COPYRIGHT. Reservoir Rock Properties Fundamentals. Saturation and Contacts. By the end of this lesson, you will be able to:
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1 Learning Objectives Reservoir Rock Properties Fundamentals Saturation and Contacts By the end of this lesson, you will be able to: Describe the concept of fluid contacts Describe how saturations change when crossing contacts 1
2 Oil-Water Contact Oil Water Contact Gas-Oil Contact Gas Oil Contact DATUM DEPTH OIL Oil Zone Aquifer Gas Cap DATUM DEPTH OIL 2
3 Gas-Water Contact Gas Water Contact No Contact DATUM DEPTH GAS Gas Zone GAS DATUM DEPTH OIL 3
4 Super-Critical Fluid LIQUID CRITICAL POINT Pressure Oil Reservoir Temperature VAPOR DATUM DEPTH OIL 4
5 Oil Zone Sand Grains Oil Connate Water Aquifer Sand Grains Connate Water 5
6 Gas-Cap Gas Cap Reservoir Sand Grains DATUM DEPTH OIL Gas Connate Water 6
7 Summary Gas Cap Oil Leg Oil Zone Water Leg Aquifer Gas Zone Please PAUSE pause the video. Learning Objectives Gas-Oil Contact Oil-Water Contact Gas-Water Contact Near Critical Fluids Geologic Time Describe the concept of fluid contacts Describe how saturations change when crossing contacts 7
8 Learning Objectives Reservoir Rock Properties Fundamentals Wettability By the end of this lesson, you will be able to: Describe wettability Describe interfacial tension Describe how residual oil saturation is controlled by the interplay of different forces 8
9 Water Wet Sand Grains Oil Connate Water Oil Wet Sand Grains Connate Water Oil 9
10 Rock Types Disappearing Trail Sandstone Limestone Potential Wettability Changes Diffusion of Mud Components Oxidation Storage Drying Pollution Handling Pollution Temperature and Pressure Drop Drilling Mud Invasion 10
11 Fatty Acids O HO trans-oleic acid HO O By Edgar181 Own work, Public Domain, Wettability Air cis-oleic acid Water Glass Plate Please PAUSE pause the video. 11
12 Non-Wetting Air Non-Wetting Please PAUSE pause the video. Mercury Glass Plate 12
13 Neutral Wet Air Surface Tension Surface film Meniscus Molecules Oil Glass Plate Surface molecules pulled toward liquid causes tension in surface Oil Internal molecules pulled in all directions 13
14 Surface Tension Interfacial Tension Water Oil 14
15 Effect of Gravity Water Effect of Rock Rock Oil Water Oil 15
16 Residual Oil Oil Wet Sand Grains Residual Oil Connate Water Residual Oil 16
17 Summary Oil wet with respect to water Water wet with respect to oil Sandstone wettability at room conditions Limestone wettability at room conditions Residual oil saturation Please PAUSE pause the video. Learning Objectives Fatty acids Naphthenic acids Surface tension Interfacial tension Adhesive forces Buoyancy forces Describe wettability Describe interfacial tension Describe how residual oil saturation is controlled by the interplay of different forces 17
18 Learning Objectives Reservoir Rock Properties Fundamentals Capillary Pressure By the end of this lesson, you will be able to: Define capillary pressure Explain how capillary pressure is a combination of several related phenomena Describe how capillary pressure can be used to explain macroscopic reservoir phenomena Show how collecting capillary pressure data can actually save money 18
19 Different Pressures Sand Grains Oil Connate Water Resolution of Forces Water Oil 19
20 Resisting Movement Water Adhesive Forces Water Oil Oil 20
21 Meniscus Surface Film Meniscus Molecules Oil Meniscus Surface Film Meniscus Molecules Surface Molecules pulled toward liquid causes tension in surface Internal molecules pulled in all directions Surface Molecules pulled toward liquid causes tension in surface Oil Internal molecules pulled in all directions 21
22 Unbalanced Forces Water Counter-Balance Water Oil Water 22
23 Counter-Balance Water Counter-Balance Capillary Pressure Water The pressure in the OIL blob is higher than the pressure in the water on either side. Water = The difference in pressure between two fluids sharing the same pore in equilibrium. Water 23
24 Counter-Balance The capillary force is a function of the interfacial tension between the oil and the water and the differences in adhesive forces between the oil-rock interface and waterrock interface. Gravity Water Water 24
25 Capillary Forces Surface tension Angle between interface and pore walls Buoyancy Forces Difference in density between oil and water Distance to the elevation 2 cos 2 cos Radius of the pore Acceleration due to gravity Engineering Oil Water Contact 25
26 Oil Wet Engineering Oil Water Contact Has to be negative Interfacial Tension Greater than 90 2 cos 2 cos 26
27 Interfacial Tension Curvature 2 cos 2 cos 27
28 Curvature Bundle-of-Tubes X Y OIL 2 cos WATER 28
29 Measurement Bundle-of-Tubes X OIL P C OIL Y 100% S W FREE WATER LEVEL WATER WATER SATURATION 0 100% OIL SATURATION 100% 0 SMALL PORE RADIUS BIG 29
30 Capillary Pressure Curves Oil Pressure Capillary Pressure Curves Capillary Pressure Water Saturation Water Saturation 30
31 Threshold Pressure P e Capillary Pressure Threshold Pressure Sand Grains Water Saturation P e Connate Water 31
32 Irreducible Water Saturation S wi S wi Capillary Pressure Irreducible Water Saturation Sand Grains Water Saturation Oil Connate Water Please PAUSE pause the video. 32
33 Hysteresis Imbibition Capillary Pressure Residual Oil Saturation S orw Capillary Pressure Drainage Water Saturation S orw Water Saturation 33
34 Residual Oil Saturation Applications Residual Oil 34
35 Saturation-Height Capillary Pressure Capillary Pressure How High? Water Saturation Depth Depth Water Saturation OWC (G) Water Saturation OWC (E) Water Saturation 35
36 Capillary Pressure Curves Please PAUSE pause the video. How Low? P C Kg f /cm h m % S W m HIGHEST ELEVATION 100% WATER WATER SATURATION 0 100% 36
37 Capillary Pressure Curves Sample Number Porosity (%) Perm. (md) A B C D E Please PAUSE pause the video. Tilted Contacts OWC (G) LOW PERMEABILITY WELL NO. 1 MEDIUM PERMEABILITY WELL NO. 2 HIGH PERMEABILITY WELL NO. 3 P C OR H S W P C OR H S W P C OR H S W OWC (E) 37
38 Active Aquifers Active Aquifers (A) WATER (B) (C) GAS OIL (A) WATER (B) (C) 38
39 Summary Active aquifers Tilted oil-water contacts Saturation-height functions Capillary pressure curves Free water level Engineering oil-water contact Geological oil-water contact Buoyancy forces Meniscus Please PAUSE pause the video. Learning Objectives Capillary forces Adhesive forces Interfacial tension Hysteresis Drainage Imbibition Threshold pressure Irreducible water saturation Residual oil saturation Bundle-of-Tubes Define capillary pressure Explain how capillary pressure is a combination of several related phenomena Describe how capillary pressure can be used to explain macroscopic reservoir phenomena Show how collecting capillary pressure data can actually save money 39
40 Learning Objectives Reservoir Rock Properties Fundamentals Relative Permeability By the end of this lesson, you will be able to: Describe how oil saturation affects the flow of water in the reservoir Describe how water saturation affects the flow of oil in the reservoir Describe how liquid saturation affects the flow of gas in the reservoir Describe how rock properties affect the flow of multiple phases through the reservoir 40
41 Water not Moving Sand Grains Oil Connate Water Absolute Permeability Sand Grains Oil Connate Water 41
42 Absolute Permeability Sand Grains Oil Relative Permeability to Oil Oil effective permeability Absolute permeability 42
43 Increasing Water Saturation Rock Rock Irreducible Water Oil Irreducible Water Rock Residual Oil Saturation Rock Irreducible Water Oil Irreducible Water Moveable Water Oil Moveable Water Irreducible Water Rock Rock Rock Irreducible Water Water Moveable Water Oil Oil Irreducible Water Rock Moveable Water Irreducible Water Rock 43
44 Oil Behavior Relative Permeability [dimensionless] Relative Permeability to Water Water Saturation [no units] kro Water effective permeability Absolute permeability 44
45 Increasing Water Saturation Rock Irreducible Water Moveable Water Oil Moveable Water Irreducible Water Rock Increasing Water Saturation Rock Irreducible Water Oil Rock Irreducible Water Moveable Water Oil Irreducible Water Rock Moveable Water Irreducible Water Rock 45
46 Residual Oil Saturation WATER IN Residual Oil Saturation WATER IN Residual Oil WATER OUT WATER OUT Residual Oil 46
47 Water Behavior 1.0 Relative Permeability [dimensionless] 0.9 k ro Water Behavior Relative Permeability [dimensionless] k ro Water Saturation [no units] krw kro k rw k rw Water Saturation [no units] krw kro 47
48 Water Behavior 1.0 Relative Permeability [dimensionless] Aquifer 0.9 k ro Sand Grains Water Saturation [no units] krw Practical Maximum Water Relative Permeability kro k rw Connate Water 48
49 Aquifer Correction 1.0 Relative Permeability [dimensionless] k ro Measurement Water Saturation [no units] krw kro k rw 49
50 Pressures vs. Pressure Drops Presentation Relative Permeability [dimensionless] Where: k ro = Oil relative permeability Δp = Pressure drop in flow direction k rw = Water relative permeability ΔL = Length in flow direction k = Absolute permeability μ o = Oil viscosity A = Cross sectional area perpendicular to flow μ w = Water viscosity Please PAUSE pause the video. Water Saturation [no units] k rw k ro 50
51 Moderate Permeability RELATIVE PERMEABILITY Low Permeability RELATIVE PERMEABILITY k ro WATER SATURATION (%) k ro k air : 440 md k air : 175 md k air : 132 md k rw k air : 440 md k air : 175 md k air : 132 md 0.1 k rw WATER SATURATION (%) 51
52 Low Permeability k ro k air : 440 md k air : 175 md k air : 132 md k ro k air : 440 md k air : 175 md k air : 132 md RELATIVE PERMEABILITY Relative Permeability [dimensionless] 0.2 k rw WATER SATURATION (%) Please PAUSE pause the video. Water-Wet k ro k rw RELATIVE PERMEABILITY k rw WATER SATURATION (%) Water Saturation [no units] 52
53 Water-Wet vs. Oil-Wet k ro k rw Relative Permeability [dimensionless] Hysteresis k rw Water Saturation [no units] Relative Permeability [dimensionless] k ro Oil Saturation [no units] k ro imbibition k ro drainage k rw Relative Permeability [dimensionless] Water Saturation [no units] 53
54 Hysteresis Hysteresis Relative Permeability [dimensionless] Relative Permeability [dimensionless] k ro drainage Water Saturation [no units] k ro imbibition k ro drainage Water Saturation [no units] 54
55 Hysteresis k rw Gas k ro & k rg Relative Permeability [dimensionless] k ro imbibition k ro drainage Water Saturation [no units] k rg k ro S Wirr TOTAL LIQUID SATURATION = (s o + s w ) (%) 55
56 Three-Phase Relative Permeability Ternary Diagram 56
57 Vertices 100% Gas 100% Water Sides 100% Gas 0% Oil 0% Water 100% Oil 100% Water 0% Gas 100% Oil 57
58 Contours k ro 100% Gas 100% Water Three-Phase 0% Oil 0% Water % Gas % Oil 58
59 Three-Phase Applications 59
60 Relative Permeability Ratios k ro / k rw CURVES FOR WATER-WET ROCKS CEMENTED SANDSTONES, OGLITE LIMESTONES, OR ROCKS WITH REGULAR POROSITY POORLY SORTED UNCONSOLIDATED SANDS WELL SORTED SANDS Water-Oil Ratios k ro /k rw k ro /k rw Where: q w = Oil rate q o = Water rate k ro = Oil relative permeability k rw = Water relative permeability μ o = Oil viscosity μ w = Water viscosity B o = Oil formation volume factor = Water formation volume factor B w WATER SATURATION, % WATER SATURATION, % 60
61 Saturation-Height Depth [length units] Depth [length units] Water Saturation [no units] WOR-Height k ro /k rw k ro / k rw CURVES FOR WATER-WET ROCKS CEMENTED SANDSTONES, OGLITE LIMESTONES, OR ROCKS WITH REGULAR POROSITY POORLY SORTED UNCONSOLIDATED SANDS WELL SORTED SANDS Water Saturation [no units] WATER SATURATION, % 61
62 Summary Water-oil ratios Transition zones Rel. perm. ratios Ternary diagrams Gas dominance 3-phase rel. perm. Oil-water rel. perm. Gas-oil rel. perm. Gas-water rel. perm. Irreducible water saturation Please PAUSE pause the video. Learning Objectives Residual oil saturation Hysteresis Oil-wet rel. perm. Water-wet rel. perm. Aquifer adjustments Effect of texture Effect of sorting Effective vs. absolute permeability Describe how oil saturation affects the flow of water in the reservoir Describe how water saturation affects the flow of oil in the reservoir Describe how liquid saturation affects the flow of gas in the reservoir Describe how rock properties affect the flow of multiple phases through the reservoir 62
63 Learning Objectives Reservoir Rock Properties Fundamentals Laboratory Procedures Relative Permeability By the end of this lesson, you will be able to: Discuss the various choices available for measuring relative permeability in the laboratory 63
64 Permeability Core Sample Permeability d Diameter x Length 64
65 Permeability Gas in Darcy s Law δp Gas Out Pressure drop Where: q g = Gas rate k g = Gas effective permeability d = Diameter of core sample = Circle constant (~3.14) p = Pressure drop in flow direction x = Length in flow direction g = Gas viscosity 65
66 Relative Permeability Relative Permeability Relative Permeability Relative Permeability Steady State Unsteady State Centrifuge Steady State Unsteady State Centrifuge 66
67 Relative Permeability Core Sample Relative Permeability d Diameter x Length 67
68 Relative Permeability (Steady State) Oil in Water in Oil in Water in Water in Relative Permeability (Steady State) Oil out Water out δp Pressure drop 68
69 Relative Permeability (Steady State) Relative Permeability (Steady State) Oil in Water in 1. Wait for steady state 2. Measure the pressure drop 3. Measure the mass 4. Repeat workflow 69
70 Apparatus STEADY STATE FLOW TECHNIQUE Darcy s Law P OIL IN WATER IN OIL OUT WATER OUT PORCELAIN PLATE Where: q o = Oil rate k o = Oil effective permeability d = Diameter of core sample = Circle constant (~3.14) p = Pressure drop in flow direction x = Length in flow direction o = Oil viscosity 70
71 Darcy s Law (2 Phase) OIL rate and OIL viscosity WATER rate and WATER viscosity 2 Where: k o = Oil effective permeability k w = Water effective permeability d = Diameter of core sample = Circle constant (~3.14) p = Pressure drop in flow direction x = Length in flow direction o = Oil viscosity w = Water viscosity Effective Permeabilities Run k o K w No. [md] [md] Please PAUSE pause the video. 71
72 Relative Permeability to Oil Relative Permeabilities Run k o K w No. [md] [md]
73 Relative Permeability to Water Relative Permeabilities Run k o K w K ro k rw No. [md] [md] [ ] [] Please PAUSE pause the video. 73
74 Saturations Saturations Mass of saturated core sample Mass of oil in saturated core sample 74
75 Saturations Saturations Mass of water in saturated core sample Mass of rock (solid material) in saturated core sample 75
76 Saturations Where: m s = Mass of saturated core sample m o = Mass of oil in saturated core sample m w = Mass of water in saturated core sample m r = Mass of rock (solid material) in saturated core sample o = Oil density = Water density w 1 2 Please PAUSE pause the video. Saturations 1 2 r s w = Rock (solid material) density = Core sample water saturation φ = Core sample porosity d = Diameter of core sample x = Length in flow direction π = Circle constant (~3.14) 1 2 Please PAUSE pause the video. 76
77 Saturations Please PAUSE pause the video. Saturations 1 2 Run k o K w K rw m s No. [md] [md] [ ] [g]
78 Saturations Run k o K w K ro k rw m s o [g/cc] No. [md] [md] [ ] [] [g] w [g/cc] r [g/cc] [ ] d [cm] x [cm] Complete Table Run k o K w K ro k rw m s o [g/cc] s w No. [md] [md] [ ] [ ] [g] w [g/cc] [ ] r [g/cc] [ ] d [cm] x [cm]
79 Normalization Normalized Run k o K w K ro k rw m s o [g/cc] s w k ro k rw No. [md] [md] [ ] [] [g] w [g/cc] [ ] [] [ ] r [g/cc] [ ] d [cm] x [cm] Plot Please PAUSE pause the video. Relative Permeability [ ] k ro k rw Water Saturation [ ] 79
80 Relative Permeability Relative Permeability Relative Permeability (Steady State) Oil in Steady State Unsteady State Centrifuge Oil in Water in δp Pressure drop 80
81 Relative Permeability Relative Permeability Relative Permeability (Centrifuge) HEAVIER FLUID GRADUATED TUBE CENTRIFUGE SYSTEM CORE SAMPLE Steady State Unsteady State Centrifuge LIGHTER FLUID AXIS OF ROTATION 81
82 Relative Permeability Relative Permeability Measures capillary pressure concurrently with relative permeability Relative Permeability Relative Permeability More math 1 fluid injecteded Steady State Unsteady State Centrifuge Steady State Unsteady State Centrifuge 82
83 Summary Absolute permeability measurement Steady state relative permeability measurement Unsteady state relative permeability measurement using a permeameter Unsteady state relative permeability measurement using a centrifuge Please PAUSE pause the video. Back to Work Suggestion Search for as many relative permeability tests as you can find in your well files that apply to your reservoir Compare them to the capillary pressure tests Are they consistent? 83
84 Learning Objectives Discuss the various choices available for measuring relative permeability in the laboratory 84
85 Learning Objectives Reservoir Rock Properties Fundamentals Laboratory Procedures Capillary Pressure By the end of this lesson, you will be able to: Discuss the various choices available for measuring capillary pressure in the laboratory 85
86 Capillary Pressure Capillary Pressure Mercury Injection Porous Plate Centrifuge Mercury Injection Porous Plate Centrifuge 86
87 Mercury Injection Apparatus N 2 Bottle 250kg Hg In Pc Hg mano Hg Windows Sample Volumetric mercury pump 87
88 Air Injection Capillary Pressure Air In Mercury Injection Porous Plate Centrifuge H 2 O Out 88
89 Apparatus Capillary Pressure Mercury Injection Porous Plate Centrifuge 89
90 Water Expulsion Water Out Apparatus CENTRIFUGE SYSTEM LIGHTER FLUID HEAVIER FLUID GRADUATED TUBE CORE SAMPLE Oil In AXIS OF ROTATION 90
91 Comparison Comparison Capillary Pressure Mercury Injection Porous Plate Centrifuge Method Wetting Phase Non-Wetting Phase Mercury Injection Air Mercury Porous Plate Water Air Centrifuge Water Oil 91
92 Conversion Conversion Where: Pc res = Capillary pressure reservoir conditions Pc lab = Capillary pressure laboratory conditions Where: Pc res = Pc lab = res = lab = res = lab = Capillary pressure reservoir conditions Capillary pressure laboratory conditions Interfacial tension reservoir conditions Interfacial tension laboratory conditions Contact angle reservoir conditions Contact angle laboratory conditions 92
93 Summary Mercury Injection Porous Plate Centrifuge Corrections Back to Work Suggestion Search for as many capillary pressure tests as you can find in your well files Compare them against each other Compare them to the relative permeability data Are they consistent? 93
94 Learning Objectives Discuss the various choices available for measuring capillary pressure in the laboratory 94
95 Learning Objectives Reservoir Rock Properties Fundamentals Laboratory Procedures Wettability By the end of this lesson, you will be able to: Discuss the various choices available for measuring wettability in the laboratory 95
96 Wettability Wettability Contact Angle Amott Contact Angle Amott USBM USBM 96
97 Step 1 Water Step 2 Solid Rock Water Solid Rock 97
98 Step 2 Water Step 3 Solid Rock Water Oil Oil Solid Rock 98
99 Contact Angle Water Solid Rock Interpretation Old School Oil Contact Angle <90 Contact Angle >90 Water Wet Oil Wet 99
100 Wikipedia Please PAUSE the video. Wikipedia Please PAUSE the video. 100
101 Interpretation Contact Angle < 60 Water Wet New School 60 < Contact Angle < 120 Old School Contact Angle < 90 o Contact Angle >90 o Interpretation Water Wet Oil Wet New School Contact Angle > 120 Contact Angle < 60 Neutral Wet Oil Wet Water Wet 60 < Contact Neutral Neutral Wet Angle < 120 Wet Contact Angle < 90 o Water Wet Old School Contact Angle >90 o Oil Mixed Wet? Contact Angle > 120 Oil Wet 101
102 1. Cloudy Water 2. Porous Rock Wikipedia 1. If produced water is cloudy: Change wavelength of the light to one not scattered by suspended solids in the water Filter the water 2. If rock sample is porous and permeable Non-porous rock samples are used Wikipedia 102
103 Contact Angle Wettability Amott USBM Step 1 103
104 Step 2 Oil Step 3 Displaced Water (Spontaneous) V 2 Displaced Water (Forced) V 3 104
105 Step 4 Displaced Oil (Spontaneous) V 4 Step 5 Displaced Oil (Forced) V 5 105
106 Calculations Oil Index Calculations Where: I o = Oil Index V 2 = Oil spontaneously entering core V 3 = Oil entering core under force 106
107 Calculations Oil Index Calculations Oil Index Water Index Where: I o = Oil Index V 2 = Oil spontaneously entering core V 3 = Oil entering core under force I w = Water Index V 4 = Water spontaneously entering core V 5 = Water entering core under force 107
108 Calculations Oil Index Variations Water Index Amott-Harvey Index Step 1 Where: I A = Amott Index I w = Water Index I o = Oil Index Start Step 2 Step 3 Step 1 Step 3 Start Step 4 Step 4 Step 5 Step 5 Step 2 End Step 3 End 108
109 Example Jadhunandan and Morrow, 1991 Owolabi and Watson, 1993 Chen et al, 2004 S or From Anderson, I A w Totally Oil Wet Totally Water Wet Water Wet (left) vs. Oil Wet (right) 109
110 Summary Contact Angle Neutral Wet Mixed Wet Amott Spontaneous vs. Forced Oil vs. Water Index Amott-Harvey Residual Oil Saturation Relative Permeability Please PAUSE pause the video. Back to Work Suggestion Search for as many wettability tests on your reservoir as you can find Is the data consistent? If not, how do you explain the inconsistencies? How are you going to resolve the inconsistencies? 110
111 Learning Objectives Discuss the various choices available for measuring wettability in the laboratory 111
112 Learning Objectives Reservoir Rock Properties Fundamentals Modeling By the end of this lesson, you will be able to: Show how reservoir engineers model relative permeability Show how reservoir engineers model capillary pressure 112
113 Relative Permeability Water Relative Permeability Modified-Corey Equation 113
114 Water Relative Permeability 2-phase water relative permeability end-point 2-phase water saturation exponent Relative Permeability [ ] Water Relative Permeability Relative Permeability [ ] k rw Water Saturation [ ] k rw Water Saturation [ ] 114
115 Water Relative Permeability Relative Permeability [ ] Normalized water saturation Critical water saturation Oil Relative Permeability k ro Relative Permeability [ ] k rw Water Saturation [ ] Water Saturation [ ] 115
116 Oil & Water k ro Relative Permeability [ ] End Point Changes Water Saturation [ ] Relative Permeability [ ] k rw k ro k rw Water Saturation [ ] 116
117 End Point Changes k ro End Point Changes Relative Permeability [ ] Relative Permeability [ ] Water Saturation [ ] k rw k ro k rw Water Saturation [ ] 117
118 Exponent Changes k ro Exponent Changes Relative Permeability [ ] Relative Permeability [ ] k rw Water Saturation [ ] k ro k rw Water Saturation [ ] 118
119 Exponent Changes k ro Relative Permeability [ ] 3-Phase Relative Permeability Oil Water Water Saturation [ ] Gas Oil k rw 119
120 3-Phase Relative Permeability Stone Where: k ro = 2-phase oil relative permeability k rw = 2-phase water relative permeability k row = 2-phase oil relative permeability from oil-water table k rog = 2-phase oil relative permeability from gas-oil table k rg = 2-phase gas relative permeability Please PAUSE pause the video. 3-Phase Relative Permeability S S S S g Where: k ro = 2-phase oil relative permeability k rw = 2-phase water relative permeability k row = 2-phase oil relative permeability from oil-water table k rog = 2-phase oil relative permeability from gas-oil table k rg = 2-phase gas relative permeability 120
121 Thomeer Capillary Pressure Water Saturation Interporosity Coefficient Capillary Pressure Threshold Pressure Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure 121
122 Thomeer P c Fit The original version of this equation used bulk volumes instead of saturations. The results are equivalent, so we ll keep things simple by using saturations. Thomeer (68,948) (6,895) (689) Fit to Data Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure P c Fit Capillary Pressure [psi] (kpa) (69) Oil Saturation [ ] 122
123 Thomeer (68,948) Threshold Pressure Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure Thomeer Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure (6,895) (689) (69) (68,948) P c Fit P d P c Fit Oil Saturation [ ] Infinite Pressure (6,895) (689) Capillary Pressure [psi] (kpa) Capillary Pressure [psi] (kpa) (69) Oil Saturation [ ] 123
124 Thomeer (68,948) Raw Data P c Fit Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure Thomeer Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure (6,895) (689) (69) (68,948) Oil Saturation [ ] P c Raw Increase Threshold Pressure P c Fit (6,895) (689) Capillary Pressure [psi] (kpa) Capillary Pressure [psi] (kpa) (69) Oil Saturation [ ] P c Raw 124
125 Thomeer (68,948) Restore Threshold Pressure P c Fit Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure Thomeer Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure (6,895) (689) (69) (68,948) P c Fit Oil Saturation [ ] Increase G-Factor (6,895) (689) P c Raw Capillary Pressure [psi] (kpa) Capillary Pressure [psi] (kpa) (69) Oil Saturation [ ] P c Raw 125
126 Thomeer (68,948) Restore G-Factor P c Fit Where: P c = Capillary pressure S w = Water saturation G = Interporosity coefficient P d = Threshold pressure (6,895) (689) (69) Please PAUSE pause the video. Summary Threshold pressure Interporosity coefficient Saturation exponent Relative permeability endpoint Normalized saturation Thomeer Corey Oil Saturation [ ] P c Raw Capillary Pressure [psi] (kpa) Please PAUSE pause the video. 126
127 Back to Work Suggestion Learning Objectives Build a relative permeability and capillary pressure model for your reservoir using correlations How does it compare with the laboratory data? If you have no laboratory data for your reservoir, how do you decide what parameters to use? Show how reservoir engineers model relative permeability Show how reservoir engineers model capillary pressure 127
128 Learning Objectives Reservoir Rock Properties Fundamentals Saturations By the end of this lesson, you will be able to: Describe how reservoir engineers define saturations 128
129 Water Saturation Relative Permeability [dimensionless] Irreducible water saturation Initial water saturation Critical Connate water saturation Critical water saturation Water Saturation [no units] krw kro 129
130 1.0 Relative Permeability [dimensionless] Sand Grains Water Saturation [no units] krw Oil kro Irreducible Connate Water 130
131 Sand Grains Connate Water Water Saturation Initial water saturation Connate water saturation Irreducible water saturation Critical water saturation 131
132 Oil Saturation Oil Saturation Where: S o = Oil saturation = Residual oil saturation 132
133 Oil Saturation Residual oil saturation to water Water Displacing Oil Water In Residual oil saturation to gas Water Out Residual Oil 133
134 Gas Displacing Oil Sand Grains Residual Oil Connate Water Gas Out Gas In Gas Saturation 134
135 Gas Saturation Where: = Gas saturation S g Gas Saturations Residual gas saturation Critical Critical gas saturation Where: S g = Gas saturation Residual 135
136 Summary S w S wi S or S orw S wc S wirr S wcr S o Please PAUSE pause the video as needed. Learning Objectives S org S g S gc S gr Describe how reservoir engineers define saturations 136
137 PetroAcademy TM Applied Reservoir Engineering Skill Modules Properties Analysis Management This is Reservoir Engineering Core Reservoir Rock Properties Core Reservoir Rock Rock Properties Fundamentals Reservoir Fluid Core Reservoir Fluid Fundamentals Reservoir Flow Properties Core Reservoir Flow Properties Fundamentals Reservoir Fluid Displacement Core Reservoir Fluid Displacement Fundamentals Reservoir Material Balance Core Reservoir Material Balance Fundamentals Decline Curve Analysis and Empirical Approaches Core Decline Curve Analysis and Empirical Approaches Fundamentals Pressure Transient Analysis Core Rate Transient Analysis Core Enhanced Oil Recovery Core Enhanced Oil Recovery Fundamentals Reservoir Simulation Core Reserves and Resources Core Reservoir Surveillance Core Reservoir Surveillance Fundamentals Reservoir Management Core Reservoir Management Fundamentals 137
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