3b- Interfacial Tension, Wettability & Capillary Pressure PDF

CONCEPTS OF INTERFACIAL TENSION AND WETTABILITY Prof. T. Kumar Dept. of Petroleum Engg. IIT(ISM) Dhanbad-826004 Interfacial or surface tension exists when two phases are present. These phases can be gas/oil, oil/water, or g...

CONCEPTS OF INTERFACIAL TENSION AND WETTABILITY Prof. T. Kumar Dept. of Petroleum Engg. IIT(ISM) Dhanbad-826004 Interfacial or surface tension exists when two phases are present. These phases can be gas/oil, oil/water, or gas/water. Interfacial tension is the force that holds the surface of a particular phase together and is normally measured in dynes/cm. The surface tension between gas and crude oil ranges from near zero to approximately 34 dynes/cm. It is a function of pressure, temperature, and the composition of each phase. The simultaneous existence of two or more fluids in a porous rock requires that terms such as capillary pressure, relative permeability, and wettability be defined. When only one fluid exists in the pore spaces, there is only one set of forces to consider, the attraction between the rock and the fluid. When more than one fluid is present, there are at least three sets of active forces affecting capillary pressure and wettability. Concepts of Surface and Capillary forces: In dealing with multiphase systems, it is necessary to consider the effect of the forces acting at the interface when two immiscible fluids are in contact. When these two fluids are liquid and gas, the interface is normally referred to as the liquid surface. All molecules are attracted one to the other in proportion to the product of their masses and inversely as the square of the distance between them. Considering water and oil, fluids commonly found in petroleum reservoirs, it is found that an interfacial tension always exists between the fluids. A water molecule which is remote from the interface is surrounded by other water molecules, thus having a resulting net attractive forces on the molecule of zero. However, a molecule at the 1 interface has a force acting upon it from the oil lying immediately above the interface and water molecules lying below the surface. The resulting forces are underbalanced and give rise to interfacial tension. The underbalanced attractive force between the molecules creates a membrane like surface. A certain amount of work is required to move a water molecule from within the body of the liquid through the interface. This work is frequently referred to as the free surface energy of the liquid. Free surface energy, in ergs per square centimeter, may be defined as the work necessary to create a unit area of new surface. The interfacial tension and surface tension are commonly expressed in dynes per centimeter, which is numerically equal to the surface energy in ergs per square centimeter. Surface tension is measured in the laboratory by standard means such as tensiometer, the drop method, etc. Water-hydrocarbon surface tension The surface tension of a water-hydrocarbon system varies from approximately 72 dynes/cm for water/gas systems to 20 to 40 dynes/cm for water/oil systems at atmospheric conditions. In 1973, Ramey published methods to evaluate the surface tension of water- hydrocarbon mixtures. 2 Effect of different types of surface on contact angles: The degree of spreading as affected by the contact angle of the system is illustrated in Figure below wherein various multi-liquid systems are in contact with silica and calcite surfaces. It is noted that when water and iso-octane are used, the water preferentially wets both the calcite and silica surfaces. Dependence of interfacial curvature upon pore size and contact angle: Figure below illustrates the effect of varying the wetting characteristics of the system and of varying the radius of the capillary tube. If the 3 wetting characteristics remain constant and the radius of the tube is increased, the weight of the water column increases as the square of the radius whereas the magnitude of the adhesion force increases in direct relation to the radius. Therefore, the height of the water column will be decreased proportionately to the increase in the tube radius. This fact is illustrated in this figure wherein it is noted that the smaller the radius of the tube, the higher the water column will rise before an equilibrium system is obtained. The changes in wetting characteristics are such that the greater the adhesion tension, the greater the equilibrium height obtained. If the only variable is the wetting characteristic of the solid, it is noted that the smaller the contact angle, the stronger the adhesion tension and the greater the height to which the liquid column will rise before equilibrium is obtained. This fact is illustrated in part (b) of the figure, wherein it is noted that for small values of the contact angle, a large height is obtained. WETTABILITY CONCEPTS AND MEASUREMENTS 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 4 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 the particular reservoir’s wettability is a difficult problem. However a few methods are available which fairly estimates it. 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 distribution of the wetting and non-wetting phases is commonly classified as pendular, finicular (sometimes called funicular), or insular, depending on their saturations. With reference to a typical relative permeability curve, the aqueous phase mainly exists as pendular rings when the wetting phase saturation is irreducible. Similarly when the wetting and non-wetting phases are mobile the saturation in both phases is referred to as the funicular. As water saturation continues to increase, oil saturation is finally reduced to the point where the connecting threads break and oil becomes discontinuous at the residual oil saturation. In this region the oil exists 5 in small, isolated groups of pores (islands) or in a state of insular saturation. The practical significance of this behaviour 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 oil in the cores and cuttings will produce 100% water. This means that So is less than Sor. Likewise, water will not be produced if Sw less than Swi. Predictions of the future producing behaviour of entire fields are based on the calculation of future production rates at steadily decreasing oil saturations; these predictions require that relative permeabilities to oil, oil, gas/and or water at the proper saturations be known. The measurement of relative permeability in the laboratory normally does not consider the wettability aspects due to the fact that the reservoir conditions are difficult to simulate in the laboratory determinations of the relative permeabilities. Therefore 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, hold 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. Wettability describes the preference of a solid to be in contact with one fluid rather than another. Although the term “preference” may seem odd when describing an inanimate object, it aptly describes the balance of surface and interfacial forces. A drop of a preferentially wetting fluid will displace another fluid; at the extreme it will spread over the entire 6 surface. Conversely, if a non-wetting fluid is dropped onto a surface already covered by the wetting fluid, it will bead up, minimizing its contact with the solid. If the condition is neither strongly water wetting nor strongly oil-wetting, the balance of forces in the oil/water/solid system will result in a contact angle, θ , between the fluids at the solid surface (below). Reservoir rocks are complex structures, often comprising a variety of mineral types. Each mineral may have a different wettability, making the wetting character of the composite rock difficult to describe. Typically, the primary constituents of reservoirs—quartz, carbonate and dolomite—are water-wet prior to oil migration. Strictly speaking, the term imbibition refers to an increase in the saturation of the wetting phase, whether this is a spontaneous imbibition process or a forced imbibition process such as a waterflood in a water-wet material. Conversely, drainage refers to an increase in saturation of the nonwetting phase. However, in practice, the term imbibition is used to describe a process with increasing water saturation, and drainage is used to describe a process with increasing oil saturation. The Practical Importance of Wettability The current, favourable oil price has improved the economics of waterflooding and some enhanced oil recovery methods. With multiple phases flowing in the reservoir, understanding wettability becomes important. However, even during primary recovery, wettability influences productivity and oil recovery. The original wettability of a formation and altered wettability during and after hydrocarbon migration influence the profile of initial water saturation, Swi, and production characteristics in the formation. Most reservoirs are water-wet prior to oil migration and exhibit a long transition zone, through which saturation changes gradually from mostly oil with irreducible water at the top of the transition zone to 7 water at the bottom. This distribution is determined by the buoyancy based pressure difference between the oil and water phases, which is termed the capillary pressure, Pc (below). Measuring Wettability Measurements may be made without using core material from the formation. One example is the contact-angle test (below). A contact angle of zero would indicate complete wetting by the denser phase, an angle of 900 indicates that neither phase preferentially wet the solid, and an angle of 1800 indicates complete wetting by the less dense phase. The contact angle is, therefore, a measure of the relative wetting of a solid by a fluid. In this test, a crystal of quartz or calcite is cleaned, or a new mica surface is cleaved, and aged in a simulated formation brine. A drop of crude oil placed in contact with the surface is aged. Several methods are used for creating moving contact lines, from which the water- advancing and receding contact angles are measured. The assumption in this test is that the crude oil will change the model surface—under the conditions of the brine temperature, pH and salt concentrations—to that of the formation. Wettability is often inferred from other measurements such as sessile drop ratio, defined as the height of a droplet on a surface to the breadth of the droplet. Sessile drop ratio of 1 indicates complete non-wetting, whereas a ratio of zero indicates complete wetting. Wettability can be also estimated from the capillary pressure curve discussed later. Wetting in idealized pores of reservoir rocks: The wettability of a reservoir rocks to the fluids present in these rocks is of great importance in that the distribution of the fluids within the interstices is a function of the wettability. The figure below is an idealized representation of the change in fluid distribution in a given pore due to a change from oil wetting to water wetting. Because of the attractive forces, the wetting fluid tends to occupy the smaller 8 interstices of the rock and the non-wetting fluid occupies the more open channels. Relation between wettability and capillary pressure: Since reservoir rocks are, for the most part, aggregates of small mineral and rock fragments, it is not possible to determine the wetting properties by direct measurement of contact angles of sessile drop ratios. However, by analogy with the effect of wetting properties on capillary pressure in capillary tubes,, an indirect measurement is indicated. In the figure below are shown the capillary rise of water in a tube and the capillary depression of mercury. A wetting fluid tends to enter a pore or tube spontaneously, while a non-wetting fluid resists entry. It has been suggested that the contact angle and some degree of wettability can be calculated from the threshold pressure (pressure just causing non-wetting fluid entry) of a porous system. 9 The wettability number and apparent contact angle are both defined by the following two equations: Cos θwo PTwo σoa Wettability number = --------------------- Cos θoa PToa σwo PTwo σoa Contact angle = Cos θwo = ------------- PToa σwo Where, Cos θoa = 1 Cos θwo = contact angle between water and oil in core Cos θoa = contact angle between air and oil in core PTwo = threshold pressure of core for oil to enter when core initially saturated with water PToa = threshold pressure of core for air to enter when core is initially saturated with oil 10  σoa and σwo = interfacial tensions between air and oil and oil and water, respectively A wettability number of 1.0 would indicate complete wetting by water; of zero, complete wetting by oil. In general, intermediate wetting is exhibited for the core samples with the values in between. The effect of wettability must be considered in all laboratory determinations of residual oil saturations, capillary pressure, and other similar tests. 11 CAPILLARY PRESSURE AND ITS MEASUREMENTS Capillary pressure is the pressure difference existing across the interface separating two immiscible fluids. The forces that hold these fluids in equilibrium with each other and with the rock are expressions of capillary forces. If the wettability of the system is known, then the capillary pressure will always be positive if it is defined as the difference between the pressures in the non-wetting and wetting phases. That is: Pc PnwPw Thus for an oil-water system (water wet) Pc Po Pw For a gas-oil system (oil-wet) Pc Pg Pw What Causes Capillary Pressure? Capillary pressure is as a result of the interfacial tension existing at the interface separating two immiscible fluids. The interfacial tension itself is caused by the imbalance in the molecular forces of attraction experienced by the molecules at the surface as shown below. 12 For molecules in the interior: Net forces = 0 since there are enough molecules around to balance out. For molecules on the surface: Net result of forces is a pull toward the interior causing a tangential tension on the surface. The net effect of the interfacial tension is to try to minimize the interfacial area in a manner analogous to the tension in a stretched membrane. To balance these forces and to keep the interface in equilibrium, the pressure inside the interface needs to be higher than that on the outside. Forces reducing interface are due to: a) Interfacial tension and b) External pressure The effect of interfacial tension is to compress the non-wetting phase relative to the wetting phase. The force created by the internal pressure is balancing it. 13 EXPRESSIONS FOR CAPILLARY PRESSURE UNDER STATIC CONDITIONS Pc in terms of radius of capillary tube Since the interface is in equilibrium, force can be balanced on any segment. The interfacial forces are eliminated by taking as a free body, that part of the interface not in direct contact with the solid. A force balance would give: (Internal pressure - External pressure) * Cross-sectional area = Interfacial tension * Circumference aw Pnw w  air water Pw Thus, Pnwr2Cos2rPwr2 Therefore, Pnw Pwr Cos2r 2 2Cos Pc  And since by definition, Pc PnwPw , we have: r For an air-water system, the air is the non-wetting phase and 2 Cos Pc  aw aw r 14 This equation is referred to as Laplace's Equation in some texts. Pc In terms of height of fluid column. Air -water system air Pa1 (1) Pw1 air hw air Pa2 Pw2 (2) water Pw2 Pa2 Pw2 because there is no capillary pressure across a horizontal interface. Pa1 Pa2 Pw2 but Pw2 Pw1 hwg therefore, Pa1 Pw1 hwg Since Pc Pa1 Pw1 then Pc hwg Oil-water system oil oil Po1 Pw1 (1) oil hw Pw2 Po2 Pw2 (2) water 15 Pa2 Pw2 because no capillary exists across any interface that is horizontal. Pw2 Pw1 hwg Po2 Po1 hog Since Pw2 Po2 , then, Pw1 hwgPo1 hog Therefore, Po1 Pw1 w ohg That is, Pc w ohg Cgs Units: Field Units: Pc dynescm2 h hw o Pc  w orP c psi(orIb sqin )  gmcc 144 144 w, o Ib ft3 gcmsec2 h ft hcm The two expressions for capillary pressure in a tube, one in terms of height of a fluid column and the other in terms of the radius of the capillary tube can be combined to give an expression for the height of a fluid column in terms of the radius of the tube as follows: 2cos hg r Therefore for an air-water system, 2awCos hw  rwg Similarly, for an oil-water system, 16  2owCos  hw  rw  og These two equations show an inverse relationship between fluid height and capillary radius. The smaller the radius is, the higher the height of the fluid column will be. Pc In terms of radii of curvature of interface The general expression for capillary pressure that is applicable to the systems with reference to the porous medium as shown below is: 1 1  Pc    R1 R2 Example Using the drainage capillary pressure curve of the Venango Core (shown below). How many feet above the free water table is the water/oil contact? (1 ft = 30.48 cm) w 1 gmcm3, o 0.75gmcm3,1 cmof mercury = 13,322.2dynescm 17 Solution From the figure, the capillary pressure at the water-oil contact can be read as 4 cm. Since Pc hww  og4*13,322 dynes / cm Then, hw  Pc   ,222.2 217.5 cm 413 w og 10.75980 =217.5/30.48 = 7.1 ft. LABORATORY METHODS OF MEASURING CAPILLARY PRESSURE Three generally accepted methods of measuring capillary pressure in the laboratory are: a) The Porous Diaphragm (or restored state) Method b) The Centrifugal Method c) The Mercury Injection Method All three tests are conducted on core plugs cut from reservoir whole core samples. 18 Drilling fluids, coring fluids, coring procedure, core handling and transportation, storage and experimental processes can alter the natural state of the core. Therefore, special precautions are necessary to avoid altering the natural state of the core. If the natural state of saturation of the core had been altered, then it must be restored to its natural state before conducting any capillary pressure tests. Fresh Core: Samples from core taken with either water or oil-base muds that are preserved (with invaded fluids) and subsequently tested without cleaning and drying are referred to as fresh cores. Native State Cores: Samples from core recovered with lease crude or special oil base fluids known to have minimal influence on core wettability, and that are tested as fresh samples, are referred to as Native State. These cores are in their native state (i.e. without invaded fluids). Such cores coming from above the transition zone should have the same quantity and distribution of water as in the reservoir. These samples are preferred for water displacement tests. Restored Cores: Core samples cleaned and dried prior to testing are referred to as restored cores. An advantage is that air permeability and porosity are available to assist in sample selection. A disadvantage is that core wettability and spatial distribution of pore water may not match that in the reservoir. The following precautions can be helpful in obtaining representative cores if the drilling conditions permit. 1. Use oil-base drilling mud to minimize clay swelling 2. Use non-oxidized lease crude as a coring fluid. 3. Suitable storage procedures include submersion under degassed water, and preservation with saran foil, and wax. 19 Refined oil versus crude oil: Refined oils are suitable for most tests, and are preferred when tests are at ambient conditions. Crude oils to be used in ambient tests should be sampled from non-water producing wells upstream from chemical or heater treaters. Crude oils often precipitate paraffin or asphaltenes at ambient conditions, resulting in invalid test data. Reservoir condition test utilizing live crude oil at reservoir pressures and temperatures often overcome difficulties experienced with crude at ambient conditions. Reservoir fluid samples for special core tests may be recovered using bottom-hole sampling techniques, or recombined from separator gas and oil samples. 1. Rotate at a fixed constant speed. The centrifugal force displaces some liquid, which can be read at the window using a strobe light. Thus, the saturation can be obtained. 2. The speed of rotation is converted to capillary pressure using appropriate equations. 3. Repeat for several speeds and plot capillary pressure with saturation. 20 1. Place core sample in a chamber and evacuate it. 2. Force mercury in under pressure. The amount of mercury injected divided by the pore volume is the non-wetting phase saturation. The capillary pressure is the injection pressure. 3. Continue for several pressures and plot the pressure against the mercury saturation. Advantages: 1. Fast (minutes) 2. No threshold pressure limitation Disadvantage: 1. Can only be used for shaped cores. 21  Pore volume - Volume produced Saturation = Pore volume 1. Saturate both the core sample and the diaphragm with the fluid to be displaced. 2. Place the core in the apparatus as shown 3. Apply a level of pressure, wait for the core to reach static equilibrium. The capillary pressure = height of liquid column + applied pressure 4. Increase the pressure and repeat step (3) 5. Plot capillary pressure versus saturation Disadvantages: 1. Have to work within threshold pressure of the diaphragm 2. Takes too long to reach the equilibrium, therefore a complete curve takes from 10 - 40 days Mercury injection technique was developed to reduce this time. 22 Capillary Hysteresis It is generally agreed that the pore spaces of reservoir rocks were originally filled with water, after which oil moved into the reservoir, displacing some of the water and reducing the water to some residual saturation. When discovered, the reservoir pore spaces are filled with a connate water saturation and an oil saturation. All laboratory experiments are designed to duplicate the saturation history of the reservoir. The process of generating the capillary pressure curve by displacing the wetting phase, i.e., water, with the nonwetting phase (such as with gas or oil), is called the drainage process. This drainage process establishes the fluid saturations which are found when the reservoir is discovered. The other principal flow process of interest involves reversing the drainage process by displacing the nonwetting phase (such as with oil) with the wetting phase, (e.g., water). This displacing process is termed the imbibition process and the resulting curve is termed the capillary pressure imbibition curve. The process of saturating and desaturating a core with the nonwetting phase is called capillary hysteresis. Figure below shows typical drainage and imbibition capillary pressure curves. The two capillary pressure-saturation curves are not the same. This difference in the saturating and desaturating of the capillary- pressure curves is closely related to the fact that the advancing and 23 receding contact angles of fluid interfaces on solids are different. Frequently, in natural crude oil-brine systems, the contact angle or wettability may change with time. Thus, if a rock sample that has been thoroughly cleaned with volatile solvents is exposed to crude oil for a period of time, it will behave as though it were oil wet. But if it is exposed to brine after cleaning, it will appear water wet. At the present time, one of the greatest unsolved problems in the petroleum industry is that of wettability of reservoir rock. Explanations for capillary hysteresis "Ink bottle effect: For porous media modelled as a bundle of tubes with varying diameters, a given capillary pressure exhibits a higher fluid saturation on the drainage curve than on the imbibition curve. 24  This mechanism that has been proposed by McCardell (1955) to account for capillary hysteresis is called the ink-bottle effect. This phenomenon can be easily observed in a capillary tube having variations in radius along its length. Consider a capillary tube of axial symmetry having roughly sinusoidal variations in radius. When such a tube has its lower end immersed in water, the water will rise in the tube until the hydrostatic fluid head in the tube becomes equal to the capillary pressure. If then the tube is lifted to a higher level in the water, some water will drain out, establishing a new equilibrium level in the tube. When the meniscus is advancing and it approaches a constriction, it jumps through the neck, whereas when receding, it halts without passing through the neck. This phenomenon explains why a given capillary pressure corresponds to a higher saturation on the drainage curve than on the imbibition curve. 25 The effect of pore size distribution on capillary pressure curve The more uniform the pore sizes, the flatter the transition zone of the capillary pressure curve. 26 Conversion of Laboratory Capillary Data to Reservoir Capillary Data Water (brine) - oil capillary pressure data are difficult to measure in the laboratory. Generally, air - brine or air - mercury data are measured instead and it becomes necessary to convert these data to equivalent oil - water data representative of reservoir fluids. If we denote (P c)aw or (Pc)aHg as (Pc)lab, and (Pc)ow as (Pc)res the conversion equation can be derived as follows: 2 Cosaw 2 Cos  From Pclab  aw r , we obtain r  aw aw Pc lab 2 Cos 2 Cos  From Pcres ow ow r , we obtain r  ow ow Pc res Assuming that the same porous medium applies in both laboratory and field, we equate the r’s to obtain, Pcres 22owCos ow P aw c lab awCos ignoring the contact angles, Pcres resPclab lab An identical equation would be obtained by starting from the two equations: 1 1      Pclab R1 R2lab 1 1      Pc res R1 R2res Assuming the radii of curvature in the laboratory is the same as that in the reservoir, the RHS's can be equated and (Pc)res : Pcres resPclab lab 27 AVERAGING CAPILLARY PRESSURE CURVES Consider a reservoir cross-section from which four core samples are taken at different depth as shown below. Each core will generate its own complete capillary pressure curve in the laboratory which can be converted to a reservoir capillary pressure curve. Thus four different laboratory capillary pressure curves are obtained as shown below. The question then arises: How do we get a single Pc or height vs. Sw curve to represent the reservoir? The answer is to use the Leverett J-function Leverett J-function The Leverett J-function is defined as: 1 P K2 J  c   Cos   where, K = permeability  = interfacial tension  = contact angle  = porosity 28 The J-function has the effect of normalizing all curves to approach a single curve and is based on the assumption that the porous medium can be modelled as a bundle of non-connecting capillaries. How to use the Leverett J-function to calculate Average Water Saturation The correct method of obtaining the average saturation, Swi for the four pieces is to calculate J for each piece, determine the corresponding water saturation, Swi of each piece by using the J-curve and then taking the arithmetic average of the saturations with the equation. Reference: 1. Amyx, J. W., Bass, Jnr. D. M., Whiting, R. L.: Petroleum Reservoir Engineering 2. Tareq Ahmed: Handbook of Reservoir Engineering 29