## Comparing the Performance of 5-Spot and Inverted 9-Spot Patterns by Reservoir Simulation using CMG Suite (Cont~)

RESULTS

1. Recovery and Cumulative Oil Production

The difference of reservoir fluids recovery for 5-spot and inverted 9-spot patterns from simulation results is listed in Table 4, and the cumulative oil production could be found from Fig. 3.

Table 4. Recovery for 5-Spot and Inverted 9-Spot Patterns

 Parameters 5-Spot Pattern Inverted 9-Spot Pattern Percentage Recovery (%) Oil 42.128 41.148 STO as a % of Mobile Oil 83.011 81.080 Total Gas 93.901 93.280 Water -214.84 -246.91

From the simulation results, the recovery of oil, Stock Tank Oil (STO) as a percentage of mobile oil, and total gas for 5-spot pattern is higher than inverted 9-spot pattern, and less water injection is needed.

Fig. 3 Cumulative Oil Production for 5- and Inverted 9-Spot Patterns

2. Water Cut

The filed water cut for 5-spot and inverted 9-spot patterns from reservoir simulation are shown in Fig.4.

Fig. 4 Field Water Cut for 5- and Inverted 9-Spot Patterns

The water cut curve for inverted 9-spot pattern has two peaks, one in the year of 2003 and the other in the year of 2005, while the water cut curve for 5-spot pattern has only one peak in the year of 2019.

To understand the difference between field water cut curves for two patterns, it is better to investigate the well water cut curves for two patterns in Fig. 5.

Fig. 5 Well Water Cut for 5- and Inverted 9-Spot Patterns

In Fig. 5, well water cut curves of producers for the two patterns could be found. The pink and blue curves represent Well 1 and Well 4, the two diagnosed producers for inverted 9-spot pattern, both of which reached the water cut of 0.95 in the year of 2003. After that, due to the constraints, Well 1 and Well 4 shut in, while Well 3 continued producing until the year of 2005. After the three producers reached the water cut limit, the filed production stopped. As for well water cut curve of Well 1 for 5-spot pattern, the peak occurred in the year of 2019.

For water cut curve of 5-spot pattern, after it reached the peak, it did not turn to zero instantly, which is different from others. Double check with the output file, on Dec. 29, 2019, there is no oil or water produced, and the water cut should be zero. The curve shows 20% water cut on Jan. 1, 2020. The paradox between the data and curve is still not understandable, maybe a numerical solution error.

As for this concept petroleum production unit, 5-spot pattern could produce more oil and gas, but inject less water, comparing with inverted 9-spot pattern.

In addition, whether 5-spot pattern or inverted 9-spot pattern could only produced no more than 45% of oil by water flooding for such a homogeneous reservoir, if proper EOR methods used, such as polymer flooding, the recovery should be increased at 10% more or less.

3. Average Reservoir Pressure, Liquid and Oil Production Rate

Because the oil production rate is highly dependent on the reservoir pressure, the average reservoir pressure, liquid and oil production rate data are combined in Fig. 6.

Fig. 6 Average Reservoir Pressure and Oil Rate for 5- and Inverted 9-Spot Patterns

From the initial conditions and constraints, the initial reservoir pressure is around 34000 k Pa, and the bubble point pressure is 30000 k Pa, while the maximum bottom hole pressure is 80000 k Pa, thus, the injection started on Jan. 1, 1995 for both cases. At this phase, the major mechanism for oil production is depletion. Each producer has a constant oil rate which is 30 m3 per day, with high gas rate. With the reservoir pressure decreases, more and more solution gas came out. After produced two years (the year of 1997), the solution gas rate reached the peak, and the reservoir pressure could not provide enough energy for oil rate at such a high level for inverted 9-spot pattern, the oil rate dropped very quickly. Then, water flooding supported the oil production. Until the year of 2001, only oil produced comparing the liquid rate and oil rate. Afterwards, the oil rate decreased and liquid rate increased very quickly. If we checked the water cut in Fig. 3 or 4, we could found that water cut increased sharply. When the two producers reached 0.95 water cut, they were shut in. The oil rate and liquid rate lowered to 30 m3 per day until the water cut reaches the upper limit. Once the three producers were shut in, the reservoir pressure will maintain at 80000 k Pa, the upper limit for the injection.

As for 5-spot pattern, after produced eight years (the year of 2003), the solution gas rate reached the peak, and the reservoir pressure could not provide enough energy for oil rate at such a high, the oil rate dropped very quickly. Then, water flooding supported the oil production. Until the year of 2004, only oil produced comparing the liquid rate and oil rate. Afterwards, the oil rate decreased and liquid rate increased very quickly. If we checked the water cut in Fig. 4 or 5, we could found that water cut increased sharply. When the producer reached 0.95 water cut, it will be shut in.

Comparing the two cases, inverted 9-spot pattern could be regarded as the compressed 5-spot pattern on the time scale. If we stretched the pressure curve of inverted 9-spot pattern, the curve may match that of 5-spot pattern.

4. Gas-Oil Ratio

Figure 7 shows the gas oil ratio changes with time. The curves prove the production history explained above.

Fig. 7 Gas Oil Ratio for 5- and Inverted 9-Spot Patterns

5. Oil Saturation Distribution

Figures 8 and 9 provide the oil saturation on Jan. 1, 1997, and on Jan. 1, 2017, respectively. According to the scale bar on the right of the figures, dark green shows lower oil saturation, and light green (or yellow) shows high oil saturation. The difference of oil saturation between layers could show the gravity effect on the water flooding.

Fig. 8 Oil Saturation for 5-Spot Pattern on Jan. 1, 1997

Fig. 9 Oil Saturation for 5-Spot Pattern on Jan. 1, 2017

CONCLUSIONS

From the simulation results, we can conclude that

1. For this reservoir, 5-spot pattern has higher recovery, but inverted 9-spot pattern produces oil more efficiently;
2. Inverted 9-spot pattern seems to be the compressed 5-spot pattern due to the high injection rate;
3. A decision should be made if more conditions provided;
4. From the PVT data and relative permeability data, this reservoir is homogeneous, but the mobility ratio became more and more unfavorable, inverted 9-spot pattern should be considered;
5. The oil saturation distribution shows the gravity effect during water flooding;
6. Whether 5-spot pattern or inverted 9-spot pattern could only produced no more than 45% of oil by water flooding for such a homogeneous reservoir, if proper EOR methods used, such as polymer flooding, the recovery should be increased at 10% more or less.

Reference:

1. Rose, S.C., J.F. Buckwalter and R.J. Woodhall, “The Design Engineering Aspects of Waterflooding”, SPE Volume 11 of the Henry L. Doherty Series, Richardson, TX (1989).

APPENDIX

Mobility Ratio:

$M=\frac{\left ( \frac{k_{r}}{\mu } \right )_{w}}{\left ( \frac{k_{r}}{\mu } \right )_{o}}=\frac{ \frac{k_{rw}}{\mu_{w}}}{ \frac{k_{ro}}{\mu_{o}}}=\frac{ \frac{\mu_{o}}{\mu_{w}}}{ \frac{k_{ro}}{k_{rw}}}$

## Comparing the Performance of 5-Spot and Inverted 9-Spot Patterns by Reservoir Simulation using CMG Suite

Note: Reservoir simulation is a must for a petroleum engineer. During the past 10 years, I focus on experimental studies of EOR processes. I have been waiting for a formal training on reservoir simulation for years. This spring, our PE program opens a course on reservoir simulation using CMG suite, which is easy for a beginner, and has a special component STARS to simulate the enhanced oil recovery processes, especially conformance control using superabsorbent polymer (also called “preformed particle gel” in literatures). In this post and the next, I will show the CMG reservoir simulation results to compare the performance of 5-spot and inverted 9-spot patterns using black oil model, which is part of team project for that reservoir simulation course.

INTRODUCTION

The objective is to study and compare the performance of five-point and nine-point patterns. The tasks included are:

1. Construct models for a reservoir model with five-spot and inverted nine-spot patterns using CMG;
2. Run reservoir simulations for both models;
3. Compare the simulation results by Dec. 31, 2020 for recovery, water cut, average reservoir pressure, oil production rate, gas-oil ratio, cumulative oil production, oil saturation, and pressure distribution between 5-spot and inverted 9-spot patterns.

RESERVOIR DESCRIPTION

A conceptual petroleum production unit with 400 m*400 m*20 m in size is to be simulated. The unit is approximated into 20 * 20 regular grids in horizontal layers and each cell is 20 m in length; and 3 layers in the vertical direction (as 8m, 8m, and 4m respectively).

The grid top, grid thickness, porosity, and permeability in x, y, and z directions are listed in Table 1.

Table 1. Reservoir Properties

 Grid Top (m) Grid Thickness (m) Porosity (fraction) Kx (mD) Ky (mD) kz (mD) 3120 8 0.2 200 200 20 3128 8 0.2 200 200 20 3138 4 0.2 200 200 20

Some other information about the reservoirs could be found below:

• Rock Compressibility: 6e-7 1/k Pa, Reference Pressure: 1379 k Pa
• Reference Pressure: 34000 k Pa @Reference Depth: 3170 m
• Constant Bubble Spot Pressure: 30000 k Pa
• Water-Oil Contact: 3250 m
• Gas-Oil Contact: 2990 m

Black-oil model is chosen, and PVT data is listed in Table 2 and relative permeability is listed in Table 3.

Table 2. PVT Data for Reservoir Fluids in Conceptual Petroleum Production Unit

 MODEL BLACKOIL PVT EG 1 **$p Rs Bo Eg viso visg 700 6.8 1.121 5.77 1.11 0.01262 1600 17.29 1.173 12.41 0.96 0.01349 2270 21.85 1.179 17.08 0.95 0.01371 3160 26.91 1.182 23.98 0.88 0.01401 4640 33.99 1.214 35.33 0.83 0.01434 6430 41.66 1.217 48.84 0.79 0.01485 8500 52.16 1.245 65.49 0.74 0.01535 12490 70.89 1.295 96.05 0.7 0.01657 17280 93.19 1.343 132.78 0.59 0.01849 20960 107.78 1.386 159.54 0.54 0.0204 34470 201.68 1.49 257.76 0.3 0.02741 48260 359.65 1.596 357.98 0.23 0.03456 68950 596.61 1.755 613.66 0.2 0.05281 DENSITY OIL 830.0 DENSITY GAS 1.330 DENSITY WATER 1153.0 CO 1.1360e-6 CVO 3.0120e-5 BWI 1.01 CW 4.3510e-7 REFPW 102.0 VWI 1.290 CVW 0.0 **$ Property: PVT Type  Max: 1  Min: 1 PTYPE CON            1

Table 3. Relative Permeability Data for Conceptual Petroleum Production Unit

 *SWT ** SW     KRW    KROW    PCOW 0.200  0.0000  1.0000  195.84 0.229  0.0001  0.7407   95.20 0.255  0.0003  0.6829   60.00 0.308  0.0012  0.5722   22.00 0.334  0.0023  0.5194   18.80 0.412  0.0102  0.3715   12.60 0.464  0.0219  0.1526    8.43 0.557  0.0416  0.0822    4.40 0.606  0.0721  0.0000    1.32 0.647  0.1448  0.0000    0.00 0.700  0.1780  0.0000    0.00 0.800  0.2604  0.0000    0.00 1.000  1.0000  0.0000    0.00 *SLT ** SL     KRG    KROG    PCOG 0.200  1.0000  0.0000 3891.60 0.316  0.6784  0.0000  579.60 0.435  0.6215  0.0000  372.40 0.562  0.5456  0.0000  242.50 0.614  0.3939  0.0020   60.80 0.702  0.1399  0.0280   37.21 0.812  0.0515  0.1721   13.65 0.875  0.0297  0.3395   10.45 0.906  0.0226  0.4395    9.00 0.937  0.0173  0.5500    7.51 0.969  0.0131  0.6702    5.90 1.000  0.0000  1.0000    0.00

BASIC MODEL SETUP

Based on the reservoir conditions, a black oil model with 20*20*3 grid blocks are created by Builder, a CMG component. Each grid block in layer 1 (top layer) and layer 2 (mid layer) is 20 m* 20 m*8 m, and each grid block in layer 3 (bottom layer) is 20 m* 20 m*4 m.

FIVE-SPOT PATTERN

Injector (Well-2) and producer (Well-1) are defined in the diagnosed corner cells in Fig. 1, the grid top model for five-spot pattern. The producer started working on Jan. 1, 1995 at liquid production rate is 30 m3 per day. The water injection rate is 30 m3 per day. Layers 1, 2, and 3 are perforated for both producer and injector. Constraints for producer are: minimum bottom hole pressure as 1500 k Pa and maximum liquid production rate as 100 m3/day for operation, and maximum water cut is 0.95 for monitor and shut-in conditions; and constraints for injector are: maximum bottom hole pressure is 80000 k Pa, and maximum water injection is 2000 m3/day for operation.

Fig. 1 Grid Top Model for Five-Spot Pattern

INVERTED NINE-SPOT PATTERN

Injector (Well-2) and one producer (Well-3) are defined in the diagnosed corner cells, and another two producers (Well-1, 4) are defined in another two diagnosed corner cells at phase 90 degrees in Fig. 2, the grid top model for inverted nine-spot pattern.

The producer started working on Jan. 1, 1995 at liquid production rate is 30 m3 per day. The water injection rate is 90 m3 per day. Layers 1, 2, and 3 are perforated for both producer and injector; and well constraints are same with five-point pattern.

Fig. 2 Grid Top Model for Inverted Nine-Spot Pattern

(to be continued)

## Calculation of Laminar Flow through Fracture

The calculation of laminar flow through fracture is very fundamental (), and it is very important for my research, also. Late last year, I derived the equation for both Newtonian fluid and non-Newtonian fluid by hand. Now I am going to make a note for that derivation for Newtonian fluid, which could be regarded as the answer to an exercise on Transport Phenomena, 2nd Ed. by Bird, R.B., et al., a classical textbook on this topic.

At first we need to describe the physical properties of the fracture model (as shown in Figure.1).

Figure 1. Physical Properties of Fracture Model

A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls with length, L, a distance B (fracture width) apart. It is understood that the fracture height, B《W, so that “edge effects” are unimportant. Make a differential momentum balance, and obtain the following expressions for the momentum-flux and velocity distributions:

$\tau_{yz}=\left ( \frac{p_{0}-p_{L}}{L}\right)x$

$v_{z}=\frac{\left (p_{0}-p_{L}\right)B^{2}}{2\mu L}\left [ 1-\left ( \frac{x}{B} \right )^{2} \right ]$

Obtain the slit analog of the Hagen-Poiseuille equation.

$w=\frac{1}{12} \frac{\left (p_{0}-p_{L}\right)B^{3}W\rho }{\mu L}$

## Microsoft Office 2010 Beta Trial

On April 15 2010, Microsoft announced that Office 2010 had been released to manufacturing, with those Volume Licensing customers who have Software Assurance being able to download the software from April 27. Availability in retail stores in the US is to be from June. [1] Now, Office 2010 Beta is available to download on Microsoft’s official website for free trial. The day before yesterday, I downloaded it into my hard drive. Today I have a chance to install it into my desktop at home. I do not use Office 2010 very long, but I still want to share in my feelings about this new version. At a glance at the Office 2010 Beta, its appearance has no big difference from its predecessor Office 2007. If you started Word 2010, the colorful screen won’t disappoint you. The round MS office icon on the top left has been modified into File menu, which seems to be more direct. That reminds me that for the first time I used Word 2007, I did not know where I could find the Print icon or menu. In addition, the File menu provides more choices than before. Through submenu Info, you can set up and view the information of the file, such as permissions. The trend for Microsoft Office is to integrate the components with Internet. This time, it is easily to publish and share the file with other users. At last, I want to say, as one of common Office 2007 users, it is easy to upgrade to Office 2010, but I won’t upgrade with extra cost.

## Fracture Core Model

Today I am going to post some photos of the fracture core model I made.

Fig. 1 Fractured Sandstone Core by Water-jet Cutting Technology

Fig.2 Nylon Mesh Strip for Plugging the Fracture on the Core

Fig. 3 Fractured Core Adhesion to Nylon Mesh Strip with 5-min Expoly

Fig. 4 Fracture Core Casing

Fig. 5 Polycarbonate Square and Connector

Fig. 6 Fracture Core in the Casing

Fig. 7 Fracture Core Filled with Casting Epoxy

## Superabsorbent Polymer

Note: In this post, I would like to introduce the superabsorbent polymer (SAP),which could be used as conformance control agent in oil and gas field. SAPs could absorb and hold a large amount of water or aqueous solutions even under high pressure and high temperature. Just as described in the summary of my proposal, in my research, I mainly test the flow properties of SAP through the fracture or fracture-like model, and the rheological properties with rheometer. Some of the swelling and deswelling behaviors and the effects on the injectivity of SAP through fractures were investigated also. Today SAPs will be introduced in general here. Later,  The following context is modified from an unpublished paper by my advisor and me. All rights reserved.

The superabsorbent polymers (SAPs) most commonly available are hard, dry, granular or powdered products made up of a cross-linked polymer with a three dimensional network structure that absorbs and holds a large amount of water and swells up to 200 times its original size and weight in fresh water or aqueous solutions while maintaining its physical structure. [1-4] SAPs are increasingly used in multiple fields of human activity, such as biomedical, agricultural, personal care, and industrial because of its high water absorbing capability. [4-6] Recently, SAPs have been applied in conformance control and water shutoff because they have significant advantages over the bulk gels used in in situ gelling processes, such as controllable size and strength, high chemical and temperature resistance, minimum formation damage, less surface facility requirements, and environmental friendly. [7] Except for the super water absorbency, the mechanical properties of SAPs are very important to the conformance control processes, such as the strength and injectivity. Dynamic mechanical analysis (DMA), rheometry and core flooding experiments are commonly used to determine the mechanical properties. Comparing to core flooding experiments, DMA and rheometry are much more cost-effective.

The SAP used in the research is LiquiBlock™ 40K (40K), a commercial product from Emerging Technology Inc. 40K is crosslinked acrylamide/potassium acrylate copolymer and the major component is 2-Propenoic acid, potassium salt, polymer with 2-proenamide. Its molecular structure is shown in Scheme 1.

Scheme 1. The molecular structure of 2-Propenoic acid, potassium salt, polymer with 2-proenamide.

In preparation for the rheological experiments, preselected dried SAP particles between 20- and 30-mesh were dispersed in 0.05%, 0.25%, 1.00%, and 10.00% sodium chloride solutions for 24 hours to achieve the maximum swelling. Because the density of both dried SAP and swollen SAP is higher than the density of brine, the swollen SAP always precipitated at the bottom of the centrifuge cell. The original and ultimate volumes of SAP in a centrifuge cell were recorded. The swelling ratio of the SAP was calculated from the following equation:

$S_{w}=\frac{V_{s}}{V_{d}}\times 100\%$

where Vs is the volume of swollen SAP and V0 is its original volume. Table 1 shows the ultimate swelling ratios for SAPs in various concentrations of brine.

Table 1. Swelling Ratios for SAP in Brine

 Brine Conc. (%) Swelling Ratio (%) Original Dia. (mm) Swollen Dia. (mm) 0.05 20455 0.595-0.841 3.506-4.955 0.25 9659 0.595-0.841 2.730-3.859 1.00 5682 0.595-0.841 2.287-3.233 10.00 3125 0.595-0.841 1.874-2.649

REFERENCES

1. Tang, H. (ChemEOR, Inc.) U.S. USPTO 20,070,204,989

2. Bai, B.; Liu, Y.; Coste, J.-P.; Li, L. SPE Res Eval & Eng 2007, 10, 415-422.

3. Das, M.; Zhang, H.; Kumacheva, E. Annu. Rev. Mater. Res. 2006, 36, 117-144.

4. Buchholz, F. L.; Graham, A. T. In Modern Superabsorbent Polymer Technology; John, Wiley & Sons, Inc.: New York, 1997; chapter 1, 7, pp 22.

5. Raju, K. M.; Raju, M. P.; Mohan, Y. M. Polym. Int. 2003, 52, 768-772.

6. Samchenko, Y. M.; Ul’berg, Z. R.; Komarskii, S. A. Colloid J. 2004, 66, 350-354.

7. Liu, Y.; Bai, B.; Wang, Y. Oil Gas Sci. Technol. – Rev. IFP. 2010. http://ogst.ifp.fr/index.php?option=article&access=standard&Itemid=129&url=/articles/ogst/pdf/first/ogst09046.pdf

## Schematic of Core Flooding Experiment

During this weekend, I tried to draw the schematic of core flooding experiments for transport of SAP through fracture models. This plot shows the basic elements in the core flooding experiments. Swollen SAP particles and/or brine were injected into the fracture model by the hydraulic pressure from the pumps. The flow rate of effluent from fracture and matrix were recorded with the various pressure on the different sections of the model. The major difference between fracture core model, glass bead pack, and transparent open fracture model is that for glass bead pack and transparent open fracture model, there is no outlet for fluid through matrix. The procedure should be almost the same.

Note: If the volume of water the pump can deliver each time and the volume of the swollen SAP particles are sufficient for one experiment, one set of pump and accumulator is needed only.

Figure 1. Schematic of Core Flooding Experiment for Transport of SAP through Fracture Models