Four curves designated as I, II, III, and IV are shown in the figure. \(q_f\) is the bottomhole oil flow rate, \(q_s\) is the surface oil flow rate, and \(B_o\) is the oil formation volume factor.
Which ONE of the following curves depicts the minimum wellbore storage effect?
\begin{center}
\includegraphics[width=0.7\textwidth]{04.jpeg}
\end{center}
Show Hint
- I
- II
- III
- IV
The Correct Option is D
Solution and Explanation
Step 1: Interpret the plotted quantity.
The ordinate is \( \dfrac{q_f}{q_s\,B_o} \).
If there were \emph{no} wellbore storage, then whatever rate leaves the reservoir at the sandface (\(q_f\)) appears at surface as \(q_s B_o\) (after volumetric conversion). Hence, \[ \dfrac{q_f}{q_s\,B_o} \xrightarrow[\text{no storage}]{} 1 \quad \text{(immediately).} \] Step 2: Effect of wellbore storage.
With wellbore storage, early–time surface flow is partly (or wholly) used to fill/empty the wellbore, so \(q_s B_o\) initially \emph{lags} behind \(q_f\). Therefore the ratio \(\dfrac{q_f}{q_s B_o}\) starts below 1 and gradually approaches 1 as the storage effect dies out.
\(\Rightarrow\) The weaker (smaller) the storage, the faster the curve rises to 1 and the less pronounced the early–time lag. Step 3: Select the curve with minimum storage effect.
Among I, II, III, IV, the curve that climbs to \(1.0\) \emph{most rapidly} (smallest lag) corresponds to the minimum wellbore storage. From the figure, curve IV rises the fastest and hugs \(1.0\) earliest; curve I is the slowest (largest storage). Final Answer:
\[ \boxed{\text{IV}} \]
Top Questions on Reservoir and channel routing
For a hydrocarbon reservoir, the following parameters are used in the general material balance equation (MBE):
\[ \begin{aligned} N & = \text{Initial (original) oil in place, stb} \\ G & = \text{Initial volume of gas cap, scf} \\ m & = \text{Ratio of initial volume of gas cap to volume of oil initial in place, rb/rb} \\ S_{wi} & = \text{Initial water saturation} \\ S_{oi} & = \text{Initial oil saturation} \\ B_{oi} & = \text{Initial oil formation volume factor, rb/stb} \\ B_{gi} & = \text{Initial gas formation volume factor, rb/scf} \end{aligned} \]
The total pore volume (in rb) of the reservoir is:
- GATE PE - 2025
- Reservoir Engineering
- Reservoir and channel routing
- Which of the following logging tool(s) underestimate(s) porosity in a gas-bearing formation?
- GATE PE - 2025
- Reservoir Engineering
- Reservoir and channel routing
The drainage oil-water capillary pressure data for a core retrieved from a homogeneous isotropic reservoir is listed in the table. The reservoir top is at 4000 ft from the surface and the water-oil contact (WOC) depth is at 4100 ft. \[ \begin{array}{|c|c|} \hline \textbf{Water saturation (\%)} & \textbf{Capillary pressure (psi)} \\ \hline 100.0 & 0.0 \\ \hline 100.0 & 5.5 \\ \hline 99.0 & 5.6 \\ \hline 89.2 & 6.4 \\ \hline 81.8 & 6.9 \\ \hline 44.2 & 11.2 \\ \hline 29.7 & 17.1 \\ \hline 25.1 & 36.0 \\ \hline \end{array} \] Assume the densities of water and oil at reservoir conditions are 1.04 g/cc and 0.84 g/cc, respectively. The acceleration due to gravity is 980 cm/s2. The interfacial tension between oil and water is 35 dynes/cm and the contact angle is 0 degree. The depth of free-water level (FWL) is at ________ ft (rounded off to one decimal place).
- GATE PE - 2025
- Reservoir Engineering
- Reservoir and channel routing
The formation resistivity factor \((F)\) is related to the formation porosity \((\phi)\) in a water-bearing carbonate formation by the following correlation: \[ F = 0.9 \phi^{-2} \] where \(\phi\) is in fraction. The resistivity of the invaded zone of the formation obtained by the Microspherically Focused Log (MSFL) is \(4.5 \, \Omega m\), and the resistivity of the mud-filtrate is \(0.05 \, \Omega m\). The formation porosity is ________ % (rounded off to one decimal place).
- GATE PE - 2025
- Reservoir Engineering
- Reservoir and channel routing
- Which of the following option(s) is/are CORRECT for well testing analysis of a reservoir?
- GATE PE - 2025
- Reservoir Engineering
- Reservoir and channel routing
Questions Asked in GATE PE exam
Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
Statement:
P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could.
Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts, and inimical local lords—all of which would reduce their chances of getting gold to almost zero.
R. All of them thought that easily they could lay their hands on gold and become wealthy overnight.
S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.
- The eigenvalues of the matrix \[ A = \begin{bmatrix} 3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3 \end{bmatrix} \] are \(\lambda_1, \lambda_2, \lambda_3\). The value of \(\lambda_1 \lambda_2 \lambda_3 (\lambda_1 + \lambda_2 + \lambda_3)\) is:
- GATE PE - 2025
- Eigenvalues
A stationary tank is cylindrical in shape with two hemispherical ends and is horizontal, as shown in the figure. \(R\) is the radius of the cylinder as well as of the hemispherical ends. The tank is half filled with an oil of density \(\rho\) and the rest of the space in the tank is occupied by air. The air pressure, inside the tank as well as outside it, is atmospheric. The acceleration due to gravity (\(g\)) acts vertically downward. The net horizontal force applied by the oil on the right hemispherical end (shown by the bold outline in the figure) is:
- GATE PE - 2025
- Integration
- If a function \(f(x)\) is continuous in the closed interval \([a, b]\) and the first derivative \(f'(x)\) exists in the open interval \((a, b)\), then according to the Lagrange's Mean Value Theorem: \[ \frac{f(b) - f(a)}{b - a} = f'(c) \] If \(a = 0, b = 1.5\), and \(f(x) = x(x - 1)(x - 2)\), then the value(s) of \(c\) in \([a, b]\) is/are:
- GATE PE - 2025
- Mean value theorems
The effect of pressure on various properties of black oil is shown in the figure. The bubble point pressure is \(P_b\).
Which of the following option(s) is/are CORRECT?
- GATE PE - 2025
- Multiphase Flow