FORMATION WATER RESISTIVITY ( RW ) DETERMINATION : THE SP METHOD

Formation water resistivity represents the resistivity value of the water (uncontaminated by drilling mud) that saturates the porous formation. It is also referred to as connate water or interstitial water. Its resistivity can be determined by a number of methods, one of which is by the SP curve discussed in this work. Analysis of wire-line log data depends on the assumption that the only conductive medium in a formation is the pure water which supplies the energy and drive in reservoirs. So, physical properties of this formation water can be determined, one of which is its electrical resistivity and this eventually leads to water saturation determination – an important aspect of reservoir evaluation. This paper presents a review and comparative assessment of the graphical, vis-a-vis the calculative means of Rw determination by the SP method

aquatic environments.Consequently, these sedimentary beds were originally saturated by salt water.Part of this water was displaced in the process of diagenesis and oil accumulations, the other remains, suspending the hydrocarbons because of their density contrast.That which remains generally is known as "Connate" or "Interstitial" water because the water was "born with" and is stored in the interstices of the sediments.Schlumberger (1989) defined formation water as the water uncontaminated by drilling mud that saturates the formation rock.Analysis of wire line log data depends on the assumption that the only conductive medium present in the formation is the pore water; the matrix and hydrocarbons are non-conductive.Physical properties of this formation water can be determined, one of which is electrical resistivity.Formation water is the free water which supplies the energy for the water drive in reservoirs; and its resistivity is variable depending on the salinity, temperature and whether or not the formation contains hydrocarbons.At a given salinity, the higher the temperature the lower the resistivity, and the water resistivity at any formation temperature, can be calculated from the water resistivity at another formation temperature, knowing both the temperature and temperature offsets using this formula: R w at FT 2 = R w FT 1 , (FT 1 + C)(FT 2 + C).Where FT 1 = Initial formation temperature FT 2 = Formation Temperature for which R w is being determined.C = 21.5 for Temperature in °C (Smolen, 1977).
It has also been established (Schlumberger, 1989) that the water resistivity determined from a hydrocarbon-bearing zone is usually greater than that from the zone bearing only formation water.Determination of formation water resistivity is very important in calculating water and/or hydrocarbon saturation, in the determination of salinity if temperature is known and in understanding the variations of resistivity from the well wall into the formation by comparing it with the resistivity of the mud filtrate.In both SP and R wa comparison methods, wire-line logs provide all the needed parameters to determine the formation water resistivity.

THE SP METHOD
In many cases, a good value of formation water resistivity R w can easily be found by the SP curve read in clean (non-shale) formations because the SP can be used to distinguish lithology such as shaly from sandy formations.The static SP (SSP) value in a clean formation is related to the chemical activities (a w and a mf ) of the formation water through the formula: Where K = Constant and varies in direct proportion with temperature especially in NaCl solutions K = 61 + 0.133T in °F K = 65 + 0.24T in °C a w = Chemical activity of water a mf = Chemical activities of mud filtrate.
For pure Nacl solutions that are not too concentrated, resistivities are inversely proportional to activities.
Therefore, Where R we = 0.075/S w at 77°F (25°C) and is the equivalent formation water resistivity; and R mfe = equivalent mud filtrate resistivity.
After we have been able to relate these resistivities to the SP value for a particular zone, we would then follow the procedure below in determining the formation water resistivity (R w ) using the SP method.8. Check whether the SP needs correction.If need be, correct for bed thickness, hole diameter, invasion and resistivity contrasts using the appropriate charts.9. Now, knowing the formation temperature (T f ), the static SP or SP (Corrected), recorded opposite a porous and permeable, non-shaly formation can be transformed into the resistivity ratio R mf /R we in two ways: graphically as in figure 1 and by calculation.

Graphically by use of chart:
With the ratio R mfe /R we now determined and the resistivity R mf of a sample of mud filtrate measured, the equivalent formation resistivity, R we , is easily calculated.However, the mud filtrate resistivity reported on the log heading or calculated at the formation temperature is its actual resistivity not its equivalent resistivity (Edwards et al 1963).To convert the measured mud filtrate resistivity (R mfe , the following rules are employed: (a) For predominantly NaCl Muds.
i.If R mf at 75°F is greater than 0.1ohm-m, use R mf 0.85ohm-m at Formation Temperature.This relationship is based on measurements made on many typical muds.
ii.If R mf at 75°F is less than 0.1ohm-m, use the NaCl (solid curves) in figure 2 to derive a value of R mfe from the measured R mfe value corrected to formation temperature.
(b) For fresh water or gypsum muds: the dashed curves of the chart in fig. 2 are used to convert R mf to R mfe .
(c) Lime-based muds, despite their name, usually have negligible amounts of calcium and are treated as regular mud (see rule a).
iii.If R mf at 75°F is greater than 0.1ohm-m, use R mf 0.85ohm-m at Formation Temperature.This relationship is based on measurements made on many typical muds.
iv.If R mf at 75°F is less than 0.1ohm-m, use the NaCl (solid curves) in figure 2 to derive a value of R mfe from the measured R mfe value corrected to formation temperature.
(e) For fresh water or gypsum muds: the dashed curves of the chart in fig. 2 are used to convert R mf to R mfe .

(f)
Lime-based muds, despite their name, usually have negligible amounts of calcium and are treated as regular mud (see rule a).
the bottom hole temperature and the total depth with the formula: Where T f = Temperature of the formation in °F or °C.T TD = Temperature at total depth (Bottom hole Temp.) in °F or °C.T 0 = Mean surface temperature (in °F or °C).D f = Depth to formation (in ft or m).T D = Total depth (in ft or m). 5. Now, from the R mf and R m values recorded on the log heading, determine the R mf and R m values at that particular formation temperature using the formula: R mf at T f = R mf at T 0 (T 0 + C/Tf + C) Where C is the temperature offset.C = 6.8 if imperial units are used and 21.5 if metric units are used.T 0 = Initial temperature at which R mf was first measured.R m = Resistivity of mud, usually recorded on the log heading 6.Now read off SP amplitude from shale baseline to maximum constant deflection.7. Determine bed thickness from SP deflection points.