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CAPILLARY PRESSURE -- Pc
Accumulation of hydrocarbon in a reservoir is a drainage process and production by aquifer drive or waterflood is an imbibition process. The capillary pressure curve is different for these two processes.
phase increases. Mobility of nonwetting fluid phase increases
as nonwetting phase saturation increases.
phase increases. Mobility of wetting phase increases
as wetting phase saturation increases
There are four key parameters that are related to a capillary curve :
Si = irreducible wetting phase saturation
Sm = 1 - residual non-wetting phase saturation
Pd = displacement pressure, the pressure required to force non-wetting fluid into largest pores
LAMDA = pore size distribution index; determines shape of capillary pressure curve
Si is the initial, or irreducible, water saturation in a hydrocarbon-bearing, water-wet, reservoir at initial pressure, prior to the start of production. It is termed SWir elsewhere in this Handbook.
(1 - Sm) is the residual oil saturation in a
fully depleted water-wet reservoir, called Sor elsewhere in this
Petrophysicists use cap pressure minimum saturation (SWir) and residual oil saturation (Sor) to help calibrate log derived water saturation in oil and gas reservoirs above the transition zone, and to help detect depleted reservoirs. It will not help calibrate SW in partially depleted zones.
LAMDA increases with decreasing permeability, poor grain sorting, smaller grain size, and usually with lower porosity. These effects shift the cap pressure curve upward and to the right, resulting in higher SWir values.
A capillary pressure curve on Cartesian coordinates is difficult to fit with simple equations. By transforming the SW axis to Sw* and plotting Pc vs Sw* on log - log graph paper, the curves become straight lines.
1: Sw* = (Sw - SWir) / (1 - SWir - Sor)
2: Pc = Pd * (Sw*) ^ (1 / LAMDA)
The slope of the line is (1 / LAMBDA) and the intercept at 100% Sw* is Pd. SWir is obtained from the Cartesian plot. Steeper slope equals higher LAMDA equals poorer quality rock. The typical range of LAMDA is 0.5 for good quality sands to 4 or 8 for poor quality sands and carbonates. Type curve matching of Sw* can be used to assess cap pressure curves and reservoir quality.
a glass capillary tube is placed in a large open vessel containing
water, the combination of surface tension and wettability of tube to
water will cause water to rise in the tube above the water level in
the container outside the tube. The water will rise in the tube
until the total force acting to pull the liquid upward is balanced
by the weight of the column of liquid being supported in the tube.
Assuming the radius of the capillary tube is R, the total upward
force Fup, which holds the liquid up, is equal to the force per unit
length of surface times the total length of surface:
Assume density of air is negligible and set Fup = Fdown, solve
for surface tension:
Rearranging equation 5:
To convert Pc in dynes/cm2 to psi, multiply by 1.45 * 10^-5.
values for air-brine conversion to oil-water are:
Solving equation 13 for H, and using reservoir (oil-water) Pc
<== Example of conversion of lab air-brine capillary
pressure data to reservoir conditions, then into saturation-height
H; results plotted in graph above..
All of the above assumes the lab data is an air-brine
measurement. For mercury injection capillary, pressure (MICP) measurements,
the density of the non-wetting phase (mercury) is 13.5 g/cc, so ΔDENS
is much larger than the air-water case. As a result, Pc values from
an MICP measurement are about 13.5 times higher than an air brine
measurement (for the same SW value in the same core plug). To
compare an air-brine cap pressure curve to an MICP curve, it is
merely necessary to change the Pc scale on one of the graphs by the
appropriate factor, or to convert both Pc scales to a
Porous diaphragm method
• Mercury injection method
• Centrifuge method
Detailed operation of the laboratory equipment is beyond the scope of this Handbook. The illustrations are not fully self-explanatory, but the general principles are relatively visible.
POROUS DIAPHRAGM METHOD
MERCURY INJECTION METHOD
AVERAGING Capillary pressure
The Leverett J-function was originally an attempt to convert all capillary pressure data to a universal curve. •A universal capillary pressure curve does not exist because the rock properties affecting capillary pressures in reservoir have extreme variation with lithology (rock type).• But, Leverett’s J-function has proven valuable for correlating capillary pressure data within a lithologic rock type.
Leverett J-Function is described by
By substitution and
•J-function is useful for averaging capillary pressure data from a given rock type from a given reservoir and
•can sometimes be extended to different reservoirs having the same lithology. Use extreme caution in assuming this can be done. J-function is usually not an accurate correlation for different lithologies. If J-functions are not successful in reducing the scatter in a given set of data, then this suggests that we are dealing with variation in rock type.
In higher permeability rock, the cap pressure curve quickly reaches an asymptote and the minimum saturation usually represents the actual water saturation in an undepleted hydrocarbon reservoir above the transition zone. In tight rock, the asymptote is seldom reached, so we pick saturation values from the cap pressure curves at two heights (or equivalent) Pc values) to represent two extremes of reservoir condition.
Only sample 1 in the above table behaves close to asymptotically, as in curve A in the schematic illustration at the right. All other samples behave like curves B and C (or worse). The real cap pressure curves for samples 1 and 2 are shown below.
The summary table shows wetting phase saturation selected by observation of the cap pressure graphs at two different heights above free water, namely 100 meters and 425 meters in this example. In this case, the 100 meter data gives water saturations that we commonly see in petrophysical analysis of well logs in hydrocarbon bearing Bakken reservoirs in Saskatchewan. This is a pragmatic way to indicate the water saturation to be expected when a Bakken reservoir is at or near irreducible water saturation. The data for the 450 meter case is considerably lower and probably does not represent reservoir conditions in this region of the Williston Basin.
Two other columns in the table are calculated from the primary measurements.
The first is the product of porosity times saturation, PHI*SW, often called Buckle’s Number. It is considered to be a measure of pore geometry or grain size. Higher values are finer grained rocks. These values vary considerably in the Bakken, between low and medium values, indicating the laminated nature of the silt / sand reservoir. The values in the Torquay are uniformly high, indicating that the reservoir is poor quality in all samples.
The second is the square root of permeability divided by porosity, sqrt(Kmax/PHIe), which is another measure of reservoir quality, directly proportional to pore throat radius and Pc. High numbers represent good connectivity and low values show poor connectivity. Again, the Bakken shows the variations due to laminations, and the Torquay shows low values and unattractive reservoir quality.
Average pore throat radius and detailed pore throat distribution data are now routinely available in the capillary pressure spreadsheet provided by the core analysis laboratory. Examples are shown below.
By comparing cap pressure and pore throat distribution graphs from each sample with the quality indicator values in the summary table, it becomes more evident as to which parameters in a petrophysical analysis might be the best indicator of reservoir quality. Since both Buckle’s Number and the Kmax/PHIe parameter can be determined from logs, it has been relatively common to assess reservoir quality from these parameters as a proxy for capillary pressure and pore throat measurements.
However, in thinly laminated reservoirs like the Bakken, this is not always possible since the logging tools average 1 meter of rock. This means we cannot see the internal variations of rock quality evident in the core data.