Am responding to the broader community since I though the below pm may be of interest to others

CGM – Craig-Geffen-Morse Analytical Waterflood MethodHi dear

I have a problem for handlign a problem in CGM ( Criag, Gefer, Morse ) in water Flooding with CGM method.

Unfortunately, the CGM is not explained well in the Wilhite waterflooding book, could you give me a hand if I can find an clear example of CGM to calculate or an Excel file :

*To Determine areal sweep efficiency, cum water injected, and cum oil produced at breakthroug

*To Predict areal sweep efficiency, cumulative oil production, water/oil ratio, oil production rate and recovery factor as functions of time till WOR = 50

for both Immobile and Mobile water saturaions.

I have constructed the fractional flow curve, but I dont know what are the next steps?

Thanks a million

Regards

Imanol

A steady-state technique combining areal sweep effects, displacement mechanism, stratification and variable injectivity to predict waterflood performance in a 5-spot pattern.

Valid with or without initial free gas, as long as no trapped gas behind the flood front. Assumes 100% vertical sweep efficiency in each layer of stratified reservoir and zero crossflow. In order to test multi-layer cases, simply repeat the below workflow for each of your layers and sum volumes/rate in time.

I’ve omitted a lot of the intermediary equations and commentary for brevity – please go to the original paper for more details.

Yes, I have made a spreadsheet which does all of this (for multilayers as well), but no sorry I will not share it. It was developed on company time so is not really mine to give. In my opinion it is best for your understanding to go through it yourselves anyway :-)

Stage 1:

Begins when water injection starts and ends when oil banks around adjacent injectors meet. This meeting is termed interference. If there is no free gas present at the start of the flood, skip stage 1 and stage 2 and go directly to stage 3

Stage 2:

Extends from start of interference until all gas space is filled by injected water. Only primary oil production occurs during this stage.

Stage 3:

Extends from gas fillup to water breakthrough at producing wells. Oil production caused by the waterflood begins at start of stage 3. Oil production during this stage is a combination of incremental waterflood production and primary recovery. Total oil recovery rate equals injection rate at reservoir conditions.

Stage 4:

From onset of water break through until economic limit is reached

Initial calculations

Calculate pattern pore volume Vp = 7758 x A x h x Phi (Eq 1)

Vp = bbls, A = acres, h = ft, Phi = fraction

Calculate oiil in place at beginning of waterflood

No = Vp x So / Bo (Eq 2)

No = stb, So = fraction, Bo = rb/stb

Calculate mobility ratio prior to water breakthrough

M = (krw@Swbt / Kro@Swc) x (Muo/Muw) (Eq 3)

krw@Swbt = rel perm to water at average water saturation in water swept region at water breathrough

Kro@Swc = rel perm to oil at the connate water saturation at start of waterflood

Determine sweep efficiency at water breakthrough

Eabt = 0.5460 + (0.0317/M) + (0.3022/e^M) – 0.0051M

M = mobility ratio per Eq. 3

Calculate cumulative water injected at the time of interference

Wii = pi x rei^2 x h x phi x Sg / 5.615 (Eq 4)

Wii = bbls, rei = half distance between adjacent injectors (ft)

Calculate cumulative water injected at gas fillup

Wif = Vp x Sg (Eq 5)

Wif = bbls

Calculate cumulative water injected at breakthrough.

Wibt = Vp x Eabt x (Swbt – Swc) (Eq 6)

Wibt = cum water inj at breakthrough (bbls)

Swbt = Average water saturation in swept region at breakthrough (fraction)

Swc = Connate water saturation

Stage 1: Performance prior to interference

Injection rate prior to interference is

iw = 0.00708kh.deltaP / ((muw/krw)ln(r/rw’)+(muo/kro)ln(re/r)) (Eq 7)

iw = bwpd injection

h = net pay (ft)

k = base perm used to define rel perm – ususlly effective perm to oil at Swir (mD)

kro = rel perm to oil in oil bank at Swc

krw = rel perm to water in water bank at Swbt

r = radius of water bank (ft)

re = radius of oil bank (ft)

rw’ = effective wellbore radius = rw.e^-Si

rw = wellbore radius (ft)

Si = skin factor at injection well

deltaP = applied pressure differential between BH injection pressure and pressure in reservoir at outer edge of oil bank – usually assumed as average reservoir pressure at start of injection (psi)

re = SQRT(5.615 x Wi / (pi x h x poro x Sg) (Eq 8)

Wi = cumulative injected water (bbls)

r = re x SQRT(Sg / (Swbt – Swc)) (Eq 9)

Summary Stage 1 calculations:

1. Select values of Wi from zero to Wii (suggest 10 intervals)

2. Compute re for each value of Wi using Eq 8

3. Compute r for each value of Wi using Eq 9

4. Compute iw for each value of Wi using Eq 7

5. Compute average water injection rate for each increment

a. (iw_avg)n = ((iw)n + (iw)n-1) / 2 (Eq 10)

6. Compute time required for each increment of water injection

a. (deltaT)n = ((Wi)n – (Wi)n-1)/(iw_avg)n (Eq 11)

7. Compute cumulative time for each value of Wi

a. tn = Sum((deltaT)n) (Eq 12)

Stage 2: From interference to fillup

Time between interference and fillup = (Wif – Wii)/(0.5*(iwi + iwf)) (Eq 13)

iwi = injection rate at end Stage 1

iwf (injection rate at fillup) as well as injection rates from fillup to water breakthrough are calculated as;

iw = CR . ibase (Eq 14)

CR = Conductance ratio (see below)

ibase = base water injection rate (bwpd)

For a 5-spot pattern,

ibase = 0.003541 x (ko @ Swir) x h x deltaP / (muo x (ln(d/rw) – 0.619 + 0.5Sp + 0.5Si)) (Eq 15)

ibase = base water injection rate (steady-state injection in a oil-filled 5-spot pattern with unit mobility ratio) – bwpd

d = diagonal distance between adjacent inj and prod wells (ft)

Sp = Skin factor in producer

Si = Skin factor in injector

deltaP = BHP pressure difference between injection and producer wells after fillup

Conductance Ratio CR ~ 1/(1+Ea((1/M)-1)) (Eq 16)

Areal sweep efficiency Ea = Wi / (Vp(Swbt-Swi)) (Eq 17)

Summary Stage 2 calculations:

1. Obtain values of Wif and Wii from initial calculations

2. Obtain value of iwi from stage 1 calculations where Wi = Wii

3. Compute Ea at fillup using Eq 17

4. Calculate mobility ratio M from Eq 3

5. Determine CR at fillup from Eq 16

6. Compute ibase using Eq 15

7. Compute water inj rate at fillup iwf using Eq 14

8. Compute time interval required for stage 2 using Eq 13

Stage 3: Performance from fillup to breakthrough

The beginning of secondary oil production. It is assumed that on reservoir volume basis, total oil rate = water injection rate. Water injection rate determined using Eq 14, so;

qo = iw / Bo x fo@swc (Eq 18)

fo@swc = oil cut at the producing well before breakthrough. If Swc = Swir, then fo = 1.0

Cumulative oil production Np since beginning of Stage 3 can be computed in terms of cumulative water injected during stage 3 as

Np = [(Wi – Wif) / Bo] x fo (Eq 19)

Summary Stage 3 calculations:

1. Select values of Wi from Wif to Wibt using user defined interval

2. Determine Ea for each value of Wi using Eq 17

3. Determine CR for each value of Wi using Eq 16

4. Compute iw using Eq 14

5. Compute avg iw for each interval

6. Compute incremental and cumulative times associated with each interval

7. Compute qo using Eq 18

8. Determine fo at Swc from fraction flow graph

9. Compute cumulative oil recovery using Eq 19

Stage 4: Performance after waterflood breakthrough

The beginning of water breakthrough, characterized by increasing mobility ratios, increasing areal sweep efficiency, increasing WOR and reducing oil rates.

Ea = 0.2749 x ln(Wi/Wbt) + Eabt (Eq 20)

Ratio of pore volumes of water injected vs pore volumes injected at breakthrough can be looked up from a table of Qi/Qibt as a function of Eabt and Wi/Wibt, I have regressed these tables to a 3D function as follows (makes calc in Excel easier!)

Qi/Qibt = (Wi/Wibt)^(0.8888-(0.07515/Eabt)) + 0.2284 x ln(Wi/Wibt) (Eq 21)

(dfw/dSw)@Sw2 = 1/(Qi)@Sw2 (Eq 22)

Qi = pore volumes of water injected at time in question

Sw2 = Saturation at producing well

Average water saturation in reservoir at time of interest

Sw_avg = Sw2 + Qi x fo2 (Eq 23)

Lambda = 0.2749 x (1/(Wi/Wibt)) (Eq 24)

Oil swept from previously unswept portion of the reservoir;

dNpu = Lambda x (Swf – Swc)/(Eabt x (Swbt – Swc)) As fraction of total fluid production (Eq 25)

Swf = water saturation immediately behind the stabilized zone

Incremental oil from previously swept region;

dNps = fo2 x (1-dNpu) As fraction of total fluid production (Eq 26)

WOR = WORp x (Bo/Bw) (Eq 27)

WORp = (1 - dNps – dNpu) / (dNps + dNpu)

Np = Vp(Ea(Sw_avg – Swc)-Sg)/Bo (stb) (Eq 28)

Average mobility ratio after breakthrough;

M = (krw)@Sw_avg x muo / ((kro)Swc x muw) (Eq 29)

Oil producing rate (stb/day);

qo = iw (dNps + dNpu) / Bo (Eq 30)

Water producing rate (stb/day);

qw = iw (1 - dNps + dNpu) / Bw (Eq 31)

Cumulative water produced (stb);

Wp = (Wi – NpBo – VpSg)/Bw (Eq 33)

Cumulative oil produced (stb);

Np = (Np)@End Stage 3 + Sum(Np)Stage 4

Summary Stage 4 calculations:

1. Select values of Wi from Wibt to the economic limit and tabulate as ratio of Wi/Wibt

2. Compute Ea using Eq 20

3. Determine values of Qi/Qibt from Eq 21, and calculate Qi = Qibt x (Qi/Qibt)

4. Compute the slope of the fractional flow curve dfw/dSw using Eq 22

5. Use slope from step 4 and fractional flow curve to determine Sw2

6. Using Sw2, determine fw2 from fractional flow curve, then fo2 = 1.0 – fw2

7. Compute Sw_avg using Eq 23

8. Compute lambda using Eq 24

9. Compute dNpu using Eq 25

10. Compute dNps using Eq 26

11. Compute WOR using Eq 27

12. Compute Np using Eq 28

13. Determine mobility ratio M using Eq 29

14. Determine CR using Eq 16

15. Compute iw using Eq 14

16. Compute incremental and cum times associated with each interval

17. Compute qo using Eq 30

18. Compute qw using Eq 31

19. Compute Wp using Eq 32

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