TDS Determination using Geophysical Well Logs

The Geophysical Logging Division of Youngquist Brothers, Inc, has combined the classic well log analysis equations developed by Archie in the 1940’s with the work done by Ron Reese of the USGS to accurately determine the water quality in South Florida wells. This technique has been successfully used for over 12 years to predict the base of the USDW.

The technique first determines the water resistivity from the Deep Induction Log and Sonic Log. Archie’s first equation states that a Formation Factor (F) is related to porosity by the equation:

Where a is a constant and m is the cementation exponent. The cementation exponent is related to lithology and ranges in value from 1.5 to 2.3 typically. Through empirical analysis Youngquist Brothers Geophysical Logging has determined that the two variables in Equation 1 are a=1 and m=2. The Greek letter  represents porosity and it is calculated from the Bore Hole Compensated Sonic Log (BHC). The calculation uses the Raymer Hunt equation (equation 2) to compute sonic porosity from sonic travel time (t) the parameter measured by the BHC. In summary F is calculated by using the BHC.

Archie’s second equation states that F is also related to the resistivity of the saturating solution filling the pore space, or the resistivity of the water (Rw).

In this equation, Ro is the resistivity of the ROCK when it is 100% saturated with water. It is different that the resistivity of the water. The Deep Induction Log accurately reads the Ro value when invasion and borehole size are not too severe. If needed, the Deep Induction can be corrected for invasion and borehole effects through the use of “Tornado Charts”. For our case in South Florida aquifers we set Ro equal to Rild (resistivity of Deep Induction).

It can be seen then if we combine the 2 Archie equations we can get an equation that relates Rw to Rild and F.

Part of the work Ron Reese did was to derive a relationship between water conductivity (the inverse of water resistivity) and chloride concentration for Floridan Aquifer waters. This equation is:

Where Cw = 10,000/Rw

A second equation developed by Ron Reese related chloride concentration to total dissolved solids or TDS. This equation is:

These equations have been programmed into the Warrior Well Logging system, Geophysical Logging Division of Youngquist Brothers, Inc; We can calculate this important parameter in real time on location.