Multiply-fractured horizontal wells are an efficient way to produce from tight gas, shale gas and tight oil formations. In this work, we present a linear composite model with a dual porosity inner zone to model production from a multiple fractured horizontal well. The composite solution uses linear dual porosity flow solution for the inner reservoir and a linear single porosity solution for the outer reservoir combined with continuity of pressure and flux at their interface. Solution to the problem was obtained in Laplace space. The solution that we have obtained is simple and fast, yet effective and can be applied to model production from fractured horizontal wells.
For the cases of interest, we observe three linear flow periods in this model. The first linear flow is from the fractures into the wellbore, followed by linear flow in the matrix to the fractures and lastly linear flow in the outer single porosity reservoir to the inner reservoir. Each of these three linear flow periods is separated by a transition depending on the properties of the fracture, matrix and the outer reservoir.
We use a numerical simulator to examine the validity of some of the assumptions made in the development of the work. While the model that we have made consists of only linear flow solutions, the numerical model accounts for two dimensional flows in all media. New solutions are presented in the form of type curves.