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# Displacement efficiency of immiscible gas injection

The conceptual aspects of the displacement of oil by gas in reservoir rocks are discussed in this article. There are three aspects to this displacement: gas and oil viscosities, gas/oil capillary pressure (Pc) and relative permeability (kr) data, and the compositional interaction, or component mass transfer, between the oil and gas phases.

## Gas/oil viscosity and density contrast

One must first understand the viscosity and density differences between gas and oil to appreciate why the gas/oil displacement process can be very inefficient. Gases at reservoir conditions have viscosities of ≈0.02 cp, whereas oil viscosities generally range from 0.5 cp to tens of centipoises. Gases at reservoir conditions have densities generally one-third or less than that of oil. Thus, gas is generally one to two orders of magnitude less viscous than the oil it is trying to displace. Regarding the fluid density difference, gas is always considerably "lighter" than the oil; hence, gas, when flowing, will segregate by gravity to the top of the reservoir or zone and oil will "sink" simultaneously to the bottom of the reservoir or zone.

Another gas/oil property that must be known for calculations at reservoir conditions is the interfacial tension (IFT) between the oil and gas fluid pair. This value is needed at reservoir conditions for the conversion of gas/oil capillary pressure data from surface to reservoir conditions. A number of technical papers discuss the calculation of IFT from compositional information about the oil and gas phases.[1][2][3][4][5] Table 1 from Firoozabadi et al.[4] shows several reservoir oil-gas fluid-pair IFT values (measured and calculated) as a function of temperature and pressure. As the pressure increases, the IFT values decrease, although not low enough for miscible displacement to occur. Although not illustrated in the table, it should be noted that the IFT between nitrogen and oil is higher than that between a lean natural gas and the same oil.

## Gas/oil capillary pressure and relative permeability

The gas/oil capillary pressure and relative permeability data are typically measured by commercial laboratories using routine special core analysis procedures. Gas-oil capillary pressure data can be measured with either porous-plate or centrifuge equipment. One approach for obtaining gas/oil relative permeability data is the viscous displacement method in which gas displaces oil. A second method is the centrifuge method, which is generally used to obtain capillary pressure and relative permeability information simultaneously.

In all cases, gas is the nonwetting phase in this displacement; hence, it will preferentially flow through the largest pores first. However, what is very important in the determination of the oil relative permeability is the distribution of the oil phase in the core sample because in real reservoirs connate water occupies the smallest pores. As shown by Hagoort,[6] initial water saturation has a significant effect on oil relative permeability during the gas/oil displacement (centrifuge experiments). The water phase will occupy a greater percentage of the smaller pore spaces as the connate water saturation increases. As a result, the pore structure appears more streamlined to the oil and gas phases. The oil relative permeability at higher connate water saturations is considerably higher (see Fig. 1 and the discussion of capillary pressure and relative permeability concepts in Relative permeability and capillary pressure).

The other key aspect of the oil relative permeability (kro) is the determination of its value as the oil saturation decreases. Because oil relative permeability becomes quite low but nonzero, the time to reach equilibrium in laboratory core plug measurements can be very long. Fig. 12.1 presents experimental results for cumulative oil recovery as a function of drainage time and shows that the oil continues to flow but more and more slowly (linearly as a function of the logarithm of tD); Hagoort[6] found similar behavior for the four different rock types he tested.

If the gas/oil relative permeability data were measured with the viscous displacement technique (the extended Welge technique as described by Johnston et al.),[7] extra care is needed in applying these data. First, the displacement of oil by gas is at an unfavorable mobility ratio (see discussion below) that makes the process unstable. Second, a displacement is adversely affected by capillary end effects that, for the gas/oil system, cannot be overcome by high gas throughput rates. At low oil saturations, the region of most interest, the capillary end effect is the greatest.[6]

Finally, one method developed to affect the gas/oil relative permeability and to reduce gas mobility is to inject water alternately with gas (WAG). This procedure was proposed by Caudle and Dyes.[8] Although the method was proposed for use in miscible gasfloods, the concept applies equally to immiscible gas displacements. This technique has been used in many west Texas CO2 miscible gas projects, in the Prudhoe Bay miscible flood,[9] and in the Kuparuk immiscible and miscible gas injection processes.[10][11] The three-phase gas, oil, and water relative permeabilities are calculated in numerical reservoir simulators with algorithms developed over the past several decades.[12]

## Mobility ratio

The mobility of a fluid (Eq. 1) is defined as its relative permeability divided by its viscosity. Mobility combines a rock property, permeability, with a fluid property, fluid viscosity. Gas-oil relative permeabilities are assumed to be dependent on the saturations of the two fluid phases and independent of fluid viscosity:

....................(1)

A fluid’s mobility relates to its flow resistance in a reservoir rock at a given saturation of that fluid. Because viscosity is in the denominator of this definition, gases, which are very-low-viscosity fluids, have very high mobility.

Mobility ratio is generally defined as the mobility of the displacing phase (in the gas/oil case, gas) divided by the mobility of the displaced phase, which is oil. Eq. 2 presents two forms of the mobility ratio equation:

....................(2)

Eq. 2 can also be written in more familiar engineering terms as the ratio of the two fluids’ relative permeability values multiplied by the ratio of the two fluids’ viscosities.

....................(3)

For simple calculations, the mobility ratio is calculated at the endpoint relative permeability values for the two phases. Hence, the equation that practical engineers use for the gas/oil mobility ratio is

....................(4)

All displacements of oil by gas are at "unfavorable" mobility ratios, with typical values of 10 to 100 or more.

## Gas/oil linear displacement efficiency

The equations that characterize the mechanics of oil displacement by an immiscible fluid were developed by Buckley and Leverett[13] using relative permeability concepts and Darcy’s law describing steady-state fluid flow through porous media. The resulting fractional flow equation describes quantitatively the fraction of displacing fluid flowing in terms of the physical characteristics of a unit element of porous media. Assumptions inherent in their work are steady-state flow, constant pressure, no compositional effects, no production of fluids behind the gas front, no capillary effects, movement of advancing gas parallel to the bedding plane, immobile water saturation, and uniform cross-sectional flow (no gravity segregation of fluids within the element). Subsequent work by Welge[14] made solving the displacement equations easier.

The Welge equation for the fractional flow of gas at any gas saturation (Sg) is calculated as follows:

....................(5)

where

 A = area of cross section normal to the bedding plane, ft2, fg = fraction of flowing stream that is gas, k = permeability, darcies, kro = relative permeability to oil, fraction, krg = relative permeability to gas, fraction, M = mobility ratio, , qT = total flow rate through area A , res ft3/D, α = angle of dip, positive downdip, degrees, Δρ = density difference, ρg – ρo, lbm/ft3, μo = viscosity of oil, cp, and μg = viscosity of gas, cp.

When gravity is negligible, this equation becomes the more familiar Buckley-Leverett equation:

....................(6)

Fig. 2 is a typical plot resulting from these calculations. The importance of the gravity term is indicated.

To relate the fraction of gas flowing to time, Buckley and Leverett developed the following material-balance equation:

....................(7)

where

 L = length, ft, Sg = gas saturation, fraction, t = time, days, and ϕ = porosity, fraction.

The value of the derivative dfg/dSg may be obtained for any value of gas saturation by determining slopes at various points on the fg vs. Sg curve. These slopes can be determined manually or, more precisely, using the method presented by Kern[15] for computer spreadsheets. Fig. 3 illustrates calculated gas-saturation distributions derived from the no-gravity and with-gravity fractional flow curves shown in Fig. 2. The area beneath each curve represents the gas-invaded zone. The saturation profile calculation results in lengths that first increase as saturation decreases and then decrease at lower saturations. While correct from a material-balance standpoint, it has been customary to square off the leading edge of the curve at the breakthrough saturation to account for capillary pressure that was neglected in the original derivation of the equation.

The gas/oil displacement efficiency, the percent of the oil volume that has been recovered, can be calculated for any period of gas injection by integrating the volume of the gas-invaded zone as a function of gas saturation (Sg). Hence, the fractional flow curves (Fig. 2) are used to generate saturation profiles (Fig. 3) that lead to values for the gas/oil displacement efficiency. In the next section, several of the factors affecting this efficiency are discussed.

## Factors affecting gas/oil displacement efficiency

The fractional-flow and material-balance equations discussed above are important for understanding the effects on the efficiency of the gas/oil displacement process of:

1. Initial saturation conditions
2. Fluid viscosity ratios
3. Relative permeability ratios
4. Formation dip
5. Capillary pressure
6. Factors of permeability, density difference, rate of injection, and cross section open to flow.

### Initial saturation conditions

If gas injection is initiated after reservoir pressure has declined below the bubblepoint, the gas saturation will decrease the amount of displaceable oil. If the free gas saturation exceeds the breakthrough saturation, no oil bank will be formed. Instead, oil production will be accompanied by immediate and continually increasing gas production. Laboratory investigations and mathematical analyses have demonstrated this influence of gas saturation on gas displacement performance.[16]

Swi has been shown to have no influence on displacement efficiency at gas breakthrough, but it directly affects the displaceable oil volume.[17] If Swi is mobile, the displacement equations are not directly applicable because they were developed for two-phase flow. Approximations of gas displacement performance can usually be made when three phases are mobile by treating the water and oil phases as a single liquid phase. Displacement calculations can then be made with krg and kro data determined from core samples containing an immobile water saturation. Oil recovery can be differentiated from total liquid recovery on the basis of material balance calculations incorporating an estimated minimum interstitial water saturation.

### Fluid viscosities

The effect of oil viscosity on fractional flow is illustrated in Fig. 4. In this plot, the Sg at breakthrough increases from 12 to 38% with a 10-fold decrease in oil viscosity.

### Relative permeability ratios

The concepts of relative permeability can be applied equally well to complete or partial pressure-maintenance operations. Relative permeability, a characteristic of the reservoir rock, is a function of fluid saturation conditions. It is important that calculations be based on dependable data obtained by laboratory analyses at reservoir conditions using representative core samples. If possible, the laboratory-determined data should be supplemented by relative permeabilities calculated from field performance data.

### Formation dip

When formation dip aids gravity, as illustrated in Fig. 2, fractional flow behavior is significantly improved if permeability is high enough and withdrawal rates do not exceed gravity-stable conditions. {See Vertical or gravity drainage gas displacement)

### Capillary pressure

Capillary forces are opposite gravity drainage forces and directionally decrease displacement efficiency. However, capillary forces can often be ignored as insignificant for projects with rates of displacement normally used. Only at extremely low rates of displacement, where viscous forces become negligible, is the saturation distribution controlled to a significant extent by the balance between capillary and gravitational forces. Another place where capillary forces are considered important is many of the large carbonate reservoirs of the Middle East where the matrix-blocks/fracture-system interaction can significantly affect overall reservoir performance.

### Other factors

Higher permeability, greater density difference between oil and gas, and a lower displacement rate all improve the displacement efficiency.

## Unfavorable mobility ratio causes viscous flow instabilities

Displacements that take place at very unfavorable mobility ratios are unstable, and viscous fingering occurs. This is the situation for essentially all gas/oil displacements, especially if the displacement is occurring horizontally. The impact of such instabilities is illustrated in Figs. 5 and 6.[18][19] Both figures were drawn from technical literature concerning miscible displacement laboratory experiments using homogeneous sandpacks, but the observed effects would be the same for immiscible gas displacing oil at very unfavorable mobility ratios. Fig. 5 shows, in cross-sectional view, the nature of viscous fingering for two highly unfavorable mobility ratios (the two fluids have equal densities). The flood front in both cases is very unstable. Fig. 6 shows, in areal view, the effect of mobility ratio on the displacement process in a quarter of a five-spot pattern for mobility ratios from 0.151 to 71.5. For mobility ratios from 4.58 to 71.5 (cases D through F), the flood front is very unstable, and breakthrough occurs via narrow fingers of the injected fluid; these cases show how the process of gas displacing oil would occur.

In both of these illustrations, the cause of the viscous fingering was a slight perturbation in the flow field that grew into the viscous finger once the perturbation occurred. In real reservoir situations, there are two physical aspects that enhance the viscous-fingering phenomenon. First, real reservoirs are very heterogeneous, so a variety of styles of permeability heterogeneities can initiate viscous fingering. Second, in a cross-section immiscible gas/oil displacement process, gas is always less dense than oil. Hence, there is a gas/oil density difference, and the force of gravity causes the gas to override the oil and initiate a viscous finger of the high-mobility gas phase along the top of the reservoir interval.

If the gas/oil displacement is occurring vertically with gas generally displacing oil downward, gravity will work to stabilize the flood front between the gas and oil, although if the rate is too high, instabilities in the form of gas cones or tongues can occur.

## Nomenclature

 A = cross-sectional area, ft2 Fg = fractional gas flow, fraction k = permeability, darcies kro = relative permeability to oil, fraction krg = relative permeability to gas, fraction L = distance along the bedding plane, ft M = mobility ratio, krgμo/kroμg qT = total flow rate through area A , ft3/D Sg = gas saturation, fraction PV Sorg* = irreducible oil saturation in presence of gas, fraction PV Swi = initial water saturation, fraction PV t = time, days α = angle of dip (positive downdip), degrees μg = gas viscosity, cp μo = oil viscosity, cp ϕ = porosity, fraction

## References

1. Katz, D.L., Monroe, R.R., and Tanner, R.P.: "Surface Tension of Crude Oils Containing Dissolved Gases," Pet. Tech. (September 1943) 1.
2. Hough, E.W. and Warren, H.G.: "Correlation of Interfacial Tension of Hydrocarbons," SPEJ (December 1966) 345.
3. Katz, D.L. and Firoozabadi, A.: "Predicting Phase Behavior of Condensate/Crude-Oil Systems Using Methane Interaction Coefficients," JPT (November 1978) 1649–1655.
4. Firoozabadi, A. et al.: "Surface Tension of Reservoir Crude-Oil/Gas Systems Recognizing the Asphalt in the Heavy Fraction," SPERE (February 1988) 265.
5. Broseta, D. and Ragil, K.: "brchors in Terms of Critical Temperature, Critical Pressure and Acentric Factor," paper SPE 30784 presented at the 1995 SPE Annual Technical Conference and Exhibition, Dallas, 22–25 October.
6. Hagoort, J.: "Oil Recovery by Gravity Drainage," SPEJ (June 1980) 139.
7. Johnston, E.F., Bossler, C.P., and Naumann, V.O.: "Calculation of Relative Permeability From Displacement Experiments," Trans ., AIME (1959) 216, 61.
8. Miscible Processes, Reprint Series, SPE, Richardson, Texas (1957) 8, 111–114.
9. Simon, A.D. and Petersen, E.J.: "Reservoir Management of the Prudhoe Bay Field," paper SPE 38847 presented at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5–8 October.
10. Ma, T.D. and Youngren, G.K.: "Performance of Immiscible Water-Alternating-Gas (IWAG) Injection at Kuparuk River Unit, North Slope, Alaska," paper SPE 28602 presented at the 1994 SPE Annual Technical Conference and Exhibition, New Orleans, 25–28 September.
11. Stoisits, R.F., Scherer, P.W., and Schmidt, S.E.: "Gas Optimization at the Kuparuk River Field," SPE 28467 presented at the 1994 SPE Annual Technical Conference and Exhibition, New Orleans, 25–28 September.
12. Aziz, K. and Settari, A.: Petroleum Reservoir Simulation, Applied Science Publishers Ltd., London (1979) 30–38.
13. Buckley, S.E. and Leverett, M.C.: "Mechanism of Fluid Displacement in Sands," Trans ., AIME (1942) 146, 107.
14. Welge, H.J.: "A Simplified Method for Computing Oil Recovery by Gas or Water Drive," Trans., AIME (1952) 195, 91.
15. Kern, L.R.: "Displacement Mechanism in Multi-well Systems," Trans., AIME (1952) 195.
16. Craft, B.C. and Hawkins, M.F.: Applied Petroleum Reservoir Engineering, Prentice-Hall Inc., Englewood Cliffs, NJ (1959) 370.
17. Anders, E.L. Jr.: "Mile Six Pool: An Evaluation of Recovery Efficiency," JPT (November 1953) 279; Trans ., AIME, 198.
18. Miscible Processes, Reprint Series, SPE, Richardson, Texas (1965) 8, 197.
19. Miscible Processes, Reprint Series, SPE, Richardson, Texas (1965) 8, 205.