Saturation Petroleum Engineering

W» = 5L05 p„ ~ 2.63 23.6 - 19.4 23.6

  • 19.4 cc
  • 0.178 or 17.8%
  • 2) Sa = - ^ - 0357 or 36%


Numerous other miscellaneous core tests are performed by commercial laboratories. Some of these will be discussed in a later section on special core testing; some, however, such as chloride content, core oil density, and grain size distribution tests will not be considered. Other texts which devote more space to these topics are listed as recommended outside readings and should be consulted. Also, the references at the end of this chapter contain specific information on more detailed analysis.

Before proceeding into more involved core testing, it is necessary to introduce certain fundamental concepts regarding the spatial distribution of fluids within a rock and the resulting effects of such distribution on flow behavior.

10.5 Fundamental Fluid Distribution Concepts — Multiphase Systems

In Chapter 2, mention was made of the fact that petroleum reservoir rocks always contain at least two, and sometimes three, separate or immiscible fluids. Water and oil; water and gas; or water, oil, and gas are the combinations of interest. The portion of the pore space which each occupies depends on the amount of each present and the wettability of the system. Wettability refers to the relative affinity between the rock and each fluid present, i.e., which fluid is preferentially adsorbed on the rock surface and is held in the most minute portions of the interstices. The determination of a particular reservoir's wettability is a difficult problem and lies beyond the scope of present treatment. In general, most rocks are wetted by water, a few are wetted by oil, and some deep high pressure reservoirs may be wetted by gas, although the latter occurrence is not definitely established. An oil-wet condition is believed to be due to the presence of polar impurities or surface active materials in the oil which, over geologic time, have been adsorbed by the rock thereby increasing its surface affinity for oil and rendering it oil-wet. The significance of fluid distribution in a porous network will become apparent as we discuss multiphase flow concepts.

Up to this time, our discussion of permeability has been restricted to the absolute permeabilities, which are relevant to rock completely saturated with flowing fluid. It is now necessary to expand the permeability concept to include cases where fractional saturations to two or three fluids exist. Two basic definitions must be introduced:

1. Effective permeability: the permeability of a rock to a particular fluid at saturations less than 100%, i.e., when other fluid (s) is present. This is measured in darcys or millidarcys and is therefore the dimensional equivalent of absolute permeability, hence:

k0 = effective permeability to oil, darcys or md kw = effective permeability to water, darcys or md kg = effective permeability to gas, darcys or md Individual values of ka, kg, ka may vary from zero up to the absolute value, k: —

2. Relative permeability: this is merely a convenient, dimensionless quantity defined by:

krw k where kr.

kr kri

~ k " ~ k krg = relative permeability to water, oil, and gas, respectively.

Since the effective permeabilities may range from zero to k, the relative permeabilities may have any value between zero and one:

Another widely used parameter is the ratio of the effective (or relative) permeabilities of water and oil, and gas and oil:

kw ko or kr krt and kg k0

These ratios pre dimensionless and may vary from zero to infinity.

Consider the two-phase flow behavior depicted in Figure 10.16. The entire pore space is filled with water and oil so that Sw + S0 = 100% at all times. To visualize what is happening, assume that the rock is originally 100% saturated with oil. Further, assume that we introduce water into every pore simultaneously and that a water-wet equilibrium is instantaneously established. This, of course, we cannot do, except mentally to visualize the mechanism involved. When water is first introduced, it is adsorbed by the rock and held immobile both on the rock surfaces and in the small corners around the junctions of the individual grains. This immobility is indicated by krw = 0 in region A. Note, however, that kro is essentially constant at 1.0 over the same saturation range. As this process continues, the water saturation reaches some critical value Swc at which water becomes mobile, (krw > 0). At this time, both oil and water flow; as water saturation is increased (and oil saturation is decreased), however, kr„ decreases and krw increases, as shown in region B. Continued increase of Sw causes the oil saturation to reach a residual value Sor at which oil becomes immobile (kro = 0) and only water flows. This is the minimum saturation to which oil may be reduced by injecting water. If it were possible to remove the oil by some other means, krw would continue to increase and finally reach the value of one as shown. This process could have been visualized in reverse just as well. It should be noted that this example portrays oil as non-wetting and water as wetting. The curve shapes _Region B_

oil Anicular «rater pendular both oil and «rater finicular

.Region C.

oil insular «rater finie

oil Anicular «rater pendular both oil and «rater finicular

.Region C.

oil insular «rater finie

-t— i i

1 1


i i


1 1




1 1 1





AS /

1 1



r/ /

i i

1 1 1




1 1



1 1






60 40

60 40

Fig. 10.17. Idealized conception of pendular rings around sand grain junctions. After Leverett,11 courtesy AIME.

shown are typical for wetting and non-wetting phases and may be mentally reversed to visualize the behavior of an oil-wet system. Note also that the total permeability to both phases, krw + kr„, is less than 1, in regions B and C.

The distribution of the wetting and non-wetting phases is commonly classified as pendular, finicular, or insular, depending on their saturations. In region A, the aqueous phase exists mainly as pendular rings around the grain junctions which may only contact each other via an extremely thin adsorbed layer on the rock surface (Figure 10.17). In region B, both phases exist in continuous flow paths through their own pore networks, and both are said to be in finicular saturation. As water saturation continues to increase, the oil saturation is finally reduced to the point where the connecting threads break and oil becomes discontinuous at the value S„r. Thus in region C the oil exists in small, isolated groups of pores (islands) or in a state of insular saturation. Again, this discussion has considered water as the wetting phase and oil as non-wetting; however, the general concepts apply to any system of wetting and non-wetting fluids.

Therefore, in summary:

Region A B C

Wetting saturation pendular finicular finicular

Non-wetting phase saturation finicular finicular insular

Fig. 10.16. Typical two-phase flow behavior.

The practical significance of this behavior is extremely important. First, it becomes obvious that the mere presence of oil in a rock is not proof that oil will be produced. Actually, many rocks which show traces of oil in cores and cuttings will produce 100% water. This means that S„ ^ Sor- Likewise, water will not be produced if Sw ^ Swc. Predictions of the future producing behavior of entire fields are based on the calculation of future production rates at steadily decreasing oil saturations; these predictions require that relative (or effective) permeabilities to oil, gas, and/or water at the proper saturations be known.

The Darcy equations derived in Chapter 2 may now be altered such that the effective permeability to the phase of interest replaces the absolute permeability. For example, the linear incompressible fluid equation

kAAp pL

becomes for multiphase flow systems:

k0AAp or


where q„, qw = oil and water flow rates, respectively n„, pw = oil and water viscosities, respectively

Example 10.6

A well is producing from a reservoir having the relative permeability characteristics of Figure 10.16. The following data are available:

pe = 2500 psi p0 = 5.0 cp pw = 1000 psi pw = 0.6 cp re = 700 ft h = 25 ft rw = 0.33 ft k = 50 md (absolute)

B0 = 1.30 (formation volume factor)

(a) What will the steady state tank oil production rate be if the water saturation Is at the critical value?

Solution: Recall equation (2.27)

where q = bbl/day h = ft k = darcvs Pe, Pw = psi P = cp

Altering the above to the problem conditions: (7.07) (25) (0.050) (2500 - 1000)

However, qot — = = 270 bbl/day of tank oil since the 0 ' flowing volume q0 will shrink prior to reaching the tanks

(b) What will the tank oil flow rate be when S0 = 0.50, Pe Pw = 1000 psi, Po = 7.0 cp, and B0 = 1.20? Solution:

k0 = (kro)(k) = (0.45)(50) = 22.5 md Combining B0 in the flow equation, (7.07) (0.0225) (25) (1000)

qot =

  • 7.0) (7.64) (1.20)
  • 62 bbl/day n„ 1.30 1000 .0225 5.0 „„,,,, = 270 X L20 X 1500 X TOSO X 7^0 " 62 bW/day
  • c) What will the producing water-oil ratio be when S0 = 0.40 and p0 = 7.5 cp? Assume same Ap and Ba as part (b).

Solution: Since:

the water-oil ratio is then:

(10.6) X Bo qot ICoPw KroPw

Note: The term kwp0/k0Pw is called the mobility ratio of water to oil, \w/\0-

From Figure 10.16, krw = 0.23 and kro = 0.23 at S0 = 0.40. . qw_ = (0.23) (7.5) '' qot (0.23)(0.6)

Similar problems involving gas vs. oil, or gas vs. water behavior may be solved in the same manner.

This has been a brief but necessary discussion of a basic concept. Later sections and chapters require some fundamental knowledge of multiphase flow. It might be mentioned that three-phase flow sometimes occurs, further complicating the picture. Fortunately, most practical calculations may be resolved as two-phase problems with the third phase (if present) being considered immobile or constant. Oil and gas flow commonly occurs with water present in pendular saturation. Relative permeability curves for oil and gas may then be used, assuming water saturation constant. Similarly, occasions arise where simultaneous water and oil flow occur at some constant, insular gas saturation. Three-phase relative permeability data are scarce; however, the classic work of Leverett and Lewis12 is suggested as a basic reference.

10.6 Special Core Analysis Procedures

If the literature on special core tests were bound in a single volume, its size would probably approach that of an unabridged dictionary. Consequently, this section will merely introduce the subject and cite a few basic references which may be used as a starting point. Since relative permeability has just been discussed let us start with its measurement.

10.61 Relative Permeability Measurements

A common method for measuring two phase relative permeability utilizes the apparatus shown in Figure 10.18. This is a slight modification of the Penn State method developed by Morse et al.13 The test sample is confined at the ends between samples having similar properties. Intimate contact is maintained between the three cores to eliminate any capillary effects at the ends (particularly the downstream end) of the test sample. This insures that the saturation distribution of each fluid will be uniform during a steady state flow test. The upstream plug also serves as a mixing head for the injected fluids. The cores are first saturated with the fluid to be displaced, (which is commonly oil), and the weight of the test section is recorded. A constant oil flow rate is then established such that the desired pressure drop occurs. The oil flow rate is then reduced slightly and the displacing fluid (gas or water) is simultaneously injected at a rate sufficient to maintain the originally established pressure drop. Equilibrium is established when the respective input and outflow volumes are equal. Saturations are determined either gravimetrically by removing and weighing the test section, or electrically by measuring resistivity. The oil rate is then decreased further and the gas or water flow rate increased proportionally. Repetition of this





Fig. 10.18. Modified Penn State permeability apparatus. After Geffen, et al.,™ courtesy AIME.


procedure in sufficiently small steps allows calculation of the permeability to each phase at various saturations. Saturations are, of course, measured at each step. The porosity and absolute permeability of the test core are measured prior to the test.

There are numerous other methods for measuring relative permeability which are also capable of defining the flow behavior of the rock-fluid system used. Papers by Osoba et al.,14 and Richardson et al.,16 have summarized existing techniques and compared the results obtained from each; a discussion of the basic factors affecting such measurements has been presented by Geffen et al.16 While space does not permit anything like a complete discussion of the subject, it seems pertinent to mention some precautions regarding the validity of basing field or well behavior predictions on core test data.





xxxx xxxxx


(A) Completely water -wet system. Oil drop tangent to rock surface. Contact angle, 0,-0





  • B) System of neutral wettability. Contact angle, 0, « 90*
  • C) Completely oil-wet system. Water drop is tangent to rock surface. Contact angle, 0,»180*

Fig. 10.19. Idealized oil-water-rock systems showing three stages of wettability as defined by contact angle.

The first rather obvious question to arise is whether or not a small core sample can represent the average behavior of a reservoir. This is a problem in all core analysis work. The apparent answer is that sufficient, properly selected cores must be analyzed to obtain a reasonable m <

Li s


Li s



1 1 i ■ : ' : 1 i :

ST 1 ST 2 ST 3

\\ \\

/ /


\\ \\ \\ \\ \\



)C\ y'

BRINE SATURATION, per cent pore spoce

  1. 10.20. Effect of wettability on flow behavior of a sandstone core. After Geffen, et al.,16 courtesy AIME.
  2. 10.18. Modified Penn State permeability apparatus. After Geffen, et al.,™ courtesy AIME.

BRINE SATURATION, per cent pore spoce

Fig. 10.20. Effect of wettability on flow behavior of a sandstone core. After Geffen, et al.,16 courtesy AIME.

statistical sampling. The reservoir behavior will then be the properly weighted average of the individual observations. Aside from the problems of sampling or laboratory technique, there are two other factors of great fundamental importance.

1. Wettability alterations: Laboratory flow tests are normally conducted on core samples which have been thoroughly cleaned and dried. The test fluids used are usually synthetic brines, close hydrocarbon cuts (C10 to C12 for example), and air or nitrogen. Use of the actual reservoir fluids introduces severe problems in technique and handling and is not generally practiced. Also the reservoir temperature and pressure are usually not simulated. Therefore the wettability of the normal laboratory system is the same as that of the reservoir only by accident. In our earlier discussion of interstitial fluid distribution, it was shown that the shapes of the individual relative permeability curves were functions of the fluid which wetted the rock surface. Consequently, it may be expected that alterations in wettability will change the relative permeability behavior. Wettability may be visualized in terms of contact angle, as shown by Figure 10.19. A zero contact angle implies complete wettability by the water as shown in A. A contact angle of 180° denotes complete wetting by the oil (C). Intermediate wettabilities are indicated by angles between these extremes. In oil-water-rock

BRINE SATURATION par cant pora ipoce

BRINE SATURATION par cant pora ipoce

oil saturation, per e«nt port space

Fig. 10.21. Comparison of data from Fig. 10.20 on effective permeability ratio bases. After Geffen, et cd.,u courtesy AIME.

oil saturation, per e«nt port space

Fig. 10.21. Comparison of data from Fig. 10.20 on effective permeability ratio bases. After Geffen, et cd.,u courtesy AIME.

systems it is the convention to measure contact angle through the aqueous phase as shown.17

Experiments have been conducted to show the effect of wettability on flow behavior, the sandstone sample's wettability being altered by a surface active material (Dri-film). The relative permeability behavior is shown in Figure 10.20. Figure 10.21 shows the data of tests 1 and 2 replotted in terms of relative permeability ratio. Note that the curves of kw/k„ for test 3 (oil-wet) and k0/kw for test 1 (water-wet) are almost identical, which implies that the fluids merely changed positions in the core.

BRINE SATURATION, par cent pore space

Fig. 10.22. Typical effect of saturation history on relative permeability behavior. After Geffen, et al.,u courtesy AIME.

BRINE SATURATION, par cent pore space

Fig. 10.22. Typical effect of saturation history on relative permeability behavior. After Geffen, et al.,u courtesy AIME.

Thus it is apparent that wettability alterations may cast considerable doubt on the validity of laboratory flow test data. Apparently, most laboratory tests are made on the assumption of water-wet conditions which, fortunately, holds true in most cases. However, it should be realized that wettability is a gradational phenomenon, and a particular system may be completely water-wet, oil-wet, or any condition between. A further complication of this problem is the lack of any completely satisfactory means of measuring wettability. Temperature and pressure also affect the magnitude of surface forces, thereby altering wettability.18 The solution to the wettability problem has not been attained; however, its possible effects on flow behavior must be recognized. 2. Saturation history effects: It has also been demonstrated that relative permeability is not a unique function of saturation but depends on the direction from which the saturation is approached. This means that the curves obtained by displacing oil with water will not be the same as those from the reverse process. Practically speaking, there are two saturation histories or directional changes which are of interest. These are:

  • a) Gas drive process: displacement of oil by gas. Oil is assumed to be the wetting phase with respect to gas. This is also called the drainage process.
  • b) Water drive process: displacement of oil by water, where water is the wetting phase. This is an imbibition process.

The typical behavior of these processes is shown in Figure 10.22, in which the arrows denote the direction of saturation change. Note that in the gas drive, (in which water, rather than oil, was used as wetting phase) permeability to gas exists at a very high water saturation. In the reverse procedure, however, gas permeability approaches zero at a much lower water saturation. Therefore, laboratory measurements must have the proper saturation history which applies to the field problem at hand.

The relative permeability concept is one which is sometimes difficult to grasp. It is often helpful to consider it as a correction factor which must be applied to the absolute permeability to account for the presence of other immiscible fluids. This is precisely what it amounts to, although the determination of its correct magnitude may be extremely difficult. For a particular rock, it is a function of saturation, wettability, and saturation history.

10.62 Determination of Connate Water Saturation

The determination of the actual (or connate) water saturation in the reservoir rock is not obtainable from routine analysis, due to the environmental factors mentioned earlier, except when the rock exists at its critical (minimum or irreducible) water saturation and is cored with oil or an oil base mud.* In this case the water, being immobile, is not disturbed by the mud filtrate. If the cores are expediently handled and properly preserved, the routine water saturation determinations will be indicative of the original reservoir. In most cases, however, this procedure is not followed, and many special laboratory methods have been used to procure an irreducible water saturation value. In order to discuss this topic it is first necessary to review the elementary concept of capillary behavior.

The familiar rise of a liquid in a capillary tube is shown in Figure 10.23. Equating of the upward and downward forces on the elevated column results in the well known expression for the surface tension of the liquid:

  • 1) Fu - 2wra cos 6 and
  • 2) Fd = icrHpg where Fu = upward force on the elevated liquid column Fd = downward force r — capillary radius a- = surface tension of the liquid or interfacial tension if two liquids are involved.

6 = contact angle of the system

I = height of the column p = liquid density g = gravitational constant

At equilibrium, Fu = Fd, hence:

If the downward force Fd is expressed as a pressure, then or from Eq. (10.7) (10.8) Pc =

  • capillary pressure
  • The term connate water is widely used as a synonym for critical water saturation. Here we will use it as the actual reservoir water saturation, which may or may not be the irreducible value.

Capillary pressure may also be defined as the pressure necessary to displace a wetting fluid from a capillary opening. Obviously, this definition will result in a negative value if the fluid does not wet the tube, i.e., if 8 > 90°. The factors which govern this capillary or displacement pressure are the surface or interfacial tension of the fluids involved, the system wettability 0, and the size (radius) of the capillary. The significance of capillary pressure becomes apparent when one considers that most oil-containing porous media may be visualized as a heterogeneous and tortuous bundle of capillary tubes.

Nearly all petroleum reservoirs occur in marine sediments which were originally saturated with water. As oil was formed and it migrated into the rock, it displaced water to an extent dependent on its driving pressure opposed to the rock's capillary pressure. Over geologic time, the oil accumulated in traps where differential pressure became sufficient to reduce the water saturation to its minimum value. This minimum or critical value will normally exist in formations which produce clean (water-free) oil. Oil reservoirs underlaid by, and in intimate contact with, water have a transition

Wetting liquid of density,p

Fig. 10.23. Capillary rise of a liquid which wets the walls of the capillary tube.

zone through which water saturation decreases from 100% in the water zone to some irreducible value in the oil zone. Wells completed in the transition interval produce both oil and water. Similarly an oil-gas transition zone will exist in fields having a gas cap. The thickness of these zones depends on the same factors appearing in the capillary pressure equation: interfacial tension, wettability, and average pore radius. Equation (10.8) is normally altered to Eq. (10.9) when applied to porous media, as indicated by Figure 10.24(A), (B).

  • 10.9) Pc = l(pw - Po)g
  • quot;-0Î + k)

cos 6

where r, are the radii of curvature of the oil water interface measured as was shown in Figure 10.17. The term 1 /rx + l/r2 may be considered as the mean curvature of the surface.19

With these concepts in mind, let us consider some methods of measuring critical water saturation. 1. Restored-state method: This is a well known, and widely used method which was proposed in 1947 by Bruce and Welge.20 Its name derives from its similarity to the original reservoir process. A typical apparatus is shown in Figure 10.25. A reservoir core of known pore volume is saturated 100% with water



Water p rm


Fig. 10.24. Analogy between simple capillary tube and porous media.

and placed in contact with the water-wet membrane, as shown. The membrane has extremely small pores and will not allow a non-wetting fluid to enter it at the pressures to be used in the test. A non-wetting fluid (oil, air, nitrogen, etc.) is then introduced into the cell at slightly elevated pressure. The air (or non-wetting fluid) will enter all the pores in the core sample having a capillary pressure less than that applied. The water displaced from the core is forced through the membrane and collected in a suitable graduate. When the displaced water volume becomes constant at a given pressure, it is recorded. The saturation may then be computed at that particular pressure. This procedure is repeated in subsequent, higher pressure, steps until an increase in pressure forces no more water from the core. This is then the irreducible value. The resultant plot of capillary pressure vs. saturation is shown in Figure 10.26. The minimum pressure which will displace water from the largest pore is called the displacement or entrance pressure. Note also the analogy between the curve obtained and the reservoir condition of Figure 10.24.

Fig. 10.25. Restored state apparatus for determination of capillary pressure curve.


Fig. 10.25. Restored state apparatus for determination of capillary pressure curve.

The principal disadvantage of this technique is the time required to carry it out. Several days may be required to reach a satisfactory equilibrium at each step. However, by installing batteries of cells, one may conduct numerous tests simultaneously. 2. Mercury injection method: This is similar in principle to the restored state method. The dry sample is placed in a mercury cell. Pressure is then applied incrementally as before, with the volume injected into the rock pores being noted at each pressure. A curve of capillary pressure vs mercury saturation is thus obtained. This must be corrected as shown by Purcell:21

Pew where <rHg = 480 dynes/cm aw = 70 dynes/cm 0Hg = 140° Bw = 0°

Reasonable checks are obtained between this and the previous method. The primary advantage of the method is speed, since only a few hours are required to obtain a complete curve. A disadvantage is that the sample is ruined for subsequent testing.

Much may be determined from the capillary pressure curve, besides the irreducible water saturation. Certainly, the curve affords soihe measure of pore size distribution. If all the pores were essentially one size, a very flat curve would result. A steep slope implies that many pore sizes exist. Stepwise calculations of pore radii may be made with Eq. (10.8) at various pressures along the curve, providing a and 0 are known. Methods for computing both absolute and relative permeability from such data are in use.21-26 Such calculations are based on the fundamental relationship between permeability and pore size.

In this regard, it is also logical to expect that the critical water saturation should correlate with absolute



Fig. 10.26. Typical capillary pressure curve showing significant features.


Fig. 10.26. Typical capillary pressure curve showing significant features.

permeability, other factors being reasonably constant. A correlation of this type is given as Figure 10.27. Note that height above the water table is also a parameter. Such curves may be developed for a particular formation, providing data over a sufficient permeability range are available. This is a further illustration of the need for proper sampling.

3. Evaporation method: This is a simple and unique method which was proposed by Messer27 in 1951. A sample of known porosity is completely saturated with water. It is then placed in a suitable oven and dried under constant conditions. The weight loss is recorded, either continuously or in increments, and plotted against time. Adsorbed water evaporates at a slower rate than the free or mobile water, due to the capillary and surface forces which oppose its escape. This difference in drying rate exhibits a break in the drying curve which may be taken as the critical value. Other liquids such as toluene, benzene, or tetrachloroethane may be used instead of water, provided that the proper volume correction is made. Satisfactory correlation between this method and the restored state or capillary pressure technique was obtained by Messer.

The advantage of the evaporation method is the speed of measurement; usually, a test can be completed in twenty minutes to an hour. Some theoretical objections have been raised regarding the validity of the method; however, it is a fast, cheap, and reasonably accurate means of obtaining an irreducible water saturation value.

All methods used for connate water determination may be criticized on one basis or another. A serious drawback to capillary pressure measurements lies in the general use of synthetic fluids which may not reproduce the proper values of a and/or 0. The seriousness of these procedural shortcuts may be considerable, in some instances. It has also been shown that core weathering and aging can affect the obtained values.

Fig. 10.27. Connate water saturation vs. height above water table for various permeabilities. Courtesy Core Laboratories, Inc.


  1. 10.27. Connate water saturation vs. height above water table for various permeabilities. Courtesy Core Laboratories, Inc.
  2. 63 Water Flood Tests

Freshly cut cores may be flooded with water (usually a synthetic brine) to determine the residual oil content So, after flooding. Such data are often useful in estimating the quantity of oil which may be recovered from an actual field water flood. These tests are often referred to as flood pot tests and are performed under radial flow conditions with a full diameter section. In some cases the cores are cleaned, resaturated to simulate initial reservoir conditions, and flooded in a manner similar to that mentioned with regard to relative permeability measurements.

10.64 Miscellaneous Special Tests

These are, of course, numerous and varied. Water permeabilities are often measured to determine the compatibility of a particular water-sand system. The principal factor involved in such tests is the hydration














Shale, N Shale, N 3000 2800 3500

o Analysis o Analysis 31 31 33

0.0 2.0 1 0

45.0 47.0 42 0

4,000 8,000 6,000








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