EFFECT OF MOBILITY RATIO ON PATTERN BEHAVIOROF A HOMOGENEOUS POROUS MEDIUM

Y. Wang, A. R. Kovscek, and W. E. BrighamDepartment of Petroleum Engineering

Stanford UniversityStanford, CA 94305-2220

ABSTRACT

It is well known, for unit mobility ratio, that the areal sweep efficiency of a staggered-line-drive pattern is always better than a five-spot pattern. However, this observation does not hold forvery favorable mobility ratios. We present simulation results and, with the help of streamline andsaturation distributions, explain the differences between unit and favorable mobility ratios.Simulations compare well with experiments conducted elsewhere. Accurate definition ofbreakthrough time is also discussed for multiphase, streamline, simulation results. The exactdefinition of breakthrough is difficult due to physical dispersion in experiments and numericaldispersion in simulations.

INTRODUCTION Pattern geometry plays a major role in determining oil recovery during secondary and

enhanced oil recovery operations. Although simulation is an important tool for design andevaluation, the first step often involves rough calculations based upon areal sweep efficiencies ofdisplacements in homogeneous, two-dimensional, scaled, physical models1-3 . These results areavailable as a function of the displacement pattern and the mobility ratio, M. The mobility ratio issimply the mobility of the displacing phase over that of the displaced, or resident, phase. Becauseit is possible to compute sweep efficiency analytically when the displacing and displaced phasehave the same mobility4, 5 , scaled physical model results have been verified for unit mobility ratios.

Convincing verification of the non-unit mobility ratio cases does not appear in the literature.Typical finite difference solutions of the reservoir flow equations suffer from numerical dispersion,the effects of which are hard to evaluate. Furthermore, the scaled physical model results at lowmobility ratios (M << 1) are provocative. For instance, Fig. 1a shows that recovery from a five-spot pattern at breakthrough for 1/M greater than about 7.5 is virtually 100%, whereas recovery atbreakthrough in Fig. 1b for a staggered-line-drive pattern at an 1/M of 7.5 is a little more than88%. This contradicts the common notion that areal sweep efficiency from a staggered-line-drivepattern is always better than that from a five-spot pattern.

We use a 3D streamline simulator6 to analyze displacements in five-spot and staggered-line-drive patterns for stable displacements, that is M less than 1. In the following sections, we presentstreamline distributions, saturation distributions, and fractional flow at the producer versusdimensionless time, tD. The dimensionless time is equal to the number of pore volumes of liquid

2

injected. With the streamline and saturation distributions at different times, we explain why and atwhat mobility ratio the five-spot pattern can recover more oil than a staggered-line-drive pattern.

The streamline calculation method is advantageous in that the results suffer from much lessnumerical dispersion than typical finite-difference approximations, but some dispersion insimulation results is evident. Therefore, we discuss how to treat the numerical dispersion to obtainaccurate estimates of breakthrough times. We discuss the proper way to calculate fractional flowbased on the flow rates at the producer. In comparing the simulation results with the experimentalresults of Dyes et al 1, physical dispersion in the experiments is found even though a piston-likedisplacement was assumed.

SWEEP EFFICIENCY Before proceeding, it is useful to recall the representation of experimental data in Fig. 1 and

the meaning of sweep efficiency. Dyes et al.1 used various oils as both the injected and displacedphases. These hydrocarbons were miscible and they assumed piston-like displacement. An X-rayshadowgraph technique was used to observe the position of the displacing front. Areal sweepefficiencies are plotted versus displaceable pore volumes injected for different mobility ratios. Inthe figure, the x axis is the reciprocal of mobility ratio. Each curve in the graphs corresponds to aspecific tD / ∆ S , or displaceable pore volume injected. The bottom curves show sweepefficiencies at breakthrough. It is assumed that the displacement has a piston-like front and there isno physical dispersion. Likewise, the porous medium is assumed to be perfectly homogeneous.

For piston-like displacement, the areal sweep efficiency is

EA = AS / AT (1)

where As is the swept area and AT is the total area. Before and at breakthrough, the amount ofdisplacing fluid injected is equal to the displaced fluid produced, disregarding compressibility.Assuming piston-like displacement, injected volume is related to area swept

VI = AS hφ∆ S (2)

where VI is the volume of displacing fluid injected, h is the thickness of the formation, and φ isporosity. Hence,

EA = AS / AT = VI / (AT hφ ∆ S) = tD / ∆ S (3)

where tD = VI / (AT hφ ) is the pore volume of fluid injected, also commonly called dimensionless

time. For ∆ S = 1, EA = tD before and at breakthrough.After breakthrough,

EA = (VI − VP ) / (AT hφ ∆ S) (4)

where VP is volume of displacing fluid produced.

3

SIMULATION RESULTS We use a three-dimensional streamline simulator, called 3DSL, written by Batycky et al 6, 7

to simulate the displacement for the five-spot and staggered-line-drive patterns. It uses the pressurefield to decompose the flow problem into a series of streamtubes that span from injector toproducer and carry identical volumetric flowrates. In the simulations, we set the conditionsidentical to those in the experiments and choose relative permeability curves that ensure a piston-like displacement. The conditions are

1. Homogeneous permeability field, i.e., k is constant.2. Straight line relative permeability curves with end point relative permeability of 1, i.e.,

krw = Sw , k Sro o= (5).Therefore, krw + kro = 1 for any Sw.

4. Mobility is altered by changing viscosity, and the mobility ratio is the reciprocal ofviscosity ratio.

5. We set ∆ S = 1 which means that ahead of the displacing front, the displacing phasesaturation is zero, and behind the front, it is unity.

3DSL is very fast compared to conventional finite difference simulators and exhibits muchless numerical dispersion6, 7. For our problem, it offers us the streamline distribution whichfacilitates explanation of displacement behavior.

We use many pressure solves (time steps) and very fine uniform grids (100 by 100 cellsfor the five spot and 140 by 70 cells for the staggered line drive) to ensure converged simulationresults. A grid refinement study showed these grids to be optimal in that further refinement of thegrid did not yield noticeable changes in breakthrough time, the oil production curve, ordisplacement patterns8. For unit mobility ratio (M = 1), we actually only need one pressure solve.But for mobility ratios far from 1, we need many pressure solves. For 1/M = 20, we used up to1000 pressure solves to ensure that the results were converged. In the streamline approach, apressure solve is accompanied by a re-determination of streamline paths and, hence, the flow fieldon the underlying fixed grid.

Figure 2 displays areal sweep efficiencies as a function of pore volume injected fordiffering mobility ratios, and compares simulation and experimental results1. The solid lines aresimulation results, solid circles experimental results, and dotted lines connect circles for ease ofviewing. In this figure, we concentrate on only the favorable mobility ratios, M < 1. We noticedmore numerical dispersion for unfavorable mobility ratio cases, not reported here.

Figure 3 shows the displacing fluid fractional flow at the producer as a function ofdimensionless time for several mobility ratios. To compute fractional flow from the numerical datawe use a central finite-difference formula rather than backward differences. The shapes of thefractional flow curves at breakthrough (tD from roughly 0.7 to 1) indicate some numericaldispersion. We expect the fractional flow to increase sharply rather than gradually at waterbreakthrough. As expected, the numerical dispersion decreases as M becomes more favorable9.The most numerical dispersion occurs for unit mobility ratio, as shown in Fig. 3. We modify thebreakthrough time by trimming the numerical dispersion as will be described next.

4

BREAKTHROUGH DETERMINATION Due to numerical dispersion, injected fluid breaks through earlier at the producer than it

should. However, the numerical dispersion does not have much effect on the late-time displacingfluid production. The fractional flow versus tD plots shown in Fig. 3 illustrate the earlybreakthrough caused by numerical dispersion.

To correct for numerical dispersion in breakthrough times and approximate thebreakthrough time more accurately, we use fractional flow data after breakthrough which isrelatively free from the effects of dispersion and extrapolate back to the breakthrough time. A least-squares method is used with second order polynomials:

tD = a + bf w + cf w2 (6)

The data points employed lie between 0.1 < f w < 0.5. The dashed lines in Fig. 3 illustrate thisprocedure. All the breakthrough times reported here are modified using this method.

We caution that using the approach embodied in Eq. (6) to estimate the shape of the water-cut curve for times exceeding breakthrough incurs a mass balance error. The amount of productionprior to breakthrough that is trimmed from the original data is not added back to the productioncurve at later times. For this reason, we use Eq. (6) only to estimate breakthrough time and not toanalyze post breakthrough behavior.

Numerical dispersion is also related to the number of time steps (i.e., pressure solves). Inthe streamline approach applied here, dispersion can be introduced through the process of mappingthe streamline saturation distribution onto the underlying Cartesian grid used to compute thepressure field6. Hence, for a unit mobility ratio where the pressure field does not change, the mostaccurate results are obtained when a single time step is used. By performing various single timestep simulations, we determine a breakthrough time of 0.7178 for the five spot (d/a = 1/2) with Mequal to 1. This is in good agreement with the analytical solution4 of 0.7177. Likewise,analytically4 and numerically determined breakthrough times for a staggered-line-drive (d/a = 1)pattern are both equal to 0.785. With multiple time steps (50) breakthrough times were sooner, butusing the method discussed above, we obtain the same values for the breakthrough times, atM = 1.

DISCUSSION Comparing simulation results and experimental results in Fig. 2, we notice that

breakthrough occurs earlier in the experiments than predicted by the simulations. Note that theexperimental breakthrough time for the five spot at unit mobility ratio is 0.70 while the simulatedvalue agrees to within 4 significant figures with the analytical result. This discrepancy is consistentwith physical dispersion in the experiments. For the staggered-line-drive pattern in Fig 2b,experimental data indicates that EA at breakthrough is roughly 0.75 for M equal to 1. In theexperiments, there is physical dispersion even though a piston-like front is assumed. In thesimulation results presented in Fig. 2a, the sweep efficiency at breakthrough is 99.7% when 1/M =20. An almost negligible area immediately around the producer is not completely swept atbreakthrough due to either a very small amount of dispersion in the simulations or perhaps cuspingof the displacement front toward the production well (refer to Fig. 3, five spot, 1/M = 20).

5

After breakthrough, the differences in areal sweep efficiencies between the experiments andsimulations become much smaller (Fig. 2). After breakthrough, the numerical dispersion consistsof only a portion of the displacing fluid produced. As time increases, this portion decreases and thedispersion has less effect on areal sweep efficiency. However, the differences between theexperimental results and the simulation results are consistent, i.e. the areal sweep efficiencies of thesimulations are generally higher than those of the experiments. As shown in Fig. 2(a), thesimulated breakthrough curve levels off at large 1 / M with near zero slope, and does not exceed 1.However, the experimental curve shows EA equal to 1 at 1 / M equal to about 7.5. We note that inthe plot drawn by Dyes et al, the point where the breakthrough curve hits the EA equal to 1 line isonly an extrapolation from other data points (refer to Fig. 8 of ref. 1 or equivalently Fig. 6-2 of ref3).

Areal Sweep Efficiency Figure 4 plots computed breakthrough, tD , versus the conventional shape factor d/a for

various mobility ratios. The analytical solution for the unit mobility ratio4 is also plotted on thesame figure for comparison. We find a good match of the sweep efficiency at breakthroughbetween the analytical solution and simulation results. The greatest differences are about 1% at d/avalues of 0.75 and 3.0.

For unit mobility ratio, Fig. 4 teaches that a staggered-line-drive pattern (d/a = 1) alwayshas better areal sweep efficiency than a five-spot pattern (d/a = 1/2). As the staggered-line-drivepattern becomes longer relative to its width (d/a increases), the displacement pattern approacheslinear flow. High sweep efficiency results.

As the mobility ratio becomes more favorable, the advantage of staggered line drive onsweep efficiency diminishes. When the mobility ratio decreases to 0.2, the five-spot patternbecomes better than the staggered-line-drive pattern with d / a = 1. However, if d / a is increased,the staggered line drive recovery can be better than the five-spot pattern for this mobility ratio.

When the mobility ratio decreases to 0.05 or lower (very favorable), the areal sweepefficiency for the five-spot pattern is very close to 1 at breakthrough. That is, sweep out iscomplete at breakthrough. At this mobility ratio, the five-spot pattern is as good as a very longstaggered line drive (d a/ ≈ 15, almost linear flow), and much better than the common staggeredline drive (d / a = 1). The transition point for five spot sweep efficiency exceeding that from astaggered line drive is around a mobility ratio of 0.3. When the mobility ratio is higher than 0.3, astaggered line drive is always better than a five spot. If mobility ratio is lower than 0.3, then thefive spot can be higher in sweep efficiency than a staggered line drive.

These results are rooted in the geometry of each pattern. The symmetry of the five-spotpattern about the diagonal connecting injector and producer coupled with the favorable mobilityratio leads to almost perfect sweep of the pattern area at breakthrough. In the common staggeredline drive, a portion of the pattern is always left unswept at breakthrough regardless of the mobilityratio. Increasing d / a of the staggered line drive reduces the fraction of the pattern volume that isnot swept at breakthrough. Presentation and support of these observations form the core ofdiscussion for the remainder of this paper.

The excellent displacement from a five-spot pattern for very favorable mobility ratios isexplained with the help of streamline distributions. Streamlines are presented in equal incrementsof the stream function. Every pair of streamlines forms a stream tube, and the volumetric flow rateis the same in all of the stream tubes. Streamlines must extend from injector to producer. All of thestream tubes connect with the same injector and producer, and the pressure drop for all the

6

streamtubes is the same. With the same pressure drop and the same volumetric flow rate, the flowresistance is the same for all the streamtubes.

For our straight-line relative permeability assumption, we have

Ri = −∆p / q = µkA

dl0

Li∫ (7)

where Ri and Li are the resistance and length of streamtube i , respectively, that vary with time.The quantity k is the homogeneous permeability and A is the cross sectional area of thestreamtube. The cross-sectional area is

A = hw

where h is the constant thickness of the layer and w is the variable width of the streamtube.Resistance in streamtube i is the same as that in streamtubej and thus

µkA

dl C tLi

0∫ = ( ) (8)

for all the streamtubes at a given time, where C (t) is constant. Moving the constant parameters kand h to the right hand side, we have

µw

dl C tLi

0∫ = ( ) (9)

For a piston-like displacing front,

µ µ10

21 1

wdl

wdl C t

l fi

l fi

Li

∫ + ∫ = ( ) (10)

where µ1 and µ2 are the constant viscosities of the displacing and displaced fluids, respectively,

and l f i is the time-dependent distance from the injector to the displacing front.

Unit Mobility Ratio For a unit mobility ratio, the pressure field remains unchanged throughout the

displacement, and so do the streamlines. The streamline distributions at M = 1 for the five-spotand staggered-line-drive (d / a = 1) patterns are shown in Fig. 5.

For unit mobility ratio, Eq. (10) is

µ 1

0 wdl C

Li

∫ = (11)

and C is independent of time. From Eq. 11, we know that if the ith streamtube is longer than thejth streamtube, then the average width of the ith streamtube wi is greater to maintain the same

7

resistance and flow rate. Therefore, the volume of the ith streamtube is larger than the jthstreamtube. The greater the difference in streamtube length, the bigger the difference in streamtubewidth, and, when breakthrough happens in the jth streamtube, the front has not progressed as farin the ith streamtube.

For a five-spot pattern, the longest streamline is that along the boundary, which is 2a. Theshortest streamline is the one along the diagonal, at a length of 2 a . The ratio of the longeststreamtube length over the shortest is2 . The average width of the longest streamtube is obtainedby equating volumetric flowrates in the longest and shortest streamtubes, substituting Darcy'sLaw, employing the result above regarding the lengths of the longest and shortest streamtubes, andcanceling identical terms such as pressure drop. Hence, the average width of the longeststreamtube is also 2 times as great as the shortest streamtube and it follows that the volume ofthe longest streamtube is twice that of the shortest.

However, for a staggered-line-drive pattern with d/a = 1, the ratio of the length along theboundary (3a/2) over the diagonal( / )5 2a is 3 / 5 ≈ 1.34 . From the streamline distribution inFig. 5, we know that the shortest streamline is longer than diagonal5, and therefore the ratio of thelongest streamline over the shortest is less than 1.34. This ratio is about 1.3 and, therefore, lessthan that for a five-spot pattern which is 1.41. The streamlines are more evenly distributed in thestaggered-line-drive than in a five-spot pattern. Therefore, when the shortest streamtube breaksthrough, a larger portion of the other streamtubes have been swept in a staggered-line-drive than ina five-spot pattern. When d / a increases, the streamtube length ratio (longest to shortest)decreases. When breakthrough happens in the shortest streamtube, a greater portion is swept in thelongest streamtube resulting in higher sweep efficiency at breakthrough.

Five-Spot Pattern, Very Favorable Mobility Ratio For a favorable mobility ratio (M < 1), the displacement is stable. For equal volumetric

flow rate streamtubes, Eq. 10 holds. Here, we consider the case of very favorable mobility ratio,i.e., the displacing fluid viscosity is much higher than that of the displaced fluid. When the frontmoves a portion of the way down the streamtube, the pressure drop is mainly in the displacingphase. After a short injection time (compared to breakthrough), the pressure drop in the displacedphase is negligible. Therefore, Eq. 10 can be simplified to the following form

1

0 wdl C t

lti

∫ ≅ ( ) (12)

In this extreme case, the displacement front is not influenced by the producer until the front is veryclose to the producer because the pressure drop between the front and the well plays a negligiblerole in the displacement (c.f., ref 10 for a discussion of cusping when M is near but not equal to 0).Initially, flow around the injector is radial, because the pattern appears to be infinite at short times.For example, examine Fig. 6b for tD = 0.583. However, after the front reaches a corner of thepattern, the no-flow boundary condition along pattern borders alters the radial flow pattern.Pressure isobars must intersect the no-flow boundaries at 90o. This constrains the streamlines inthe region adjacent to a boundary to be parallel to the boundary. Because the fluids areincompressible, streamlines cannot terminate. The flow field in the region near the front transitionsfrom radial to quasi-radial. From the figure, we also see that streamtubes ahead of the front arenarrower along the boundary than those in the center, which makes the front in the boundary

8

streamtubes move faster than in the central streamtubes. Little area is unswept and the sweepefficiency at breakthrough approaches unity.

As in the previous discussion, a long streamtube must be wider in the swept region, ascompared to a short streamtube, in order to maintain equal resistance (same flow rate and pressuredrop) in all streamtubes. Therefore, the streamtubes along the boundary widen near the corners.Streamlines must remain smooth as is apparent in Fig. 6b.

In summary, the very favorable mobility ratio conspires with boundary conditions todetermine streamline paths and displacement patterns. Since the mobility ratio is very favorable, thedisplacement front is not influenced by the production well and remains very similar in shape to thepressure isobars until immediately prior to breakthrough. Thus, sweep efficiency at breakthroughis near unity.

Staggered Line Drive, Ver y Favorable Mobility Ratio For the staggered-line-drive pattern, the displacement at the beginning is similar to that in

the five-spot pattern. That is, the displacement pattern is radial around the injector before the frontreaches the nearest corner. The differences in displacement behavior between the two patternsoccurs after the front reaches the near corner. For a five spot, because of the symmetry, the frontreaches the two corners at the same time. However, for a staggered line drive, the front reaches theclosest corner first.

After the front passes the near corner, the streamlines evolve in a way similar to the fivespot. The streamtubes along the boundary are wide near the corner but narrow near the front.This makes the front near the boundary move faster because the streamtubes are narrower thanthose in the center of the pattern. Therefore, the front near the boundary on the near no-flow cornerside catches up, and the displacement approaches linear flow (see the relevant streamlinedistribution in Fig. 7 at tD = 0.60 and 0.80). If the aspect ratio is large, flow in the center of thepattern must become nearly linear because the pressure isobars are nearly straight and intersect thepattern boundary at 90o.

Similar to the discussion above for a five-spot pattern, for a very favorable mobility ratio,the displacing front is perpendicular to the borders of the pattern both before and after the frontpasses the nearest corner. As a result, we see linear displacement for some time until the front onthe near-corner side approaches the producer as shown in Fig. 7.

When the front approaches the producer, the streamtubes narrow due to the confinement ofthe pattern boundary and the well. And therefore, with the same flow rate, the displacing fluid willbreak through relatively quickly in the streamtubes closest to the producer. The front on the far no-flow side progresses more slowly. This streamline distribution does not change greatly as themobility ratio becomes more favorable. Sweep out of the pattern is not complete at breakthrough.For instance, a small amount of the resident fluid remains along the right hand boundary as shownby the saturation distribution in Fig 7a at tD = 0 94. .

If the length of staggered line drive is increased (increasing d / a ), then the displacementwill approach linear flow and the sweep efficiency at breakthrough will approach unity. Theproportion of unswept area decreases as d / a increases.

With the piston-like displacement behavior now well understood, an obvious extension ofthis work is to consider sweep efficiency for the more general case of non piston-likedisplacements. For displacements with M close to 1, we expect that fractional flow versus timecurves at the producer could become more spread as the amount of oil displaced by the frontdecreases and significant oil production from each streamtube continues after breakthrough.

9

However, for very favorable mobility ratios, the large viscosity of the displacing phase dominatesdisplacement behavior. It is very hard to achieve a displacement front that is not piston like in thislimit. Recovery from a five-spot pattern will remain near 1 at breakthrough for very favorablemobility ratios.

CONCLUSIONS Pattern performance changes with mobility ratio. For unit mobility ratio, unfavorable

mobility ratios and some favorable mobility ratios (M > 0.3), a common staggered-line-drive (d/a= 1) pattern has larger areal sweep efficiency than a five-spot (d/a = 0.5) pattern. However, forvery favorable mobility ratios (M < 0.3), a five-spot pattern has better sweep efficiency than acommon staggered-line-drive.

The reason for this behavior is the evolution of the pressure distribution and the resultingstreamlines with mobility ratio. For very favorable mobility ratios, the displacing front nearlyparallels an isobar and intersects the pattern boundary at 90o. This causes the fronts at times nearbreakthrough to become radial around the producer for a five-spot pattern. This displacing frontshape is due to the symmetry of the five-spot pattern.

For a staggered line drive undergoing displacement at a very favorable mobility ratio, thedisplacing front is also perpendicular to the border of the pattern. However, because the pattern isnot symmetric, sweepout at breakthrough is not complete. Only in the limit of very large d/a willthe areal sweep efficiency approach 1.

The simulation results are quite close to the analytical solutions for unit mobility ratio. Theresults are also very close to the experimental data, Dyes et al1, after breakthrough at variousmobility ratios. We find physical dispersion in the Dyes et al experimental results that causesearlier breakthrough time.

We observed some numerical dispersion in our simulation results. For very favorablemobility ratios, the dispersion is small. We corrected the simulation results by fitting the fractionalflow curves with second order polynomials to estimate breakthrough times.

ACKNOWLEDGMENT We thank R. P. Batycky, M. R. Thiele, and M. J. Blunt for making 3DSL available and forhelpful discussions. This work was supported by the Assistant Secretary for Fossil Energy, Officeof Oil, Gas, and Shale Technologies of the U.S. Department of Energy under contract No. DE-FG22-96BC14994 to Stanford University. Likewise, the support of the SUPRI-A IndustrialAffiliates is gratefully acknowledged.

NOMENCLATURE A area, L2

AS area swept, L2

AT total area of the pattern, L2

a distance between like wells (injection or production) in a row, Ld distance between adjacent rows of injection and production wells, LEA areal sweep efficiencyfw fractional flow of waterh bed thickness, L

10

k permeability, L2

kro relative permeability of oilkrw relative permeability of waterl length, LLi length of stream tube i, Llfi distance of the displacing front from the injector in stream tube i, LM mobility ratiop pressure, M/L• T2

q flow rate, L3/TRi flow resistance of stream tube i, M/L4• TS saturationSw water saturationtD dimensionless timeVI volume of displacing phase injected, L3

w width of a stream tube, L

φ porosityµ viscosity, M/L• T

REFERENCES

1. Dyes, A.B., B.H. Caudle, and R.A. Erickson, "Oil Production after Breakthrough--asInfluenced by Mobility Ratio," Petroleum Transactions AIME, 201, 27-32, (1954).

2. Craig, F.F.Jr., The Reservoir Engineering Aspects of Water Flooding, Society of PetroleumEngineers Monograph, Dallas, TX, 1971.

3. Lake, L.W., Enhanced Oil Recovery, Prentice Hall Inc., Englewood Cliffs, NJ, 1989.4. Morel-Seytoux, H.J., "Unit Mobility Ratio Displacement Calculations for Pattern Floods in

Homogeneous Medium," Soc. Pet. Eng. J., 6, 217-227, (1966).5. Prats, M., "The Breakthrough Sweep Efficiency of the Staggered Line Drive," Trans. AIME,

207, 67-68, (1956).6. Batycky, R.P., M.J. Blunt, and M.R. Thiele: "A 3D Streamline Simulator with Gravity and

Changing Well Conditions," SPE 36726, in Proceedings of the Soc. Pet. Eng. Ann. Tech.Conf. and Exhibition, Denver, CO (Oct. 1996).

7. Thiele, M.R., R.P. Batycky, M.J. Blunt, and F.M. Orr Jr., "Simulating Flow inHeterogeneous Systems Using Streamtubes and Streamlines," Soc. Pet. Eng. Res. Eng., 11,5-12, (1996).

8. Wang, Y., "A Study of the Effect of Mobility Ratios on Pattern Displacement Behavior andStreamlines to Infer Permeability Fields", MS Report Dept of Petroleum Engineering, StanfordUniversity, 1998.

9. Peaceman, D.W., Fundamentals of Numerical Reservoir Simulation, Elsevier ScientificPublishing Co., New York, 1977.

10. Claridge, E.L., "Prediction of Recovery in Unstable Miscible Flooding," Soc. Pet. Eng. J. ,12, 143-155, (1972).

11

(a) Five Spot Pattern (b) Staggered Line Drive, d/a = 1

0.5

0.6

0.7

0.8

0.9

1.0A

real

Sw

eep

Effi

cien

cy

10-1 1 10Reciprocal of Mobility Ratio, 1/M

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

aa

a

a

a

aa

a

a

a

a

a

aa

a

a

a

aa

Breakthrough

0.8

1.0

1.21.41.61.82.0

tD/∆S

0.5

0.6

0.7

0.8

0.9

1.0

Are

al S

wee

p E

ffici

ency

10-1 1 10Reciprocal of Mobility Ratio, 1/M

a

a

a

a

a

a

a

aa

a

aa

a

a

aa

a

a

a

a

a

aa

a a a a a

a

a

a

a

a

aa

aa

a

aa

a

aa

a

a

aa

a

aa

a

aa

a

a

a

aa

aa

Breakthrough

0.8

1.01.2

1.41.61.82.0

tD/∆S

FIG. 1 Dyes et al experimental areal sweep results.

12

(a) Five Spot Pattern (b) Staggered Line Drive, d/a = 1

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Are

al S

wee

p E

ffici

ency

1 10Reciprocal of Mobility Ratio

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

SimulationDyes et alBreakthrough

0.8

1.0

1.21.41.61.82.0

tD/∆S

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Are

al S

wee

p E

ffici

ency

1 10Reciprocal of Mobility Ratio

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa

a

a

a

a

a

a

a

a

a

a

aa

a

a

SimulationDyes et al

Breakthrough0.8

1.0

1.21.41.6

tD/∆S

FIG. 2 Comparison of simulated and experimental areal sweep behavior

13

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

5 spot,1/M=1

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

b

bbbbbbbbbbbbbbbbbbbbb

a

b

Original dataExtrapolation

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

5 spot, 1/M=2

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a

a

a

a

a

a

a

a

a

a

a

aaaaaaaaaaaaaaaa

b

b

b

b

b

b

b

b

b

b

b

bb

a

b

Original dataExtrapolation

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

5spot, 1/M=3

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a

a

a

a

a

a

a

a

a

a

a

a

a

aaaaa

b

b

b

b

b

b

b

b

a

b

Original dataExtrapolation

0.0

0.2

0.4

0.6

0.8

1.0

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

5spot, 1/M=20

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a

a

aaaaa

a

b

Original dataExtrapolation

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

Staggered, 1/M=1

a a a a a a a a a a a a aa

a

a

a

a

a

a

a

a

a

a

a

a

b

b

b

b

b

b

b

a

b

Original dataExtrapolation

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

Staggered, 1/M=2

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a

a

a

a

a

a

a

a

a

a

a

a

aaaaaaaaaaaaaaaaaa

b

b

b

b

b

b

b

b

b

b

b

b

b

a

b

Original dataExtrapolation

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

Staggered, 1/M=3

a a a a a aa a a a a a a a a a a a a aa

a

a

a

a

a

b

b

b

b

a

b

Original dataExtrapolation

0.0

0.1

0.2

0.3

0.4

0.5

0.6

f-w

0.5 0.6 0.7 0.8 0.9 1.0tD

Staggered, M=20

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

b

bb

b

b

b

b

b

b

b

b

b

b

b

b

b

b

a

b

Original dataExtrapolation

FIG 3. Fractional flow versus dimensionless time at producer -- determination of breakthrough time

14

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Are

al S

wee

p E

ffici

ency

1 10Aspect Ratio, d/a

a

a

a

a

a

a

a

aa

b

b

b

b

b

b

b

b

a

aa

a

a

aa

a

a

aa

a

aa

a

a a

a

a

a

b

a

a

a

a

M = 1.00M = 1.0, AnalyticalM = 0.33M = 0.30M = 0.20M = 0.05

FIG. 4 Effect of mobility ratios and pattern geometry on areal sweep efficienc yat breakthrough.

15

(a) Five Spot Pattern

(b) Staggered Line Drive

tD = 0.204

tD = 0.408

tD = 0.612

tD = 0.68

tD = 0.714

tD = 0.748

tD = 1.02

aa a a a a aa a a a aa

a a a a aa a a a a

a aa a a aa a a a a

a a aaa aa a a a a

a a aaa aa a a a

a aaa aa a a

a aaaa a a

aaaa a

aaaa a

aaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa a aa a aa

a a aa a aa

a a aa a aa

a a aa aaa

a a aa aaa

a a aa aaa

a a aaaa a

a a aaa a

a aaaa

a aaaa

a aaa a

aaaa a

aaa aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa a aaaa

a aaaa

a aaaa

a aaaa

a aaaa

a aaaa

a aaa a

a aaa a

a aaa a

a aaa a

aaaa a

aa aaaa

a aaaa aaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa aaaa

a aaa a

aa aa aa

a aaa a

a aaa a

aa aaaa

a aaa a

aaaa a

aaa aaa

a aaa a

aaa aaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa aaa

aaaa aaa

aaaaaa

a aaa

aaaaaa

a aaa

aaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a

aaaa aa

a aaaa

a aa aaa

a a aaaa a

a a a aaaa a a

a a a aa aaa a a

a a a a aaaa a a a

a a a a aaaa a a a

a a a a aa aaa a a

a a a a aa aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a aaa a

aa aa aa

a aaaa

a aaaa

a aa aaa

a a aaa a a

a a aaa a a

a aaaa a a

a aaaa a a

aaa aa a a

aaa aa a a

aaa aa a aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaa a

aaa aaa

a aaa

a aaa a

a aaa a

aaaa a

aaaa a

aa aa a

aa aa aa

a aa aa

a aa aa

a aa aa

a aa aa

a aaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaa

aaaa aaa

aaaa a

aaa aaa

a aaa a

aa aaaa

a aaaa aaa

a aaa

a aaa

a aaa a

aaaa aa

a aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaa

aaaa

aaaaaa a

aaaaaa

aaa aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

tD = 0.208

tD = 0.416

tD = 0.624

tD = 0.763

tD = 0.783

tD = 0.797

tD = 0.832

tD = 1.04

aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a a a aa a

aaa

aa

aa

a

aaa

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a a a a a a a aaa a a a a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aaa a a a a a a a a a a a aa a a a a aa a

aaaaaaa

aaaaaa

aa

aaa

aaa

a

aaa

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a aaa a a a a a a aa a a a a a a a a a aaa a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a aaa a a a a a a a a a aaa a a a a aa a a a aaaaaaaaaaaaaaaaa

aa

aaa

aaa

aaa

a

aaa

a

aaa

a

a

a

aa

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

a

a

aa

aa a a a aa a a a a aa a a a a a aaa a a a a aaa a a a a a a a aaa a a a a a a a a a a a aa a a a a a a a a a a a a a aa a a a a a a a a aaa a a a a aa a

a a aa aaaaaaaaaaaaaaaaaaaaaa

aaa

aa

a

aa

a

aaa

a

aaa

a

aaa

a

a

aaa

a

a

aaa

a

a

a

aa

a

a

a

aa

aa a a aaa a aaa

a a aaaa a a aa a a a a aa a a a a a aa a a a a a a a aa a a a a a a a a a a aa a a a a a a a a a a aa a a a a a a a aa a a a a aaa

a a aaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aaa

aaa

aaa

aaa

a

aaa

a

aa

a

a

aaa

a

aaa

a

a

aaa

a

aa

aa a aaaa aa

a a aa a a aaaa a aa a a a aa a a a a aa

a a a a aaa a a a a a aaa a a a a a a a aaa a a a a a a a a aa a a a a a a aa aa a a aaa

a a aaaaaaaaaa

aaa

aaaaaaaaaaaaa

aa

aa

aaa

aa

a

aa

a

aa

a

aa

a

aaa

aaa

a

aaa

a

aa

a

a

aa

a

aa

aa aaaaaaaaaaaaaaaaaaa aa a a aaa

a a aa a a a aaaa a a a aa

a a a a a aaa a a a a a a aaa a a a a a a aaa a a a a a aa a a a a aa a a a aaaa aaaaaaaaaaaaaa

aa

aaaaaaaa

aa

aa

aaa

aa

aaa

aaa

aaa

aaa

aaa

aaa

a

aa

a

aaa

aa

aaaaaaaaaaaaaaaaa

aaaaa aaaaaaa a aa

a a aaaa a aaa

a a a aaaa a a a aaa a a a a a a aa a a a a a a aa a a a a a aa a a a a aa a a aaa

aaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaa

aa

aaa

aa

aaa

aaa

aa

a

aa

a

aa

a

aa

a

aa

aa

aaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a a aa a a a aa a a a a aaa a a a aaa a a a a a aa a a a a a aaa a a a a aaa

a a a aa a a a aaaa aaaaaaaaaaaaaaaaaaa

aaaaaaaa

aa

aa

aa

aaa

aa

aaaaa

aaa

aa

aaa

aaa

aa

aa

aaaa

aaaaa

aaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaa a aaa

a a aa aa a a aa

a a a a aa a a a a a aa a a a a a aaaa a a a aa a a a aaa

a a aa a aaaaa aaaaaaaaaaa

aaaaa

aa

aa

aaaaaa

aa

aa

aa

aaaaa

aa

aaa

aa

aaa

aa

aaaa

aaaaaa

aaaaaaaaaaaaaaaaaaaaaaa

aaa

aaaaaaaaaaa a aaa

a a aa a a a aaaa a a aaa

a a a a aaaa a a a aaa

a a a aaaa a a aa a a a aa

a a aaaaaaaaa

aaa

aaaaaaaa

aaaaaaaaaaaaaaaaaa

aa

aa

aaaaa

aa

aaaaaa

aaaaaaaaaa

aaaaaaa

aaaaaaaaaaaaaaaaaa

aaaaaaaaaaaa aa a a aaa

a a a aaa a a a aa

a a a a aaaa a a a aa a

a a a aaaa a a aa a a aaa

a aaaaaaaaaaaaa

aaa

aaaaa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaa

aaa

aa

aaaaaaaaaaaaa

aaaaaaa

aaaaaaaaaa

aaaaaaaaaaaaaaaaa

a a aa a a a aa a a a a aa a a a a aaaa a a a aa a

a a a aaaa a a aa a a aaa

a a aaaaaaaaaaaaaaaaaa

aaaaa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

aaa

a

aa

aaaaaa aa a a a a a a a a aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

a

aa

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

aaa

a

aaa

aaa

aa

aaaa

aaaaaaaaa a aa a a a a aaa a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aaa a a a a a a a a a a a a a a a a a a aaa a a a a a a a a a a a a

a

aa

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

aaa

a

a

a

aa

a

a

aaa

a

aaa

aaa

aaa

aa

aaaaaa

aaaaa

aaaaaaa

a a aa a a a a a aa a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a aaa a a a a a a a a a a a a a a aa a a a a a a a a a aa a a a a a a a aa a a a a a aa

aa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

aaa

a

aaa

a

aaa

a

aa

a

aa

aaa

aa

aaaaaaaaaa

aaaaaaaaaa aa a

a a aa aa a a a aa a a a a a a a a aaa a a a a a a a a a a a a aaa a a a a a a a a a a a aa a a a a a a a aaa a a a a a aaa

a a a a aa a a a a aa a a a aa

aa

a

aaa

a

a

aaa

a

aaa

a

aaa

a

aaa

a

aa

a

aaa

aaa

aaa

aa

aaaaaaaaaaaa

aaaaa

aaaaaaaa aa a a a aa a a a a aaa a a a a a a a aa a a a a a a a a a a aa a a a a a a a a a aaa a a a a a a aa a a a a a aa a a a a aa a a a aaa

a a aaaa a aa a

a aa

aa

a

aa

a

a

aa

a

aaa

a

aaa

aaa

a

aa

a

aa

a

aa

aaa

aaaaa

aa

aa

aa

aa

aaaaaaa

aaaaaaaaaaa aa a a a aa a a a a aaa a a a a a a aa a a a a a a a a aa a a a a a a a a aa a a a a a a aa a a a a aaa

a a a aa a a a aa a a aaaa a aa a

aaaaaaa a aa

aa

aaa

a

aa

a

aa

a

aaa

aaa

aaa

aaa

aa

aaa

aaaaa

aa

aa

aa

aa

aa

aaaaa

aaaaaaaaaaaaa aaa

a a aaaa a a a aa

a a a a a aaa a a a a a a aaa a a a a a a aaa a a a a a aaa a a a aa a a a aa a

a a aa a a aa aaaaaaaaaaaaaaaaaaaaa

aa

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aa

aaaaa

aa

aaaaaaaaaaaa

aaaaa

aaaaaaaaaa aaa a aa a a a aa

a a a aaaa a a a a aa a a a a a a aa a a a a a a aa a a a a a aa a a a a aa a a a aa a a aaa

aaaaaaaaaaaaaaaaaaaaa

aaa

aaa

aa

aa

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aa

aa

aa

aa

aaaaaaa

aaaaaaaa

aaaaaaaa a aa

a a aaaa a a aaa

a a a a aaa a a a a a aa a a a a a aaaa a a a aa a a a aaa

a a aaaa aaa

aaaaaaaaaaaaaa

aaaaaaaaa

aaa

aaaaaaa

aaaa

aa

aaa

aa

aaa

aa

aa

aaaaa

aa

aa

aa

aa

aa

aaaaaaa

aaaaa

aaaaaaaaaaaaa a aaa

a a aaaa a a aa a a a a aaa

a a a a a aa a a a a a aaa a a a aa a a a aaa

a a aa a aaaaaaaaaaaaaa

aaaaaaaaa

aaaaaaaa

aaaaaaaa

a

aaaaaa

aa

aaaaaaa

aa

aa

aaaaaaaaaaaa

aaaaaaa

aaaaa

aaa

aaaaaaaaaaa a aa a a aaa

a a a aaaa a a a aa

a a a a a aaa a a a aaa

a a a aaaa a aaa

a a aa aaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaa

aaaaa

aaaaaaaa

aaaaaaaaaaaa

aa

aa

aa

aa

aa

aaaaaaaaa

aaaaaaaaaa

aaa

aaa

aaaaa aa

a a aa a a a aa a a a aaaa a a a aa a a a a a aa

a a a a aa aa a a aa a a a aa a a aaa

aaaaaaaaaaaaaaaaaaaaaa

aaaaa

aaaaaaa

aaaaaaaaa

aaa

aaa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaa

aaaaa

aaaaa

aaaaaaaaaaaaaa aa

a a aa a a a aa a a a aaaa a a a aa a a a a a aa

a a a a aa aa a a aa a a a aa a a aa a

aaaaaaaaaa

aaa

aaa

aaaaa

aaaaa

aaaaaaaaaaaaaaa

aa

aa

aaa

FIG. 5Streamline and saturation distributions, unit mobility ratio.

16

(a) Saturation Distribution

(b) Streamline Distribution

tD = 0.583

tD = 0.796

tD = 0.837

tD = 0.878

tD = 0.918

tD = 0.938

tD = 0.969

tD = 0.998

tD = 0.583

aa a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a aaa a a a a a a a a a a aa

aaaa

aa

aa

aa

a

aa

a

a

aa

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a aa a a a a a a aa a a a a a a aa a a a a a a aaa a a a a a aaa a a a a a aaa a a a a a aa a a a a a aaa

a a aaaa

aa

aaa

aaa

a

aaa

a

a

a

aa

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

aaa

a

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

a

a

aa

aa a a aaaa a a aa a a a aaa

a a a aa a a a aaaa a a aa a a a aaa

a a a aa a a a aaaa a a aa a a a aa a a a aaa

a aaa a

aaa

aaa

a

aa

a

a

a

aa

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

aaa

a

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

aa

aa a aaaa aaa

a a aaa a aa

a a aaaa a aa

a a aaa a aa

aa aaa

a a aaaaaaaaaaaaaaaaaaaaa aa

aa aa

aaaaaaa

aaa

a

a

aa

a

a

a

aaa

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

aa

a

a

aaa

a

a

aa

a

a

aa

a

a

aaa

a

aaa

a

aa

aaa aaaaaaa aaaaaaa aa

aaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a

a

aaa

a

a

a

a

aa

a

a

a

a

aa

a

a

a

aa

a

a

aaa

a

aaa

a

aa

a

a

aa

a

aaa

a

aa

a

aaa

a

aaa

a

aa

a

aaa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaa

aaa

aaa

aaa

aaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

a

a

aaa

a

a

a

aaa

a

a

aaa

a

aaa

a

aa

a

aaa

a

aa

a

aa

a

aaa

aaa

aaa

aaa

aaa

aaa

a

aa

a

aa

aa

aaaa

aaaaaaaa

aaa

aaaaaaaa

aaaaaaaa

aaa

aaaaaaaa

aaaaaaaa

aaaaaaaa

aaa

aaaaa

aaa

aaaaa

aaa

aaaaa

aa

a

a

a

aa

a

a

a

aa

a

aaa

a

aa

a

aaa

aa

a

aa

a

aa

aaa

aaa

aaa

aa

aaa

aaa

aa

a

aa

aaa

aa

aa

aaaaaa

aaaaa

aaaaa

aaaaaaaaaaaa

aaaaa

aaaaa

aaaaaaa

aaaaa

aaaaa

aaaaaaaaaaaa

aaaaa

aaaaaaa

aaaaa

aaa

a

a

aaa

aaa

a

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aa

aaa

aa

aaaa

aaaaaaaa

aa

aaaaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aaaaaa

aaa

aaa

aaa

aa

aa

aaa

aa

aa

aaaaa

aa

aaaaaaa

aa

aa

aaaaa

aa

aa

aaaaaaaa

aaa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

aaa

aaa

aa

aa

aaaaaaa aa a a a a a aa a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a

a

aa

a

a

a

a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

aaaa

aaaaaaaaaaaa

a a a aa aa a a a a a aaa a a a a a a a a a aa a a a a a a a aaa a a a a a a aa a a a a a a aa a a a a a a

a

aa

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

a

aa

a

a

a

aa

aaaa

aaaaaaa a a aa a

a a a a aa a a a a a a aaa a a a a a aaa a a a aa a a a a aa a a a aaa

a a a aa a a a aaaa a aa

aa

a

aaa

a

aaa

a

a

aa

a

a

aa

a

a

aaa

a

aaa

a

aaa

a

a

aa

a

a

aa

a

a

aaa

a

aaa

a

a

aa

a

a

aa

a

a

aa

a

a

aaa

a

aaa

a

aaa

a

aaaaaa a aaa

a a a aa aa a a a aa a a a a aa a

a a a aaa a aaa

a a aa a a aaaa a aa

a aaaa a

aaa a

aaa a aa

aa

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aaa

aaa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

aaa

aaa a a aaa

a a a aaaa a a aaa

a a aaaaaaaaaaaaaaaaaaaa aaaaaaaaa

aaaaaaa

aaaaaa

aa

aa

a

aa

a

aa

a

aa

a

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa a a a aa

a a a aaaa a aa

aaaaaaaaaaaaaaaaaaaaaaaa

aaa

aaa

aaa

aaa

aaa

aaa

aa

aa

aa

aaa

aa

a

aa

aaa

aa

a

aa

aaa

aa

a

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aa

aaaa

a a a aa a aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaa

aaa

aaaaa

aaa

aaaa

aaaa

aa

aaaaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaaaa

aa

aaaaa

aaaaaaaaaaaaaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaaaa

aaaaa

aaaaa

a

aaaaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaa

aa

aa

aa

aaaaa

aa

aa

aa

aaaaa

aa

aa

aa

aaaaa

aa

aaaaaaaaaaa

aaaaa

aa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aaaaaaa

aaa

aaa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aaa

tD = 0.796

aa a a a a a a a a a a a a aa a a a a a a a a a a a a a aaa a a a a a a a a a a a a aa a a a a a a a a a a a aa a a a a a a a a aa a a a a aa

aa

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a aa a a a a a aaa a a a a a aa a a a a a a aa a a a a a aaa

a a a a a aaa a a a a aa

a a a a aaaa a a aaa

a a a aa a a a aaa a aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

aa

aa a a aaaa a a aa

a a a aa a a a aaaa a a aa a a a aa a a a aaa

a a aaaa a a aa

a a a aaa a aaa

a a aa a a aaaaa aa

aa aa

aaaaaaaaaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

aa

aa a aaaa aa

aaaaaaa aa

aa aa

aaaaaaaaaaaaaaaaaaa aaaa aa

aa aa

aa aa

aa aaaaaaaaaaaaa

aaaaaaa

aaaaaaaaaaaaaa

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

aa

a

a

aaa

a

aaa

a

aaa

a

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaa

aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaa

aa

aaa

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

aa

a

a

aa

a

a

aa

a

aaa

a

aa

a

aaa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaa

aaa

aaaaaaaaaaa

aaaaaaaa

aaaaa

aaaaa

aa

aaa

a

a

a

a

a

a

aaa

a

a

a

aaa

a

a

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aa

a

aa

aa

aaaa

aaaaaaaa

aaaaaaaa

aaaaaaaa

aaaaaaaa

aaaaaaaa

aaaaaaaa

aaaaaaaa

aaaaa

aaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaa

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

aa

a

aa

a

aa

a

aa

aaa

aa

a

aa

aaa

aa

aa

aaaaaa

aaaaa

aaaaaaa

aaaaa

aaaaa

aaaaaaa

aaaaa

aaaaaaa

aaaaa

aaaaaaa

aaaaaaa

aaaaa

aaaaaaa

aa

aaaaaaa

aaaaaaa

aa

aaaaaa

a

a

a

a

a

a

a

a

aaa

aaa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaaa

aaaaaaaaaa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aaaaaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaaaa

aa

aa

aaaaaaaaaaa

aa

aa

aaaaaaaa

a

a

aaa

a

aa

aaa

aa

aaa

aa

aa

aaaaaaa

aa

aa

aaaaaaaa

aaa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaa

aa

aa

aaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

aaa

a

a

a

a

aa

aaa a a a a a a a a a a aaa a aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a

a

aa

a

a

a

a

aaa

a

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

aaa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a aa a a a a a a

a

aa

a

a

aaa

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

a

aa

a

a

a

aa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

aa

a

a

aaa

a

a

aa

a

a

aaa

a

aaa

a

aa

a

aaa

a

aaa a a a a a a a a a a a a a a a a aaa a a a a a a a a a a a a a aaa a a a a aaa

a a a aa aa a aaa

a a aa

aa

a

aaa

a

aaa

a

aaa

a

aaa

a

a

aa

a

a

aa

a

a

aa

a

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aa

a

a

aa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aa

aaa a a a a a a aaa a a a a a a a a a a a a a a a a a a a a aa a a a aa a a aaa

aaaaaa aa a aa

aa

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aaa

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aa

aaaaa a a a a a a a aa a a a a a a a a a a a a aaa

a a aaaaaaaaaaaaaaaaaaaaaaa

aa

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aaa

aaa

aa

a

aa

a

aa

aaa

aaa

aa

aaa

aa

a

aa

aaa

aa

aaaaaaa a a a a a a aa a a a a a a aaa

a a a aaaaaaaaa

aaa

aaa

aaaaaaaaa

aa

aa

aa

aaa

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aa

a

aa

aaa

aa

a

aa

aaa

aa

aaa

aa

a

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaaaaa a a a a a aaa a aa a a a a aa

aaaaaaaaaaaa

aaa

aaaaaaaa

aaaa

aaaa

aa

aaaaa

aa

aaa

aa

aa

aaa

aa

aaa

aa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aa

aaa

aa

aa

aaa

aa

aa

aaaaa

aa

aaaaaaa

aa

aaaaaaa

aa a a aa a a aa a aa aaaaa

aaa

aaaaa

aaaaa

aaaaaaa

aaaaaa

aaaaaaaa

aa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aa

aaaaa

aa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aaaaaaaaaaa

aaa a a aa

aaaaaaaaaaa

aa

aaaaaaa

aa

aa

aaaaaaa

aaa

aaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaa

tD = 0.837

aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a a a a a aaa a a a a a a a a a a aa a a a a a a a a a a aa a a a a a a a a a aaa a a a a a a a aa a a a a a aa a a a aaa

aaaaaaaaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a aa a a a a a aa a a a a a aa a a a a a aa a a a a a aa a a a a aaaa a a a aa a a a a aa a a a aaa

a a aa aa a a

aaaaaaaaaaaaaaaaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

a

aa

aa a a aa a a a aa a a a aa a a a aa a a a aa a a a aa a a a aa a a a aa a a aaaa a aa a

a a aaaa aa

aaaaaaaaaa aaaaaaaaaaaaaaaaaaaa

aa

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

aa

a

a

a

aa

a

a

aa

aa a aaaaaaaaaaaaaaaaaaaaaaaaaaaa aa

aa aa

aa aaaaaaaaaaaaaaaaa

aaaaaaa

aaaaaaaaaa

aaa

aaa

aaaaaaaaaaa

aaaaa

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

aaa

a

a

aa

a

a

aa

a

a

aa

a

aa

aaaaaa aa

aaaaaaaaaa

aaaaaaaaaa

aaaaaaaaaa

aaaaaaaaaa

aaa

aaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaa

aaaaa

aaaaa

aa

a

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

aaa

a

a

a

a

aa

a

a

aa

a

aaa

a

aa

a

aa

a

aaa

aa

aaaaaaa

aaa

aaa

aaa

aaaaaaaaaaaaaaaaaaaaaaaaaa

aaa

aaaaaaaaaaaaaa

aaa

aaaaaaaa

aaaaa

aaaaaaaaaaaaaaa

aaaaa

aaaaaa

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

aa

a

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

aa

aaaa

aaaaa

aaaaaaaa

aaaaa

aaaaaaaa

aaaaa

aaaaaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aa

a

a

a

aaa

a

a

a

a

a

aaa

a

aaa

aaa

aaa

aaa

aa

aaa

aa

aaa

aaaa

aaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aaaaa

aaaaaaa

aaaaaaa

aaaaaaaaa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aaaaaaaaa

aa

aa

aa

aaa

a

a

a

aa

a

a

aa

a

aa

aaa

aa

aaa

aa

aa

aaa

aa

aa

aaaa

aaa

aaaaaaaaa

aa

aa

aaaaaaaaa

aa

aa

aaaaaaaaaaa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

a

a

aaa

aaaaa

aa

aaaaaaa

aa

aa

aa

aaaaaaa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

aaa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

a

aa

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

aaa

a

a

aa

a

aaa

aaaa a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a a a a a

a

aa

a

a

a

a

aa

a

a

a

a

aaa

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

a

aaa

a

a

a

a

aaa

a

a

a

aaa

a

a

a

aaa

a

a

a

aa

a

a

a

aa

a

a

aaa

a

aaa

a

aa

a

aaa

aaa

aaa a a a a a a a a a a a a a aaa a a a a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a aa a a a a aa

aa

a

a

aa

a

a

a

aa

a

a

a

aa

a

a

aaa

a

a

aaa

a

a

aaa

a

a

aaa

a

a

aa

a

a

a

aa

a

a

aaa

a

a

aa

a

a

aa

a

a

aaa

a

aa

a

a

aa

a

aaa

aaa

aaa

aaa

aaa

aa

aaa a

a a a a a a a aaa a a a a a a a a aaa a a a a a a a a a a aa a a a a a aa a a a aa a a a aa a a aa

aa

a

aa

a

a

aa

a

a

aa

a

a

aa

a

a

aa

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aa

a

a

aa

a

aaa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aa

aaa

aa

aa a a a aa a a a a a a aaa a a a a a a a a a a a a a a aa a a a aaaaaaaaaaaaaaa aa

aa

aaa

aaa

a

aa

a

aaa

aaa

a

aa

a

aaa

aaa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aaa

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aaa

aa

aaa

aaa

aa

aaa

aa

aaaaaa a a a a aa a a a a a a aa a a a a a aaa a a a aa

aaaaaaaaaaa

aaaaaaaaa

aa

aa

a

aa

a

aa

aaa

aaa

aaa

aaa

aaa

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aaa

aa

a

aa

a

aa

aaa

aaa

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaa a a a aa a a a a a a a a a a a aa a

aaa

aaaaaaaaaaaaaaaaaaaa

aaaa

aaa

aa

aaa

aa

aaa

aa

a

aa

aaa

aa

aaa

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaaaa

aa

aaaaa

aa

aa

aaaaaa a a aa a a a a a a aaa

aaaaaaa

aaa

aaaaaaaa

aaaaa

aaaa

aaaaaa

aa

aaa

aa

aa

aaa

aa

aa

aaa

aa

aa

aaa

aa

aa

aaa

aa

aaaaa

aa

aa

aaa

aa

aa

aaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

a a a a a a aaaaaaaaa

aaa

aaaaaaa

aaaaa

aaaaaaaa

aaa

aaaaaaa

aa

aa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa a aaaaaaaaa

aaaaaaaaa

aa

aa

aaaaaaaaa

aaa

tD = 0.878

aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a aaa a a a a a a a a a a a a a a a a aa a a a a aa

aaaa

aa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a a a a aa a a a a a a a a aaa a a a a a a a a aa a a a a a a a a aa a a a a a a aa

a a a a aa a a a aa aaaaaaaaaaaaaaa

aa

aaaaaaa

aa

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

aa

aa a a a aaaa a a a aa a a a a aaa

a a a a aa a a a a aaaa a a aaa

a a a aa a a a aaaa a aa a a

aaaaaaaaaaaaaaaaaa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

a

a

aaa

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

aaa

a

a

a

aa

aa a a aaa a aaa

a a aaaa a aa a

a a aa a a a aaa a aaa

a a aa a a aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaa

aaaaaaaaa

aa

aa

aaaaaaaa

aaa

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

aaa

aa

a

a

a

a

a

a

a

aa

a

a

a

aaa

a

a

aa

a

a

aa

aa a aaaa aa

aaaaaaaaaaaaaaaaaaaaaaa

aa aaaaaaaaaaaaaaaaaaaaaaa

aaa

aaa

aaa

aaaaaaaa

aaaaa

aaaaaaaaa

aaaaaaaaa

aa

aa

a

a

a

a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

aaa

a

a

a

aa

a

a

aa

a

a

aa

a

a

aa

a

aa

aaaaaaaaaaa

aaaaaaaaaa

aaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaa

aaaaaaa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaaa

aa

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

aa

a

a

aa

a

aaa

a

aa

a

aaa

aaa

aa

aaaaaaa

aaa

aaaaaaaaaaaaaaaaa

aaa

aaaaaaaaaaaaaa

aaa

aaaaaaaa

aaaaa

aaaaaaaaaa

aaaaa

aa

aaaaaaa

aaaaaaaaa

aa

aaaaaaaaa

aa

a

aaa

a

a

a

a

a

aa

a

aa

a

a

a

a

aa

a

aaa

aaa

aaa

aaa

aa

a

aa

aa

aaaa

aaaaa

aaaaa

aaaaaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aa

aaaaaaaaa

aa

aa

aaaaaaaaa

aa

aa

aa

a

aa

a

a

a

a

a

a

a

aa

a

aaa

aaa

aaa

aa

aaa

aaa

aa

aaaa

aaaaaa

aa

aaaaa

aaaaaaa

aaaaaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aa

aaaaaaaaa

aa

aa

aa

aaaaaaaaaaaaa

aa

aa

aa

a

a

a

a

a

aaa

a

aa

aaa

aa

aaa

aa

aaaaa

aa

aaaaaa

aaa

aaaaaaaaaaa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

a

a

aa

a

aa

aa

aaaaa

aa

aa

aa

aaaaaaaaa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

aaa

aaa

aa

aaaaa

aa aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

a

aa

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

aaa

a

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

aa

a

a

aa

a

aa

a

aa

aaaaaaaaaaaaaa

aaaaa a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a a a a

a

aa

a

a

a

aaa

a

a

a

a

aa

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

a

aa

a

a

a

a

aa

a

a

a

a

aa

a

a

a

aa

a

a

a

aa

a

a

aa

a

a

aa

a

aa

a

aa

a

aa

aaa

aa

aaaaaaaaaaaaaaaaaaaa a aa a a a a a a a a aaa a a a a a a a a a a a a a a a a a a a a aaa

a a a a aaaa a a aa

aa

a

a

aa

a

a

aaa

a

a

aaa

a

a

aa

a

a

a

aa

a

a

aaa

a

a

aa

a

a

aaa

a

a

aa

a

a

aaa

a

aaa

a

aa

a

aaa

a

aa

a

aa

a

aa

a

aa

aaa

aa

aaa

aa

aa

aaaaaaa

aa

aa

aa

aaaa aaa a a a a a aa a a a a a a a a a aa a a a aa a a a a a a aa a a a aaa

a a aa a a aa

aa

a

aa

a

aaa

a

aaa

a

aaa

a

aaa

a

aa

a

a

aa

a

aaa

a

aaa

a

aa

a

aaa

a

aaa

aaa

a

aa

a

aaa

aaa

aaa

aaa

aa

a

aa

aaa

aa

aaaaa

aa

aaaaa

aa

aa

aa

aaaaa

aaa a a a a aa a a a a a aa a a a a a a a a a aa

a a a aa aaaaaaaaaaaaa aa

aa

aaa

aaa

a

aa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aaa

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aaaaa a a a a a aa a a a a a a a a a a a aa a

aaaaaaa

aaaaaaaaaa

aa

aa

aa

a

aa

aaa

aaa

aaa

aa

a

aa

a

aa

aaa

aaa

aaa

aa

a

aa

aaa

aaa

aaa

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaa aa a a a a a aa a a a aa a a a

aaaaaaaaaaaaaaaaaaaaaa

aaaa

aa

aaa

aa

a

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aa

aaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaa a a a a a a a a aa

aaaaaaa

aaa

aaaaa

aaaaa

aaa

a

aaaaaa

aa

aaaaa

aa

aa

aaa

aa

aa

aaaaa

aa

aaaaa

aa

aa

aaa

aa

aa

aaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aaaaaaaa a a a a a aa

aaaaaa

aaaaa

aaaaaaa

aaaaaaaa

aaa

aaaaaaaaaaa

aa

aa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaa

aaaaaaaaaaa

aa

aa

aaaaaaaaaaa

aa

aaa

tD = 0.918

aa a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a a aaa a a a a a a a aaa

a a a aa aaaaaaa

aa

aa

aa

a

aa

a

aaa

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a a aaa a a a a a a a aa a a a a a a a aa a a a a a a aa a a a a a aaa

a a a aaaa a aa

aaaaaaaaaaaaa

aaaaaa

aa

aaa

aa

a

aa

a

aaa

a

aa

a

a

aaa

a

a

aa

a

a

aa

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

aa

aa a a a aa a a a a aa a a a a aa a a a a aa a a a a aaa a a aa a

a a aaaa a aa a a

aaaaaaaaaaaaa

aaaaaaaaaa

aa

aaaaaaa

aa

a

aa

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

aa

aa a aaaa a aa a a aaa

a a aa a a aaaa a aa a a aaa

aa aaaa aaaaaaaaaaa aaaaa

aaa

aaa

aaaaa

aaaaaaaaaaaa

aa

aa

aaa

aa

aaa

aa

a

aa

aaa

aa

aaa

aa

aa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

aa

a

a

aaa

a

aa

aa a aaaaaaaaaaaaa

aaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaa

aa

aa

aa

aa

aa

aaaaa

aa

aa

aaa

aa

aa

aaa

aa

aa

aaaaaa

aa

a

a

a

a

aaa

a

a

a

a

aaa

a

a

a

aaa

a

aaa

a

aaa

a

aa

a

aa

aaaaaaaaaaaaaa

aaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaa

aaaaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

a

a

a

a

a

a

a

a

aa

a

a

aaa

a

aa

a

aaa

aaa

aaa

aa

aaaa

aaa

aaaaaaaa

aaa

aaaaaaaaaaa

aaa

aaaaaaaa

aaaaa

aaaaaaaa

aaaaaaa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aaaa

a

a

a

a

a

a

a

a

aa

a

a

aa

a

aa

a

aa

aaa

aaa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaa

aaaaa

aaaaaaa

aaaaaaa

aaaaaaaaa

aa

aa

aa

aaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

a

a

a

a

aa

a

a

aa

a

aa

a

aa

aaa

aa

aaa

aa

aaaa

aaaaaaaa

aaaaaaaaa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aaa

a

a

aa

a

aa

aaa

aa

aaaaa

aa

aa

aaaaaa

aaa

aa

aaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaa

aaa

aa

aa

aa

aaaaaaaaaaaaa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

aaa

a

a

aa

a

aa

aaa

aa

aaaaa

aaa

aa aa a a a aaa

a a a a a a aa a a a a a a a aaa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

a

aa

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

a

a

aa

a

a

a

a

aa

a

a

a

aa

a

a

aa

a

aaa

aaa

aa

aaaaaaaaaa

aaaaa

aaa

aaaaaaaa a

aaaa a a

aaa aaaaa

a a a a a a a a a a a a a a a a a a a a a a a a aa a a a a a a aa

aa

a

a

a

aa

a

a

a

a

aa

a

a

a

aaa

a

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

aaa

a

aaa

a

aaa

a

aa

a

aa

a

aa

aaa

aa

aa

aaaa

aa

aaaaaaa

aaaaaaaaaaaaaaaaaa

aaa

aaaaa a a a a a a a a a a a a a a a a a a a a aa a a a a aa a a a aa

aa

a

aaa

a

a

aa

a

a

aaa

a

a

aa

a

a

aaa

a

aaa

a

a

aa

a

a

aa

a

a

aaa

a

aa

a

aaa

a

aa

a

aaa

aaa

aa

a

aa

aaaaa

aa

aa

aa

aa

aa

aaaaaaa

aaaaa

aaa

aaaaa

aaaaa

aa

aa

aaa a a a a a a a aa a a aa a a a a a a aa a a a aa a a aaa

a aa

aa

a

aa

a

aaa

a

aa

a

aaa

a

aaa

a

aa

a

aaa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aa

aaa

aa

aaaaaaaaaaaaaaaaaa

aaaaaaa

aaaaaaa

aaaaaaaaaaaaa a a a aa a a a a a a aa a

a a a aaaa aa

aaaaaaaa aa

aa

aaa

aaa

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aaa

aaa

aaa

aaa

aaa

aaa

aa

a

aa

aaa

aa

aaa

aa

aaa

aa

aa

aaaaaaaaaaaaaaaaaa

aa

aa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

a a a a a a a a a a aaaaa aaaaaaaaaaaa

aaa

aa

aa

aa

aaa

aaa

aa

a

aa

aaa

aaa

aa

a

aa

aaa

aaa

aa

a

aa

aaa

aa

a

aa

aaa

aa

aaa

aa

aaaaa

aa

aa

aaaaaaaaa

aa

aa

aa

aaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaa a a a a a a a aa

aaaa

aaaaaa

aaa

aaaaaaa

aaaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaa

aa

aa

aaaaa

aa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaa

aa

aa

aa

aaa a a a aa a

aaaaaaaaa

aaaaaaaaaaaaa

a

aaaaaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aaaaaaa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a a

aaaaaaaa

aaaaaaa

aa

aaaaaaaa

aaa

aa

aaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaa

aaaaa

aa

aaaaaaaaaaaaa

aa

aa

aaa

tD = 0.938

aa a a a a a a a a a a a a a a a a a a a aa a a a a a a a a a a a a a a a a aaa a a a a a a a a aaa a a a a aa a a

aaaaaa

aaaaaaaa

aa

a

aaa

a

aaa

a

a

a

a

aa

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a a aa a a a a a a a aa a a a a a a aaa a a a a a aaa

a a a a aaaa a a aaa

a a aaaaaaaaaa

aaa

aaaaa

aa

aa

aa

aaa

aa

aaa

a

aa

a

aaa

a

a

aa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

aa

aa a a a aa a a a a aaa a a aaa

a a a aa aa a a aa a a a aa a a a aa a

a a aaaaaaaaaa

aaaaaaaaaaaa

aaaaaaaaaaaa

aa

aaa

aa

a

aa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

aa

a

a

a

aa

aa a aaaa a aa

a a aaaa a aa

a a aa a a aaaa a a

aaa aa

aaaa

aa aaaaaaaaa

aaa

aaa

aaa

aaaaa

aaaaaaaaaaaa

aa

aa

aaa

aa

a

aa

aaa

aaa

aaa

aaa

aaa

aaa

aa

aaaaa

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

aa

a

a

aaa

a

aa

aa a aaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaa

aaa

aaa

aaaaaaaa

aaaaaaa

aa

aa

aa

aa

aaaaaaa

aa

aaa

aa

aaa

aa

a

aa

aaa

aa

aaa

aa

aaaaaaa

a

a

a

a

a

a

a

a

a

a

aaa

a

a

aa

a

aaa

a

aa

a

aa

aaaaaaaaaaaaaaaaaaaa

aaa

aaaaaaaaaaaaaaaaaaaaa

aaa

aaaaaaaa

aaaaa

aaaaaaaaa

aa

aa

aa

aa

aaaaaaa

aa

aaaaa

aa

aaa

aa

aa

aaa

aa

aa

aaaaaaaaa

a

aa

a

aaa

a

a

a

aaa

a

aaa

aaa

aaa

aaa

aa

aaaa

aaaaaaaaaaa

aaaaaaaaaaa

aaaaaaaa

aaa

aaaaa

aaaaaaaaaaaaaaa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaa

aa

aa

aaaaa

aa

aa

aaaaaaaaaaaaa

a

a

a

a

aaa

a

a

aa

a

aa

a

aa

aaa

aaa

aa

aa

aaaaaaaaaaa

aaaaa

aaaaa

aaaaa

aaaaa

aaaaaaa

aaaaa

aaaaaaa

aaaaaaaaa

aa

aaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

a

a

a

a

aa

a

aa

a

aa

aaa

aa

aaa

aa

aaaa

aaaaaaaa

aa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaa

aa

aaaaaaaaa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaa

aa

aa

aa

aaaaaa

aa

a

a

aa

aaa

aa

aaaaa

aa

aa

aaaaaa

aaa

aa

aa

aaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aaaaaaaaaaaaa

aa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

aaa

a

aa

a

aa

aaaaaa

aaaaa

aaaa a a aa a a a a a aa a a a a a a a aaa a a a a a a a aa a a a a a a a a a a a a a a a a a a a a a a a a a a a a

a

aa

a

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

a

a

aa

a

a

a

a

aa

a

a

a

aa

a

a

aaa

a

aa

a

aa

aaa

aa

aaaaaaaa

aaaaa

aaa

aaaaa aa

a a aa aa a aa a a a aa a a a aa

aa aa

a a a a a a a a a a a a a a a a a a aa a a a a a a aa

aa

a

a

a

aa

a

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

aa

a

a

aaa

a

aa

a

aaa

aaa

aaa

aaaaa

aa

aa

aa

aa

aaaaaaa

aaa

aaaaaaaaa

aaaaaaaaa aaaaaaaaaaa

a a a a a a a a a a a a a a a aa aa a a aa a a a aa

aa

a

aaa

a

a

aa

a

a

aa

a

a

aaa

a

a

aa

a

a

aa

a

a

aaa

a

aaa

a

aaa

a

aa

a

a

aa

a

aa

a

aaa

aaa

aa

a

aa

aaaaa

aa

aa

aa

aa

aaaaaaa

aaaaa

aaaaaaaaaaaaaaaaaaaa

aaaaa

aaa a a a a a a a a a a a a aa a

a a aa a a aaa a aa

aa

aaa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aaa

aaa

a

aa

a

aaa

aaa

aaa

aaa

aa

a

aa

aaa

aa

aa

aaaaaaaaaaaaaaaa

aaaaaaa

aaaaa

aaaaaaaa

aaaaa

aaaaaaaaa a a a a a a a a a a a aa

aaaaaaaaaaaa aa

aa

aa

a

aaa

aaa

aaa

aaa

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aa

a

aa

aaa

aa

aaa

aa

aa

aaaaaaaaaaaaaaaaaa

aa

aaaaaaa

aaaaa

aaaaaaa

aaaaaaaaaaaaa aa a a a aaa a a a aa

aaaaaaaaaa

aaa

aa

aa

aa

aaa

aaa

aa

aaa

aaa

aa

a

aa

aaa

aaa

aa

a

aa

aaa

aa

aaa

aaa

aa

aaa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aa

aa

aa

aa

aaaaaaaaa

aa

aaaaaaaaa

aaaaaaaaa

aa

aa

aaaaa a a a a aa a

aaa

aaaaaa

aaa

aaaaaaa

aaaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaa

aa

aaa

aa

aa

aaa

aa

aaaaa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaaaaaaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aaa a a a

aaaaaaaaaaa

aaaaa

aaaaa

a

aaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aaaaaa a

aaaaaa

aaaaaaa

aa

aaaaaaaa

aaa

aa

aa

aaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaa

aa

aa

aa

aaa

tD = 0.969

aa a a a a a a a a a a a a a a aa a a a a a a a a a a a a a aaa a a a a a a a a a aaa a a a a a aa a

a a aaaaa aaaaa

aaaaa

aa

aaa

aa

a

aaa

a

aaa

a

a

aaa

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a aa a a a a a a aa a a a a a a aa a a a a a aaa

a a a a aa a a a a aa a a a aa a aaaaaaaaaaaaaaaa

aa

aa

aa

aa

aaa

aa

aaa

a

aa

a

aaa

a

aaa

a

a

aaa

a

a

a

aaa

a

a

a

aaa

a

a

a

a

aa

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

aa

aa a a aaaa a a aa a a a aaa

a a a aa a a a aa a a a aa aa a aa a a a aa

aa aa

aa aaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aaa

aa

aaa

aaa

aaa

a

aa

a

a

aa

a

a

aa

a

a

aaa

a

a

aa

a

a

aaa

a

aaa

a

aaa

a

a

a

a

a

aaa

a

a

a

a

aaa

a

a

aa

aa a aaaa aa

aa a aa

aa aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaa

aa

aa

aa

aa

aaa

aa

aaa

aa

aaa

aaa

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aaa

a

aa

a

aa

a

aaa

a

a

aa

a

a

a

a

a

aaa

a

aaa

a

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaa

aaaaa

aa

aaaaaaaaaaaaaa

aa

aaaaa

aa

a

aa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aaa

aa

aaa

a

a

a

a

a

aa

a

a

aa

a

aaa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaa

aaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaa

aa

aa

aaa

aa

aaa

aa

aaa

aa

a

aa

aaa

aaa

aa

a

aa

aaa

aa

aaa

aa

aa

a

a

a

a

aa

a

aaa

a

aa

a

aa

aa

aaaa

aaaaaaaa

aaaaaaaa

aaaaaaaa

aaa

aaaaa

aaaaaaaaaaaaaaaaaaaa

aa

aaaaaaa

aa

aa

aa

aa

aa

aa

aaaaaaa

aa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aa

a

a

aaa

a

aa

a

aa

aaa

aa

aa

aaaaaa

aaaaa

aaaaaaaaaaaa

aaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aa

aa

aaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aaaaaaa

aa

aaaaa

aa

aa

aaa

aa

aa

aaaaa

aa

aa

aaaa

a

aaa

aaa

aa

aaa

aa

aaaa

aaaaaaaaaa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaaaa

aa

aaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

a

aa

aaa

aa

aa

aaaaaaaa

aaa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

aaa

a

a

aa

a

aaa

aa

aaaaaaaaaa

aaaaaaaa aa a

a a a aa a a a a a a aa a a a a a a a a a aa a a a a a a a a a aa a a a a a a a a a a a a a a a a a aa

aa

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

a

a

aaa

a

a

a

a

aa

a

a

a

a

aa

a

a

a

aa

a

a

aaa

a

aa

a

aaa

aaa

aa

aaaaaaaaaa

aaaaa

aaaaaa

aaaaa a aa

a a a aaa a a aaa

a a a aaaa a a a aa a a a aa a a a a a a a a a a aa a a a a a a

a

aa

a

a

aaa

a

a

a

aa

a

a

a

aa

a

a

a

aaa

a

a

aaa

a

a

aaa

a

a

aaa

a

a

aa

a

a

aa

a

a

aa

a

aaa

aaa

aaa

aaa

aa

aaaaaaaaaaaa

aaaaa

aaaaaaaaaa aaaaaaaaaaa a aa

a a aaaa a aa

aaaaaaaa

a a a a a a aa a a a a aaaa a aa

aa

a

aaa

a

aaa

a

aaa

a

a

aa

a

a

aa

a

a

aa

a

a

aa

a

a

aa

a

a

aa

a

aaa

a

aa

a

aaa

aaa

aaa

aaa

aa

aaa

aa

aaaaaaaaaaaaaa

aaaaa

aaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaa a a aa a a a a aaa

aaaa a aa

aa

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aa

aaaaa

aa

aa

aaaaaa

aa

aa

aaaaaaaaaaaaaaa

aaa

aaaaaaaaaaaa

aaa

aaa

aaa

aaa

aaaaa a a a a a aa

aaaa

aaaaaa

aa

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aa

aaa

aaa

aa

aa

aaa

aa

aa

aaaaaaaaaaaa

aa

aaaaaaa

aaaaaaaaaa

aaaaaaaa

aaaaaaaa

aaa

aaaaa

aa

aaa a a a aa

aaaa

aaa

aaa

aa

aa

aa

aaa

aa

aaa

aaa

aa

a

aa

aaa

aa

a

aa

aaa

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aa

aaa

aa

aa

aaaaaaaaa

aa

aa

aaaaaaaaaaa

aaaaaaa

aaaaaaa

aaaaa

aaaaa

aaaaa

aaaaaaa

aa

aaa a aa

aaaaaaa

aaa

aaaa

aaaa

aa

aaaaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aaaaa

aa

aaa

aa

aa

aaa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaaaaaaa

aa

aa

aa

aaaaaaaaa

aaaaaaa

aaaaaaaaa

aaaaaaaaa

aa

aa

aaa aa

aaaa

aaaaa

aaaaaa

aaaaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aaaaa

aaa

aa

aaaaaaa

aaa

aaa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aaa

tD = 0.998

aa a a a a a a a a a a a a aa a a a a a a a a a a a a aaa a a a a a a a a a aa a a a a a a aaa

a a a aaaaa aaaaaaaaaaaaaaaa

aa

a

aa

a

aa

a

a

aaa

a

a

a

aaa

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

a

a

aa

aa a a a a a aa a a a a a aaa a a a a a aa a a a a a aa a a a a a aa

a a a aaaa a a aa

a aaaaaaa

aaaaaaaaa

aaaaaaaa

aa

aaa

aa

a

aa

a

aa

a

a

aa

a

a

aaa

a

a

aaa

a

a

a

aa

a

a

a

a

a

aa

a

a

a

a

a

aa

a

a

a

a

aaa

a

a

a

aaa

a

a

a

a

a

a

a

aa

aa a a aaaa a aaa

a a a aa a a a aa a a a aaaa a aaa

a a aa a a a aaaa aa

aa aaaaaaaaaaaaaaaaa

aa

aaaaaa

aa

aa

aaa

aa

aaa

aaa

aaa

a

aaa

a

aa

a

a

aa

a

a

aaa

a

a

aaa

a

a

aaa

a

a

aaa

a

a

aa

a

a

aa

a

a

a

a

a

aaa

a

a

aa

aa a aaaaaaaaaaaaaaaaa aa

aa aa

aa aa

aa aa

aa aaaaaaaaa

aaaaaaaaaaaaaaa

aaaaa

aaaaaaaaaa

aa

aa

aaa

aa

aaa

aaa

aaa

aaa

a

aa

a

aaa

a

aa

a

a

aa

a

a

aa

a

a

aa

a

aaa

a

aaa

a

aa

a

a

aa

a

a

a

aaa

a

aa

aaaaaaaaaaaaaaa

aaaaaaa

aaaaaaaaaaaaaaaaaaaa

aaa

aaa

aaa

aaaaaaaa

aaaaaaa

aa

aa

aa

aa

aa

aaaaa

aa

aaa

aa

aaa

aaa

aa

a

aa

a

aa

a

aaa

aaa

a

aa

a

aa

a

aaa

aaa

a

aa

a

aa

aaa

a

a

aaa

a

aaa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaa

aaa

aaa

aaaaaaaaaaa

aaaaaaaaaa

aaaaaaa

aa

aa

aa

aa

aa

aa

aa

aaaaa

aa

aaa

aa

aaa

aa

a

aa

aaa

aaa

aa

a

aa

a

aa

a

aa

aaa

aaa

aaa

aa

aaa

aaa

a

a

aa

a

aa

aa

aaaa

aaaaaaaa

aaaaaaaa

aaaaa

aaa

aaaaa

aaaaaaaa

aaaaa

aaaaaaa

aaaaaaa

aa

aaaaaaaaaaaaaaaa

aa

aa

aa

aaaaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aa

aaa

aaa

aa

aaa

aa

aaaaaaa

a

aaa

aaa

aa

aa

aaaaaa

aaaaa

aaaaaaa

aaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaa

aa

aa

aaaaa

aa

aa

aaaaa

aa

aaa

aa

aa

aaa

aa

aa

aaa

aa

aa

aa

aaa

aaa

aa

aaaa

aaaaaaaaaa

aa

aaaaaaaaa

aa

aa

aaaaaaaaa

aa

aaaaaaaaaaa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aaaaaaaa

aaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaa

aa

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

a

a

aa

a

a

a

a

a

a

a

a

a

aaa

a

a

a

a

a

a

aa

a

a

a

a

aaa

a

a

aa

a

aaa

aaa

aaaaaaaaaa

aaaaaaaaa

a a aaaa a a a aa

a a a a a a aa a a a a a a a a a aaa a a a a a a a a a a aa a a a a a a a a a a a a aa

aa

a

a

a

a

aaa

a

a

a

a

a

aa

a

a

a

a

a

aa

a

a

a

a

a

aa

a

a

a

a

aaa

a

a

a

aaa

a

a

aaa

a

a

aa

a

a

aa

a

aaa

aaa

aa

aaaaaaaaaaaaaaaaa

aaa

aaaaa aa

a a aaaa a aaa

a a a aa aa a a a aa

a a a a aaaa a a a aa a a a a a aa a a a a a a aa

aa

a

a

aaa

a

a

aaa

a

a

aaa

a

a

a

aa

a

a

a

aa

a

a

a

aa

a

a

aaa

a

a

aa

a

a

aa

a

a

aa

a

aaa

a

aa

a

aa

aaa

aa

aaaaa

aa

aa

aaaaaaa

aaaaaaaaaaaaaaa

aa aaaa aa

a a aaaa a aa a a a aa a a a aa

a a aa aaaaa a a a a aaa

a a aa

aa

a

aa

a

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aaa

a

aa

a

aaa

a

aa

a

aa

a

aa

a

aa

aaa

aa

aaaaa

aa

aa

aa

aa

aaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaa aa a a a a a

a a aa

aa

aaa

a

aa

a

aaa

a

aa

a

aa

a

aaa

a

aa

a

aaa

aaa

a

aa

a

aaa

aaa

aaa

aaa

aaa

aa

a

aa

aaa

aa

aa

aaaaaaaaaaaaaaaaaa

aaaaa

aaaaa

aaa

aaaaaaaaaaaaaaa

aaaaaaaaaaaaa

aaaaaa

aaa

a a a aaaaaaaa

aa

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

a

aa

aaa

aaa

aaa

aaa

aa

a

aa

aaa

aa

a

aa

aaaaa

aa

aaaaaaa

aa

aa

aa

aa

aaaaaaa

aaaaaaa

aaaaa

aaaaaaaa

aaa

aaaaaaaaaaaaaa

aaa

aaaaaaaaaaa

a aaa

aaa

aa

aa

aa

aaa

aa

aaa

aaa

aa

aaa

aa

a

aa

aaa

aa

aaa

aaa

aa

aaa

aa

aaa

aa

aaaaa

aa

aaaaa

aa

aa

aa

aaaaaaaaaa

aa

aa

aaaaaaaaa

aaaaa

aaaaaaaaaaaaaaa

aaaaa

aaaaa

aaaaaaaaaaaa

a aaaaaa

aaaa

aaaa

aa

aa

aaa

aa

aaa

aa

aa

aaa

aa

aaaaa

aa

aaa

aa

aa

aaa

aa

aa

aaaaa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaa

aa

aaaaaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aaaaaaa

aa

aa

aaaaaa

aaaaaa

aaaaaaaa

aa

aa

aa

aaaaaaa

aa

aa

aaaaaaa

aa

aa

aa

aaaaaaaaa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aaaaaaaaa

aa

aa

aaaaaaaaa

aa

aa

aaaaaaaaaaaaaaaaaa

aaa

aaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aa

aaa

FIG. 6Five-spot pattern, very favorable mobility ratio, 1/M = 20.

17

FIG. 7Staggered-line-drive pattern, very favorable mobility ratio, 1/M = 20 .