ENPE 523_Lecture 3 - Fluid Flow in Oil and Gas Reservoirs.pdf

# ENPE 523_Lecture 3 - Fluid Flow in Oil and Gas Reservoirs.pdf

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Introduction to Reservoir Engineering ENPE 523 Hassan Hassanzadeh EN B204M [email protected]

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Learning objectives develop governing equations of flow of oil and water for various flow geometries, identify different flow regimes and recognize factors affecting flow of oil and 2 water around wellbores. apply superposition principle to solve a variety of transient flow problems in oil reservoirs and aquifers.
Fluid flow in oil and gas reservoirs Darcy’s law linear and radial flow average permeability the Klinkenberg effect steady-state flow diffusivity equation boundary conditions 3 constant rate and constant solutions pseudo-steady-state flow in oil & gas reservoirs skin factor productivity index superposition principle multi-well multi rate transient well testing boundary effect

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Darcy’s law assumptions The fluid is homogenous, single-phase, and Newtonian There is no chemical reaction between the fluid and the porous medium Laminar flow conditions prevail Permeability is a property of the porous medium that is 4 independent of pressure, temperature, and the flowing fluid There is no slippage effect (Klinkenberge effect phenomenon) There is no electrokinetic effect
Darcy’s law L p p kA q 2 1 - = μ ( ) C x kA q x p dp dx kA q dx dp kA q + = - = - = μ μ μ p1 p2 q L p2 p1 0 L 5 SI unit, Q in m 3 /sec, L in m, p in Pa, μ in Pa-s, A in m 2 , k in m 2 L p p B kA q 2 1 127 . 1 - = μ Darcy’s unit, q in cc/sec, L in cm, p in atm, μ in cp, A in cm 2 , k in Darcy Field unit, q in STB/D, L in ft, p in psi, μ in cp, A in ft 2 , k in D 1 Darcy=0.987x10 -12 12 m 2

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Darcy’s equation in field units 2 2 dx dp kA q μ - = in Darcy’s units we have In field units: Darcy’s units, q in cc/sec, L in cm, p in atm, μ in cp, A in cm 2 , k in Darcy 6 ( ) ( ) ( ) = × ft cm ft dr psi atm psi dp m cm ft m ft kA m cm bbl m s D D bbl q 28084 . 3 100 7 . 14 100 28084 . 3 100 1 2898 . 6 3600 24 2 3 3 μ dx dp B kA q μ 127 . 1 - = Field units, q in STB/D, L in ft, p in psi, μ in cp, A in ft 2 , k in D
Velocity Apparent velocity (Darcy velocity) Actual velocity (pore velocity) A q V app = A q V ac φ = Single- phase 7 Phase apparent velocity Phase actual velocity A q V o o app = ( ) w o o ac S A q V - = 1 φ Two-phase oil & water

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General form of Darcy’s law ± - = θ ρ μ sin g ds dp B kA q θ + If flow is upward 8 - If flow is downward Horizontal flow L p p B kA g ds dp B kA q 2 1 sin - = ± - = μ θ ρ μ 0 p1 p2 L
Special cases Vertical flow Case 1: both ends are at atmospheric pressure 1 1. If flow is downward - 2. p 1 =p 2 =0 3. sin θ =1 9 2 L - - - = g L p p B kA q ρ μ 1 2 B g kA q μ ρ =

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Special cases Vertical flow Case 2: downward flow when the driving head at the inlet is h and
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