Analytical coupled axial and radial productivity model for steady-state flow in horizontal wells

Abstract

A new analytical model for coupled radial well inflow and axial flow has been developed and applied to horizontal well productivity calculations. This analytical model results in a linear pressure distribution in the axial direction and a logarithmic pressure distribution in the radial direction. The analytical solution is investigated for two special cases where a one-dimensional analytical solution already exists. It is proven that the model reduces to the classical radial inflow model in the case when the axial pressure gradient is zero and to the linear Darcy equation when there is zero radial inflow. The new equations are also used to evaluate the well flow rates when the skin effect is included. The analytical solution verifies that the axial flow in the reservoir, in general, cannot be ignored, particularly in reservoirs with high permeability and high well productivity. The analytical model is used to quantify the importance of frictional losses in well productivity calculations. An example on how the analytical model can be used in hand calculations to determine well productivity and frictional losses is presented.

Productivity Models of Infill Complex Structural Wells in Mixed Well Patterns

“…In the semi-analytical model, each branch of the complex structural well is divided into several infinitesimal sections, thus the productivity can be obtained by solving the system of linear equations combined with fluid flow rate and pressure drawdown for each infinitesimal in the wellbore. However, these methods mainly focus on building models of single well or regular well patterns, and little research has been conducted on the seepage theory of mixed well patterns of vertical wells and complex structural wells [24][25][26][27][28][29][30]. In view of the field problems involving the productivity prediction of infill wells in irregular well patterns, there are limitations in current mathematical models [31][32][33][34][35].…”

Productivity Prediction Model for Stimulated Reservoir Volume Fracturing in Tight Glutenite Reservoir Considering Fluid-Solid Coupling

“…Doe et al (2013) carried out discretization of complex fracture network in the fractured region, established the productivity model of multiple porosity media, and calculated the contribution rate of natural fractures in the productivity. Cao et al (2015) established a full analytical mathematical productivity model considering friction, and compared and analyzed the difference between the analytical method and the finite-difference solution results, proving that the model is more accurate in spatial discretization and other aspects (Johansen et al, 2015). Taking the tight reservoir of Daqing Oilfield as the study object, Hu et al (2017) established a numerical model of production capacity based on the theory of unsteady seepage mechanics and superposition principle, which was used to calculate and analyze the production capacity of fracturing horizontal wells.…”