Dimensionless scaling

When R(t) is plotted versus √ according to eq.2.70 , the wettability index is obtained from the slope of the straight line, the highest slope, is set equal to 1. A modified capillary dimensionless time containing the normalization index can then be used for an appropriate scaling of data. To be able to take account of all parameters affecting the imbibition rate, a dimensionless time for gravity can be incorporated (Shahri et.al., 2012).

(4.5) √ _√

109 (4.6) √ _√

(4.7)

√

= Capillary dimensionless time, with normalization index

= Capillary dimensionless time

= Dimensionless time for gravity t = time

K = absolute permeability Φ = porosity

σ = interfacial tension μ = viscosity

L = length of the core

LC = characteristic length, shape factor NI = Normalization index, see table 4.5.

Figure 4.32: Semi-log plot of normalized recovery vs. dimensionless time with wettability index at room temperature. In the legend the core number is listed first, and then I for imbibition brine, and last F, for flooding sequence performed on the core.

110 Figure 4.33: Semi-log plot of normalized recovery vs. dimensionless time without wettability index at room temperature. In the legend the core number is listed first, and then I for imbibition brine, and last F, for flooding sequence performed on the core.

The modified dimensionless time, which is the sum of capillary and gravity dimensionless times, are plotted above both with and without the normalization index. Even with the normalization index there is incongruity between the imbibition curves, meaning that other existing factors are affecting the imbibition rate. The recovery data for the different cores have the same trend, but the overall dimensionless time depends on different parameters. Permeability, interfacial tension and density differences have a positive effect on the magnitude of dimensionless time. Negative parameters include porosity, oil water and water viscosities. Wettability could increase the imbibition rate, for example a water wet rock has a higher imbibition rate, which reduces imbibition time and

dimensionless time.

Density differences, oil and water viscosities, and IFT should be equal for all the cores with SSW as initial imbibition fluid. According to figure 4.30 core #5 and #6 had the highest imbibition rate, the straight line indicates capillary driven imbibition. The dimensionless time however, are high compared to the other cores, even with the normalization index. This could be due to the overall effect of the different parameters, for example permeability. A reduction in permeability would reduce the dimensionless time, supporting the theory that mobilization of fines from the LSW injection have led to blocking of pores and reduced permeability.

111 Dissolution, mobilization of fines, release of clay particles and an increase in pH are all reported to increase water-wetness. Adsorption of polar components onto the clay surface is believed to be dependent of pH of initial brine / formation water, if the LSW flooding causes a local pH increase as proposed by Austad et.al., 2010, it might reduce the clays ability to adsorb organic material.

Core #7 was flooded with SO4 brine, and core #13 had SO4 as initial imbibition brine. Both performs similarly to the core flooded with SSW, initial imbibition rate is high, but equilibrium is quickly reached and the SI stops. A decrease in oil recovery is mainly dependent by at which water

saturation the capillary pressure falls to zero. Imbibition rate effects are probably related to change in imbibition capillary pressure and mobility to water. As the water saturation increases there are opposing effects determining the imbibition rate; the driving force of capillary pressure decreases, but the mobility of the water phase increases. The relative permeability to water is low and that to oil is high during the beginning of imbibition. Ratio of the capillary to gravity forces is given by the inverse Bond number (NB^-1):

(2.10) ^√

At large inverse bond numbers capillary forces dominate the flow, and as NB^-1 approaches zero, gravity forces dominate. Numerator is a measure of capillary entry pressure, denominator is the gravity head over the length, H. Al-Lawati et.al., 1996, reported that for high permeability cores with high to intermediate IFT, the imbibition fluid rapidly imbibed into the core. In the low IFT case, imbibition rate was slow, but with a higher oil recovery at the end in comparison with the

intermediate and high IFT fluids. The IFT measurements showed that SO4 has a IFT at 31.1 mN/m, compared to SSW at 20.1 mN/m. At low IFT it was observed that gravity forces were the dominant imbibition force. At intermediate values of the inverse bond number, gravity is still strong enough to cause considerable segregation of the flow, keeping relative permeabilities high, while capillary forces are still strong enough to boost the driving force of fluid flow. As a result the imbibition rate can be higher at intermediate IFT values, compared to either capillary of gravity dominated flow. On the other hand, imbibition rate is more rapid for cores with high permeability.

A deviation from a straight line in a log-log plot of recovery versus time (figure 4.34) may indicate that the imbibition process is dominated or affected by forces other than capillarity. It can be observed that the initial imbibition rate is high, but after a period of time the oil recovery more or less ceases. The results indicate that early oil production appears to be obtained from capillary imbibition, as the imbibition process progresses gravity will become more dominant and to a lesser extent from capillarity. Imbibition behavior can be explained on the basis that capillary forces are at

112 their highest the first instant the imbibition is initiated, caused by imbibition in the smallest

pores/capillary tubes, at this instant the capillary force dominate the gravity forces. The rate of imbibition and capillary pressure decreases proportionally to the capillary radius as larger capillaries becomes available, after a certain time a transition occurs, and the capillary forces are no longer the dominating mechanism for oil recovery. It is reported in the literature that residual oil saturation decreases with a reduction in IFT. It seems that a critical IFT value exist, below this value a significant reduction in the oil trapping or increase in oil mobilization were observed, correlated to the breakup of oil into smaller bubbles (Saleh et.al.,1993; Morrow et.al., 1982; Morrow et.al., 1985; Mohanty et.al., 1987).

Figure 4.34: Log-log plot of recovery fraction at room temperature vs. time in hours. In the legend the core number is listed first, and then I for imbibition brine, and last F, for flooding sequence performed on the core

113 Figure 4.35: Log-log plot of cumulative oil recovery [ml] vs. time in hours. In the legend the core number is listed first, and then I for imbibition brine, and last F, for flooding sequence performed on the core. Equation for each core is listed below the legend key.

(2.67) ( )

According to the eq.2.67, derived in section 2.10.4, a log-log plot of cumulative oil production versus imbibition time should yield a straight line with a slope equal to 0.5. Assuming that gravity forces are negligible compared to capillary forces. However, a countercurrent flow will be slower than a cocurrent flow, as the movement of both oil and water in opposite directions will reduce the total mobility. It is interesting to observe that the different cores maintain a straight slope at early oil production, but the time period before a deviation occurs, differs widely. Especially for core #5, which maintain a straight slope almost twice as long as core #4. Explaining the increase in displacement efficiency observed might be essential to understanding the LSW mechanism.

114