Formation Temperature Calculation Using Gradient Method in Excel

Formation temperature is the temperature of the rock and the fluid inside it at a certain depth. It is important to know the formation temperature for various applications, such as estimating the properties of reservoir fluids, predicting the occurrence of gas hydrates, and evaluating the geothermal potential of an area.

One way to estimate the formation temperature is to use a temperature gradient, which is the rate of change of temperature with depth. The temperature gradient can vary depending on the location and the geology of the area, but a typical value is about 25°C per kilometer. This means that for every kilometer deeper you go, the temperature increases by 25°C.

Using this temperature gradient, you can calculate the formation temperature at any depth by adding the surface temperature to the product of the temperature gradient and the depth. For example, if the surface temperature is 15°C and the depth is 3 km, the formation temperature is:

15°C + (25°C/km) x 3 km = 90°C

This is a simple and approximate method that does not require any formulas, but it has some limitations and assumptions. For instance, it assumes that the temperature gradient is constant and uniform throughout the area, which may not be true in reality. It also ignores the effects of drilling, circulation, and shut-in on the temperature measurements. For more accurate and detailed methods, you may need to use some formulas and data from bottom-hole temperature logs, as explained in some of the web search results.

Basic Theory:

The formation temperature (Tf) is determined using the temperature gradient (G) and the depth of the formation (D) with the following formula:

$Tf = T_{\text{surface}} + (G \times D)$

Where:

$T_{\text{surface}}$ is the surface temperature,
$G$ is the temperature gradient,
$D$ is the depth of the formation.

Procedures in Excel:

Input Parameters:
- Enter the surface temperature in cell A1.
- Specify the temperature gradient in cell A2.
- Define the depth of the formation in cell A3.
Excel Formula:
- In cell A4, input the formula: =A1 + (A2 * A3).
- This formula calculates the formation temperature based on the gradient method.
Scenario:
- Assume $T_{\text{surface}} = 25 \, ^\circ \text{C}$ , $G = 0.02 \, ^\circ \text{C/m}$ , and $D = 2000 \, \text{m}$ for our scenario.
Excel Calculation:
- Input the scenario values into the respective cells.
- Excel will automatically calculate the formation temperature in cell A4.

Excel Table:

Surface Temperature	Temperature Gradient	Depth of Formation	Formation Temperature
25 °C	0.02 °C/m	2000 m	=A1 + (A2 * A3)

Result:

In our scenario, the calculated formation temperature using the gradient method in Excel is obtained by evaluating the formula in cell A4, resulting in $T_f = 25 + (0.02 \times 2000) = 65 \, ^\circ \text{C}$ .

MATLAB Comparison:

For MATLAB, the same calculation can be performed using the following code snippet:


% Input parameters
T_surface = 25;   % °C
G = 0.02;         % °C/m
D = 2000;         % m

% Formation temperature calculation
Tf = T_surface + (G * D);

% Display the result
disp(['Formation Temperature (MATLAB): ' num2str(Tf) ' °C']);