Flow Convergence and Pressure Loss Characteristics in Viscous Flow through Rectangular Orifices with Applications in Porous Media

• Author / Creator

  Yusuf, Yishak

• The enhanced oil recovery process known as steam assisted gravity drainage (SAGD) uses horizontal wells with perforations on their lateral surfaces to inject steam into, and produce oil from, oilsand reserves. Slotted liners that are used external to these wells serve as screens to minimize sand production. The flow contraction caused by the presence of these slots leads to significant pressure loss in the flow increasing the probability of well failure due to plugging. Scrutinizing the underlying physics reveals a flow convergence phenomenon in the incoming flow of produced oil which is characterized by flow acceleration and streamline curvature.

  The thesis considers the problem of flow into a single slot defining the geometry as a rectangular orifice of high aspect ratio, AR. The flow configuration in the SAGD flow scenario consists of the coupled regions of the porous media and the rectangular orifice. The research first investigates the flow through an open slot to model the pressure loss as a function of AR and the flow Reynolds number.

  A semi-empirical model is developed for the pressure loss coefficient as a function of AR and flow convergence. The analytical modeling is based on the 1 dimensional Navier-Stokes equation and an asymptotic velocity transition model for a Gaussian velocity distribution. The loss coefficient decreased for increasing AR as per the model, agreeing with the hypothesized relationship regarding the streamline curvature and AR.

  A large scale flow measurement facility is used to measure the pressure drop across rectangular orifices of various aspect ratio in the range 1 ≤ AR ≤ 250. The orifices all have equal cross sectional area while the hydraulic diameters were varied to change AR. The flow rates in the experiments are selected to maintain the same Reynolds number across all orifices in the range 0.05 ≤ Re ≤ 0.1 which was selected based on field conditions in SAGD. The static pressure drop ΔP increased with increasing AR and Re. The effect of AR on the pressure drop was attributed to varying flow blockage and convergence effects which become apparent in their respective planes of investigation.

  The changing flow convergence/blockage characteristics with changing AR is closely investigated by using particle image velocimetry (PIV) experiments to measure the velocity field from which the streamlines are determined. The streamlines for the flow through orifices having lower AR started to curve farther upstream than for higher AR. The trend in the axial distribution of streamline curvature were also reflected in the pressure gradients determined in both the streamwise and spanwise directions. Calculation of these pressure gradients is achieved by applying the equations of motion in streamline coordinates along the streamlines calculated using PIV data. The maximum streamwise pressure gradient occurred along the center streamline since the maximum velocity gradient also occurs along the centerline. The spanwise pressure gradient reached maximum wherever there is maximum curvature.

  The study also considered the flow through the coupled media by including a representative porous region on the upstream side of the orifice using spherical glass beads with mean diameter of 1 mm. Modelling of the pressure loss through the coupled system developed a relation combining Ergun’s equation for the porous bed and the model developed for the open-orifice scenario. The model described that higher AR leads to higher pressure drop across the coupled system due to dominating effect from flow blockage. Comparison of the pressure drop relation obtained from the model with that from experimental measurements showed that the flow convergence due to the orifice contributes more to the losses than the preceding porous region.

• Subjects / Keywords

  • Pressure loss characteristics
  • Gaussian velocity transition
  • Pressure measurement flow loop
  • Flow convergence
  • Steam assisted gravity drainage (SAGD)
  • Velocity transition
  • Particle image velocimetry
  • Streamline curvature
  • 1D Navier_Stokes Equation
  • Slotted liners
  • tortuosity calculation
  • Rectangular orifices
  • streamline calculation
  • Porous media-Orifice coupled flow domain

• Graduation date

  Spring 2020

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-wzcw-ya88

• License

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