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Equations

Layer Data Input
Program Internal Calculations
Results: Initial Calculations
Results: Relative Permeability Data
Results: Derivative of Fractional Flow Curve
Results: Performance to Interference
Results: Performance to Fillup
Results: Performance from Fillup to Breakthrough

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.'
 rw :
Well radius , ft.
d :
Distance between adjacent rows of wells , ft.
K
Absolute Permeability - Base permeability is permeability to oil at irreducible water saturation , (Ko ) @ Swi.
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
Eabt : Program calculates the areal sweep efficiency at water breakthrough using Figure E.6
Sg* : Program calculates maximum gas saturation, Sg*, for which the CGM method is valid
  Sg* : C * (Soi-Sobt ) figure E.7
Sobt Program calculates the average oil saturation in the swept zone at water breakthrough
Test Program tests validity of program by comparing calculated Sg, the current gas saturation at flood start to Sg*
  The condition Sg < Sg* 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
Vp Reservoir Pattern Pore Volume 7,778 * A * hnet * f bbls
Nwf Reservoir Pattern Stock Tank Oil in Place @ start of flood ( Vp*So ) / Bo STB
M Mobility ratio calculated by program prior to water breakthrough [(Krw) Swbt  * mo ] / [ mw * (Kro)Swi ]  
Eabt Areal sweep efficiency calculated by program at water breakthrough From : M vs. Conductance Ratio Graph  
Wii Cumulative water injected @ interference ( p * hnet * f * Sg * rei2 ) / 5.615 bbls
Wif Cumulative water injected @ fillup Vp * Sg bbls
Wibt Cumulative water injected @ breakthrough Vp * Eabt * (Swbt  - 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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