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These are caused not only by the frictional effect, but also by the kinematic effect, which consists of the accelerational and fluid inflow effects inside a wellbore.
Without inclusion of a dynamic reservoir model, conventional time-lapse interpretation remains limited to describing time variations of fluid inflow rates produced from or injected into fluid-producing rock formations.
The problem of the hydraulic fracture evolution over time is modeled as stable quasi-static crack growth where time is the result of upholding the mass conservation principle between the fluid inflow and the crack volume.
Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.
The aim of this study is to investigate the possible pathways for fluid inflow into the Soultz and adjacent geothermal fields (e.g. the Rittershoffen field).
This fluid inflow from the surface displaces hotter fluid at depth and, thus, relocates the heat coming from deeper parts of the basin by advective heat transport from the south to the north.
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Therefore fluid inflows and outflow are relatively insensitive to changes in D34.
After removal of the hypertonic urea fluid, inflows via the transporter and membrane resume immediately.
When the characteristic set on the boundary satisfies a certain assumption, the authors in [24, 25] can show the well-posedness to both isentropic fluids and heat-conductive fluids containing inflow boundary with small Reynolds number, but not infinitesimally small, and small Mach number.
Considering the steady compressible fluids with inhomogeneous boundary conditions, the authors in [20 23] study the existence and regularity of compressible fluids with inflow boundary conditions in different domains when the Reynolds number is small.
Inflow fluid velocity, L/t, ft/s.
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