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Petrophysicist Role• Petrophysics is the study of rock properties and their interactions with fluids (gases, liquid hydrocarbons, and aqueous solutions).• Petrophysicist is considered to be responsible for integration of all available data from wireline logging together with core analysis data in order to generate a complete picture for the reservoir in hand.• Petrophysicist is responsible for generating field study based on wireline logs to be provided further for the geologists and reservoir engineers to work on the static and dynamic modeling. AbdelRahman Elkhateeb
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Archie Equation• Archie Equation is the most famous equation used by petrophysicists to determine the water saturation in the reservoir in hand.• Considered to be effective in clean reservoirs.• Used by petrophysicists and log analysts in manual interpretation to have a quick look evaluation.• Presence of any shale content within the reservoir decreases the reliability of the water saturation calculated by Archie Equation.• Using Archie in shaly reservoirs of high resistivity generates high water saturation values should be corrected further on the CPI log. AbdelRahman Elkhateeb
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Extracting Archie Equation• Resistivity Index:• Considering Rt is the true resistivity of the reservoir, and Ro is the resistivity of the reservoir fully saturated with water, RI = Rt / Ro, Where RI is the resistivity Index.• If the reservoir is fully saturated with water, then the true resistivity should be the same as the Ro value. (SW) n = 1 / RI (n) Is the saturation exponent (SW)n = Ro/Rt AbdelRahman Elkhateeb
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Extracting Archie Equation • (F) The Formation Factor of the reservoir is characterized F= by two factors, the tortuosity and the porosity. Where (a) is Tortuosity Factor, () is the porosity Resistivity of Brine and (m) is the saturation exponent Water Ro = F * RwThe saturation equation (SW )n = = will be Where (Rw) is the water resistivity And (Rt) is the true resistivity AbdelRahman Elkhateeb
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Extracting Archie Equation (SW )n = ∗ ∗ Archie Equation Ф • The generalized equation that had come from study of 152 core of oil producing sandstone reservoirs indicated that (m) = 2, (n) = 2 and (a) equal (0.81) in sand with porosity higher than 0.15 and (1) in carbonate and low porosity sand, while the other parameters are all could be detected from the logs, then finally the following general equation has been the standard Archie Equation. (SW ) 2 = ∗ ∗ Ф Or ∗ SW = Ф ∗ Simple Archie Equation AbdelRahman Elkhateeb
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Humble Equation• Humble Plot was the first graphical attempt to solve the water saturation equation.• This equation was extracted based on core plugs, where F vs. ϕ were plotted on a chart, and the following formation factor parameters were obtained, F = 0.62 / ϕ2.15• This Equation later simplified to the famous formation factor equation that is extensively used in sandstone formations F = 0.81 / ϕ2 AbdelRahman Elkhateeb
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Humble Equation (m)Depends on the slope of the line. (a) Values AbdelRahman Elkhateeb
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Archie Parameters Rock Grains Porosity (Ф)(a) Is the tortuous Path between grains AbdelRahman Elkhateeb
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Determining the Archie Equation Parameters• Total Porosity: The ratio of the volume of all pores to the bulk volume of the rock. (ϕt = Vp/VB)• Effective Porosity: The ratio of only the interconnected pores to the bulk volume of the rock.• (m) is the cementation exponent that differs according to the degree of cementation.• (n) is the saturation exponent that is determined from special core analysis.• (a) is the tortuosity factor depends on the path that the fluid will flow through. AbdelRahman Elkhateeb
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Determining the Archie Equation Parameters Bulk Volume = 1 V +t =1 M Bulk Volume of the Rock VM = 1-Фt Rock Matrix Porosity Fluids BVW = Sw* Ф AbdelRahman Elkhateeb
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Determining the Archie Equation Parameters What is the difference between water saturation (Sw) and Bulk Volume of Water (BVW)? Shale VolumeRock with shale content AbdelRahman Elkhateeb
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Water Saturation and Bulk Volume Water• Bulk Volume of Water is volume of the water in relation to the total bulk volume of the rock. BVW = Sw * ϕeff• Water saturation is the amount of water in relation to the pore spaces only. ФT = VP / VB Sw= BVW/ϕeff AbdelRahman Elkhateeb
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Example• A rock with true resistivity around 20 ohm.m has been encountered in Bahariya Formation in Western Desert with porosity ranging from 0.20 to 0.25, Determine the water saturation within this rock if the water resistivity is 0.035 ohm.m? AbdelRahman Elkhateeb
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Example• A sandstone rock with 30% porosity and 10 ohm.m resistivity, What is the water saturation of this rock if the water resistivity is 0.12 and derive the bulk volume of water? AbdelRahman Elkhateeb
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How to detect thelithology and the zone of interest? AbdelRahman Elkhateeb
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Detecting the Lithology from the D-N Crossplot Ρb = 2.4 g/cc ФN = 0.20 0.20 L.St. Ρb = 2.38 g/cc ФN = 0.165 0.20 SLB L.St or S.S ?? AbdelRahman Elkhateeb
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Calculating Porosity in the Formation• In order to calculate the porosity of the formation, it is necessary to have an idea about how to detect the lithology, how to read the logs, and the most important thing, How to feel the wireline logs and visualize the formation?• Moreover, the log analyst as well as the petrophysicist should have an idea about the equations that will lead him to give a quick look evaluation for the reservoir in hand. AbdelRahman Elkhateeb
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Calculating Porosity in the Formation• Calculating porosity from the density curve − ϕD = − Bulk DensityPorosity From Density S.S = 2.65 mat is the matrix density L.St = 2.71 Dol. = 2.847 Fresh = 1 Fluid Density Salt = 1.1-1.2 AbdelRahman Elkhateeb
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Calculating Porosity in the Formation Determine the porosity from density curve if the ρb curve27.5 % reads around 2.4 g/cc? SLB AbdelRahman Elkhateeb
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Calculating Porosity in the Formation• Calculating porosity from the Sonic curvePorosity From Sonic − Sonic Reading Fresh = 189 μs/ft. ϕS = − Fluid Transit time Salt = 185 μs/ft. S.S = 55.5 μs/ft.mat is the matrix Transit Time L.St = 47 μs/ft. Dol. = 43 μs/ft.• Primary Porosity Could be calculated from sonic curve in conjunction with the density and neutron curves. AbdelRahman Elkhateeb
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Calculating Porosity in the Formation Determine the porosity from sonic curve if the tlog curve reads around 70 μs/ft.?10.7 % SLB AbdelRahman Elkhateeb
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Calculating Porosity in the Formation• Calculating porosity from the Neutron curvePorosity From Neutron ϕN = Reading of the neutron curve • The higher the porosity of the formation, as well as the hydrogen content, the higher the neutron curve value. • Interpret the high value of the neutron curve in the shale beds? AbdelRahman Elkhateeb
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Calculating Porosity in the Formation Determine the porosity in26 % sandstone from neutron curve if the ФN curve reads around 18% in limestone scale? SLB AbdelRahman Elkhateeb
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Calculating Porosity in the Formation• Calculating the total porosity from the curves within hand ϕ+ϕ+ϕTotal Porosity φ T = 3 ϕ+ϕ φ Or T = 2 Or ϕ+ϕ φ T = 2 For Gas Intervals AbdelRahman Elkhateeb
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Example• In the following log example, determine the interested zones, calculate the porosity, detect the resistivity, then determine the water saturation within the zones of interest if the water resistivity of the same formation was detected from water sample and the results were around 0.03 ohm.m? AbdelRahman Elkhateeb
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Log Example RXO NPHI RHOB AbdelRahman Elkhateeb
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Detecting the Water Resistivity• Water resistivity is the most important parameter in Archie equation, and plays very important role in the equation.• Inaccurate water resistivity value results in totally unreliable water saturation and wrong true bulk volume of water.• Water resistivity could be determined through different equations and methods, the most easiest and fastest one is from the porosity with resistivity value in the clean water zone. AbdelRahman Elkhateeb
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Methods of Detecting the Water Resistivity• Form Archie Equation, in a clean 100% water interval with high porosity. Ф ∗ Rw = • If the cementation exponent is known from core analysis, this will typically enhance the accuracy of water resistivity value. Otherwise use the standard (m) value as usual. AbdelRahman Elkhateeb
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Log Example • Determine the high porosity value from the logs against the lowest resistivity through the logs , then enter both in the reversed Archie Equation to get water resistivity value. AbdelRahman Elkhateeb
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Methods of Detecting the Water Resistivity• Form Picket Plot, which is considered to be an integration for the reversed Archie Equation with crossplot. Ф ∗ Rw = • This crossplot has to be in coherent with the value calculated from the reversed Archie Equation (more or less the same). AbdelRahman Elkhateeb
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Methods of Detecting the Water Resistivity• Form Picket Plot, which is considered to be an integration for the reversed Archie Equation with crossplot. Rt AbdelRahman Elkhateeb
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Methods of Detecting the Water Resistivity• Form Salinity value from the logs or water sample in conjunction with the formation temperature using salinity chart.• Considered to be the most effective method as the measured value is much more accurate than any value calculated from the logs.• Water resistivity calculated from the logs using true resistivity could have some error due to the influence of the mud on its readings. AbdelRahman Elkhateeb
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Methods of Detecting the Water Resistivity SLB AbdelRahman Elkhateeb
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Methods of Detecting the Water Resistivity• From SP Log, we can determine the Water Resistivity value using the following equation SSP = -Kc Log • Kc = Temperature coefficient = - (61 + 0.133 T degF)• Rmfe= Resistivity of mud filtrate (When Rmf @ 75° F 0.1, then Rmfe = Rmf x 0.85.• When Rmf @ 75°F 0.1, use Schlumberger Chart SP-2 to find Rmfe.• SSP = Static Spontaneous Potential. AbdelRahman Elkhateeb
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Methods of Detecting the Water Resistivity SLB AbdelRahman Elkhateeb
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Methods of Detecting theCementation Exponent Value• Form Picket Plot, (m) is the slope of the line that detecting the Rw value. AbdelRahman Elkhateeb
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Methods of Detecting the (m) Value • From Special Core Analysis. • A log-log plot of F vs. ϕ yields a straight line that can be extrapolated m= -Y/X to ϕ =1 to find (a) value. The slope of the line is –m (Due to that Log ϕ always will be with (– value) . • A best fit line drawn through the points intersects the representing ϕ =1. at a value of 1.4 then a=1.4 .The slope of the line is -1.8, so a value m=1.8. • (a) value is detected at the point of the intersection between the drawn line and (X = 1) AbdelRahman Elkhateeb
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Methods of Detecting the (m) Value• These methods were discussed extensively and finally it is found that in order to use a specific (m) value but the standard one, there must be a core taken in the field under observation.• Different (m) values affect the water saturation dramatically and of course leads to completely unreliable petrophysical interpretation, while difference in (a) or (n) values does not affect the water saturation as much as (m). AbdelRahman Elkhateeb
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