PETE311_06A_Class10_(Maggard)

PETE311_06A_Class10_(Maggard) - Average Permeability Flow...

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Average Permeability Flow in Layered Systems Some figures were taken from Amyx, Bass and Whiting, Petroleum Reservoir Engineering (1960).
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Average Permeability • If permeability is not a constant function of space (heterogeneity), we can calculate the average permeability – Common, simple flow cases are considered here • Linear, Parallel (cores, horizontal permeability) • Linear, Serial (cores, vertical permeability) • Radial, Parallel (reservoirs, horizontal layers) • Radial, Serial (reservoir, damage or stimulation) • Average permeability should represent the correct flow capacity – For a specified flow rate, average permeability results in same pressure drop (and vice versa ) • Review Integral Averages (Self Study, e.g. Average Velocity)
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Linear Flow, Pressure Profile • Review, Darcy’s Law: – horizontal flow ( Φ =p) L q A 1 2 = = ds dp μ k A q v s dp μ kA ds q = = 2 1 p p L 0 dp μ kA ds q () 2 1 p p L μ A k q =
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Linear Flow, Pressure Profile • We can determine how pressure varies along the flow path, p(x), by considering an arbitrary point, 0 x L – Integral from 0 x – We could also integrate x L L q A 1 2 = p(x) p x 0 1 dp μ kA ds q A k x μ q p p(x) 1 = OR , equivalently = 2 p p(x) L x dp μ kA ds q A k x) (L μ q p p(x) 2 + =
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Linear Flow, Pressure Profile • Pressure profile is a linear function for homogeneous properties – slope depends on flow rate L q A 1 2 x 0L p p 1 p 2 0 x p(x)
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Linear, Parallel Flow – Discrete changes in permeability
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This note was uploaded on 12/03/2009 for the course PETE 311 taught by Professor Staff during the Spring '08 term at Texas A&M.

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PETE311_06A_Class10_(Maggard) - Average Permeability Flow...

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