Equations: Drive mechanisms and material balance

consistent units of pressure and compressibility: MPa and 1/MPa, or psi and 1/psi

Holds when: The pressure is above the bubble point, there is no free gas, and the aquifer is not working. The compressibilities are constant over the pressure range considered. The pressure is the same throughout the accumulation: a “tank” material balance.

consistent units; volumes in m³, gas in standard m³ (m³ of gas measured at standard conditions)

Holds when: The accumulation is treated as one “tank”: the pressure is the same throughout, and the phases are in equilibrium. The fluid properties from PVT studies refer to the average pressure. There is no injection; if there is, its volumes are added to the right side.

both sides are volumes at reservoir conditions, in m³; in oilfield units they are reservoir barrels, with $G$ in scf and $B_g$ in rb/scf

Holds when: There is no water influx, and no water is produced. The pore volume occupied by gas is constant: the expansion of the connate water and the decrease of the pore volume are neglected (the correction is in the advanced section). The reservoir temperature is constant, and the pressure is the same throughout the accumulation. The gas in the reservoir stays single-phase, and $G_p$ includes all the gas produced.

any units of pressure and gas volume: the formula contains only ratios

Holds when: The same as for the balance of a closed accumulation. $Z$ matches the composition of the reservoir gas and does not change because the composition changes during development.

a dimensionless share; pressures are absolute

Holds when: Depletion drive: there is no water influx. The whole accumulation is brought down to one pressure $p_a$ by the end of development.

m³ at reservoir conditions; in oilfield units, reservoir barrels

Holds when: The expansion of the connate water and the decrease of the pore volume are neglected. The pressure is the same throughout the accumulation, including the part flooded by water. $W_e$ is the whole volume of water that has entered the initial gas-filled volume, no matter how much gas it displaced and how much it bypassed.

m³ at standard conditions

Holds when: The compressibility of the pores and the connate water is neglected. The pressure measurements are accurate enough. When the pressure has fallen only a little, the difference $B_g - B_{gi}$ is small, and the error is large.

a dimensionless share

Holds when: At the end of development, all the remaining gas is at one pressure $p_a$. In the swept part the gas saturation equals $S_{gr}$, and in the unswept part it equals the initial value, $1 - S_w$. The compressibility of the pores and the connate water is neglected.

$\rho_c$ in kg/m³, $M_c$ in kg/kmol; the result is m³ of gas per m³ of liquid at 20 °C and 0.101325 MPa

Holds when: The vapour of the condensate at standard conditions is taken as an ideal gas ($Z = 1$). The density and molar mass refer to the liquid whose volume is counted in the production.

m³ at reservoir conditions; pressure and compressibilities in consistent units

Holds when: The compressibilities are constant over the pressure range considered. $c_f$ is the compressibility of the pore volume with respect to the fall of the pore pressure (Rock compressibility and the effect of stress on core properties).

m³; in oilfield units, reservoir barrels (rb), with $N_p$ in barrels of stock-tank oil (STB), $R$ in standard cubic feet per barrel (scf/STB) and $B_g$ in rb/scf

Holds when: the properties are taken at the same average reservoir pressure $p$ all the gas produced is counted, including gas burned at a flare and gas used for the field's own needs; gas injected into the wells for gas lift (to help the oil rise) is subtracted from the production above the bubble point pressure $R_p = R_s = R_{si}$, and the free-gas term is zero

m³/m³; in oilfield units rb/STB, with $B_g$ in rb/scf and $R_s$ in scf/STB

Holds when: $B_o$, $R_s$ and $B_g$ belong to the average reservoir pressure and to the laboratory way of releasing the gas that is closest to what happens in the reservoir (Laboratory PVT tests) the composition and properties of the oil are the same throughout the accumulation gas that has come out of the oil has either stayed in the accumulation or been counted in the production; the left side of the equation takes care of this

m³/m³

Holds when: the gas of the cap and the gas coming out of the oil are described by one formation volume factor $B_g$ the cap is at the same average pressure as the oil zone condensate dropping out of the gas of the cap is neglected

consistent units of pressure and compressibility: MPa and 1/MPa, or psi and 1/psi

Holds when: the compressibilities are constant over the pressure range considered $c_f$ is the compressibility of the pore volume, measured against the fall in pore pressure at reservoir conditions, not the compressibility of the rock as a whole the water saturation and the pore compressibility in the gas cap are the same as in the oil zone; otherwise the terms for the cap and for the oil zone are written separately

consistent units: volumes in m³, gas in standard m³ (sm³), pressure in MPa, compressibilities in 1/MPa; in oilfield units STB, scf, rb, psi and 1/psi, with no conversion constants

Holds when: the accumulation is one “tank”: the pressure is the same throughout the volume and the phases are in equilibrium the reservoir temperature is constant the fluid properties are described by the black oil model (oil taken as two components, stock-tank oil and gas) and belong to the average reservoir pressure there is no injection; injected volumes, $W_{inj}B_w + G_{inj}B_g$, are added to the right side time does not enter the equation: it links states, not rates

consistent units, as in the general equation

Holds when: the water influx $W_e$ and the gas cap ratio $m$ are known or equal to zero the pressure drop is large compared with the error in finding it

consistent units of pressure and compressibility

Holds when: the pressure is above the bubble point pressure; there is no gas cap and no water influx, and no water is produced the compressibilities are constant from $p_i$ to $p$

dimensionless fractions; volumes in the same units

Holds when: all the quantities belong to one date the oil in place $N$, the gas cap ratio $m$ and the water influx $W_e$ have already been found

m³ at reservoir conditions

Holds when: the same as for the general equation the split of the produced gas into gas of the cap and gas that came out of the oil is conventional: only their sum enters the final equation

m³ (in oilfield units, STB)

Holds when: there is no gas cap; there is no injection, or it has been subtracted from $F$ the pressure has fallen enough for its error to be small compared with $\Delta p$

m³

Holds when: there is no water influx one formation volume factor $B_g$ describes both the cap gas and the gas that came out of the oil; the cap is at the same average pressure as the oil zone

m³ (in oilfield units, STB)

Holds when: there is no water influx the pressure drop is large compared with the error of its measurement

m³; the units of $C$ and $w$ are such that their product is in m³ at reservoir conditions

Holds when: the type of the aquifer model and its geometry are chosen in advance, and only the parameter $C$ is unknown the pressure at the contact with the aquifer is taken as equal to the average pressure of the accumulation the gas cap ratio is known, or there is no gas cap

m³ at standard conditions; the integral in MPa·d

Holds when: a steady-state aquifer model the expansion of the connate water and the pores is neglected; the gas in the reservoir is single-phase

consistent units: m³ (oil and gas at standard conditions: 0.101325 MPa and 20 °C), $B_g$ in m³/m³; in oilfield units, STB, scf, rb/STB, rb/scf

Holds when: the accumulation is closed: no gas cap, no water influx or water production, no injection the pressure is the same throughout the volume (the “tank”), the phases are in equilibrium, and the properties are those of the black oil model at the average pressure $E_t$ is counted from the initial pressure of 30 MPa. If the accumulation started development above the bubble point pressure, $E_t$ includes the elastic expansion of the oil, the connate water and the pores gained there.

any consistent system: in metric units $R$ and $R_s$ in m³/m³, $B_g$ in m³/m³; in oilfield units $R$ and $R_s$ in scf/STB, $B_o$ in rb/STB, $B_g$ in rb/scf; the viscosities in the same units

Holds when: gas and oil flow to the well under the same pressure drop (capillary pressure is neglected) the relative permeabilities are taken at the average gas saturation of the drainage area, and in a tank forecast at that of the whole accumulation all the gas in the production is either dissolved in the oil produced or free gas of the same reservoir: there is no breakthrough of gas from a gas cap or from neighbouring formations

m³/m³ (scf/STB)

Holds when: gas used for gas lift and injected gas are excluded from the production figures in the step-by-step calculation $\bar R_i$ is the average of the gas–oil ratios at the two ends of the interval, so the intervals are taken shorter where $R$ changes fast

fractions; volumes in m³, pressure and compressibilities in MPa and 1/MPa

Holds when: the saturation is the same throughout the accumulation: the gas does not collect at the top in a secondary gas cap the accumulation is closed, and no water is produced the compressibilities are constant over the pressure range considered

m³ of gas at standard conditions

Holds when: within a step the gas–oil ratio changes linearly with the oil production (the trapezoid rule), so the pressure steps are taken small, a fraction of a megapascal where $R$ grows fast all the assumptions of the tank balance and of the gas–oil ratio equation

a dimensionless ratio; $R$ and $R_s$ in the same units

Holds when: the gas in the production is only dissolved and free gas of the oil zone: no gas cap, no gas injection and no crossflow the gas saturation on the same date is taken from the balance, from the cumulative oil production and the average pressure the gas measurements are complete: gas burned at a flare and gas used for the field's own needs are counted

MPa; volumes in any, but the same, units

Holds when: the drainage areas do not overlap and together make up the accumulation the pressures belong to one date and to one reference depth

MPa; $\Delta F_j$ and $\Delta p_j$ are for the same period

Holds when: the areas are closed: there is no crossflow between them, and the pressure drop of each is determined by its own withdrawal the total compressibility is the same in all areas, with the same fluids and saturations; below the bubble point pressure, where $c_t$ is set by the free gas, this assumption is rougher the pressure drop over the period is clearly larger than the error in finding it

metric oilfield units: $k$ in mD, $h$ in m, $\mu_o$ in mPa·s; $J^*$ in m³/(d·MPa)

Holds when: pseudo-steady-state flow, with the well at the centre of a round drainage area $k_{ro}$, $\mu_o$ and $B_o$ are taken at the average saturation and pressure of the accumulation, as in the “tank” the skin factor and the thickness do not change

m³; $\Phi_g$ is per 1 m³ of gas at standard conditions

Holds when: the accumulation is closed, with no water; water influx is added as the term $-(W_e - W_pB_w)\Phi_w$ with $\Phi_w = 1/E_t$

1/MPa; all the functions are positive below the bubble point pressure, so the oil saturation decreases together with the pressure

Holds when: the pore volume and the connate water saturation are constant (the compressibility of the water and the pores is not counted), which suits an accumulation that started development at the bubble point pressure the saturation is uniform, and the gas does not separate into a cap the derivatives of the properties (their rates of change with pressure) are taken from smoothed PVT data, because random scatter in the points is magnified in them

m³ of gas at standard conditions

Holds when: one $B_g$ describes both the cap gas and the gas that came out of the oil; the cap is at the same average pressure the cap gas does not break through to the wells; if it does, the gas–oil ratio equation of the oil zone no longer describes the production, and the cap gas is counted separately