# CGM – Craig-Geffen-Morse Analytical Waterflood Method

• 03-28-2011, 08:53 AM
vinomarky
CGM – Craig-Geffen-Morse Analytical Waterflood Method
Am responding to the broader community since I though the below pm may be of interest to others
[QUOTE]Hi 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 [/QUOTE]

CGM – Craig-Geffen-Morse Analytical Waterflood Method

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
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
• 03-29-2011, 05:40 AM
Imanol
Thanks a lot, that was a lot of informative post, it worked out

Best regards
Imanol
• 06-11-2011, 08:57 PM
Nunzio_44
You seem to know a lot about waterflooding. Do you have any suggestions about injection well design in soft sands(k>1 D) to avoid premature failure/reduction of injectivity if injecting at fracture conditions?
• 06-12-2011, 12:37 AM
vinomarky
Work reduce local velocities - horizontal wells for injectors immediately springs to mind. Lower injection pressures for a given rate, lots of alternate pathways should (or when) injection damage occurs.
• 06-12-2011, 03:23 AM
Nunzio_44
Thanks for the suggestions. Horizontal wells will be preferred but the cost is high and therefore trying to make vertical ones work longer is and will be a worthy cause. Some suggest downhole check valves but I am not so sure about them.
• 06-12-2011, 08:02 AM
vinomarky
Yes, I guess about the only route you then have is in your procedures to bean up/down the injection rates - trying to avoid as much as possible surges, backflow and general pressure pulses/surging that tend to destabilize formation
• 03-17-2012, 11:08 PM
bendorf
Re: CGM – Craig-Geffen-Morse Analytical Waterflood Method
Anybody here has Larson CGM? i realy need it badly.