Pressure Transient Analysis of the Vertical Fractured Well in Three-Separate Zone With Crossflow in Boxed Reservoirs
Notice bibliographique
Résumé
Abstract For low permeability or damaged formations, hydraulic fracturing is a broad applied technology. A new mathematical model of the well with infinite-conductivity vertical fractures is described in a three-separate-zone with crossflow in a boxed reservoir, Based on the model, pressure transient behaviors of the vertically fractured well intercepting a three-separate-zone with crossflow is described through the methods of Laplace transform, Fourier integral transform and Stehfest numerical inversion. The influences of parameters of the three-separate-zone with crossflow in a boxed reservoir such as rectangular boundary length (yeD), half fracture length (xfD), the permeability ratio (K1, K2, K3), interporosity flow parameter (λ 1, λ 2), and storability ratio (ω1, ω2, ω3), have the pressure response of a fractured well.Loglog diagnosis graphs of the vertically fracture well pressure are given and analyzed here. The methods can instruct the allocation of production and injection rates, dynamic forecast and development technology of the three-separate-zone with crossflow with infinite-conductivity hydraulic vertically fracture. Introduction Hydraulic fracturing usually creates vertical fractures, unless in shallow layers. Many formations consist of multi-layers due to sedimentary dynamics reasons, and multi-layered formation are fractured to open by hydraulic fracturing operation. Thus, research on pressure transient characteristics of hydraulic fracturing multilayered zone, can help optimizing fracturing treatment design, analyze commingled producing wells performance in a multilayered reservoir after hydraulic fracturing, and give explanations correspond to reality. Choosing fair and reasonable production pressure drop, and obtaining appropriate production and injection allocation systems, has important theoretical directive functions to develop hydraulic fracturing multi-layered reservoirs. In the literature of vertical well pressure analysis in layered reservoirs, Lefkovits (1961) obtained pressure solution of commingled producing wells without crossflow; Tariq (1961) began to consider wellbore storage and skin effects on Lefkovits' solution. Kuchuk (1984) presented well test methods applicable to vertical wells in communication zones by using wellbore pressure and fluid flux; Bourdet (1984) presented vertical wells pressure and derivative type curves in a two-layered reservoir with crossflow in pseudo-steady state and with wellbore storage and skin effects. Using maximum effective wellbore radius concept, Sun (2003) established the maximum wellbore radius model in an infinite three-layered reservoir with crossflow. Zhang (2001) analyzed pressure behavior of multi-layered reservoir, the difference of interflow between depleted zones, and mechanism of interlayer crossflow after well shut-in. Wang and Liu (1999) obtained the method and equation for calculating wellbore pressure in a circular multi-layered infinite extension heterogeneous medium without crossflow. The above mentioned models for calculating pressure behavior in multi-layered reservoirs are mainly aimed at vertical wells, the performance of commingled producing vertically fracture wells are short of careful analyses. Little research on hydraulic fracturing well in multi-layered reservoirs has been done in the literature, Liu and Wang (1993) only obtained some results of infinite conductivity vertically fracture wells performance in a two-layered reservoir. This paper establishes the mathematical model of the infiniteconductivity vertically fracture well
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