Question

A matrix acidizing job is planned on a sandstone pay zone at a depth of 7000 ft without formation breakdown, by keeping a safety margin of 250 psi with the help of a coil tubing unit. Consider the fracture gradient of 0.7 psi/ft, average specific gravity of the injection fluid as 1.065, and frictional pressure drop of 200 psi.
The maximum surface injection pressure (in psi) is __________. (Rounded off to one decimal place)
[Given: Hydrostatic gradient (psi/ft) = \( 0.433 \times \text{Specific Gravity} \)]

Hint:

Find the maximum allowable bottomhole pressure from the fracture pressure minus the safety margin, then work back to the surface using the hydrostatic and friction terms.

Answer 1

Correct Answer: 1622

Step 1: Compute the fracture pressure at the target depth:
The fracture gradient is given as 0.7 psi/ft and the depth is 7000 ft, so the fracture pressure is $P_{frac} = 0.7 \times 7000 = 4900$ psi.
Step 2: Find the maximum allowable bottomhole pressure:
To avoid breaking down the formation, a safety margin of 250 psi must be kept below the fracture pressure. So the maximum bottomhole pressure allowed during the job is $P_{BH,max} = P_{frac} - \text{margin} = 4900 - 250 = 4650$ psi.
Step 3: Compute the hydrostatic pressure of the injection fluid column:
The hydrostatic gradient is given as $0.433 \times SG$ psi/ft, where SG is the specific gravity of the injection fluid, 1.065. So the gradient is $0.433 \times 1.065 = 0.461145$ psi/ft. Over the 7000 ft depth, the hydrostatic pressure is $P_{hyd} = 0.461145 \times 7000 = 3228.015$ psi.
Step 4: Relate surface pressure to bottomhole pressure:
While pumping fluid down the tubing, the bottomhole pressure equals the surface injection pressure plus the hydrostatic pressure of the fluid column, minus the frictional pressure drop lost while the fluid is moving through the tubing. So $P_{BH} = P_{surf} + P_{hyd} - P_{friction}$, which rearranges to $P_{surf} = P_{BH} - P_{hyd} + P_{friction}$.
Step 5: Substitute the numbers:
Using the maximum allowable bottomhole pressure as the limiting case, $P_{surf,max} = 4650 - 3228.015 + 200 = 1621.985$ psi.
Step 6: Round to one decimal place:
Rounding 1621.985 to one decimal place gives 1622.0 psi.
Final Answer:
\[ \boxed{1622.0 \text{ psi}} \]