Abstract: Analytical and semi-analytical formulas for production calculation of horizontal wells generally require the reservoirs being homogeneous and well trajectory parallel reservoir boundary,which make them unsuitable for complex trajectory wells.In this paper,the reservoir is divided into several regions based on well trajectory and permeability.Each region has different permeability,and the well trajectory within the region may be unparallel with the boundary.The point source function method is introduced to establish the segmented integral similarity solution for the production of complex-trajectory well in heterogeneous and constant-pressure-boundary reservoir,and the Ouyang model is used to calculate the pressure loss along the wellbore.This method can avoid numerical dispersion in simulation,and provide a fast production evaluation with fewer input parameters.Case study result shows that flow rate in wellbore with complex trajectory increases from toe to heel,the reservoir inflow rate is different in each segment due to reservoir heterogeneity and is high in the high permeability reservoir region,the pressure drop within the wellbore also increases from toe to heel and is different in each wellbore segment due to the uneven distribution of flow rate.The result of this method is consistent with that of Eclipse,confirming its feasibility.In comparison with the metered oil production in field,the calculated production of complex trajectory well has an error of less than 5%,showing that it can satisfy the demand of real-field reservoir engineering research.

Key words: heterogeneous reservoir, point-source function, complex-trajectory well, production calculation