GATE Petroleum Engineering Reservoir Engineering Syllabus

Define irreducible (connate) water saturation $S_{wc}$.

$S_{wc}$ is the lowest water saturation that can be achieved in the rock by displacing water with a non-wetting hydrocarbon phase; this water is held by capillary forces in small pores and as films and is effectively immobile during hydrocarbon production.

Define residual oil saturation $S_{or}$.

$S_{or}$ is the oil saturation remaining and trapped (immobile) in the swept region of the reservoir after a displacement process such as waterflooding; it represents oil that cannot be recovered by that displacement due to capillary trapping.

Write the Buckley–Leverett fractional flow equation for water (horizontal, neglecting capillary pressure).

$$f_w = \frac{1}{1 + \dfrac{k_{ro}\,\mu_w}{k_{rw}\,\mu_o}}$$ It gives the fraction of water in the total flowing stream as a function of saturation; lower oil/water mobility ratio sharpens the displacement front.

State the Buckley–Leverett frontal advance equation.

$$x_{S_w} = \frac{q_t\, t}{A\,\phi}\left(\frac{df_w}{dS_w}\right)_{S_w}$$ The position of a given water saturation moves proportionally to the derivative of the fractional flow curve evaluated at that saturation.

Define the mobility of a fluid phase and the mobility ratio $M$ in waterflooding.

Mobility $\lambda_i = \frac{k_{ri}}{\mu_i}$. The mobility ratio is $$M = \frac{\lambda_{displacing}}{\lambda_{displaced}} = \frac{k_{rw}/\mu_w}{k_{ro}/\mu_o}$$ $M \leq 1$ (favorable) gives stable, efficient displacement; $M > 1$ (unfavorable) promotes viscous fingering.

Define capillary pressure $P_c$ in a reservoir rock.

Capillary pressure is the pressure difference across the curved interface between two immiscible fluids: $$P_c = P_{non-wetting} - P_{wetting} = \frac{2\sigma \cos\theta}{r}$$ where $\sigma$ is interfacial tension, $\theta$ the contact angle, and $r$ the pore (capillary) radius.

What is reservoir wettability and what are the two end-member types?

Wettability is the tendency of one fluid to preferentially spread on or adhere to the rock surface in the presence of another fluid. The end members are water-wet (water coats the grains, oil in pore centers) and oil-wet (oil coats grains). Wettability controls relative permeability and residual saturations.

Give the overall recovery efficiency relationship in a waterflood.

$$E_R = E_D \times E_A \times E_V$$ where $E_D$ is microscopic displacement efficiency, $E_A$ areal sweep efficiency, and $E_V$ vertical sweep efficiency. $E_A \times E_V = E_{vol}$ is the volumetric sweep efficiency.

Define displacement (microscopic) efficiency $E_D$.

$$E_D = \frac{S_{oi} - S_{or}}{S_{oi}} = \frac{\text{oil recovered from swept zone}}{\text{oil initially in swept zone}}$$ It measures how effectively the displacing fluid mobilizes oil at the pore scale within the contacted region.

State the radial diffusivity equation governing transient reservoir flow.

$$\frac{1}{r}\frac{\partial}{\partial r}\!\left(r\frac{\partial P}{\partial r}\right) = \frac{\phi \mu c_t}{k}\frac{\partial P}{\partial t}$$ The group $\eta = \frac{k}{\phi \mu c_t}$ is the hydraulic diffusivity, and $c_t$ is total compressibility.

Define the skin factor $s$ and its effect on bottomhole pressure.

Skin $s$ is a dimensionless measure of near-wellbore damage ($s>0$) or stimulation ($s<0$) relative to undamaged formation. The extra pressure drop is $$\Delta P_{skin} = \frac{q\mu}{2\pi k h}\,s$$ Damage increases $P_{wf}$ requirement; stimulation reduces it.

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

$$J = \frac{q}{\bar{P} - P_{wf}}$$ the ratio of production rate to pressure drawdown (reservoir average pressure minus flowing BHP). It quantifies a well's ability to produce, in $\text{STB/d/psi}$.

Write the dimensionless pressure solution (line-source / Ei) for transient radial flow.

$$P(r,t) = P_i + \frac{q\mu}{4\pi k h}\,\text{Ei}\!\left(-\frac{\phi \mu c_t r^2}{4 k t}\right)$$ For long times the exponential integral is approximated by a logarithm, giving the semilog straight line used in well-test analysis.

In semilog pressure drawdown analysis, how is permeability obtained from the slope $m$?

$$k = \frac{162.6\,q\,\mu\,B}{m\,h}$$ where $m$ is the slope (psi/cycle) of the $P_{wf}$ vs $\log t$ straight line in field units. The slope is inversely proportional to $kh$.

What is the Horner plot used for in pressure buildup analysis?

A Horner plot graphs shut-in BHP $P_{ws}$ versus $\log\!\left(\frac{t_p + \Delta t}{\Delta t}\right)$, where $t_p$ is producing time and $\Delta t$ shut-in time. The straight-line slope gives $kh$, and extrapolation to a Horner ratio of 1 gives the initial/average reservoir pressure $P^{*}$.

Define total compressibility $c_t$ of a reservoir.

$$c_t = c_o S_o + c_w S_w + c_g S_g + c_f$$ the saturation-weighted sum of oil, water, and gas compressibilities plus the formation (pore) compressibility. It appears in the diffusivity and material balance equations.

Classify hydrocarbon reservoir fluids into the five main types.

Based on phase behavior: (1) black oil, (2) volatile oil, (3) retrograde gas condensate, (4) wet gas, and (5) dry gas. They are distinguished by initial GOR, API gravity, and position of reservoir T relative to the critical and cricondentherm points on the phase envelope.

What is retrograde condensation in a gas-condensate reservoir?

Retrograde condensation is the anomalous formation of liquid from gas as pressure decreases (isothermally) below the dew point, occurring when reservoir temperature lies between the critical temperature and the cricondentherm. The condensed liquid can drop out around the wellbore and impair productivity.

Distinguish a wet gas from a dry gas reservoir.

In a dry gas reservoir, the fluid remains single-phase gas at all reservoir and surface conditions (no liquid). In a wet gas reservoir, no liquid forms in the reservoir, but the separator/surface conditions fall inside the two-phase envelope so liquids (condensate) are recovered at the surface.

Define net-to-gross ratio (NTG) in reservoir characterization.

NTG is the fraction of the gross reservoir interval that is productive (net pay): $$NTG = \frac{h_{net}}{h_{gross}}$$ It excludes shales and non-reservoir layers and directly scales the volumetric hydrocarbon estimate.

State Archie's equation for water saturation from log analysis.

$$S_w^{\,n} = \frac{a\,R_w}{\phi^{m}\,R_t}$$ where $R_w$ is formation-water resistivity, $R_t$ true formation resistivity, $\phi$ porosity, $a$ tortuosity constant, $m$ cementation exponent, and $n$ saturation exponent.

Define the formation resistivity factor $F$ (Archie).

$$F = \frac{R_o}{R_w} = \frac{a}{\phi^{m}}$$ where $R_o$ is the resistivity of the rock fully saturated with water of resistivity $R_w$. $F$ relates a clean rock's resistivity to its porosity through the cementation exponent $m$.

What is the Leverett $J$-function and why is it used?

$$J(S_w) = \frac{P_c}{\sigma \cos\theta}\sqrt{\frac{k}{\phi}}$$ It is a dimensionless capillary pressure used to correlate and average capillary pressure data from rock samples of differing permeability and porosity into a single representative curve.

How is the height above the free water level related to capillary pressure?

$$h = \frac{P_c}{(\rho_w - \rho_o)\,g}$$ Capillary pressure converts to a saturation-vs-height profile (transition zone) above the free water level; larger density contrast and lower $P_c$ give a shorter transition zone.

State Dake's general material balance (Havlena–Odeh) compact form.

$$F = N(E_o + m E_g + E_{f,w}) + W_e$$ where $F$ is the underground withdrawal, $E_o$ oil/dissolved-gas expansion, $E_g$ gas-cap expansion, $m$ the gas-cap-to-oil-zone ratio, $E_{f,w}$ rock-and-water expansion, and $W_e$ water influx. Straight-line plots of these groups solve for $N$, $m$, and aquifer parameters.

Define the gas-cap-to-oil-zone volume ratio $m$ used in material balance.

$$m = \frac{\text{initial reservoir volume of gas cap}}{\text{initial reservoir volume of oil zone}} = \frac{G\,B_{gi}}{N\,B_{oi}}$$ A larger $m$ means a stronger gas-cap drive contribution to recovery.

What is the apparent contradiction governing why permeability and porosity are not always correlated?

Porosity measures storage capacity (volume fraction of voids), while permeability measures flow capacity, which depends on pore-throat size, connectivity, and geometry. A rock can be highly porous but low permeability (e.g., chalk or shale with tiny, poorly connected pores), so the two are related but not uniquely correlated.

Define sweep (conformance) efficiency components and the meaning of areal sweep efficiency $E_A$.

$E_A$ is the fraction of the reservoir area contacted by the displacing fluid in plan view at breakthrough/abandonment; $E_V$ is the fraction of the vertical cross-section contacted. Both depend on well pattern, mobility ratio, and heterogeneity; favorable (low) $M$ improves both.

State Klinkenberg's gas-slippage correction for measured permeability.

$$k_g = k_\infty\left(1 + \frac{b}{\bar{P}}\right)$$ where $k_g$ is the apparent gas permeability at mean pressure $\bar{P}$, $k_\infty$ the equivalent liquid (absolute) permeability, and $b$ the Klinkenberg slip factor. Gas permeability exceeds liquid permeability at low pressure due to molecular slippage at pore walls.

List the standard surface (standard) conditions commonly used in reservoir engineering field units.

Standard conditions are typically $T_{sc} = 60^\circ\text{F} = 520^\circ\text{R}$ and $P_{sc} = 14.696\ \text{psia}$ ($1\ \text{atm}$). Volumes of gas (scf) and stock-tank oil (STB) are reported at these conditions, which is why formation volume factors are needed to convert to reservoir volumes.