Production from Two-phase Reservoirs:

- Phase diagram- Gas oil ratio in saturated reservoirs- Properties of two phase fluids, relative permeability- Comparing single and two phase flows

Steady statePseudo steady state

- Inflow performance relationship (IPR)Single phase flowTwo phase flow

Vogel’s correlationsGeneralized Vogel’s correlationsFetokovich’s approximation

Earlier flow relationships have considered only single-phase flow of oil. The effect

of simultaneously producing liquid (oil) and gas on the liquid flow rate will now be

considered.

(From, Dake, Fundamentals of Reservoir Engineering)

If the reservoir is below bubble point pressure, as depicted in fig. 2.1(b), the situation is more complicated. Now there are two hydrocarbon phases in the reservoir, gas saturated oil and liberated solution gas. During production to the surface, solution gas will be evolved from the oil phase and the total surface gas production will have two components; the gas which was free in the reservoir and the gas liberated from the oil during production. These separate components are indistinguishable at the surface and the problem is, therefore, how to divide the observed surface gas production into liberated and dissolved gas volumes in the reservoir.

In a saturated reservoir each stock tank barrel of oil is produced in conjunction with R scf of gas, where R (scf/stb) is called the instantaneous or producing gas oil ratio and is measured daily (see fig 2.3). As already noted, some of this gas is dissolved in the oil in the reservoir and is released during production through the separator, while the remainder consists of gas which is already free in the reservoir. Furthermore, the value of R can greatly exceed Rsi, the original solution gas oil ratio, since, due to the high velocity of gas flow in comparison to oil, it is quite normal to produce a disproportionate amount of gas. This results from an effective stealing of liberated gas from all over the reservoir and its production through the relatively isolated offtake points, the wells. A typical plot of R as a function of reservoir pressure is shown as fig. 2.4.

The producing gas oil ratio can be split into two components as shown in fig. 2.3, i.e.R = Rs +(R-Rs)The first of these, Rs scf/stb, when taken down to the reservoir with the one stb of oil, will dissolve in the oil at the prevailing reservoir pressure to give Bo rb of oil plus dissolved gas. The remainder, (R -Rs) scf/stb, when taken down to the reservoir will occupy a volume

and therefore, the total underground withdrawal of hydrocarbons associated with the production of one stb of oil is(Underground withdrawal)/stb = Bo + (R Rs) Bg (rb/stb)

The shapes of the Bo and Rs curves below the bubble point, shown in fig. 2.5(a) and(b), are easily explained. As the pressure declines below pb, more and more gas is liberated from the saturated oil and thus Rs, which represents the amount of gas dissolved in a stb at the current reservoir pressure, continually decreases. Similarly, since each reservoir volume of oil contains a smaller amount of dissolved gas as the pressure declines, one stb of oil will be obtained from progressively smaller volumes of reservoir oil and Bo steadily declines with the pressure.

The presence of a gas phase reduces the relative permeability of oil.

Relative permeabilities are laboratory-derived relationships, are functions of fluid

saturations and functions of specific reservoir rock.

The expansion of free gas creates an effective mechanism for the production of fluids.

The reservoir pressure, which is the driving force for the flow, decreases rapidly with

production from a reservoir containing liquid only.

Comparing the Flow Equations for Single and Two-phase Flows:

STEADY STATE INFLOW:

PSEUDO-STEADY STATE FLOW:

INFLOW PERFORMANCE RELATIONSHIP (IPR):

All well deliverability equations relate the well production rate and the driving force in

the reservoir, that is, the pressure difference between the initial, outer boundary or

average reservoir pressure and the flowing bottomhole pressure.

If the bottomhole pressure is given, the production rate can be obtained readily.

However, the bottomhole pressure is a function of the wellhead pressure, which, in turn,

depends on production engineering decisions, separator or pipeline pressures, etc.

Therefore, what a well will actually produce must be the combination of what the

reservoir can deliver and what the imposed wellbore hydraulics would allow.

It is then useful to present the well production rate as a function of the bottomhole

pressure. This type of presentation is known as an "inflow performance relationship"

(IPR) curve. Usually, the bottomhole pressure, pwf, is graphed on the ordinate and the

production rate, q, is graphed on the abscissa.

Pseudo steady state IPR calculation is the most useful and most commonly done

for the forecast of well performance. Each IPR curve reflects a “snapshot” of well

performance at a given reservoir pressure. This is time dependent calculation done in

discrete intervals. In combination with “volumetric material balances” it will allow the

forecast of rate and cumulative production versus time.

The complex analytical solutions to the two-phase flow equations will not be

considered in this course. The two-phase correlations of Vogel and Fetkovitch will

be presented.

Vogel's Correlations:

Vogel developed a set of inflow performance relationship (IPR) correlations. The

particular correlation that is appropriate is dependent on the magnitude of the average

reservoir pressure, , and the wellbore pressure, Pwf, relative to the bubble-point

pressure, Pb. These correlations are valid for a wide range of reservoir and fluid

properties. Only the properties of the oil phase associated with the two-phase flow are

required for Vogel's correlations.

Case 1: Pwf < Pb (original Vogel Correlation)

In this case there is two-phase flow throughout the reservoir:

o and B are evaluated at .

Case 2: > Pb but Pb Pwf (Vogel's Generalised Correlation)

A limiting volumetric flow, qb, is defined which represents the flow that occurs in the

specific case when the wellbore pressure is equal to the bubblepoint pressure (Pwf=Pb).

Fetkovitch Inflow Performance Relationship:

In some cases Vogel's correlations do not accurately represent well /reservoir

behavior. The correlation of Fetkovitch can also be applied to two-phase systems.

Fetkovitch developed an empirical equation based on two correlation parameters,

qo,max and n. To apply the correlation, well measurements must be performed during at

least two stable flow conditions. Fetkovich's equation is adjusted to fit to the data

using the parameters.

The following two equations are combined to give the final empirical equation: