A horizontal well in a composite system with planar interfaces

Abstract

The goal of this work is to consider the situation where the well intersects a partial hydrologic barrier. A two-region composite system where a horizontal well taps both regions is considered. The method of sources and sinks is used to build the well model to determine the drawdown in the aquifer. A model to examine a system with several contiguous regions is presented. The viability of the mathematical model where a horizontal well traverses two regions with distinct properties is demonstrated through illustrative examples of the characteristics of the drawdown response and its logarithmic derivative. Further it is shown that the numerical computations match asymptotic limits and that solutions may be correlated with homogeneous-aquifer solutions under appropriate circumstances. If the well were to tap both regions, it behaves as if its effective length is the ratio of the sum of the conductivity weighted well lengths and the average conductivity of the system. Three flow regimes with characteristic signatures over specific time intervals may be evident. Equivalent system parameters that are useful as a starting point to analyze data are provided. The influence of the trajectory of the well in a composite system is documented. In addition to quantitative results, it is shown that the long-term drawdown response in terms of the logarithmic derivative is independent of the trajectory of the well and no particular signatures are evident to suggest that the well traverses regions with distinct properties. Thus, production logs may be particularly useful.