Densities are then supplied to Eclipse as standard condition values (as in the DENSITY keyword in the “BASIC data input example”), and transforming these values to reservoir conditions is done by the formation volume factors, which is the ratio of a unit volume of fluid at reservoir conditions to the volume the same amount of fluid occupies at standard conditions,

Bl = Vl,RC , where l denotes gas, oil or water.

Vl,SC

The unit for Bl is Rm3/Sm3, reservoir cube metres on standard cube metres.

The dissolved gas-oil-ratio, Rs, is defined as the gas volume, measured at standard conditions, that can be dissolved in one standard conditions unit volume of oil, if both fluids are taken to reservoir conditions.

Then, since a volume of oil at reservoir conditions contains both pure (liquid) oil and dissolved gas, the formation volume factors can be expressed by the fluid densities as,

Oil will behave very differently depending on whether the oil pressure is above or below the bubble point. If the oil is at a higher pressure than the bubble point pressure, no gas will evaporate from the oil, and the oil behaves as a “pure” fluid, similar to water. Oil in this regime is called dead oil or undersaturated oil, while oil below the bubble point is called live, or saturated oil.

For gas, water or dead oil, increasing the fluid pressure results in compressing the fluid – it becomes heavier. Hence the volume formation factor will be decreasing with increasing pressure for such fluids. Also fluid viscosity must be expected to be non-decreasing as the fluid becomes heavier. When oil pressure is reduced below the bubble point, the behaviour is less predictable, as the oil will become heavier due to gas release, but lighter due to expansion.

Water

In the black oil model, water is pure water, and does not mix with oil or contain dissolved gas. Further, since water compressibility is low, a constant compressibility coefficient is assumed.

The coefficient of compressibility is defined as,

When Cw is constant, equation (14) can be solved easily:

Bw = Bw0 exp[Cw ( p − p 0 )]

From this expression, the volume formation factor can be calculated at any pressure from its value at a reference pressure p0.

Water viscosity can safely be assumed constant. Hence, Eclipse only needs water PVT data at a reference pressure Pref.

Eclipse syntax:

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It can safely be defaulted in almost all runs.

Example:

PVTW

Dead Oil

If the oil pressure stays above the bubble point pressure everywhere in the reservoir at all times, a simplified version of oil PVT data can be defined. In the permitted pressure regime, no gas is liberated from the oil in the reservoir, and hence the oil behaves as a pure liquid. Eclipse uses a special keyword for this situation, PVDO (PVT for Dead Oil). The table consists of three columns, with syntax for each line,

Po must be increasing down the column Bo must be decreasing down the column

µo must be non-decreasing down the column

Example

(See also Figure 11)

Po (bars)

Figure 11. Volume factor and viscosity, dead oil (from example PVDO table)

For dead oil no gas vaporises from the oil in the reservoir. When the oil flows in a producing well to the surface, the oil pressure will normally be far below bubble point when the oil arrives at the platform. The released gas volume pr. unit oil volume will however be constant, since all oil departed

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the reservoir as dead oil. The amount of released gas which must be accounted for on the surface can therefore be specified as a constant, which must be supplied to Eclipse in dead oil runs,

Note that if the pressure in any grid block falls below the bubble point pressure PBP, the run will terminate.

Example

RSCONST

--Rs P_BP

180 230 /

Dry Gas

Gas which does not contain vaporised oil is denoted dry gas, and is the only kind of gas we will look at in these notes.

PVT data for dry gas are equivalent to PVT data for dead oil, and the table syntax in Eclipse is equal: Each line,

Pg [bars] µg(Pg) [cP]

Pg must be increasing down the column Bg must be decreasing down the column

µg must be non-decreasing down the column

Pg (bars)

Figure 12. Volume factor and viscosity for dry gas (from example PVDG table)

Example

(see also Figure 12)

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PVDG

-- Pg Bg mu_g

27.20.03313 0.0130

54.40.016564 0.0135

81.60.010051 0.0140

108.80.007500 0.0145

136.00.006255 0.0150

163.20.005503 0.0155

190.40.004716 0.0160

217.60.004155 0.0165

245.00.00365 0.0170

272.00.00328 0.0175

299.20.00303 0.0180

326.40.00275 0.0185

353.60.00253 0.0190

380.80.00236 0.0195 /

Live Oil

An undersaturated oil has a well defined bubble point pressure PBP. If the oil pressure is reduced to PBP the oil starts to boil, and gas evaporates from the oil. But once this process starts, the oil itself changes

– when some gas has been liberated from the oil, the remaining liquid oil contains less dissolved gas than before the evaporation, such that the oil is heavier, and with a new, lower bubble point than originally. Hence, PVT relationships for live oil must describe both how the oil itself changes, and for “each type of oil” how properties vary with primarily oil pressure. As long as the “oil type” is constant the property variation is similar to that of dead oil, described by the PVDO keyword. Whereas the bubble point is constant for dead oil, for live oil it is directly related to the “oil type”, which can be characterized by the gas resolution factor Rs. Hence we must specify the relationship between Rs and PBP, as well as variation of oil properties – typically the liquid oil grows heavier and more viscous as the amount of dissolved gas is reduced. The table can use either PBP or Rs as primary variable, in Eclipse Rs has been chosen.

The table contains two types of data,

1.Data for saturated oil, tabulated as a function of Rs. Each line contains PVT data relating to the supplied Rs –value.

2.Data for undersaturated oil, valid for a certain value of Rs, and tabulated as a function of oil pressure. This data must be defined for the largest Rs –value in the table, and can also be defined for other Rs –values.

One record in the table is comprised of four items if data is of the first kind, and an additional subtable if it is of the second kind. Each record is terminated by a slash.

Data of the first kind are given as,

Rs [Sm3/Sm3] PBP(Rs) [bars] Bo(PBP) [Rm3/Sm3] µo(PBP) [cP]

The Rs –values should be increasing within the table.

When data of the second kind are supplied, the record takes the form,

I.e. the first four items are defined as above, and then additional data are defined, tabulated as a function of Po (which must be defined in increasing order, starting with PBP), all valid for the current value of Rs.

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