PNG405 Pennsylvania State University - Penn State Main Campus Wettability Analysis

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2017ggne

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PNG405

Pennsylvania State University - Penn State Main Campus

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Below is a portion of a phase-partitioned cross-sectional slice from a 3D computed microtomography scan of a glass bead pack post two cycles of flooding by two immiscible fluids. Of the two fluids present (orange or yellow), which is the wetting phase? How do we know this? If I told you the brine is yellow and the kerosene is orange, what is the wettability of the beads used?

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1 PNG 405 (Fall 2019) Class Notes Lecture 14 Date: 10/15/2019 Taken from Previous year’s notes (PNG 405 Fall 2017) by Prof. Karpyn; and Dandekar, Petroleum Reservoir Rock and Fluid Properties, Second Edition, (2012) Blunt, Multiphase Flow in Permeable Media: A Pore-Scale Perspective, (2017) INTERFACIAL TENSION Interfacial tension is the energy per unit area of the surface (or interface) between the two phases. It is also referred to as the energy penalty of breaking the intermolecular interactions within the two phases and instead creating an interface between them. In the figure below, the energy penalty for creating the interfaces is A < B < C, therefore, 𝜎𝑜𝑎 < 𝜎𝑤𝑎 < 𝜎𝑚𝑎 Where, 𝜎𝑜𝑎 is the interfacial tension between oil and air, 𝜎𝑤𝑎 is the interfacial tension between water and air, 𝜎𝑚𝑎 is the interfacial tension between Mercury and air. A B C Air Air Air Oil Water Mercury P. Purswani 2 This is because intermolecular forces within the oil phase are much weaker. Oil is largely nonpolar and oil molecules experience weak Vander Waal’s forces which are relatively easier to break. Water on the other hand is polar and water molecules experience stronger bonding such as Hydrogen-bonding, and are therefore difficult to break which requires more energy. Lastly, Mercury has the strongest boding (metal bonding) which would require the most energy to break its bond. SURFACE TENSION It refers to the energy per unit area of a surface between a fluid (or solid) and its vapor phase in thermodynamic equilibrium, with no other components present. In a petroleum system, we have a complex mixture of many components in the phases therefore, interfacial tension is used instead of surface tension Adhesive forces Unlike cohesive forces, adhesive forces show attraction of molecules in one phase to molecules of another phase. Case 1. When adhesion forces are stronger than cohesive forces Phase 1 Phase 2 Adhesive force Phase 1 Water rises in the capillary Cohesive force Phase 2 Cohesive force Interface Here, the force of adhesion is stronger – it produces a concave curvature. Phase 2 wets the solid surface, because it has a greater affinity to the solid P. Purswani 3 Case 2. When adhesion forces are weaker than cohesive forces Phase 1 Phase 2 Interface Adhesive force Cohesive force Resultant force Cohesive force Here, the force of cohesion is stronger – it produces a convex curvature. Phase 1 wets the solid surface, because it has a greater affinity to the solid Case 3. When adhesion forces are comparable to cohesive forces Interface Adhesive force Cohesive force Resultant force Cohesive force Here, the force of cohesion and adhesion are similar – it produces a flat curvature. Both phases have equal affinity to the solid P. Purswani 4 Wettability “It is the relative ability of a fluid to spread on a solid surface in the presence of another fluid.” (Anderson, 1986) The knowledge of reservoir wettability is critical because it affects other reservoir rock and fluid properties such as capillary pressure and relative permeability. These properties are impacted because wettability affects how fluids are distributed in the porous medium The adhesion force determines which fluid will preferentially wet the solid surface (rock) Young’s equation 𝜎12 Phase 1 Phase 2 𝜃 𝜎1𝑠 𝜎2𝑠 Solid On balancing the forces in the horizontal direction, 𝜎2𝑠 + 𝜎12 𝑐𝑜𝑠𝜃 = 𝜎1𝑠 Therefore, 𝑐𝑜𝑠𝜃 = 𝜎1𝑠 − 𝜎2𝑠 𝜎12 The difference in the interfacial tensions of the fluids with the solid phase is called the adhesion tension (AT) 𝐴 𝑇 = 𝜎1𝑠 − 𝜎2𝑠 From Young’s equation, P. Purswani 5 𝐴 𝑇 = 𝜎12 𝑐𝑜𝑠𝜃 Example cases – Oil/water systems (Water is the denser phase) Case 1. Water-wetting 𝜎𝑜𝑤 Oil Water 𝜃 𝜎𝑜𝑠 𝜎𝑤𝑠 Solid 𝑐𝑜𝑠𝜃 = 𝜎𝑜𝑠 − 𝜎𝑤𝑠 𝜎𝑜𝑤 Here, 𝜃 < 90𝑜 => 𝑐𝑜𝑠𝜃 𝑖𝑠 + 𝑣𝑒 Meaning that 𝜎𝑜𝑠 > 𝜎𝑤𝑠 because water has a higher affinity to the solid and therefore the penalty paid in the creation of water/solid interface is less Case 2. Oil-Wetting Oil 𝜎𝑜𝑤 𝜃 𝜎𝑜𝑠 𝜎𝑤𝑠 Water Solid P. Purswani 6 𝑐𝑜𝑠𝜃 = 𝜎𝑜𝑠 − 𝜎𝑤𝑠 𝜎𝑜𝑤 Here, 𝜃 > 90𝑜 => 𝑐𝑜𝑠𝜃 𝑖𝑠 − 𝑣𝑒 Meaning that 𝜎𝑜𝑠 < 𝜎𝑤𝑠 because oil has a higher affinity to the solid and therefore the penalty paid in the creation of oil/solid interface is less Types of Wettabilities • Completely water-wet (𝜃 = 0𝑜 ) Oil Water film Solid • Water-wet (0𝑜 < 𝜃 < 60 − 75𝑜 ) 𝜎𝑜𝑤 Oil 𝜃 𝜎𝑜𝑠 𝜎𝑤𝑠 Water Solid • Neutral-wet (60 − 75𝑜 < 𝜃 < 105 − 120𝑜 ) Oil 𝜎𝑜𝑤 𝜃 𝜎𝑜𝑠 𝜎𝑤𝑠 Water Solid • Oil-wet (60 − 75𝑜 < 𝜃 < 105 − 120𝑜 ) P. Purswani 7 Oil 𝜎𝑜𝑤 𝜃 𝜎𝑜𝑠 𝜎𝑤𝑠 Water Solid • Completely oil-wet (𝜃 = 180𝑜 ) Oil 𝜃 𝜎𝑜𝑠 𝜎𝑜𝑤 𝜎𝑤𝑠 Water Solid Intermediate wettability (different from neutral wettability) • Fractional wettability – some pores are oil-wet, some others are water-wet due to variability in the mineral composition of the rock • Mixed-wet – small pores are water-wet but larger pores are oil-wet P. Purswani 8 CAPILLARY PRESSURE Rise of fluid in a capillary Consider a water/air system. Water rises due to the adhesion tension. r a P 𝜃 Air h Q R Water How far does the water rise? Water rises until the total pulling force by the adhesion tension is balanced by the weight of the column Upward force due to capillarity, 𝐹𝑢𝑝 = 𝐴 𝑇 2𝜋𝑟 𝐴 𝑇 = 𝜎𝑎𝑠 − 𝜎𝑤𝑠 = 𝜎𝑎𝑤 𝑐𝑜𝑠𝜃 𝐹𝑢𝑝 = 𝜎𝑎𝑤 𝑐𝑜𝑠𝜃2𝜋𝑟 Downward force due to gravity, 𝐹𝑑𝑜𝑤𝑛 = 𝑚𝑔 = 𝜌𝑉𝑔 = 𝜌𝑤 𝜋𝑟 2 ℎ𝑔 P. Purswani 9 Balancing forces, 𝐹𝑢𝑝 = 𝐹𝑑𝑜𝑤𝑛 𝜎𝑎𝑤 𝑐𝑜𝑠𝜃2𝜋𝑟 = 𝜌𝑤 𝜋𝑟 2 ℎ𝑔 We get, the equilibrium height, h, for the rise of the fluid in the capillary 𝒉= 𝟐𝝈𝒂𝒘 𝒄𝒐𝒔𝜽 𝝆𝒘 𝒓𝒈 In the same capillary system, consider the pressures at the following points, • Pressure at point a, (Pa). This is equal to atmospheric pressure • Pressure at point P, (PW). Water pressure at point P • Pressure at point Q, (PQ). This is equal to atmospheric pressure, negligible hydrostatic head of air • Pressure at point R, (PR). This is equal to PW + 𝜌𝑤 𝑔ℎ. That is, pressure of water at P and the hydrostatic head of water We know, PQ = PR. These are pressure at the same horizontal level. Therefore, PQ = Pa = PR Therefore, Pa = Pw + 𝜌𝑤 𝑔ℎ Therefore, Pa - Pw = 𝜌𝑤 𝑔ℎ Capillary pressure (Pc) is defined as the difference in the non-wetting phase pressure and the wetting phase pressure 𝑃𝑐 = 𝑃𝑛𝑜𝑛−𝑤𝑒𝑡𝑡𝑖𝑛𝑔 − 𝑃𝑤𝑒𝑡𝑡𝑖𝑛𝑔 For the air/water system, air being the non-wetting phase, wand water being the wetting phase 𝑃𝑐 = 𝑃𝑎 − 𝑃𝑤 P. Purswani 10 Therefore, for the air/water capillary rise system, 𝑃𝑐 = 𝜌𝑤 𝑔ℎ Putting the equilibrium height, h, we get, 𝑃𝑐 = 2𝜎𝑎𝑤 𝑐𝑜𝑠𝜃 𝑟 Where, 𝑟 is the tube radius, 𝜎𝑎𝑤 is the air/water interfacial tension, 𝜃 is the wetting angle (contact angle) Note: As 𝑟 ↓ => ℎ ↑ => 𝑃𝑐 ↑ As 𝐴 𝑇 (𝜎𝑎𝑤 𝑐𝑜𝑠𝜃) ↑ => ℎ ↑ => 𝑃𝑐 P. Purswani Q5. Below is a portion of a phase-partitioned cross-sectional slice from a 3D computed microtomography scan of a glass bead pack post two cycles of flooding by two immiscible fluids. Of the two fluids present (orange or yellow), which is the wetting phase? How do we know this? If I told you the brine is yellow and the kerosene is orange, what is the wettability of the beads used? 5 6 [mm] 10 11 14 15 16 17 18 19 Imm!
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Wettability
Q: Of the two fluids present (orange or yellow), which is the wetting phase? How do we know
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Wetting phase is the preferential contact of one...


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