Frontal advance rate

Figure 2. Transient pressure drop across the porous-medium micromodel of Figure 1 for foam pregenerated in an identical upstream medium. The foam frontal advance rate is 186 m/d. In the wet case, foam advanced into the downstream micromodel which was completely saturated with aqueous surfactant solution. In the dry case, the downstream micromodel contained only air.

Frontal advance rates were 1 ft/day after initial brine saturation and 3 ft/day during brine saturation. The brine used for the Huntington Beach core test contains 0.75% NaCl, whereas the brine used for the Wilmington Field core tests contained 1.0% NaCl and 1100 ppm Calcium Ion. Sufficient back pressure was main tained on the system throughout the experiment to prevent the oil from de-gasing while within the core. 

Gogarty studied the flow of polyacrylamides in Berea sandstone. A shear-thinning region was found where the apparent viscosity decreased linearly with frontal advance rate when the data were plotted on log-log paper. Gogarty found that the power-law exponent for polymer flow in porous rock (n ) was greater than the power-law exponent (n) determined from rheometer Sata. An empirical correlation was developed between the apparent viscosity in the shear thinning region and the frontal advance rate. This correlation is defined in Equations 15-17. 

Flow experiments were completed on six Berea cores using polymer concentrations of 500, 1000 and 1500 ppm. The experimental data were fitted by the power-law model for most of the flow rate range as shown in Figure 4. Departure from the power-law model was observed at flow rates less than 0.009 cc/min (frontal advance rate - 0.1 ft/d) in several runs. This was expected since flow behavior should become Newtonian at low frontal advance rates. When Newtonian flow occurs, the power-law constant is 1 which means that the slope of the graph of AP versus Q on log-log paper is 45 degrees. Newtonian flow was not attained at the lowest frontal advance rate (0.022 ft/d). 

Typical results are shown in Tables 3-5 for the Blake-Kozeny model where polymer mobilities are compared at a frontal advance rate of 1 ft/d. For the conditions of this study, the polymer mobility was underestimated by factors ranging from 1.3 to 6.7. Best agreement was observed at 500 ppm for high permeability cores. Poorest agreement occurs at 1500 ppm and 15.5 md cores. The average reduction in polymer mobility was 0.42 for the Blake-Kozeny model and 0.36 for the modified Blake-Kozeny model. Capillary bundle models consistently predict lower polymer mobilities in porous rocks than observed experimentally. 

The development of a correlation between water permeability following polymer treatment, polymer concentration, and polymer mobility, opens several opportunities for improvement of mobility control design in laboratory experiments. By using the correlation, it is possible to estimate the polymer concentration required to obtain a given mobility in the displacement of biopolymer through Berea core. Laboratory corefloods are usually run at a frontal advance rate of 1 ft/d. The mobility of biopolymer at a frontal advance rate of 1 ft/d is given by Equation 33. 

At a frontal advance rate of 1 ft/d, the apparent shear rate is computed from Equation 35... 

Flow of Flocon 4800 polymer solutions through Berea cores is described by a power-law model at frontal advance rates ranging from 0.1 ft/d to 117 ft/d. The upper rate is the maximum frontal advance rate studied and is not a limit on power-law behavior in the rock. 

The packing technique was the same as before. After the permeability to brine measurement, oil was pumped through the pack at a 20 ft/day frontal advance rate. Approximately 40-50 pore volumes of oil were injected. Upon completing the oil saturation, a standard brineflood was performed on the sandpack. A 6 ft/day injection rate was applied. After 6 pore volumes of injected brine, negligible oil production was observed. 

Polymer injection initiated at advanced stages of waterflood. Two polymer-floods were performed in partly oil depleted sandpacks. The sequence of operations was as follows. Upon completing the brine permeability measurements, a sufficient amount of oil (20 PVI) was pumped through the sandpack. After saturation with oil, a regular brineflood was performed, applying a 6 ft/day frontal advance rate. Thereafter, the sandpacks were resaturated with oil. 

Having completed the resaturation, a volume of brine (40% of the total pore volume) was injected into the sand. The brine was followed by a slug of polymer solution (20% of the total pore volume). After the polymer slug, brine was injected again until the end of the test (6 PV). During each cycle of the flooding operations, a constant, 6 ft/day frontal advance rate was applied. 

The multilayer adsorption concept is also incapable to explain the role of pore dimensions. In a low permeability material, the shear rates are considerably greater at a given average frontal advance rate than in a high permeability material. Due... 

The experimental results indicate that different water fractional flows, for particular frontal advance rates, are needed to generate strong foams. This effect is much more pronounced in the presence of oil, i.e. higher fractional flow of water was needed to establish significant mobility reduction factors when residual oil was present. Foams generated in the presence of residual oil produced consistently lower mobility reduction factors than foams generated in cores without oil. 

The flood history is summarized in Table 3. First baseline pressure drops were determined across the 1.8 m core during simultaneous injection of brine (without surfactant) and gas at a fixed frontal advance rate and varying gas fractional flows. A frontal advance rate of 4.0 m/day was selected to ensure a flow rate higher than the critical rate for effective foam formation and propagation. A non-adsorbing tracer, tritiated water, was added to the brine so that the breakthrough of the tracer could be compared with the breakthrough of the gas. 

Foam Quality (%gas) Injection Rate = 43.3 ml/h, Frontal Advance Rate = 4 m/day Injection Rate = 21.6 ml/h, Frontal Advance Rate = 2 m/day Injection Rate = 10.8 ml/h, Frontal Advance Rate = 1 m/day ... 

In Figure 8, the experimental results from the (4 m/day frontal advance rate, oil free) short core flood are compared to the simulated pressure drops which were based on the limiting capillary pressure principle. In this particular case was chosen at 0.35 over a range of water fractional flows from 0.01 to 0.15 to closely match the experimental data. For Sw > a fractional flow curve was chosen which matched the experimental data closely by appropriately adjusting the gas phase relative permeability curve. The water relative permeability curve remains the same as defined in the Appendix under gas/water relative permeabilities. The composite foam fractional flow curve can be seen in Figure 9. Notice the vertical section in the curve for the foam flow case lies at = 0.35. 

The close match between experimental and simulated data does not continue when the same fractional flow curve is used to simulate the experimental pressure drop results at a slower frontal advance rate (2 m/day, oil free). A new fractional flow curve had to be constructed to give a closer match. In Figure 10 the experimental pressure drops are compared to the simulated curves and in Figure 9 the contrast between the new and old fractional flow curves is made clear. Due to the shear thinning nature of the foam, at slower frontal advance rates a steeper fractional flow curve is required at the same critical water saturation, = 0.35. 

Three foam models were investigated in the course of this project. All three models relied on modifying the gas relative permeability in the presence of foam. The foam model by Vassenden and Holt [24 was the most versatile platform to match steady state foam results at various frontal advance rates and foam qualities. With this steady state foam model, it was possible to history match the foaming behaviour investigated on the long and short cores. 

Darcy velocity of gas and water phase reference velocity of gas phase critical velocities of gas and water phases q/A(j), total frontal advance rate qg/A(j), gas phase advance rate q /A(j), water phase advance rate... 

Data describing the flow of polymers in porous media can be obtained by conducting steady-state flow tests in core plugs or sand-packs over the range of frontal-advance rates anticipated in the bulk of the reservoir and in the vicinity of the wellbore. In these tests, polymer of a specific concentration is injected at a constant rate. Pressure drops are measured across the entire length of the porous medium and between measuring ports spaced along the porous medium, as depicted in Fig. 5.30. A constant rate is maintained until the pressure drop reaches a steady state. A series of measurements of flow rate vs. pressure drop is taken to determine the flow properties of the polymer in the porous material. 

Fig. 5.31—Effective viscosity as a function of frontal-advance rate. ...

Fig. 5.31 presents effective viscosity data as a function of frontal-advance rate for the flow of xanthan biopolymer through Frannie reservoir core. 59 The effective viscosity decreases as the frontal-advance rate increases because the biopolymer is shear-thinning in this range of frontal-advance rates. Another common practice is to assume that kp is the permeability of the porous rock to brine, k, after the mobile polymer has been displaced and compute the apparent viscosity of the polymer. 

Example 5.2—Calculation of Polymer Mobility. Data for toe flow of a partially hydrolyzed polyaciylamide through a lO-in.-long Berea sandstone core were obtained by injecting polymer solution at a constant frontal-advance rate and measuring the pressure drop between pressure taps located 8 in. apart. The following data are avallablefiO ky,=516 md, Ap = 1.18 psi, distance between pressure taps is 0.667 ft, frontal-advance rate, v, is 1.85 ft/D, and porosity is 0.21. Determine toe polymer mobility in md/cp from these data. 

Polyacrylamides exhibit similar flow characteristics at low and moderate frontal-advance rates. A lower Newtonian regime exists at low frontal-advance rates. As frontal-advance rate increases, there is a transition to a shear-thinning region. Fig. 5.35 illustrates pressure-drop vs. flow-rate data for the flow of polyacrylamide in Berea core material. This polymer is shear-thinning because n , <1.0. However, polyacrylamides are not as shear-thinning as biopolymers. The mobility of polyacrylamide in porous rocks is strongly influenced by the reduction of permeability caused by the retained polymer. The computation of X and <, from these data is illustrated in Example 5.3. 

Fig. 5.34—Pressure-drop/flow-rate data for xanthan In an unconsolidated sandpack showing onset of Newtonian region at low frontal-advance rates.

Example 5.3—Calculation ofX and n From Flow Data. The pressure-gradient vs. frontal-advance rate data in Fig. 5.35 were obtained from Gao and French. > These data are part of the experimental data from a study of the flow through Berea core material of a 1,500-ppm solution of Pusher 500, a partially hydrolyzed polyacrylamide, in 53 meq/L NaCl. Table 5.10 summarizes pressure gradients and frontal-advance rates. These data are to be analyzed to obtain values of Xf and n. Porosity of the sandstone is 0.21. 

Solution. Beeause the plot of ApIL vs. v is linear on the log-log graph in Fig. 5.35 for frontal-advance rates within the range listed in Table 5.10, the data can be fitted to Eq. 5.20 by use of least squares. Eq. 5.20 can be rearranged in the form... 

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