JNTU B.Tech IV RESERVOIR STIMULATION Previous Question Paper (December - 2020 - R15)

A pretreatment pressure drawdown test is a transient pressure analysis conducted on an oil well to evaluate its initial reservoir characteristics and completion efficiency before any stimulation treatment. The test involves placing the well on production at a constant flow rate after a period of shut-in, while recording the bottom-hole flowing pressure as a function of time. This test helps determine the reservoir permeability, initial reservoir pressure, and the skin factor, which quantifies the damage or improvement near the wellbore.

To derive the equation for the skin factor, we start with the radial flow equation for a slightly compressible fluid in a homogeneous reservoir. The pressure at any time t is given by the line-source solution:

For a well with skin, the pressure drop includes an additional term due to the flow restriction at the wellbore. At the wellbore radius (r = r_w), the flowing pressure P_wf is expressed as:

Where s is the skin factor. Rearranging this equation to solve for s, we use the semi-logarithmic straight-line portion of the drawdown plot where pressure is plotted against log(t):

In this derivation, m is the slope of the straight line on the semi-log plot, defined as:

By determining the slope m and the pressure at one hour (P_1hr) from the field data, the skin factor s can be calculated. A positive value of s indicates wellbore damage, a negative value indicates stimulation or natural fractures, and s = 0 indicates an undamaged well.

To determine the formation permeability (k) and skin factor (S), we perform a semi-logarithmic analysis of the pressure drawdown data. The pressure is plotted against the logarithm of time (log t). The slope (m) of the straight-line portion of the semi-log plot is calculated as:

Using the data points at t = 4 hr (P = 16716 kPa) and t = 20 hr (P = 16128 kPa):

Assuming standard reservoir parameters (e.g., flow rate q = 1000 m³/day, oil viscosity μ = 1 cP, formation thickness h = 10 m, and total compressibility c_t = 10⁻⁵ kPa⁻¹), the permeability is calculated using:

Substituting the values, k is determined in mD. The skin factor (S) is then calculated from the pressure at 1 hour (P_1hr) using the equation:

By identifying the linear region on the semi-log plot, the slope m represents the reservoir flow characteristics, allowing for the calculation of permeability, while the intercept at t = 1 hour accounts for the pressure drop caused by skin effects near the wellbore.