Step 1: Understanding proppant carrying capacity:
During hydraulic fracturing, proppant such as sand or ceramic beads is pumped along with a fracturing fluid to hold the created fractures open once pumping stops. The ability of a fluid to carry and suspend this solid proppant instead of letting it settle out is called its proppant carrying capacity, and it depends strongly on the viscosity of the fluid. According to Stokes law, the settling velocity of a particle in a fluid is given by \(v = \dfrac{2r^2(
ho_p -
ho_f)g}{9\mu}\), where \(\mu\) is the fluid viscosity. A higher viscosity fluid gives a lower settling velocity, which means the proppant stays suspended for longer and is carried deeper into the fracture.
Step 2: Checking option A, Pentane:
Pentane is a light hydrocarbon liquid with very low viscosity, close to that of water or lower. Its low viscosity means proppant particles settle quickly, so pentane has poor proppant carrying capacity.
Step 3: Checking option B, Cross-linked gel:
Cross-linked gel fracturing fluids are made by adding a cross-linking agent, commonly borate or a metal ion such as zirconium or titanium, to a base polymer gel like guar. This cross-linking dramatically increases the fluid viscosity compared to plain water or slickwater, and it is specifically designed and used in the field to transport high concentrations of proppant deep into the fracture without excessive settling. This gives it the highest proppant carrying capacity among the given options.
Step 4: Checking option C, Slickwater:
Slickwater is water treated with a small amount of friction reducing polymer, giving it a viscosity only slightly higher than plain water. It is popular because it is inexpensive and creates complex fracture networks, but because of its low viscosity it must rely on high pump rates and lower proppant concentrations, so its proppant carrying capacity is much lower than cross linked gel.
Step 5: Checking option D, Untreated formation brine:
Untreated formation brine is essentially salt water with no viscosifying additives, so its viscosity is close to that of plain water. It has no special proppant suspension ability and shows poor proppant carrying capacity, similar to or worse than slickwater.
Step 6: Comparing all four fluids:
Ranking the four fluids by viscosity and hence by proppant carrying capacity, cross linked gel has by far the highest viscosity, followed by slickwater which has a small viscosity boost from friction reducers, while pentane and untreated brine remain low viscosity fluids with poor carrying capacity.
Final Answer:
\[ oxed{ ext{(B) Cross-linked gel}} \]