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# Microscopic efficiency of waterflooding

At the pore level (i.e., where the water and oil phases interact immiscibly when moving from one set of pores to the next), wettability and pore geometry are the two key considerations. The interplay between wettability and pore geometry in a reservoir rock is what is represented by the laboratory-determined capillary pressure curves and water/oil relative permeability curves that engineers use when making original oil in place (OOIP) and fluid-flow calculations. This article discusses these basic concepts and their implications for initial water- and oil-saturation distribution, relative permeability, and how initial gas saturation will affect water/oil flow behavior.

Fig. 1[1] is a schematic diagram of the water/oil displacement process.

## Wettability

Wettability is defined in terms of the interaction of two immiscible phases, such as oil and water, and a solid surface, such as that of the pores of a reservoir rock. For understanding wettability concepts and for simple laboratory determinations, the solid surface is taken as a smooth flat surface. Fig. 2[2] illustrates two styles of wettability: water-wet and oil-wet. Eq. 1 describes the force relationship that is in balance for the drop of water that is on the solid surface and is surrounded by oil. The interfacial tension (IFT) between the oil and water phases varies depending on the compositions of the phases but generally is relatively high, in the 10- to 30-dyne/cm range. The contact angle θ is used to define which fluid phase is more wetting—for low contact angles, the water phase is more wetting, whereas for high contact angles, the oil phase is more wetting.

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

where σos = the IFT between the oil and solid phases, σws = the IFT between the water and solid phases, and σow = the IFT between the oil and water phases.

The particular contact angle depends on many variables, including the composition of the crude oil and the amount of gas in solution; the salinity and pH of the connate brine; the mineralogy of the rock surfaces; and the salinity and pH of the injected water that is used for waterflooding. The concentration of surface-active components (e.g., asphaltenes) that are in the crude oil and that can adsorb on the rock surfaces affects wettability.

Reservoir rocks typically are described as being water-wet, oil-wet, or intermediate-wet. A water-wet rock surface is one that has a strong preference to be coated, or "wetted," by the water phase, so that there will be a continuous water phase on the rock surfaces. Oil-wet rocks prefer to be coated with oil instead of water. Strongly oil-wet rocks have been created for laboratory studies but, as discussed below, are unlikely to exist in real reservoirs. Intermediate-wet reservoir rocks have been found in several oil reservoirs. The term "dalmatian wetting" describes reservoir rocks that have both oil-wet and water-wet surfaces. Fig. 3 illustrates two styles of intermediate-wetting.

Two types of laboratory measurements commonly are used to estimate wettability. First, the crude-oil/brine IFT values can be measured on smooth rock surfaces of various mineralogies. Second, Amott tests can be run on the reservoir rock to determine the extents to which it imbibes oil and brine. When running the Amott tests, it is critical to initialize the core plugs as close to original reservoir conditions as possible either by using well-preserved core samples or by aging the core plugs in the presence of reservoir crude oil. High-quality water/oil capillary-pressure (Pc) and water/oil relative permeability (krwo) data, both of which are strongly affected by rock wettability, are needed as input to waterflood calculations, whether using simple engineering methods or complex numerical reservoir simulators.

## Pore geometry

The pore geometry for any reservoir rock is the result of its depositional and diagenetic history. The depositional environment determines a rock’s grain size and sorting. Post-depositional diagenetic changes caused by various types of cementation, leaching, and clay alteration will impact a rock’s pore characteristics whether the rock is primarily silica or carbonate.

Figs. 4 and 5 show photomicrographs and krwo curves for a sandstone with large, well-connected pores and for one with small, well-connected pores, respectively. These illustrate just one of many possible differences in pore geometry. Pore distributions in carbonate rocks often are more complicated because of vug networks and fractures. Also, there are many scales of pore-geometry heterogeneities; a core plug has one scale of pore-size variation, but other important variations are found at each higher scale.

## Capillary pressure

The characteristics of and differences between the drainage and imbibition capillary-pressure/water-saturation (Pc/Sw) curves are considered. Capillary pressure affects waterflood performance and engineering calculations because the extent to which the water/oil flood front is vertically and horizontally "smeared out" during the waterflood is controlled by the Pc/Sw imbibition curve.

Reservoir rocks are considered to be water-wet initially because all reservoir rocks were deposited in water-filled environments or were immersed in water soon after deposition, when their overlying sediments were deposited. The drainage Pc/Sw curve describes the drainage process, or the Pc/Sw relationship while the nonwetting-fluid phase (oil) displaces the wetting-fluid phase (brine) from various parts of the pore system, thus decreasing the wetting-phase saturation. If during the displacement process the process is reversed and the wetting-phase saturation increases, it is known as imbibition (the imbibing of the wetting phase).

Fig. 6 shows the drainage and imbibition Pc/Sw characteristics of a strongly water-wet rock. The minimum wetting or water saturation from the drainage process is termed the connate (or irreducible) water saturation. The maximum water saturation from the imbibition process defines the minimum nonwetting-phase saturation, or (for waterflooding considerations) the residual oil saturation to waterflooding Sorw. Figs. 7 and 8 show the drainage and imbibition Pc/Sw curves from the laboratory tests of an oil-wet rock and a rock with intermediate wettability, respectively. Fig. 8 includes both the spontaneous (number 2 on curve) and the forced (number 3 on curve) portions of the imbibition curve. Spontaneous imbibition occurs without any pressure being applied to the test apparatus, whereas obtaining the forced imbibition portion of the curve requires an external pressure to be applied. Note that Pc = 0 does not define the Sorw.

## Initial water-oil-saturation distribution

An oil field’s initial water-/oil-saturation distribution depends on its hydrocarbon history and has a significant effect on its waterflooding potential. The pore system in a reservoir rock contains a very large number of pore bodies whose filling by oil is controlled by the diameters of the pore throats that link them.

During the oil-filling process, the oil first enters through the largest pore throats, and all other parts of the pore system remain filled with connate brine. As more oil enters the reservoir trap, the oil column lengthens downward. Just above the oil/water contact, only the pores that are accessible from the largest pore throats fill with oil. At the top of the oil column, where the capillary pressure is greatest, not only the largest pores are oil-filled, but also some that have smaller pore throats. The very fine pore spaces remain filled with connate brine.

This process continues until the oil column reaches its maximum length. This whole process is the drainage cycle of the Pc/Sw curves. At this point in the process, oil is filling the largest pores and water is filling the smallest pores; however, the Pc/Sw drainage curve governs the percentage of each. Connate brine will remain as films on the surfaces of the largest pores, but surface-active components of the crude oil might adsorb on some of the pore surfaces, rendering them oil-wet. Hence, the overall system can have mixed-wet characteristics.

There are oil fields that, although initially filled through a drainage process, when discovered were on the imbibition cycle because of a complicated hydrocarbon or structural history. Portions of several west Texas San Andres carbonate reservoirs and the Prudhoe Bay field of Alaska are examples of such oil fields.

This original water-/oil-saturation distribution is important to understand for waterflooding because it controls the efficiency of the waterflood in portions of the reservoir. It also relates directly to the residual oil saturation that can be achieved at the end of a waterflood.

## Relative permeability

Relative permeability (kr)is an important aspect due to the characteristics of imbibition oil/water kr curves. These govern the nature and efficiency of the waterflood displacement and how much of the OOIP will be recovered before the waterflood economic limit is reached.

The shapes of the imbibition water/oil kr curves depend on pore geometry and wettability. As noted earlier, Figs. 4 and 5 show the differences between these curves for a sandstone with large, well-connected pores and one with small, well-connected pores. The krw is greatly reduced for the sandstone with small pores at all saturation levels. Fig. 9 shows the effect of wettability, as measured by the U.S. Bureau of Mines (USBM) Amott wettability index, on the water/oil kr curves. As is expected for a change from water-wet to oil-wet in such laboratory tests, the water kr curve rises with increasing oil-wetness and the oil kr curve decreases.

Most importantly, laboratory-determined water/oil kr data should be obtained at the best approximation of reservoir conditions. Salathiel describes the importance of this to actual field oil/water displacement.[3] Fig. 10 shows the results of Salathiel’s laboratory experiments that relate to the East Texas oil field. These curves show that the oil relative permeability for water-wet conditions is significantly different than for mixed-wet conditions. In water-wet conditions, the oil phase becomes discontinuous and loses its mobility quickly. In mixed-wet conditions, the oil maintains phase continuity by means of the oil-wetted rock surfaces and slowly drains to significantly lower oil saturations. The comparison of the laboratory results to the actual field production data and the residual-oil-saturation-pressure core data showed that the reservoir had mixed-wettability, yielding Sorw values of < 10% PV in many portions of the reservoir.

## Residual oil saturation

For waterflooding, the two most important numbers for a reservoir rock are the connate-water saturation Swc and the Sorw. The S wc determines how much oil initially is in each unit volume of rock when the reservoir is discovered. The Sorw is how much of the OOIP will remain in rock that will be well swept by injected-water volumes. Assuming that the oil-formation-volume factor is the same at the beginning and the end of the waterflood, the equation for the unit-displacement efficiency is:

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

where Soi = initial oil saturation (1 – Swc).

The Sorw is the endpoint of the water/oil imbibition kro curve, which was discussed above; however, for simple waterflood calculations this value is the most critical one. Table 1 compares Salathiel’s Sorw results for the water-wet conditions to those for the mixed-wet conditions.[3] The Sorw for the mixed-wet samples generally was 10% PV lower than for the water-wet samples. In the water-wet conditions, more of the oil phase gets "snapped off" and therefore trapped and immobilized as isolated oil globules by the increasing water saturation. Jerauld and Rathmell[4] found similar results for the Prudhoe Bay field.

Sorw can be measured several ways. It can be determined as part of all relative permeability laboratory studies. Historically, short core-plug "floodpot" tests have been run in the laboratory, and only the rock sample’s porosity, absolute air permeability, Swc, Sorw, and permeability at the two endpoint saturations have been reported. It is important to ensure that these laboratory tests are conducted long enough for the displacement to be taken to its true endpoint. They can be performed either as displacement tests or by using a centrifuge to measure these data. Displacement tests historically have been used, but because of improvements in centrifuge technology, the centrifuge approach is becoming more common. Usually, floodpot-test times are inadequate to reach a true Sorw. Imbibition capillary pressure measurements obtain more-reliable values for water-wet porous media.

Generally, Sorw is inversely related to Swi. This can be understood in terms of the pore spaces that become filled with water and oil. While the Swi decreases (or the Soi increases), the oil phase occupies more of the pores and fills more of the smaller pore spaces. When water displaces the oil, the advancing waterfront traps more of the oil, especially if the rock is water-wet.

The performance of a waterflood depends on the impact of viscous and capillary forces on Sorw and kr. At reservoir flow rates, the viscous forces do not vary enough to make a significant difference in kr and Sorw; however, under laboratory conditions, viscous and capillary forces are major considerations because short core-plug displacement tests actually measure pressure drops and fluid-production volumes as a function of time that include large capillary end effects. These data must be entered into interpretative calculations to derive the water/oil Pc/Sw and kr curves that are used later in field waterflood calculations. The laboratory personnel must choose what length of core plugs to test, what flow rates and pressure drops to apply, whether to make the measurements at steady-state or unsteady-state conditions, and how to interpret these data.

## Initial gas saturation

In many oil reservoirs, a free-gas saturation formed during the early production period because the waterflood was not initiated before the reservoir pressure had dropped through the oil bubblepoint pressure. For many years, the effect of this gas saturation on Sorw has been a subject of considerable technical interest. Fig. 11 summarizes the experimental results of several investigators and shows the impact of initial gas saturation (Sgt) on Sorw for water-wet rocks. The Sorw decreased as Sgt increased. Because gas is the most nonwetting of the fluid phases, the residual gas phase occupies the center of the pore bodies and hence can reduce the volume of oil that is trapped.

## Other considerations

Historically, most laboratory tests have been run at surface temperature and pressure conditions using dead crude oils and constant brine salinity when measuring water/oil Pc/Sw and kr data. More recently, researchers at the U. of Wyoming and the U. of Texas have published papers concerning studies of the effect of temperature, salinity, and oil composition on wettability and waterflood oil recovery.[5][6] Those studies show that oil recovery increases with higher temperature, and generally also with variation in salinity.

## Mobility ratio

The mobility of a phase (Eq. 3) is defined as its relative permeability divided by its viscosity. Hence, mobility combines a rock property (relative permeability) with a fluid property (fluid viscosity). The water/oil relative permeability is assumed to depend only on the saturations of the two fluid phases.

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

where λi = mobility of fluid phase i, ki = relative permeability of fluid phase i, and μi = viscosity of fluid phase i. Mobility relates to the amount of resistance to flow through a reservoir rock that a fluid has at a given saturation of that fluid. Because viscosity is in the denominator of this equation, low-viscosity fluids generally have high mobility and high-viscosity fluids generally have low mobility.

The mobility ratio M generally is defined as the mobility of the displacing phase (for waterflooding, water) divided by the mobility of the displaced phase (oil). Eqs. 4 and 5 present two forms of the mobility-ratio equation:

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

where μw = viscosity of water, cp; μo = viscosity of oil, cp; krw = relative permeability to water; and kro = relative permeability to oil.

The mobility ratio also can be expressed as the product of the two fluids’ relative permeability and viscosity ratios.

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

Mobility ratios are considered to be either "favorable" or "unfavorable." A favorable mobility ratio is a low value (≤ 1); this means that the displaced phase (oil) has a higher mobility than does the displacing phase (water). An unfavorable mobility ratio (> 1) is the other way around. In practical terms, a favorable mobility ratio means that the displaced oil phase can move more quickly through the reservoir rock than can the displacing water phase.

For simple waterflooding calculations, the mobility ratio is calculated at the endpoint relative permeability values for the two phases. Hence, the equation to be used for the waterflood mobility ratio is:

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

where krwe = relative permeability to water at the endpoint (Sorw) and kroe = relative permeability to oil at the endpoint (Swi). This mobility ratio assumes a plug-like displacement between the oil phase at connate-water saturation before the flood front and the water phase at residual oil saturation behind the flood front.

In most reservoir situations, water’s viscosity is lower than oil’s, making the viscosity ratio unfavorable for water to displace oil efficiently; however, as Figs. 4, 5, and 9 show, the relative permeability of water at residual oil saturation is lower by a factor of two to eight than that of oil at connate-water saturation. Hence, for many reservoirs, the mobility ratio is close to unity (favorable) if the oil viscosity is greater than the water viscosity at reservoir conditions only by a factor of five.

## Nomenclature

 λi = mobility of fluid phase i ki = relative permeability of fluid phase i μi = viscosity of fluid phase i krwe = relative permeability to water at the endpoint kroe = relative permeability to oil at the endpoint μw = viscosity of water, cp μo = viscosity of oil, cp krw = relative permeability to water kro = relative permeability to oil σos = the IFT between the oil and solid phases σws = the IFT between the water and solid phases σow = the IFT between the oil and water phases Soi = initial oil saturation Sorw = endpoint of the water/oil imbibition

## References

1. Craig Jr., F.F. 1971. The Reservoir Engineering Aspects of Waterflooding, Vol. 3. Richardson, Texas: Monograph Series, SPE.
2. Willhite, G.P. 1986. Waterflooding, Vol. 3. Richardson, Texas: Textbook Series, SPE.
3. Salathiel, R.A. 1973. Oil Recovery by Surface Film Drainage in Mixed-Wettability Rocks. J Pet Technol 25 (10): 1216–1224; Trans., AIME, 255. SPE-4104-PA. http://dx.doi.org/10.2118/4104-PA
4. Jerauld, G.R. and Rathmell, J.J. 1997. Wettability and Relative Permeability of Prudhoe Bay: A Case Study In Mixed-Wet Reservoirs. SPE Res Eng 12 (1): 58–65. SPE-28576-PA. http://dx.doi.org/10.2118/28576-PA
5. Sharma, M.M. and Filoco, P.R. 2000. Effect of Brine Salinity and Crude-Oil Properties on Oil Recovery and Residual Saturations. SPE J. 5 (3): 293–300. SPE-65402-PA. http://dx.doi.org/10.2118/65402-PA
6. Zhou, X., Morrow, N.R., and Ma, S. 1996. Interrelationship of Wettability, Initial Water Saturation, Aging Time, and Oil Recovery by Spontaneous Imbibition and Waterflooding. Presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, 21–24 April. SPE-35436-MS. http://dx.doi.org/10.2118/35436-MS