A new semi-analytical model developed allows making fast modeling of the heterogeneous reservoirs, drained by a single horizontal well with multiple transverse hydraulic fractures. It is assumed that: - the flow in the reservoir obeys Darcy law; - the fluid contains only one phase; - the reservoir permeability tensor is a function of the variable, directed along the horizontal wellbore; - the well trajectory is not a straight line; - the wellbore has finite conductivity. The proposed model is fast in terms of the execution time and the time required to build a new case. In the first section of this article a description of the solution method is given. The second part is dedicated to validating the proposed model. The recognized finite-difference hydrodynamic simulator (FDS) was used as reference software, though the model and FDS are not competitors because of their differing applicability. For this reason the execution times of the FDS and the Advanced Horizontal Well (AHW) model are not compared with one another. More significant is that using this model one can generate a new case in fifteen minutes even when the properties of the reservoir are complex and when there are multiple fractures. The primary focus of the AHW model is a single well productivity index analysis, and candidate selection for stimulation.