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Transitional Flow Regimes

Transitional Flow Regimes. Transitional flow regimes. Navier Stokes Well. Brinkman equations Fast … near perforations. Darcy’s law Slow … in the reservoir. Transitional flow regimes. Richard’s equation Unsaturated. Navier Stokes Free. Darcy’s law Saturated - slow. Brinkman equations

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Transitional Flow Regimes

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  1. Transitional Flow Regimes

  2. Transitional flow regimes Navier Stokes Well Brinkman equations Fast … near perforations Darcy’s law Slow … in the reservoir

  3. Transitional flow regimes Richard’s equation Unsaturated Navier Stokes Free Darcy’s law Saturated - slow Brinkman equations Saturated - fast

  4. Transitional flow regimes • Besides … • zooming in on a wellbore can be handy when you consider in- and near-well processes, like pore clogging, skin effects, wave propagation and more.

  5. Transitional flow regimes impermeable layer above axisymmetry (an approximation) perforation fluid velocity satisfies pumping rate well impermeable layer below inflow from pumped reservoir below

  6. Transitional flow regimes Brinkman Equations Dependent Variables Darcy’s Law pdl pbr, ubr, vbr Navier-Stokes Equations pns, uns, vbr weak constraints p = pressure, u =vector of velocities, h = dynamic viscosity k = permeability, r = fluid density

  7. Transitional flow regimes

  8. Transitional flow regimes • Solution requires: • weak constraints to link dependent variables from 3 different flow equations. • a good mesh. Zoom in on boundaries between flow domains and in well. • a good initial guess. Use parametric solver to get solution for unrealistically simple problem. Use results as initial guess for the next, more realistic scenario.

  9. Transitional flow regimes Low pressure drop in the well because no rocks seamless transitions In pressure and velocity Surface and contours are pressure, streamlines are velocity, arrows show direction Note: pressure in well not shown because shading obscured streamlines

  10. Transitional flow regimes High velocities in the well Low velocities in reservoir seamless transitions In pressure and velocity Surface is velocity, contours are pressure

  11. Geometry draw using COMSOL Multiphysics CAD tools Worked example file – Model Navigator > Model library > Earth Science Module > Fluid Flow > darcy_brinkman_ns.fl Coupling requires – Turning on non-ideal weak constraints from Physics > Properties Solving requires – Good mesh, Parametric solution Points of interest

  12. References • Jamiolahmady, M., Danesh, A., Terhani, D.H., Henderson, G.D., and Duncan, D.B. (2004). Flow around a rock perforation surrounded by damaged zone: Experiments vs. Theory, presented at IASME/WSEAS International Conference, Corfu, Greece, on 17-19 Aug. • Shavit, U., Rosenzweig, R., and Assouline, S. (2003). Free flow at the interface of porous surfaces: A generalization of the Taylor Brush configuration in Transport in Porous Media, Kluwer Academic Publishers, the Netherlands.

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