material balance in oil reservoirs

Material balance in oil reservoirs

The material-balance equation is the simplest expression of the conservation of mass in a reservoir. The equationmathematically defines the different producing mechanisms and effectively relates the reservoir fluid and rock expansion tothe subsequent fluid withdrawal.

Contents

1 Material balance equation

2 Nomenclature3 References

4 Noteworthy papers in OnePetro5 External links6 See also

Material balance equation

The applicable equation for initially saturated volatile- and black-oil reservoirs is[1][2][3][4]

(/File%3AVol5_page_0906_eq_001.png)....................(1)

where:

Gfgi, Nfoi, and W are the initial free gas, oil, and water in place, respectively

Gp, Np, and Wp are the cumulative produced gas, oil, and water, respectively

GI and WI are the cumulative injected gas and water respectively

Eg, Eo, Ew, and Ef are the gas, oil, water, and rock (formation) expansivities

Most of the equations regarding primary drive mechanisms (/Primary_drive_mechanisms) for oil reservoirs apply to anyconsistent set of units. A few equations, however, are written assuming English or customary units. Those equations areexpressed in SI units:


http://petrowiki.org/File%3AVol5_page_0906_eq_001.png

http://petrowiki.org/Primary_drive_mechanisms







and


Nfoi and Gfgi are related to the total original oil in place (OOIP) and original gas in place (OGIP), N and G, according to

N = Nfoi + Gfgi Rvi and G = Gfgi + Nfoi Rsi.

The expansivities are defined as




and (/File%3AVol5_page_0906_inline_001.png), where B to and B tg are the two-phase formation

volume factors (FVFs),


and (/File%3AVol5_page_0907_eq_002.png)....................(13)










http://petrowiki.org/File%3AVol5_page_0906_inline_001.png



The rock expansivity is obtained from direct measurement. See compaction driving oil reservoir(/Compaction_drive_reservoirs) for a greater discussion.

Physically, the two-phase FVF is the total hydrocarbon volume per unit volume of oil or gas at standard conditions. Thetwo-phase FVF mimics the observations noted during a constant-composition expansion test. For instance, the two-phase oil FVF is the total hydrocarbon (oil + gas) volume of a saturated oil sample per unit volume of oil at standardconditions. In contrast, the two-phase gas FVF is the total hydrocarbon volume of a saturated gas sample per unit volumeof gas at standard conditions. Bto and Btg typically are expressed in units of RB/stock tank barrel (STB) and RB/Mscf,

respectively.

For undersaturated oils, the two-phase oil FVF is equal to the oil FVFFor undersaturated gases, the two-phase gas FVF is equal to the gas FVF.

Eqs. 12 and 13 account for volatilized oil in the equilibrium gas phase. If volatilized oil is negligible, these equations aresimplified. For instance, Bto = Bo + Bg (Rsi – Rs) and Btg = Bg. These equations apply for black oils. Eq.11 ignores

dissolved gas in the aqueous phase.

Eq.1 broadly states that net expansion equals net withdrawal. More specifically, it shows the different forms of expansionand withdrawal. The different forms of expansion such as gas expansion are responsible for the different producingmechanisms.

For the sake of simplicity, Eq.1 is often written in the abbreviated form of


where:

F = total net fluid withdrawal or productionEgwf = composite gas expansivity

Eowf = composite oil expansivities

F, Egwf, and Eowf are defined in



and (/File%3AVol5_page_0908_eq_003.png)....................(17)

The composite expansivities include the connate-water and rock expansivities. Eq.15 includes Gps, which is the

cumulative produced sales gas and is defined as (Gp – GI).

F is expressed in reservoir volume units (e.g., RB or res m3)

http://petrowiki.org/Compaction_drive_reservoirs





Egwf is expressed in reservoir volume units per standard unit volume of gas (e.g., RB/scf)

Eowf is expressed in reservoir volume units per standard unit volume of oil (e.g., RB/STB)

For strictly undersaturated oil reservoirs, no free gas exists (i.e., Gfgi = 0) and the initial free oil in place is equal to the

OOIP (i.e., Nfoi = N) and Eqs.1 , 14, and 15 simplify, respectively, to[1][4][5]

(/File%3AVol5_page_0909_eq_001.png)




Eqs.18 through 20 ignore gas reinjection.

The material balance equation also helps explain most oil-recovery strategies. If the material-balance equation is solvedfor the produced fraction of the original free oil in place, then


Eq.21 succinctly shows that oil recovery increases with:

Water influx (We) (/Water_influx_models)

Initial free-gas-cap volume (which is proportional to Gfgi) (/Gas_cap_drive_reservoirs)

Surface water injection (WI) (/Surface_water_treatment_for_injection)

Surface gas injection (by minimizing gas sales through Gps)

It also shows that oil recovery increases by minimizing water production (Wp).

The material balance equation and its many different forms have many uses including:

Confirming the producing mechanismEstimating the OOIP and OGIP

Estimating gas cap sizes

Estimating water influx volumes






http://petrowiki.org/Water_influx_models

http://petrowiki.org/Gas_cap_drive_reservoirs

http://petrowiki.org/Surface_water_treatment_for_injection

Identifying water influx model (/Water_influx_models) parameters

Estimating producing indices

Nomenclature

Bg = gas FVF, RB/scf

Bo = oil FVF, RB/STB

Btg = two-phase gas FVF, RB/scf

Bto = two-phase oil FVF, RB/STB

Btw = two-phase water/gas FVF, RB/STB

Bw = water FVF, RB/STB

cf = rock compressibility, Lt2/m, 1/psi

ct = total aquifer compressibility, Lt2/m, 1/psi

Ef = rock (formation) expansivity

Eg = gas expansivity, RB/scf

Egw = expansivity for McEwen method, RB/scf

Egwf = composite gas/water/rock FVF, RB/scf

Eo = oil expansivity, RB/STB

Eow = expansivity for McEwen method, RB/STB

Eowf = composite oil/water/rock FVF, RB/STB

Ew = water expansivity, RB/STB

F = total fluid withdrawal, L3, RB

G = total original gas in place, L3, scf

Gfgi = initial free gas in place, L3, scf

Gi = cumulative gas injected, L3, scf

Gp = cumulative produced gas, L3, scf

h = pay thickness, L, ft

k = permeability, L2, md

ka = aquifer permeability, L2, md

kH = horizontal permeability, L2, md

kt = time constant, 1/t, 1/years

kv = vertical permeability, L2, md

La = aquifer length, L, ft

N = total original oil in place, L3, STB

Nfoi = initial free oil in place, L3, STB

Ng = dimensionless gravity number

http://petrowiki.org/Water_influx_models

Np = cumulative produced oil, L3, STB

p = pressure, m/Lt2, psi

pe = pressure at drainage radius, m/Lt2, psi

pw = wellbore pressure, m/Lt2, psi

q = producing rate at reservoir conditions (RB/D) or surface conditions (STB/D),v L3/t

qc = critical coning rate, STB/D, L3/t

qDc = dimensionless critical coning rate

re = reservoir drainage radius

rw = wellbore radius, L, ft

R = instantaneous producing GOR, scf/STB

Rs = dissolved GOR, scf/STB

Rsw = dissolved-gas/water ratio, scf/STB

Rv = volatilized-oil/gas ratio, STB/MMscf

Swi = initial water saturation, fraction

t = time, t, years

tmax = maximum time, t, years

tD = dimensionless time

tDmax = maximum dimensionless time

U = aquifer constant, L4t2/m, RB/psi

Vpi = initial reservoir PV, L3, RB

w = reservoir width, L, ft

W = initial water in place, L3, STB

WD = dimensionless cumulative water influx

We = cumulative water influx, L3, RB

WI = cumulative injected water, L3, STB

Wp = cumulative produced water, L3, STB

Δp = difference of time-averaged pressure, m/Lt2, psi

Δρ = density difference, m/L3, lbm/ft3 and g/cm3

μg = gas viscosity, m/Lt, cp

μo = oil viscosity, m/Lt, cp

μw = water viscosity, m/Lt, cp

References

1. ↑ 1.0 1.1 Walsh, M.P. 1995. A Generalized Approach to Reservoir Material Balance Calculations. J Can PetTechnol 34 (1). PETSOC-95-01-07. http://dx.doi.org/10.2118/95-01-07 (http://dx.doi.org/10.2118/95-01-07)

http://dx.doi.org/10.2118/95-01-07

2. ↑ Walsh, M.P. 1994. New, Improved Equation Solves for Volatile Oil and Condensate Reserves. Oil & Gas J.(22 August): 72.

3. ↑ Walsh, M.P., Ansah, J., and Raghavan, R. 1994. The New, Generalized Material Balance as an Equation of a

Straight Line: Part 2 - Applications to Saturated and Non-Volumetric Reservoirs. Presented at the Permian BasinOil and Gas Recovery Conference, Midland, Texas, 16-18 March 1994. SPE-27728-MS.http://dx.doi.org/10.2118/27728-MS (http://dx.doi.org/10.2118/27728-MS)

4. ↑ 4.0 4.1 Walsh, M.P. and Lake, L.W. 2003. A Generalized Approach to Primary Hydrocarbon Recovery.Amsterdam: Elsevier.

5. ↑ Walsh, M.P., Ansah, J., and Raghavan, R. 1994. The New, Generalized Material Balance as an Equation of aStraight Line: Part 1 - Applications to Undersaturated, Volumetric Reservoirs. Presented at the Permian Basin Oil

and Gas Recovery Conference, Midland, Texas, 16-18 March 1994. SPE-27684-MS.http://dx.doi.org/10.2118/27684-MS (http://dx.doi.org/10.2118/27684-MS)

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Material balance in water drive reservoirs (/Material_balance_in_water_drive_reservoirs)

Primary drive mechanisms (/Primary_drive_mechanisms)

Oil fluid characteristics (/Oil_fluid_characteristics)

Oil fluid properties (/Oil_fluid_properties)

PEH:Oil Reservoir Primary Drive Mechanisms (/PEH%3AOil_Reservoir_Primary_Drive_Mechanisms)

(http://www.addthis.com/bookmark.php?v=300&pubid=ra-52d6c17f4a5b0215)

http://dx.doi.org/10.2118/27728-MS

http://dx.doi.org/10.2118/27684-MS

http://petrowiki.org/Material_balance_in_water_drive_reservoirs

http://petrowiki.org/Primary_drive_mechanisms

http://petrowiki.org/Oil_fluid_characteristics

http://petrowiki.org/Oil_fluid_properties

http://petrowiki.org/PEH%3AOil_Reservoir_Primary_Drive_Mechanisms

http://www.addthis.com/bookmark.php?v=300&pubid=ra-52d6c17f4a5b0215

material balance in oil reservoirs

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