TY - JOUR
T1 - Lagrangian Transport and Chaotic Advection in Two-Dimensional Anisotropic Systems
AU - Varghese, S.
AU - Speetjens, M.F.M.
AU - Trieling, R.R.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - Enhanced geothermal systems (EGSs) are a promising concept to make geothermal power generation available in many regions worldwide. However, in current EGSs generally only a fraction of the geothermal reservoir is effectively accessed by the production fluid, resulting in suboptimal performance. Recent studies in the literature on a two-dimensional Darcy flow in a circular reservoir driven by reoriented injector–producer wells demonstrated that well configurations and pumping schemes designed on the basis of chaos theory enable efficient distribution of the production fluids throughout the entire reservoir. Key to this is accomplishment of chaotic advection, i.e. the rapid dispersion and stretching of material fluid regions, by a “proper” flow forcing. However, these studies concern isotropic reservoirs, while geothermal reservoirs typically are highly anisotropic. Our theoretical/computational study expands on said studies by investigating the impact of anisotropy on fundamental aspects of the Lagrangian transport of production fluids. This reveals that anisotropy generically eliminates key organizing mechanisms in the Lagrangian transport, viz. symmetries, and thus tends to promote disorder and, inherently, chaotic advection. However, symmetries are partially preserved—and thus order and coherence partially restored—in non-generic cases such as pumping schemes employing an even number of injector–producer wells and well configurations aligned with the anisotropy. Symmetry associated with well alignment in fact appears crucial to an intriguing “order within chaos” observed only in such cases: prolonged confinement of fluid to subregions of chaotic areas.
AB - Enhanced geothermal systems (EGSs) are a promising concept to make geothermal power generation available in many regions worldwide. However, in current EGSs generally only a fraction of the geothermal reservoir is effectively accessed by the production fluid, resulting in suboptimal performance. Recent studies in the literature on a two-dimensional Darcy flow in a circular reservoir driven by reoriented injector–producer wells demonstrated that well configurations and pumping schemes designed on the basis of chaos theory enable efficient distribution of the production fluids throughout the entire reservoir. Key to this is accomplishment of chaotic advection, i.e. the rapid dispersion and stretching of material fluid regions, by a “proper” flow forcing. However, these studies concern isotropic reservoirs, while geothermal reservoirs typically are highly anisotropic. Our theoretical/computational study expands on said studies by investigating the impact of anisotropy on fundamental aspects of the Lagrangian transport of production fluids. This reveals that anisotropy generically eliminates key organizing mechanisms in the Lagrangian transport, viz. symmetries, and thus tends to promote disorder and, inherently, chaotic advection. However, symmetries are partially preserved—and thus order and coherence partially restored—in non-generic cases such as pumping schemes employing an even number of injector–producer wells and well configurations aligned with the anisotropy. Symmetry associated with well alignment in fact appears crucial to an intriguing “order within chaos” observed only in such cases: prolonged confinement of fluid to subregions of chaotic areas.
KW - Anisotropy
KW - Chaotic advection
KW - Geothermal systems
KW - Pumping scheme
KW - Well placement
UR - http://www.scopus.com/inward/record.url?scp=85021112362&partnerID=8YFLogxK
U2 - 10.1007/s11242-017-0881-5
DO - 10.1007/s11242-017-0881-5
M3 - Article
AN - SCOPUS:85021112362
SN - 0169-3913
VL - 119
SP - 225
EP - 246
JO - Transport in Porous Media
JF - Transport in Porous Media
IS - 1
ER -