GATE Petroleum Engineering Oil and Gas Well Testing Syllabus

During pure wellbore storage, what is the relationship between pressure change and time?

$$\Delta p = \frac{q B}{24\,C}\,\Delta t$$ pressure change is linear in time, which produces the unit-slope line on a log-log diagnostic plot.

How can the wellbore storage coefficient $C$ be obtained from the early unit-slope data?

From the unit-slope line, $$C = \frac{q B}{24}\,\frac{\Delta t}{\Delta p}$$ using any point $(\Delta t,\Delta p)$ on that line ($q$ in STB/D, $B$ in RB/STB, $\Delta t$ in hours, $\Delta p$ in psi).

On a pressure-derivative log-log plot, how does wellbore storage appear?

As an early-time hump where both the $\Delta p$ curve and the derivative curve overlie on a unit-slope line; the derivative then peaks and falls to the radial-flow stabilization (horizontal $0.5$ line).

Give an estimate for the time marking the end of wellbore-storage-dominated flow (start of radial flow).

$$t_{wbs} \approx \frac{(200000 + 12000\,s)\,C}{kh/\mu}$$ (hours), or in dimensionless form $t_D = (60 + 3.5\,s)\,C_D$.

Why must early-time data affected by wellbore storage be excluded from semilog (MTR) analysis?

Because storage masks the reservoir response: the sand-face rate is not equal to the surface rate, so the data do not lie on the true semilog straight line and would give wrong $k$ and skin if included.

Define the skin factor $s$.

A dimensionless number quantifying the additional (or reduced) pressure drop near the wellbore relative to the ideal reservoir flow; positive $s$ indicates damage (extra pressure loss) and negative $s$ indicates stimulation/improvement.

Write the equation for the additional pressure drop due to skin, $\Delta p_{skin}$.

$$\Delta p_{skin} = \frac{141.2\,q\mu B}{kh}\,s$$ with $q$ in STB/D, $\mu$ in cp, $B$ in RB/STB, $k$ in md, $h$ in ft.

How is the skin-related pressure drop expressed using the semilog slope $m$?

$$\Delta p_{skin} = 0.87\,m\,s$$ where $m$ is the absolute value of the slope of the semilog straight line (psi/cycle).

State the standard equation used to compute skin $s$ from a drawdown semilog analysis.

$$s = 1.151\left[\frac{p_{1hr}-p_{wf,0}}{m} - \log\!\left(\frac{k}{\phi\mu c_t r_w^{2}}\right) + 3.23\right]$$ where $p_{1hr}$ is read from the extrapolated semilog line at $\Delta t = 1$ hr.

What is the Hawkins formula for skin due to a damaged zone?

$$s = \left(\frac{k}{k_s} - 1\right)\ln\!\frac{r_s}{r_w}$$ where $k_s$ and $r_s$ are the permeability and radius of the altered (skin) zone.

According to Hawkins' formula, what sign of skin results when $k_s < k$ versus $k_s > k$?

When $k_s < k$ (damaged near-wellbore), $s>0$ (positive skin / damage); when $k_s > k$ (stimulated), $s<0$ (negative skin / improvement).

Define the effective (apparent) wellbore radius $r_{wa}$.

The radius of an ideal (zero-skin) well that would give the same pressure drop as the actual well with skin: $$r_{wa} = r_w\,e^{-s}$$

For a highly stimulated well, why can the effective wellbore radius be much larger than $r_w$?

Because a large negative skin makes $r_{wa}=r_w e^{-s}$ grow exponentially; e.g. $s=-5$ gives $r_{wa}\approx 148\,r_w$, modeling a fracture or acidized zone as an enlarged wellbore.

Define flow efficiency (FE) of a well.

The ratio of the actual productivity to the ideal (zero-skin) productivity: $$FE = \frac{\bar p - p_{wf} - \Delta p_{skin}}{\bar p - p_{wf}}$$ where $\bar p$ is average reservoir pressure.

What does a damage ratio (DR) greater than 1 indicate?

DR $= 1/FE$; a value greater than 1 indicates a damaged well (positive skin) producing less than its ideal potential, while DR $<1$ indicates a stimulated well.

List the main physical components that can contribute to total (apparent) skin.

Formation damage, partial penetration/limited entry, perforation effects, non-Darcy (turbulent) flow, deviation/inclination of the well, phase change/relative-permeability effects, and stimulation (fractures, acidizing) which contribute negative skin.

Distinguish mechanical (true) skin from pseudo-skin.

Mechanical skin is the rate-independent near-wellbore damage/stimulation (e.g. Hawkins damaged zone). Pseudo-skin is an apparent skin from geometry or flow effects (partial penetration, deviation, non-Darcy flow) that is not true formation alteration.

How is rate-dependent (non-Darcy) skin represented in the total skin?

$$s_{total} = s + D q$$ where $s$ is the constant mechanical skin and $D$ is the non-Darcy flow coefficient; $Dq$ grows with rate, common in high-rate gas wells.

How is the non-Darcy coefficient $D$ typically determined in the field?

By running multiple tests (or a multi-rate/multi-point test) at different rates and plotting apparent skin $s_{total}$ versus rate $q$; the slope gives $D$ and the intercept gives the true mechanical skin $s$.

What is partial penetration (limited entry) skin?

A positive pseudo-skin arising when only part of the producing interval is open to flow, forcing flow to converge vertically toward the open section, which adds extra pressure drop near the wellbore.

How does well deviation (inclination) affect skin?

An inclined or horizontal well increases the effective contact with the formation, contributing a negative pseudo-skin and improving productivity relative to a fully-penetrating vertical well.

Compare positive skin and negative skin in terms of well productivity.

Positive skin ($s>0$) means near-wellbore damage and extra pressure loss, lowering productivity; negative skin ($s<0$) means stimulation and reduced pressure loss, raising productivity. Zero skin is the ideal undamaged case.

In a pressure buildup test, how is skin computed from the Horner analysis?

$$s = 1.151\left[\frac{p_{1hr}-p_{wf}(\Delta t=0)}{m} - \log\!\left(\frac{k}{\phi\mu c_t r_w^{2}}\right) + 3.23\right]$$ with $m$ the slope of the Horner straight line and $p_{1hr}$ read from it at $\Delta t = 1$ hr.

Why does wellbore storage make skin determination unreliable if early data are misused?

Storage delays the appearance of the true semilog straight line; if the line is fit too early, the slope $m$ and $p_{1hr}$ are wrong, propagating into an erroneous skin value. The correct line must begin after storage ends.

What diagnostic feature on a log-log plot marks the transition from wellbore storage to infinite-acting radial flow?

The pressure-derivative curve leaves the early unit-slope hump and flattens to a horizontal stabilization at the value $0.5$ (dimensionless), indicating radial flow has begun.

How does increasing wellbore storage coefficient $C$ affect the duration of the storage period?

A larger $C$ (bigger wellbore volume or higher fluid compressibility) prolongs the storage-dominated period, delaying the start of interpretable radial flow and requiring a longer test.

Why does a positive skin lengthen the wellbore-storage-affected period?

Because the time to reach radial flow, $t_{wbs}\propto(200000+12000\,s)C$, increases with $s$; the extra near-wellbore pressure drop delays the establishment of the true semilog response.

What is the effect of skin on the productivity index (PI) of a well?

$$J = \frac{q}{\bar p - p_{wf}} = \frac{kh}{141.2\,\mu B\left[\ln(r_e/r_w) - 0.75 + s\right]}$$ positive $s$ raises the denominator and lowers $J$; negative $s$ raises $J$.

State the inflow (pseudosteady-state) equation showing where skin enters the flow rate expression.

$$q = \frac{kh(\bar p - p_{wf})}{141.2\,\mu B\left[\ln\frac{r_e}{r_w} - \frac{3}{4} + s\right]}$$ The skin $s$ adds to the geometric term, increasing total pressure drop for $s>0$.

Why is it important to separate wellbore-storage and skin effects when interpreting a well test?

Both distort the near-wellbore early-time response: storage controls the rate the formation sees, and skin adds a constant pressure offset. Misidentifying either leads to wrong permeability, wrong skin, and wrong productivity forecasts, so type-curve/derivative matching is used to deconvolve them.