Spontaneous potential logs in water resistivity calculation

Exploring for Oil and Gas Traps
Series	Treatise in Petroleum Geology
Part	Predicting the occurrence of oil and gas traps
Chapter	Predicting reservoir system quality and performance
Author	Dan J. Hartmann, Edward A. Beaumont
Link	Web page
Store	AAPG Store

Water resistivity or R_w, is a critical component of log analysis in calculating water saturation using the Archie equation. R_w can be measured from a sample of formation water taken from the zone of interest at the well site or a nearby well, or it can be calculated using spontaneous potential (SP) log data.

Data required

To calculate R_w from SP, we need the following data:

• Resistivity of the mud filtrate (R_mf) at measured temperature, found on the log header. If only mud resistivity (R_m) is given, convert it to R_mf as explained below.
• Bottom-hole temperature (BHT) and total depth, found on the log header.
• SP reading from a porous zone at least length::20 ft thick. (A bed thickness correction is necessary if the zone SP is measured from is less than length::20 ft thick.)

Converting r_m to r_mf

If the log header gives R_m only, then R_m must be converted to R_mf using this procedure:

1. Enter R_m and move across (Figure 1) to the appropriate mud weight.
2. Project to the bottom of the chart to estimate R_mf

Steps for calculating r_w

Figure 1 SP log data. Copyright: Schlumberger.

There are five steps for calculating R_w from the SP log. The list below summarizes these steps, which are detailed in the rest of this section.

1. Estimate formation temperature.
2. Convert R_mf to formation temperature.
3. Convert R_mf to R_mfeq .
4. Read SP response and estimate R_we .
5. Convert R_we to R_w and NaCl at formation temperature.

Step 1: Estimate formation temperature

Formation temperature (T_f) can be estimated by using the following formula:

${\displaystyle {\mbox{T}}_{\rm {f}}={\mbox{T}}_{\rm {s}}+{\mbox{D}}_{\rm {f}}{\frac {{\mbox{$BHT}}-{\mbox{T}}_{\rm {s}}}{\mbox{TD}}}}

where:

• T_s = average surface temperature
• D_f = depth to the formation
• BHT = bottom-hole temperature (found on log header)
• TD = total depth (make sure BHT and TD are from same log run)

Step 2: convert r_mf to r_mf at formation temperature

Figure 2 SP log data. Copyright: Schlumberger.

Follow this procedure to convert R_mf (measured at surface temperature) to R_mf at formation temperature.

1. Enter Figure 2 along the resistivity of solution axis and the temperature axis using the measured values for R_mf and surface temperature found on the log header.
2. Follow the appropriate salinity line intercepted at step 1 to the appropriate formation temperature and mark on the chart.
3. Project down the chart from this mark to the resistivity scale and read R_mf at formation temperature. Record the value of R_mf at a specific temperature.

Step 3: convert r_mf to r_{mf eq}

Figure 3 SP log data. Copyright: Schlumberger.

Use the R_mf at formation temperature obtained above and follow the procedure below to convert R_mf to equivalent mud filtrate resistivity (R_{mf eq}).

1. Enter Figure 3 with R_mf at formation temperature on the vertical axis.
2. Move across the chart to the appropriate formation temperature contour, and mark this point on the figure.
3. Read down to R_mfeq . This value is used in the equation R_we = R_mfeq (R_mfeq /R_we value).

Step 4: convert SP to r_we

Figure 4 SP log data. Copyright: Schlumberger.

Follow the procedure below to convert SP from the zone of interest to equivalent formation water resistivity (R_we).

1. On the log, establish the shale base line for the SP curve.
2. Read the maximum SP response in a zone at least length::20 ft thick.
3. Enter the base of Figure 4 with SP (SP is negative if it deflects to the left of the shale base line). Follow the SP grid line up the chart to the appropriate formation temperature. At this point, move across the chart and read the R_{mf eq} /R_we Value.
4. Solve for R_we using the equation R_we = R_mfeq /(R_mfeq /R_we value).

Step 5: convert r_we to r_w

Follow the procedure below to convert R_we to R_w.

1. Enter Figure 3 again with R_we (along the base). Move up the chart until R_we intersects the temperature slope.
2. Directly across from the intersection point, read R_w from the vertical axis.

See also

• Determining water saturation
• Archie equation
• Determining Rt
• Pickett plot construction

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bottom hole temperature

total depth