1. E. Putra, Y. Fidra and D.S. Schechter
SCA9910
Study of Waterflooding Process in Naturally Fractured Reservoirs from Static and Dynamic Imbibition Experiments
Thank you! My name is Erwinsyah Putra.
The title of my presentation is study of waterflooding process in naturally fractured reservoirs from static and dynamic imbibition Experiments. This presentation will cover the experimental and the modeling of static and dynamic imbibitions.
E. Putra, Y. Fidra and D.S. Schechter

2. Outline Introduction Objectives Static Imbibition Dynamic Imbibition
The outline of my presentation is divided into 5 sections. One is the short introduction, and continued by presenting the objectives of this study. Then I will talk about the static and dynamic imbibitions, both experiment and modeling. I will end my presentation by presenting the conclusions from this study.
Conclusions

3. Introduction Field dimension Dynamic Static imbibition imbibition
Determine rock
wettability
Capillary
Capillary pressure curve
pressure curve
Determine laboratory
critical injection rate
Fracture
Scaling
Capillary
equations
Number
As I mentioned earlier that two studies were conducted, one is static imbibition and the other is dynamic imbibition. The difference between static and dynamic is the static does not need a water injection during the experiments and use an unfractured core. While in dynamic imbibition experiments need a water injection or we call it a force imbibition and use an artificial fractured core.
The purpose of doing static imbibition is to determine the rock wettability and the static imbibition capillary pressure. While in dynamic imbibition, we use it to determine the capillary pressure curve with fixed relative permeability and also determine the critical injection rate.
The results of these two experiments were up-scaled to field dimension.
Upscaling
Upscaling
Field dimension

4. Objectives
To investigate wettability of Spraberry Trend Area at reservoir conditions.
To investigate the contribution of the capillary imbibition mechanism to waterflood recovery.
To determine the critical water injection rate during dynamic imbibition.
The main objectives of this study are :
First is to investigate wettability of Spraberry trend area in west Texas at reservoir conditions (high pressure and high temperature). We made comparison between room and reservoir conditions and also delineate the effect of temperature and pressure on imbibition recovery.
Second is to investigate the contribution of the capillary imbibition mechanism to waterflood recovery. We made a comparison between oil recovery from static and dynamic imbibitions.
The last objective is to determine the critical water injection during dynamic imbibition. The critical injection rate at laboratory dimensions was scale-up to field dimensions using a fracture capillary number.

5. The material used for the experiments was shown here
The material used for the experiments was shown here. The fluids are spraberry crude oil and synthetic reservoir brine. Two porous media were used; Berea sanstone and low permeability spraberry rock. Berea sandstone is used as a reference.

6. Experimental Set-up for Static Imbibition Tests at Ambient Conditions
This is the experimental set-up for static imbibition tests at ambient conditions, where saturated core after establishing initial water saturation was immersed into the beaker that full of brine. The oil recovery that was produced by capillary force was record at the top of beaker, as shown in this figure, until ultimate recovery was achieved. Before the core was immersed into the brine, the core was aged for certain days. This graph shows the different oil recovery with different aging time. For our experiments, 7 days is enough to age the core.

7. Experimental Set-up for Static Imbibition Tests at Reservoir ConditionsBV NV PR
Graduate
Cylinder
Brine Tank
High
Pressure
Imbibition
Cell
N2 Bottle
(2000 psi)
Air Bath
BV = Ball Valve
NV = Needle Valve
PR = Pressure Regulator
Top View
Inlet for creating
tangential flow
Side View
core
The static imbibition experiments were also conducted in high pressure and high temperature apparatus as shown in this figure here. The core was sit in the core holder that full of brine without rubber sleeve. The core holder was placed into the air bath to keep high temperature. The pressure was increased to reservoir pressure. There is a water inlet at the side of the core holder to create the turbulent flow allowing water to push the oil sticked at the surface of the core. Similar way when the beaker was shaken in spontaneous imbibition conducted in room temperature. The oil recovery was recorded in graduated cylinder.

8. After imbibition tests, all core plugs were waterflooded with brine at reservoir temperature as shown here. The brine was subject to force injection to displace the oil left after spontaneous imbibition. The purpose of this experiment is to determine the wettability index by applying the Ammot index.

9. Effect of Pressure and Temperature on Static Imbibition in Berea Sandstone
The effect of pressure and temperature on static imbibtion in Berea Sandstone can be seen in this plot. The results were plot between oil recovery and time. Increasing the pressure up to 1000 psi from the room pressure didn’t have any significant effect on oil recovery. At the beginning, the oil recovery was delayed, but at the end of the tests, the ultimate recoveries are the same. Reference curve was performed at reservoir condition using refine oil for a very strongly water-wet system.
While, the temperature effect has a significant effect on oil recovery as shown in this figure. After oil recovery ceased at the end of the imbibition test performed under room temperature, the experimental temperature was changed to reservoir temperature. As indicated in this figure, a dramatic increase in the rate of spontaneous imbibition, due to change in fluid mobility, oil expansion and decrease in interfacial tension.
Also, higher oil recoveries were achieved at reservoir temperature compared to that at room temperature. The ultimate oil recovery is also affected by the temperature. Since there is no effect of pressure on oil recovery, this experiments were conducted at room pressure.

10. Effect of Temperature on Static Imbibition
with Spraberry Reservoir Rock
Similar effect of temperature was also found using low permeability spraberry reservoir cores. Even though, the effect of temperature on oil recovery using these cores are less than using Berea cores.
Two measurements were carried out for each temperature and good reproducibility is indicated in this figure. The results also demonstrate that during the process of brine imbibition into low permeability core, the water is imbibed by rock faster at reservoir temperature than at room temperature.

11. Wettability index vs aging time
for different experimental temperatures
Static imbibition A
Displacement
This figure shows wettability index to water vs. aging time at different temperatures during spontaneous imbibition and displacement process. The total recoveries for cores performed at reservoir temperature during the imbibition process and flooded by brine at room temperature is higher than the one with imbibition and displacement perfomed at reservoir temperature. This is indicated that the oil recovery from displacement process performed at high temperature is higher than that at room temperature. Since after 7 days aging time, the wettability remain constants, all the other experiments were aged at 7 days. B
Spraberry cores

12. Composite Imbibition Curves
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.01
0.1 1 10
100
1000
10000
100000
Dimensionless Time, tD
Normalized Recovery
SWW Berea Core
(reference curve)
Spraberry Cores
at Reservoir Condition l =
at Ambient Condition =
Aranofsky Eq. : R n
= 1 - exp (- t D )
The results of spontaneous imbibition from spraberry cores conducted in room and reservoir conditions were plot in normalized recovery against the dimensionless time. The purpose of this plot is to find the value of lambda which is a curve fitting that will be used in recovery equation derived by Aronofsky.

13. Scaling Equations for Static Imbibition;
C = 10.66
The dimensionless time for the previous plot is defined in this equation. Vis_g is a geometric mean between brine and oil viscosities. The Lc is the fracture spacing. The dimensionless recovery is defined based on Arofnosky equation.
The analytical model for decline curve analysis based on imbibition theory is expressed as follows. The lambda that previous obtained based on curve fitting is defined in this equation.

14. Up-scaled Recovery Profile
h = 10 ft
Ls = 3.79 ft
Upper Spraberry
1U Formation
(Shackelford-1-38A)
Using a decline curve analysis, we can up-scale recovery profile and predict the effect of time on oil recovery. This result shows an application that decline curve analysis to predict recovery in the upper spraberry 1 U formation based on spontaneous imbibition recovery. Several scenarios were performed at different times of imbibition. Within 10 years of waterflooding initiation, the average recovery is about 11%-13%. After about 40 years, there is no more oil recovered from 1U layers.

15. Effect of Matrix Permeability and Fracture Spacing on Oil Recovery
We conducted the scenario to see the effect of matrix permeability and fracture spacing on oil recovery. The results were plotted between oil recovery vs. imbibition time. As we can see from this figure, decreasing a permeability will significantly decrease the recovery. This graph assumes that fracture spacing is constant about 2.86 ft.
As fracture spacing increase, the oil recovery significantly increase as can be seen here with assuming constant permeability 0f 0.1 mD.
So from these two graphs we can say that higher oil recovery will be obtained in high permeable rock and more dense fracture systems.

16. Static Imbibition Modeling
Governing Equation
Brine
Core plug
Glass funnel
Oil bubble
Oil recovered
Assumptions
Because imbibition experiments usually take a long time and sometimes difficult to determine other parameter such as capillary pressure or to illustrate water saturation at different time and location, therefore, numerical modeling is needed to simulate this process. The simultaneous flow of two-phase flow formulation is described in the four basic flow equation, mass balance equation for water and oil, capillary pressure and water saturation relationship. By combining these four basic equation, the governing equation for static imbibition modeling is described here. D (sw) is a diffucitivity as highly function of water saturation. In deriving this equation, some assumptions are used; gravity terms are negligible, capillary pressure is the only driving force where total velocity is zero, and fluid and rock are incompressible. 
No gravity effect
Only Pc as driving force
Fluid and rock are incompressible  

17. Static Imbibition Modeling
The capillary pressure result was plotted in here. Initial water saturation for this particular core is 35% and the residual oil saturation is 54%. Therefore the saturation change is only 11%. Because of small change of water saturation, the solution become unstable because of numerical dispersion. So we increase the saturation change by decreasing the residual oil saturation using 3 different residual oil saturation, 0.4,0.3 and 0.2. To generate the capillary pressure, the relative permeability is assumed constant and the matching effort only alters the capillary pressure curve to match the volume oil recovered as can be seen here as example of using residual oil saturation of 0.2. The capillary pressure that was generated can be seen in this figure. Similar way for 0.3 and 0.4 residual oil saturation. For the actual residual oil saturation (0.54), we estimate that pressure curve from those previous capillary pressure curve following the trend from those curves. The estimated capillary pressure shows that the capillary pressure is very low indicating again that the spraberry cores are weakly water wet.
Match between Laboratory Experiment and Numerical Solution for Sor = 0.2
Capillary Pressure Curves Obtained as a Result of Matching Experimental Data

18. Counter-current Exchange Mechanism
Concept of Dynamic Imbibition Process
Water
Oil
Invaded Zone
Matrix
Fracture
Counter-current Exchange Mechanism
The dynamic imbibition process is visualized in term of single fracture into which water is injected at the one end with production occuring at the other end. As the injected water flows through the fracture, the water would gradually imbibe into the adjacent matrix, in which the counter curent exchange mechanism occurs. Once the oil was stored in the matrix, the oil was pushed by injected water depending on how high the injection rate on producing wells.

19. Artificially fractured core
Experimental Set-up for Dynamic Imbibition Tests at Reservoir Temperature
Air Bath
Confining pressure gauge
Brine tank
Core holder
To illustrate that process, we performed the imbibition flooding experiment in an artificially fractured core, both berea and spraberry cores with following procedure:
1. After the initial waters saturation was established, the core was cut into two pieces using hydraulic cutter to generate the fracture, then the cut sections were put back together without polishing the surface or using spacers.
2. The matrix face was seal off to allow injected only through the fracture.
3. The core was inserted back to core holder under high temperature and room pressure. The water was injected with low injection rate and the oil recovery was collected in graduated cylinder. Several cores were perfomed with different injection rate.
Graduated cylinder
Artificially fractured core
N2 Tank
(2000 psi)
Ruska
Pump
Fracture
Matrix

20. Oil Recovery from Fractured Berea and Spraberry Cores during Water Injection using Different Injection Rates
Oil recovery from fractured Berea core and Sprabbery cores during water injection using different injection rates were plotted between oil recovery and total production. As can be seen here, increasing the injection rate decreases contact time of water with the matrix resulting a weaker capillary imbibition transfer and also increase water breakthrough. While the ultimate recovery approaches the same value. The only different is the time to recover the oil and the amount of injected water. Similar results were obtained using Spraberry core. When we use unfractured core with 0.2 cc/hr injection rate, the oil recovered is about 55% IOIP while using the artificial fracture core, the oil recovered is about 30%. This difference is because of difference displacement mechanism. The experiment using unfractured core is piston displacement while countercurrent imbibition and viscous displacement were involved in the fractured core.

21. Comparison between Static and Dynamic imbibitions for Berea Core, Spraberry Brine and Crude Oil

22. Dynamic Imbibition Modeling
Single porosity, 2 phase and 3-D
Rectangular grid block with grid size : 10 x 10 x 3 (Berea) ; z = 9 layers for Spraberry
Fracture layer between the matrix layers
Inject into the fracture layer
Alter matrix capillary pressure only to match the experimental data 
zero Pc for fracture
straight line for krw and kro fracture
use krw and kro matrix from the following equations (Berea core):  

23. Match Between Experimental Data and Numerical Solution
Berea Core
Match Between Experimental Data and Numerical Solution
Cumulative water production vs. time
Cumulative oil production vs. time
Spraberry Core
Cumulative water production vs. time
Cumulative oil production vs. time

24. Capillary Pressure Curves Obtained by Matching Experimental Data (Berea and Spraberry Cores)

25. Dimensionless Fracture Capillary NumberAm w dz Af
Capillary force
( cos  Am)
Viscous force
(v w Af ) h
Lab Units:
Field Units:

26. Injection Rate versus Oil-cut

27. Upscaling of Critical Injection Rate

28. Conclusions
The capillary pressure curve and wettability index obtained from spontaneous imbibition experiments indicate the Spraberry cores are weakly water-wet.
Effect of pressure is much less important than the effect of temperature on imbibition rate and recovery.
Performing the imbibition tests at higher temperature results in faster imbibition rate and higher recovery due to change in mobility of fluids.

29. Conclusions (Cont’ed)
The capillary pressure curve obtained from dynamic imbibition experiments is higher that of the static imbibition experiments due to viscous forces during the dynamic process.
An effective capillary pressure curve can be derived from dynamic imbibition experiments as a result of matching between experimental data and numerical solution.
Imbibition transfer is more effective for low injection rates due to lower viscous forces and longer time to contact the matrix.