Maximum Height of Oil Column in Cap Rock in Excel Formulas

The maximum height of oil column in cap rock is the maximum vertical distance that oil can accumulate under a layer of rock that prevents it from escaping. This layer of rock is called a cap rock or a seal, and it acts as a barrier for the oil that is trapped in the porous rock below.

The oil column is formed by the difference in density between oil and water. Oil is lighter than water, so it tends to rise up in the pores of the rock until it reaches the cap rock. The cap rock has very small pores that create a high resistance for the oil to pass through. This resistance is called the capillary pressure, and it depends on the size and shape of the pores, the surface tension between oil and water, and the wetting properties of the rock.

The capillary pressure is the minimum pressure that the oil needs to overcome to break through the cap rock. If the oil pressure is lower than the capillary pressure, the oil will stay below the cap rock. If the oil pressure is higher than the capillary pressure, the oil will leak through the cap rock. The oil pressure is proportional to the height of the oil column, so there is a limit to how high the oil column can be before it reaches the capillary pressure. This limit is the maximum height of oil column in cap rock.

Different types of cap rocks and oil have different capillary pressures and maximum heights. For example, clay-rich cap rocks have higher capillary pressures and lower maximum heights than carbonate cap rocks. Similarly, light oil has lower surface tension and higher maximum height than heavy oil. The maximum height of oil column in cap rock can be estimated by measuring the capillary pressure of the cap rock and the density of the oil and water.

Basic Theory

The maximum height of the oil column in cap rock can be determined using the following simplified formula:

$H = \frac{P}{\rho \cdot g}$

Where:

$H$ is the maximum height of the oil column,
$P$ is the pressure difference across the oil column,
$\rho$ is the density of the oil,
$g$ is the acceleration due to gravity.

Procedures

Gather Data: Collect necessary data, including reservoir pressure, cap rock thickness, and oil density.
Calculate Pressure Difference ( $P$ ): Determine the pressure difference across the oil column by subtracting the cap rock pressure from the reservoir pressure.
Apply Formula: Utilize the formula $H = \frac{P}{\rho \cdot g}$ to find the maximum height of the oil column.
Excel Calculation: Implement the calculations in Microsoft Excel for better visualization and analysis.

North Sea Reservoir

Consider a reservoir in the North Sea with the following data:

Reservoir Pressure ( $P_{\text{reservoir}}$ ): 3000 psi
Cap Rock Pressure ( $P_{\text{cap rock}}$ ): 1500 psi
Cap Rock Thickness ( $\text{Cap Rock Thickness}$ ): 1000 ft
Oil Density ( $\rho$ ): 55 lb/ft³
Acceleration due to Gravity ( $g$ ): 32.2 ft/s²

Excel Calculation

Let’s create an Excel table to perform the calculations:

Parameters	Values
Reservoir Pressure	3000 psi
Cap Rock Pressure	1500 psi
Cap Rock Thickness	1000 ft
Oil Density	55 lb/ft³
Gravity Acceleration	32.2 ft/s²

Now, apply the formula in Excel:

$H = \frac{(3000 - 1500)}{(55 \cdot 32.2)}$

$H = \frac{1500}{1761} \approx 0.85 \text{ ft}$

Therefore, the maximum height of the oil column in the cap rock is approximately 0.85 ft.

MATLAB Comparison

Let’s write a MATLAB script to solve the same problem and compare the results:


% MATLAB script for calculating maximum height of oil column in cap rock

% Given data
P_reservoir = 3000; % psi
P_cap_rock = 1500; % psi
Cap_Rock_Thickness = 1000; % ft
Oil_Density = 55; % lb/ft³
Gravity_Acceleration = 32.2; % ft/s²

% Calculate pressure difference
P = P_reservoir - P_cap_rock;

% Calculate maximum height using the formula
H = P / (Oil_Density * Gravity_Acceleration);

disp(['Maximum height of the oil column in cap rock (MATLAB): ', num2str(H), ' ft']);

Running this script in MATLAB will yield the same result as obtained using Excel.