Semi-analytical modeling of rate transient for a multi-wing fractured vertical well with partially propped fractures considering different stress-sensitive systems

Abstract

Multi-fracture wings can be generated around vertical well after hydraulic fracturing, and damage usually occurs in far from wellbore fracture due to poor proppant transport. The existing rate transient models ignore the different stress-sensitive behaviors in propped and un-propped fractures. For tight reservoir characterization and production prediction, in this paper, a semi-analytical Blasingame decline analysis model of a multi-wing fractured vertical well (MFVW) is formulated with partially propped fractures under different stress-sensitive effects. Compared to propped section, lower initial conductivity and larger stress sensitivity are considered in un-propped section. Employing Laplace transformation, numerical inversion, node analysis, and an iteration method, the production rate is obtained and then verified. Afterward systematic sensitivity analyses are carried out. The influences of parameters such as un-propped section length and different stress-sensitive behavior on production rate are studied in detail. A big difference is observed between type curves of the uniform and non-uniform stress-sensitive models. The properties of propped fracture section mainly put an impact on the early time production rate. The stress-sensitive un-propped fracture section makes production rate reduction at the middle time, and such an influence is enhanced with a longer un-propped section. Sharper decline rate and smaller minimum conductivity both would enhance the production reduction caused by stress-sensitivity. For the first time, the flow flux and pressure along the partially propped fracture of MFVW are analyzed. It has been found that the max flux rate would not appear in the first near wellbore segment with smaller θ in MWFV. And flow flux in un-propped section is lower by order of magnitude than that of the propped section at early time, the majority of the total production at early time is contributed by the near wellbore propped fracture section. The model can help for better understand of the flow mechanism and achieve more realistically fracture flow simulation. It has practical significance for better development of tight resources.