This paper discusses an alternative approach to a horizontal well (HW) productivity evaluation. The approach is based on the exact solution to a task of the horizontal well productivity evaluation in a 3D reservoir with correct evaluation of all boundary conditions including the no cross-flow conditions at the top and bottom of the reservoir.
Validation of the new equation for the HW productivity is made by means of special asymptotic analysis. In particular, it is shown that the obtained solution asymptotically approaches well-known solutions for cases of simple flow geometry.
However, comparison of the new equation with solutions available from the literature shows some differences between them. We believe that this is mostly due to a more accurate handling of boundary conditions in the new solution. For example, comparison with Joshi’s solution [1, 2] shows that a newly obtain solution gives higher production rates for short length of horizontal sections (L in the order of tens of meters) and lower rates for long horizontal wells in thin reservoirs (Lπh, L⊇re). In the latter case reduced production rate (as compared with ) was obtained with due regard for a no cross-flow conditions at the top and bottom of the pay interval. Higher production rates in case of short length of horizontal sections can be caused by a dominating effect of 3D flow in the vicinity of a well, especially in case of a thick pay interval. The highest discrepancy between solutions reported in the literature and proposed in this paper found to be up to 19% for long wells and can exceed 30% for short sidetracks (5-20 m). More detailed analysis of similarities and differences between several solutions is given in the next sections.
A generalized solution for the inflow performance of a HW accounting for the directional values of the reservoir permeability (an orthotropic reservoir) is also given in the paper. In particular, it is shown that in case of anisotropic reservoir orientation of a horizontal well in plane has a strong impact on its productivity