Erth 571
Hydrodynamic Effects on Petroleum-Water Interface
Name __________________________
Assigned:
10/25/12
Due:
11/6/12
In M. King Hubbert’s classic paper on the hydrodynamic theory of petroleum
entrapment, he showed that the position of the oil-water (or gas water) contact could be
determined by plotting oil heads (Hubbert, 1953).
ho =
ρw
ρ − ρw
h+ o
z
ρo
ρo
(1)
where
€
ho - head in the oil phase
h – water head (h = P/ρwg + z)
ρw - water density (998 kg/m3)
ρo- oil density
z – elevation of top of carrier bed
The slope of the oil-water contact would be parallel to a line of constant ho. Hubbert
further showed that the slope of the oil water contact is given by:
∂z o
ρ w ∂h
=
∂x ρ w − ρ o ∂x
(2)
where zo is the elevation of the oil water contact. Thus the lateral hydraulic gradient is
related to the tilt of the oil-water contact through the amplification factor. The density
€
ratio in equation
(2) (ρw/ρw-ρo) is frequently referred to as the amplification factor.
If oil is trapped in an anticlinal structure and the slope dzo/dx exceeds the slope of the
anticline, then oil will be entirely flushed from the system. If the contour slope is less
than the anticline slope, then the contact will be tilted. In this lab, we will experimentally
test Hubbert’s theory using a reproduction of his Hele-Shaw model off an anticlinal
petroleum reservoir (see enclosed figure). We will glycerin density (~ 1.22 km/m3) for
brine density. We will use water as the oil density (non-wetting fluid).
Experimental Procedure.
Figure 1. Schematic of Hele-Shaw Model.
1. Fill Hele-Shaw model with dyed fresh water by adding the water to the upper
reservoir shown in figure 1. Make sure all the air is removed (tilt the model on
end so air bleeds out). If a little air is in the system, you can think of it as a gas
column.
2. Determine the slope of the two down-gradient limbs of the anticline in the HeleShaw model.
3. Now replace the fluid in the upper reservoir with glycerin (density ~ 1.2 gm/cm3)
or saline water (density ~ 1.04 gm/cm3). Allow some of the dyed freshwater to
remain in the model.
4. Turn the nozzle to the off position in the upper reservoir and verify that the
glycerin -water contact is horizontal.
5. Open the nozzle and allow flow of glycerin (or salt water). Adjust the elevation of
the outflow reservoir to control flow and the tilting of the air-water contact.
6. Adjusting the elevation of the outflow tube (h2), try to find 2-3 different flow rates
(and head gradients). Measure the different tilts in the glycerin-water interface.
Measure the slope. Use a magic marker.
7. Compute the tilt of the oil-glycerin and saltwater-freshwater contact and the head
gradient. Use the slope of this line to determine where the oil-water contact
should be.
Answer the Following Questions
1. How well does the computed slope [ρf/( ρg - ρf) x Δh/L] and the observed glycerin
-water contact compare? How well does the computed slope [ρf/( ρs - ρf) x Δh/L]
and the observed saltwater-water contact compare?
2. Did you observe some of the differences between the glycerin-water and saltwaterfreshwater experiments?
3. What would the oil/water contact look like for a natural hydraulic gradient (e.g.
0.01; ρo = 850 kg/m3)?
Work Sheet:
Density calculations:
Beaker Volume ________ ml (cm3)
Beaker Weight _______ gm
Beaker Weight with Salt water _____ gm;
Weight saltwater _______ gm
Beaker Weight with Fresh water _____ gm; Weight fresh water _______ gm
Beaker Weight with Glycerin _____ gm;
Weight glycerin _______ gm
Density Freshwater _______ gm/ cm3
Density Saltwater _______ gm/ cm3
Density Glycerin _______ gm/ cm3
Distance along Hele Shaw Model (L) __________ cm
Run #1 Glycerin
Head gradient
h1 _______ cm h2 ________ cm
Δh ________ cm Δh/L _________
ρf/( ρg - ρf) x Δh/L __________
Tilt of glycerin-water contact
z1 ______ cm z2 _________
Δz ________ cm
distance (Δx) ___________ cm
Δz/Δx _________
Run #2 Glycerin
Head gradient
h1 _______ cm h2 ________ cm
Δh ________ cm Δh/L _________
ρf/( ρg - ρf) x Δh/L __________
Tilt of glycerin-water contact
z1 ______ cm z2 _________
Δz ________ cm
distance (Δx) ___________ cm
Δz/Δx _________
Run #3 Glycerin
Head gradient
h1 _______ cm h2 ________ cm
Δh ________ cm Δh/L _________
ρf/( ρg - ρf) x Δh/L __________
Tilt of glycerin-water contact
z1 ______ cm z2 _________
Δz ________ cm
distance (Δx) ___________ cm
Δz/Δx _________
Run #4 Saltwater
Head gradient
h1 _______ cm h2 ________ cm
Δh ________ cm Δh/L _________
ρf/( ρs - ρf) x Δh/L __________
Tilt of glycerin-water contact
z1 ______ cm z2 _________
Δz ________ cm
distance (Δx) ___________ cm
Δz/Δx _________
Run #5 Saltwater
Head gradient
h1 _______ cm h2 ________ cm
Δh ________ cm Δh/L _________
ρf/( ρs - ρf) x Δh/L __________
Tilt of glycerin-water contact
z1 ______ cm z2 _________
Δz ________ cm
distance (Δx) ___________ cm
Δz/Δx _________
Run #6 Saltwater
Head gradient
h1 _______ cm h2 ________ cm
Δh ________ cm Δh/L _________
ρf/( ρs - ρf) x Δh/L __________
Tilt of glycerin-water contact
z1 ______ cm z2 _________
Δz ________ cm
distance (Δx) ___________ cm
Δz/Δx _________