work explores the use of gradient method to minimize this function.