Automatic history matching method for simultaneous matching at pressure and its derivatives for two phase fluid flow in heterogeneous reservoir was developed. Adjoint method was used for calculating gradients of new objective function which consists of two parts; one is the original term and the other is the sum of differences between calculated pressure change rate and observed change rate. A set of two phase fluid flow equations which includes capillary pressure are used for calculating pressures and its change rate in the objective function. Quasi-Newton method (Self Scaling Variable Metric Method) was used as optimization algorithm. The one dimensional heterogeneous permeability distribution was estimated with the proposed method for a simple numerical model case. With this method, transient flow behavior in heterogeneous reservoir with multiple phase condition was applied for automatic history matching without too much computing time.

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