4фото1слово крокодил смотрит в лупу, бумажный самолкт, настоящий самолет...

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

Material balance equation

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



  • 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 настоящий самолет.

    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 for oil reservoirs apply to any consistent set of units.

A few 4фото1слово крокодил смотрит в лупу, however, are written assuming English or customary units. Those equations are expressed in SI units:







and .(8)

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 + GfgiRvi and G = Gfgi + NfoiRsi.

The expansivities are defined as




and , where B to and B настоящий самолет.

are the two-phase formation volume factors (FVFs),


and .(13)

The rock expansivity is obtained from direct measurement.

See compaction driving oil reservoir for a greater discussion.

Physically, the two-phase FVF is the total hydrocarbon volume per unit volume of oil or gas at standard conditions. The настоящий самолет. 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 standard conditions. In contrast, the two-phase gas FVF is the total hydrocarbon volume of a saturated gas sample per unit volume of 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 FVF
  • For undersaturated gases, the two-phase gas FVF is equal to the gas FVF.

Eqs. 12 бумажный самолкт 13 account for volatilized oil in the equilibrium gas phase. If volatilized oil is negligible, these equations are simplified. For instance, Bto = Bo + Bg (RsiRs) 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 4фото1слово крокодил смотрит в лупу, it shows the different forms of expansion and withdrawal. The бумажный самолкт forms of expansion such as gas expansion are responsible for the different producing mechanisms.

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



  • F настоящий самолет. total net fluid withdrawal or production
  • Egwf = composite gas expansivity
  • Eowf = composite oil expansivities

F, Egwf, and настоящий самолет.

are defined in



and .(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 (GpGI).

  • F is expressed in reservoir volume units (e.g., RB or res m3)
  • Egwf is expressed in reservoir volume units per standard unit volume of gas (e.g., RB/scf)
  • Eowf is 4фото1слово крокодил смотрит в лупу 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.114, and 15 simplify, respectively, to[1][4][5]




Eqs.18 through 20 ignore gas reinjection.

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


Eq.21 succinctly shows that oil recovery increases with:

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 настоящий самолет.

    the OOIP and OGIP

  • Estimating gas cap sizes
  • Estimating water influx настоящий самолет. water influx model parameters
  • Estimating producing indices


Bg = gas FVF, RB/scf
Bo = oil FVF, Настоящий самолет.
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 настоящий самолет., Lt2/m, 1/psi
Ef = rock (formation) expansivity
Eg = gas expansivity, RB/scf
Egw = expansivity for McEwen method, RB/scf
Egwf 4фото1слово крокодил смотрит в лупу composite gas/water/rock FVF, RB/scf
Eo = oil expansivity, RB/STB
Eow настоящий самолет.

expansivity for McEwen method, RB/STB
Eowf = composite oil/water/rock FVF, RB/STB
Ew = настоящий самолет. water expansivity, RB/STB
F = total fluid withdrawal, L3, RB
G = total original gas in place, L3, scf
Gfgi = настоящий самолет.

free gas in place, L3, scf бумажный самолкт =

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
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 бумажный самолкт = volatilized-oil/gas ratio, STB/MMscf
Swi = настоящий самолет.

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 4фото1слово крокодил смотрит в лупу, m/Lt, cp


  1. 1.01.1Walsh, M.P.

    1995. A Generalized Approach to Reservoir Material Balance Calculations. J Can Pet Technol 34 (1). PETSOC-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 настоящий самолет. Straight Line: Part 2 - Applications to Saturated and Non-Volumetric Reservoirs.

    Presented at the Permian Basin Oil and Gas Recovery Conference, Midland, Texas, 16-18 March 1994.

    4фото1слово крокодил смотрит в лупу, бумажный самолкт, настоящий самолет...

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

  4. 4.04.1Walsh, 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 настоящий самолет. a Straight Line: Part 1 - Applications to Undersaturated, Volumetric Reservoirs. Presented at the Permian Basin Oil and Gas Recovery Conference, Midland, Texas, 16-18 March 1994.

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

Noteworthy papers in OnePetro

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<a href="https://www.onepetro.org/conference-paper/SPE-105982-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#" alt="https://www.onepetro.org/conference-paper/SPE-105982-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#" title="https://www.onepetro.org/conference-paper/SPE-105982-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#">https://www.onepetro.org/conference-paper/SPE-105982-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#</a>

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<a href="https://www.onepetro.org/general/SPE-4920-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#" alt="https://www.onepetro.org/general/SPE-4920-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#" title="https://www.onepetro.org/general/SPE-4920-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#">https://www.onepetro.org/general/SPE-4920-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#</a>

<a настоящий самолет.

alt="https://www.onepetro.org/conference-paper/SPE-172415-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#" title="https://www.onepetro.org/conference-paper/SPE-172415-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#">https://www.onepetro.org/conference-paper/SPE-172415-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#</a>

<a href="https://www.onepetro.org/conference-paper/SPE-62882-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#" alt="https://www.onepetro.org/conference-paper/SPE-62882-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#" title="https://www.onepetro.org/conference-paper/SPE-62882-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#">https://www.onepetro.org/conference-paper/SPE-62882-MS?sort=&start=0&q=material+balance+in+oil+reservoirs&from_year=&peer_reviewed=&published_between=&fromSearchResults=true&to_year=&rows=10#</a>

External links

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See also

Material balance in water drive reservoirs

Primary drive mechanisms

Oil fluid characteristics

Oil fluid properties


Источник: http://petrowiki.org/Material_balance_in_oil_reservoirs

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