Linear Flow

			L			Q = kA
Q
						µ
	P1		P2

	Q =	kA		P
θ		µ		1

	Q =	kA		P
		µ		1
θ

P1

−P2

L

−P2

L

−P2

L

−ρg sin θ

+ρg sin θ

Radial Flow

Pwf

Pe

h

re	rw

Q = − kA dP µ dR

Q= −k2πH R dP

µdR dRR = −2µπQkH dP

r		p
∫w	dR	= − ∫wf 2πkHdP
r	R	p	µQ
e			e

ln rw = −2πkH (Pwf −Pe ) re µQ

Q= 2πkH(Pe −Pwf )

µln(re rw )

Averaging Permeability (Parallel Sand)

						L			A1	i=n
				k1, h1, Q1
Q									A2	Q = ∑Qi = Q1 +Q2 +Qn
				k2, h2, Q2
									An	i=1
				kn, hn, Qn
		P1		= k1A1			∆P	P	2	∆P + kn An	∆P
k∑Ai			∆P					+ k2 A2
i=n
i=1			µL				µL			µL	µL
k∑Ai			= ∑ki Ai
k =		∑ki Ai			or	∑ki hi				Arithmetic averages
		∑Ai				∑hi

Averaging Permeability (Series Sand)

Q				A	i=n
					∆P = ∑∆Pi = ∆P1 + ∆P2 + ∆Pn
	k1	k2	kn
	L1	L2	Ln		i=1

∆P1 ∆P2 ∆Pn

L

Harmonic averages

		i=n
	k =	∑Li
		i=1				Prove it ?
		i=n	Li
		∑
	=		k	i
		i 1