{"title":"Nonlinear Fractal Flow Model of Fractured Vertical Wells With Stimulated Reservoir Volume Considering the Quadratic Gradient Term","authors":"Xuefeng Yang, Xin Jiang, Cheng Chang, Yizhao Chen, Xiaojing Ji, Yanze Wan, Ziqi Qiu, Junjie Ren","doi":"10.1155/gfl/3185617","DOIUrl":null,"url":null,"abstract":"<p>Although various fractal flow models have recently been developed to investigate pressure responses of fractured vertical wells, almost all of the existing fractal models ignore the quadratic gradient term (QGT), which makes them violate mass conservation. In this paper, fractal theory is introduced to develop a nonlinear flow model of fractured vertical wells with stimulated reservoir volume (SRV). The QGT is reserved so that the present model fully obeys material balance. Function transforms are used to linearize the nonlinear flow model, and then, Laplace transform and Laplace numerical inversion algorithm are employed to derive the pressure solution. Type curves are provided to analyze the flow characteristic and identify the flow regimes. The effects of some parameters on the pressure responses are discussed in detail. It is found that the existence of the QGT leads to the decrease of the pressure drop, especially at a large nonlinear coefficient and a large time scale. Fractal parameters and SRV radius not only affect type curves but also affect the relative error caused by neglecting the QGT.</p>","PeriodicalId":12512,"journal":{"name":"Geofluids","volume":"2024 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/gfl/3185617","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geofluids","FirstCategoryId":"89","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/gfl/3185617","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
Although various fractal flow models have recently been developed to investigate pressure responses of fractured vertical wells, almost all of the existing fractal models ignore the quadratic gradient term (QGT), which makes them violate mass conservation. In this paper, fractal theory is introduced to develop a nonlinear flow model of fractured vertical wells with stimulated reservoir volume (SRV). The QGT is reserved so that the present model fully obeys material balance. Function transforms are used to linearize the nonlinear flow model, and then, Laplace transform and Laplace numerical inversion algorithm are employed to derive the pressure solution. Type curves are provided to analyze the flow characteristic and identify the flow regimes. The effects of some parameters on the pressure responses are discussed in detail. It is found that the existence of the QGT leads to the decrease of the pressure drop, especially at a large nonlinear coefficient and a large time scale. Fractal parameters and SRV radius not only affect type curves but also affect the relative error caused by neglecting the QGT.
期刊介绍:
Geofluids is a peer-reviewed, Open Access journal that provides a forum for original research and reviews relating to the role of fluids in mineralogical, chemical, and structural evolution of the Earth’s crust. Its explicit aim is to disseminate ideas across the range of sub-disciplines in which Geofluids research is carried out. To this end, authors are encouraged to stress the transdisciplinary relevance and international ramifications of their research. Authors are also encouraged to make their work as accessible as possible to readers from other sub-disciplines.
Geofluids emphasizes chemical, microbial, and physical aspects of subsurface fluids throughout the Earth’s crust. Geofluids spans studies of groundwater, terrestrial or submarine geothermal fluids, basinal brines, petroleum, metamorphic waters or magmatic fluids.