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Equations

Permission Granted by the Society of Petroleum Engineers SPE, Dallas, Texas
The Reservoir Engineering Aspects of Waterflooding
Monograph Volume 3

Layer Data Input

A :

Reservoir Pattern Area , acres

h _net :

Average formation layer thickness , ft.

f :

Average Porosity , fraction

S_o :

Oil Saturation @ start of flood , fraction

B_o:

Oil formation volume factor @ start of flood , RB / STB

B_w:

Water formation volume factor @ start of flood, RB / STB

S _{wi :}

Initial water saturation ; fraction

m _o :

Oil viscosity , cp

m _w :

Water viscosity , cp

rei :

1/2 the distance between adjacent injectors, ft.'

r_w :

Well radius , ft.

d :

Distance between adjacent rows of wells , ft.

Absolute Permeability - Base permeability is permeability to oil at irreducible water saturation , (Ko ) @ S_wi.

D P

Pressure difference beween formation face injection pressure and pressure @ the leading edge of the oil bank in the reservoir , psig

Relative
Permeability
Data:

User manually inputs relative permeability data or can use default algorithm

Program Internal Auto Calculations

Calculations of the Fractional Flow Curve Calculations of the Derivative of the Fractional Flow Curve
M :	Program calculates mobility ratio prior to water breakthrough utilizing the fractional flow curve
E_abt :	Program calculates the areal sweep efficiency at water breakthrough using Figure E.6
S_g* :	Program calculates maximum gas saturation, S_g*, for which the CGM method is valid
	S_g* : C * (S_oi-S_obt ) figure E.7
S_obt	Program calculates the average oil saturation in the swept zone at water breakthrough
Test	Program tests validity of program by comparing calculated S_g, the current gas saturation at flood start to S_g*
	The condition S_g < S_g* must be met for calculations to be performed

RESULTS: INITIAL CALCULATIONS

Initial injection into the pattern assumes that the fluid banks are radial in shape and that Darcy's radial flow equation applies.
		Equation Permission Granted by the Society of Petroleum Engineers SPE, Dallas, Texas The Reservoir Engineering Aspects of Waterflooding Monograph Volume 3
Vp	Reservoir Pattern Pore Volume	7,778 * A * h_net * f	bbls
N_wf	Reservoir Pattern Stock Tank Oil in Place @ start of flood	( V_p*S_o ) / B_o	STB
M	Mobility ratio calculated by program prior to water breakthrough	[(K_rw) _Swbt * m_o] / [ m_w * (K_ro)_Swi]
E_abt	Areal sweep efficiency calculated by program at water breakthrough	From : M vs. Conductance Ratio Graph
W_ii	Cumulative water injected @ interference	( p * h_net * f * S_g * rei² ) / 5.615	bbls
W_if	Cumulative water injected @ fillup	V_p* S_g	bbls
W_ibt	Cumulative water injected @ breakthrough	V_p* E_abt * (S_wbt - Swi)	bbls

RESULTS: RELATIVE PERMEABILITY DATA

RESULTS: DERIVATIVE OF THE FRACTIONAL FLOW CURVE

RESULTS: PERFORMANCE TO INTERFERENCE

RESULTS: PERFORMANCE TO FILLUP

RESULTS: PERFORMANCE FROM FILLUP TO WATER BREAKTHROUGH

RESULTS: PERFORMANCE FROM FILLUP BREAKTHROUGH TO FLOODOUT

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