Deep insights to transient pressure behavior and stabilized productivity index of multilateral wells in laterally and spatially anisotropic reservoirs

Abstract

The objective of this paper is focusing deep insights on stabilized productivity index (PI) and transient pressure behaviors and flow regimes of multilateral wells. It introduces an integrated approach for the performance of reservoirs depleted by multilateral wells extending in arbitrary trajectories. The study introduces new practical solutions for estimating stabilized pseudo-steady state (PSS) productivity index and starting time of PSS as well as transient PI behavior of multilateral wells in single and dual porous media with laterally and spatially anisotropic characteristics.Several analytical models are used in this study for describing pressure and pressure derivative behavior of multilateral wells considering different reservoir configurations and types and different wellbore lengths and directions. These models are developed for laterally and spatially anisotropic reservoirs consisting of single homogenous and dual heterogeneous porous media (Naturally fractured reservoirs) and depleted by multilateral wells extending from single vertical wellbore at different horizons and directions. The models are modified to identify the staring time of PSS flow or the time when boundary dominated flow regime is developed. They are also applied to estimate the time variant transient PI and time invariant stabilized PSS PI for constant single lateral flow rate or constant vertical wellbore commingled flow rate.The outcomes of this study are summarized in: 1) Developing new analytical solutions for pressure distribution in porous media drained by multilateral wells. 2) Developing new integrated approach for estimating stabilized PSS productivity index. 3) Understanding pressure, pressure derivative, and PI behavior of finite acting reservoir depleted by multilateral horizontal wells during transient and PSS production. 4) Investigating the impacts of different reservoir configurations and types, wellbore lengths and directions, permeability anisotropy characteristics, and single and dual porous media petrophysical properties on stabilized PSS productivity index.The novel points in this study are: 1) The optimum reservoir configuration that gives the maximum stabilized PI is the rectangular shape reservoir with reservoir length to width ratio of (2−4). 2) The lateral with long wellbore and the slightly deviated from the horizontal directions gives the greatest stabilized productivity index. Stabilized PI is impacted by the length and direction of each multilateral as well as lateral wellbore location in the vertical plane. 3) Lateral reservoir anisotropy exhibits bad PI compared to the spatial anisotropy. 4) PI of conventional dual porous media reservoirs is greater than the index of unconventional reservoirs at early and late production time, but the index at intermediate production time demonstrates the greater value for unconventional reservoirs.