SPE-16963-PA (hall)

Analyzing Injectivity of Polymer Solutions With the Hall Plot R.S. Buell, SPE, Chevron U.S.A.; H. Kazeml, SPE, Marathon Oil Co.; and F.H. Po.ttmann, SPE Colorado School of Mines '

Summa..,. The Hall plot was originally used to analyze water-injection wells. This paper demonstrates that the Hall plot can also be used to analyze injection of polymer solutions. In particular, it is possible to determine the in-situ and residual resistance factors ?f a polymer solution fro~ the Hall plot. The analysis methods developed are used to examine two field injection tests and one hypothet-Ical example. The analytical results are verified with a reservoir simulator.

Introduction Polymer floods, micellarlpolymer floods, and injectivity- or productivity-profIle-modification treatments are the most common applications of polymer solutions. The interpretation of injection pressures and rates associated with polymer solution injection is important to the efficient application of the solutions. The Hall plot l-3 is a useful tool for evaluating performance of injection wells.

The Hall plot was originally developed for single-phase, steady-state, radial flow of Newtonian liquids. Since the advent of poly-mer and micellar solutions for EOR, it has also been applied to the injection of these solutions. Moffitt and Menzie4 used the Hall plot to evaluate injection of polymer solutions but did not verify the validity of the Hall plot for this application. This paper verifies the validity of the Hall plot for evaluating polymer solution injection.

Because of the complex nature of polymer solution flow through porous media, exact analytical solutions are generally not possi-ble. However, some relatively simple approximate analytical so-lutions can be developed. To verify the analytical solutions for polymer solution injection, a two-phase, radial, numerical reser-voir simulator was developed. 2 The simulator is designed to con-sider the more important phenomena and effects that occur when polyacrylamide or polysaccharide polymer solutions are injected into porous media. The simulator has the following characteristics: slightly compressible flow, two-phase flow, non-Newtonian rheol-ogy, adsorption/retention with permeability reduction, concentra-tion effects, skin, and wellbore storage. It was used to history match two field injectivity data sets.

Development of the Hall Plot The Hall I plot was originally proposed to analyze the performance of waterflood injection wells. Hall simply used Darcy's law for single-phase, steady-state, Newtonian flow of a well centered in a circular reservoir:

q ........................ (1) 14I.2Bwl'w[ln(relr w) +s]

Hall integrated both sides with respect to time to obtain

Wi

Separating the integral of Eq. 2, Hall then rearranged to obtain

141.2Bwl'w[ln(r elr w) +s] Wi+i'Pedt . ........... (3)

kkrwh

The relation between surface and bottomhole pressures for steady-state vertical flow is given by

pwf=ptrtlpf+pgD . ............................... (4) Copyright 1990 Society of Petroleum Engineers

SPE Reservoir Engineering, February 1990

Hall substituted Eq. 4 into Eq. 3 to arrive at

141.2Bwl'w[ln(r elr w) +s] --------Wi +J(Pe + tlprpgD)dt.

kkrwh

.................................... (5)

Hall simply dropped the second term on the right side ofEq. 5 and plotted the integral of wellhead pressures with respect to time vs. cumulative injection, which came to be known as the "Hall plot." By plotting in this format, Hall observed that if an injection well was stimulated, the slope decreased, and if a well was damaged, the slope increased. While Hall's conclusions regarding changes in slope are valid, the second term on the right side of Eq. 5 is often not negligible in comparison with the other terms and there-fore usually cannot be dropped.

In industry applications, the Hall integrals i'Pifdt and i'Pwfdt fre-quently are used. The slopes calculated from these integrals should not be used for quantitative calculations unless a correction proce-dure is applied. Fig. 1 is a Hall plot based on the data for Well A, where the integral fPwfdt has been plotted vs. cumulative in-jection. Several changes in slope can be seen on the plot, but there has been no change in transmissibility or skin. The changes in slope are caused by changes in rate, which occur because the integral fPedt has been neglected. Fig. 2 is a Hall plot based on data for Well C. The three most common forms of the Hall integral have been plotted for the same data. For each integration method, the slopes of the curves are quite different.

Injection data must be plotted in the form of Eq. 2 to make valid quantitative calculations; i.e., cumulative injection should be plot-ted vs. f(Pwf-Pe)dt. The slope of the Hall plot from Eq. 2 is then given by

1412Bwl'w[ln(r elr w) +s] ..................... (6)

kkrwh

Eq. 6 will not be appropriate when multiple fluid banks with sig-nificantly different properties exist in the reservoir.

Advantage. and DI.advantage. The Hall plot is a steady-state analysis method, whereas falloff tests, injection tests, and type-curve analysis are transient methods. Tran-sient pressure analysis methods determine the reservoir properties at essentially one point in time. The Hall plot is a continuous mon-itoring method; i.e., reservoir properties are measured over a period of weeks and months. The Hall plot, therefore, can help identify changes in injection characteristics that occur over an extended period.

Hall's method has several advantages. Integrating the pressure data with the Hall integral [f(Pwf-Pe)dt] has a smoothing effect on the data. Data acquisition for the Hall plot is inexpensive be-cause only the recording of cumulative injection and surface pres-sures is required. Surface pressures must be converted to bottomhole pressures (BHP's), correcting for hydrostatic head and friction loss-

41

M~ 350 bbl/d - 100 'r Iwfd! / I I VV, -~-~- ' I I/V I I r ! 1~ _~/f[';~_~ ~- =1=== I ~ I _--+- I I

----!----- I I I I I ' -,--,--+~, I --.----,,--,-+-,-,---~ , ,

0 ~OOO 4000 6000 8000 10000 ie-ODD HODO 16000 CUMULATIVE INJECTION (bbl)

Fig. 1-Comparlson of Hall Integration methods, Well A, P. = 1,000 psi.

es. Injection and falloff tests usually require running gauges on wire-line to depth, which is an additional expense.

The greatest disadvantage of the Hall plot is that the skin, s, and transmissibility, khl/Jo' are combined in the slope. It is possible to determine one of these if the other is known, but the determination of both skin and transmissibility is not possible with the Hall plot. To use the Hall plot effectively, running falloff or injection tests periodically is still necessary to determine the individual values of transmissibility and skin.

Quantitative Analysis Newtonian Fluids. In a mature waterflood, the transmissibility usually will not change significantly with time; therefore, any change in the slope of the Hall plot will be a result of skin effects. Assum-ing no change in transmissibility, the new skin can be calculated as follows for water injection:

kkrwh s2 =sI - (mHI -mH2), .................... (7)

141.2Bw/Jow

where subscript 1 denotes the old slope and skin and subscript 2 the new slope and skin. This relationship can be useful in recog-nizing formation damage or fracturing.

When a waterflood begins, two-phase flow will exist in the near-wellbore region. As the water moves away from the wellbore, water and oil banks form if the oil saturation is large enough. A simpli-fied method to analyze this situation is to apply Darcy's law in a series manner. Because the oil displacement is governed by the Buckley-Leverett5 equation, the saturations and relative permea-bilities are not constant within each fluid bank; however, for sim-plicity, they can be assumed to be constant within each bank. The accuracy of the results is not significantly compromised with this assumption. The slope of the Hall plot for a water and oil bank is given by

(water bank) (oil bank)

.................................... (8)

The interface between the oil and water banks is rbl. The inter-face of the oil and water banks can be estimated with Eq. 9, which results from the Buckley-Leverett equation in radial coordinates. 6

r1I = 5.615Wi (a/w ) +ra . ....................... (9) q,7rh asw F

The quantity (a/wlaSw)F is the derivative of the fractional-flow curve at the flood front. The water saturation and the derivative of the fractional-flow curve at the flood front are determined with

42

.... & I'w,d' / Go ~ .~ y ~----Og I.~ ,/ .~ // ~ f[pw'p.~, a. o /' .... g ....12 ~ ---- ~r-Co a:o /

------

CI:il w'" 1#

-------

I PHdt .,.0 ~ zg -:il ~ V :18 C:il X" ~ ~

... 10DO 2000 3000 '000 5000 6000 7000 8000 CUMULATIVE INJECTION (Barrels)

Fig. 2-Comparlson of Hall Integration methods, Well C.

Welge's7 method. As the oil bank is pushed away from the well-bore, the water-bank term will dominate owing to the logarithmic nature of Eq. 8.

Non-Newtonian Fluids. The analysis methods for non-Newtonian fluids are similar to the methods developed in the previous section, except permeability reduction must be considered. The apparent viscosity of the non-Newtonian fluids is taken to be a constant within each fluid bank. Eq. 10 is for an injection sequence of polymer and then water. The reservoir is assumed to be initially oil-saturated. Three fluid banks will be created: oil, polymer, and water.

[ /JowBw[ln(rb2Ir w) +s] /JopBw In(rbI lrb2)

mH=141.2 +--'------hkakrw hkakrp

(water bank) (polymer bank)

+ /JooBo In(relrbl) I ............................... (10) hkkro j

(oil bank)

Eq. 10 can be rewritten with just one absolute permeability and one aqueous-phase viscosity after the introduction of resistance fac-tor, Rj' and residual resistance factor, Rrj' which are defined below.

water mobility (kkrw)//Jow Rj = = ................ (11)

polymer mobility (kakrp)//Jop absolute permeability before polymer k

and Rrj= .... (12) absolute permeability after polymer ka

Because residual resistance factor and resistance factor are useful in the evaluation of polymer performance, Eq. 10 has been rewrit-ten with these definitions:


+ /JooBo In(relrbl) I ............................... (13) hkkro j

(oil bank)

In Eqs. 10 and 13, apparent viscosity is assumed to be constant through space; i.e., the non-Newtonian rheology is ignored. The variation of apparent viscosity in space can be taken into account by applying Darcy's law, with the definition of effective viscosity used in the same series manner as used to develop Eq. 10. For the simple case of a power-law fluid bank occupying the whole reser-


0 >:~ II ~ :ag e. .. III r Wat" I-

CUMULATIVE INJECTION (barrels)

Fig. 5-Hall plot, rate-contrOlled history match, Well B.

and resistance factor estimates provided by Milton et ai. were used as a first approximation and were then adjusted to obtain the best possible history match. All pressure data were recorded at the sur-face. For history-matching purposes, all surface pressures were cor-rected to BHP with friction included.

The residual resistance factor was estimated to be 1.05 on the basis of transient well testing. To obtain the best possible match with the field data, reducing the polymer solution viscosity and in-creasing the residual resistance factor was necessary. The best his-tory match was obtained with the rheology given in Table I and a residual resistance factor of 1.33.

The rate-controlled (Neumann) boundary condition and match-ing pressures were used to obtain Figs. 5 and 6. The reservoir was modeled with single-phase flow because Milton et ai. considered the reservoir to be at ROS owing to extensive waterflooding. The Hall plot generated from history matching can now be used to ap-ply the analytical procedures developed. The Hall plot shown in Fig. 5 has three distinct sections: water, polymer, and water injec-tion. Applying Darcy's law in a series manner yields an equation for each section. For this example, four unknowns will be assumed: kkrw, Rrf, Rfl, and Rj2. All other parameters are assumed to be known. Rfl is the resistance factor of the polymer bank while poly-mer solution is being injected. Rj2 is the resistance factor of the polymer bank after polymer injection has stopped and water injec-tion has begun. Rfl and Rj2 usually will not be equal because of shear thinning of the polymer solution and because adsorption/reten-tion will reduce polymer concentrations as the polymer slug prop-agates through the reservoir. The slope of the Hall plot for the first water-injection period is given by Eq. 6. The slope of the Hall plot for the polymer-injection period is given by

(polymer bank) (water bank)

................................... (15) An oil bank is assumed not to form in Eq. 15 because of the exten-sive waterflooding. The slope of the Hall plot for water injection following polymer injection is given by

[ R,frwBw[ln(rb2Ir w) +s] Rj2JlwBw In(rbl /rb2)

mH3 = 141.2 + hkkrw hkkrw


+ JlwBWh~::lrbl) J ............................. (16) (water bank)

Eq. 8 is used to calculate a permeability to water of 90.9 md with a skin of7.2. The permeability to water used by the reservoir simu-lator is 91.0 md. With one unknown eliminated, there are now three 44

i

2~. J:LLt-l~!wj-~ --0 10 20 30 40 50 60 70 80 90 100

TIME (days)

Fig. 6-BHP vs. time, rate-controlled history match, Well B.

unknowns and only two equations. To solve for all the unknowns, another equation is necessary. The residual resistance factor can be estimated by taking the ratio of the Hall plot slopes for water injection before and after polymer injection. The contributions from the banks farther away from the wellbore become smaller and smaller as injection continues when Eq. 16 is used. As injection proceeds, the Hall plot slope after polymer injection, mH3, will ap-proach the value given by

14I.2RrfJlwBw[ln(r e1r w) +s] mH3= ................. (17)

hkkrw (water bank)

The latest straight-line portion of water injection following poly-mer is used to estimate mH3, so the influence of the other banks will be at a minimum. Eqs. 6 and 17 can be combi:1ed to solve for Rrf. The residual resistance factor can then be estimated with

Rrf=mH3 /mH!' .................................. (18) The residual resistance factor is computed to be 1.42. The in-

situ residual resistance factor calculated in the simulator is 1.33. Eqs. 15 and 16 can be used to find the two remaining unknowns, Rfl and Rj2. Because this problem was simulated with one-phase flow, all displacement processes are miscible. Piston-like displace-ment, therefore, is assumed to occur. The location of the interface between banks can be calculated by volumetric calculations account-ing for polymer adsorption. Using Eq. 15 to calculate the resistance factor at the end of the polymer-injection period results in a resistance factor of 2.22 for the polymer bank. It can be seen that when numerical values are substituted into Eq. 15, the water bank is less important than the polymer bank, supporting the conclusion that the bank in contact with the wellbore will dominate. The water bank away from the wellbore can be assumed to be negligible, and the single-fluid-bank assumption can be used. When this single-fluid-bank assumption is used, the resistance factor is calculated to be 2.06. The single-fluid-bank assumption will underestimate the resistance factor because, in this case, the polymer bank is assumed to extend to the drainage radius when it actually extends only some fraction of the drainage radius. The simulator provides pressures for each cell. The average resistance factor for the poly-mer bank is calculated with the simulator results to be 2. 17.

The slope of the water injection following polymer is used to solve Eq. 16. Substituting numerical values into Eq. 16 results in a cal-culated resistance factor of 4.19 for the polymer bank away from the wellbore. The average resistance factor of the polymer bank is calculated with the simulator results to be 3.51. The resistance factor calculated for the polymer bank away from the wellbore can be significantly in error. The reason for the larger errors is that the pressure drop caused by the polymer bank is small away from the wellbore. A small error in the determination of the slope re-sults in an increased error in the calculated resistance factor. Ta-ble 2 compares the approximate analytical methods with the simulator results.


Well C. Well C was used to evaluate the injectivity of micellar and polymer solutions. The daily injection data consisted of mice 1-lar solution injection followed by polymer solution injection. The polymer solution was then displaced with water. The reservoir data, fluid properties, daily injection history, and polymer parameters are given in Refs. 2 and 8.

The injection pressures were controlled to prevent reservoir frac-turing or fracture parting. A falloff test was run before micellar solution injection began. The test indicated a water mobility of 27 md/cp [27 md/mPa' s] and a skin of -1.14. The skin and permea-bility calculated from the falloff test were used in the simulator for history matching. This reservoir had been waterflooded extensive-ly before the injection testing. The reservoir was estimated to be at ROS; therefore, the history match was done with only single-phase flow.

The history match was conducted in the same manner as for Well B. The best history match was obtained by adjusting rheology and resistance factors. All other parameters were taken from available data and assumed to be correct. The Carreau model was used to approximate the rheology of the polymer and micellar solutions. History matching was done with both the rate- and pressure-controlled boundary conditions.

The Neumann (rate-controlled) boundary condition was used for Figs. 7 and 8. Table 3 gives the rheology of the polymer solution used to obtain the best match. The amount of permeability reduc-tion was much larger than for Well B. The residual resistance fac-tor used in the best match was 11. 1. The rate-controlled boundary condition was used for cases with various levels of adsorption/reten-tion. As with Well B, the results were found to be relatively insen-sitive to the amount of adsorption/retention.

The Hall plot for Well C was analyzed in the same manner as that for Well B. There were no initial water-injection data for this well; however, the slope before polymer and micellar solution in-jection can be calculated because the skin and transmissibility are known. The Hall plot slope for water injection is calculated with Eq. 6 to be 1.68 (psi-D)/STB [0.0387 (kPa' d)/stock-tank m3] from the falloff testing data before polymer injection. The slope for the late water-injection period is 16.50 (psi-D)/STB [0.380 (kPa'd)/stock-tank m3]. Eq. 18 can now be used to estimate a residual resistance factor of 9.80, which is reasonably close to the simulator value of 11. 10. Table 4 compares the analytical solutions with the simulator results.

Eqs. 15 and 16 can now be used to calculate the average resistance factor of the polymer/micellar solution banks. At the end of poly-mer/micellar solution injection, the average resistance factor is cal-culated with Eq. 15 to be 29.53. The average resistance factor can also be approximated by assuming a single bank that extends to the drainage radius, which results in an average resistance factor of20.95. The average resistance factor calculated with the simula-tor is 29.40.

After water injection, the polymer/micellar bank is between 48 and 95 ft [15 and 29 m]. The simulator results were used to calcu-late an average resistance factor of 14.7. A resistance factor of 16.6 was calculated with Eq. 16.

The apparent viscosity for Well C is given as a function of radial distance in Ref. 8. The relative change in the apparent viscosity within the polymer bank is small. Small changes in apparent vis-

TABLE 2-COMPARISON OF ANALYTICAL METHOD WITH SIMULATOR RESULTS, WELL B

Analytical Methods, Analytical Methods, Parameter Multiple Banks Single Bank kkrw 90.9 90.9 R" 1.42 1.42 R 11 2.22 2.06 Rf2 4.13

~ 0 0 '" .~ V :g /' ." 0 , 0 ., 0 0; .... /v Q. :g Simulatot Match :!~ / .. Q. Field Cat ... 0 :I g .s ~. If' :=; Mic_Uar SO'UL :::l g I/) 0

-I V "'. N 7-polymer t---.--- ---- -Wat&r-1---

Simulator 91.0

1.33 2.17 3.51

v

f---~

00 1000 ZOOO 3000 4000 5000 6000 7000 BODO

CUMMULATIVE INJECTION (barrels,

Fig. 7-Hall plot, rate-controlled history match, Well C.

40 50 60 TIME (days,

Fig. 8-BHP vs. time, rate-controlled history match, Well C.

TABLE 3-HISTORY MATCH, APPARENT VISCOSITY AS A FUNCTION OF INTERSTITIAL VELOCITY, WELL C

Concentration Interstitial Velocity (ft/O) (ppm) 0.01 0.10 1.00 10.00 100.0 1,000.0

--

0.0 1.00 1.00 1.00 1.00 1.00 1.00 2,445.0 3.00 2.85 2.01 1.55 1.39 1.33 2,800.0 5.00 4.72 3.07 2.19 1.87 1.76 3,100.0 6.99 6.59 4.19 2.91 2.45 2.29 3,430.0 8.49 7.83 4.30 2.83 2.44 2.34 5,000.0 19.98 18.70 12.55 10.51 10.10 10.02

'Savins 13 shear-rate/velocity relation used.

SPE Reservoir Engineering, February 1990 45

TABLE 4-COMPARISON OF ANALYTICAL METHOD WITH SIMULATOR RESULTS, WELL C

Analytical Methods, Analytical Methods, Parameter Multiple Banks Single Bank Rtf 9.80 9.80 R 11 29.53 20.95 R'2 16.63

Simulator 11.10 29.40 14.73

cosity within the polymer bank also occurred with Well B. Accord-ing to the history matching of Wells B and C, the non-Newtonian flow effect is relatively small. Apparent viscosity stays relatively constant within the polymer bank.

Conclusions Using a numerical reservoir simulator, 2 we have demonstrated that quantitative analysis can be performed on the Hall plot when non-Newtonian solutions are injected. The best method for analyzing the Hall plot would be to use a reservoir simulator like that devel-oped for this study. For the practicing engineer, however, a simu-lator may not be available. Therefore, two approximate analysis methods for the Hall plot have been developed to estimate permea-bilities, resistance factors, and residual resistance factors.

1. The Hall plot can be used to estimate the performance charac-teristics of injected polymer and micellar/polymer solutions.

2. The multibank analysis method will yield more accurate an-swers than the single-bank method. When the fluid bank in contact with the wellbore has moved out a substantial distance, the single-fluid-bank analysis method can be used with acceptable accuracy.

3. The non-Newtonian rheology effect is small because the change in the in-situ apparent viscosity of the polymer solutions through space is relatively small.

4. The amount of permeability reduction has a significant effect on the Hall plot and simulator results.

5. The transient flow period has little effect on the Hall plot be-cause, in most field situations, the transient period rarely lasts more than a few days. Because most Hall plot data are recorded daily, it is usually not possible to observe the transient flow period on the Hall plot.

Nomenclature B = FVF, dimensionless D = true vertical hole depth, ft [m] fw = fractional flow of water, dimensionless g = gravity constant, 32.2 ft/sec2 [9.81 m/s2] h = formation thickness, ft [m] k = absolute permeability, md

ka = absolute permeability after polymer, md kro = relative permeability to oil, dimensionless krp = relative permeability to polymer, dimensionless krw = relative permeability to water, dimensionless mH = Hall plot slope, (psia-D)/STB [(kPa 'd)/stock-tank m3]

n = Carreau and power-law-fluid slope parameter, dimensionless

Pe = pressure at external drainage radius, psia [kPa] Ptf = surface tubing injection pressure, psia [kPa]

Pwf = bottomhole injection pressure, psia [kPa] t::..pf = pressure loss caused by friction, psi [kPa]

q = rate, BID [m3/d] rbl = Bank I radius, ft [m] rb2 = Bank 2 radius, ft [m] re = external drainage radius, ft [m] r w = wellbore radius, ft [m] Rf = resistance factor, dimensionless

Rrf = residual resistance factor, dimensionless s = skin, dimensionless S = saturation, dimensionless

46

t = time, days ilt = change in time, days Wi = cumulative injection, bbl

"y = shear rate, seconds-\ A = Carreau rheological parameter, seconds /./, = viscosity, cp [mPa's]

/'/'e = effective viscosity, cp [mPa's] /'/'0 = viscosity at zero shear, cp [mPa's]

/./,00 = viscosity at infinite shear, cp [mPa 's] p = fluid density, Ibm/ft3 [kg/m3]

cf> = porosity, dimensionless

Subscripts F = flood front o = oil P = polymer w = water wf = injection pressure at r w

Acknowledgments We thank the Colorado School of Mines Petroleum Engineering Dept., Chevron U.S.A., and Marathon Oil Co. for their support in presenting and preparing this paper.

References 1. Hall, H.N.: "How To Analyze Waterflood Injection Well Perform-

ance," World Oil (Oct. 1963) 128-30. 2. Buell, R.S.: "Analyzing Injectivity of Non-Newtonian Fluids: An Ap-

plication of the Hall Plot," MS thesis, Colorado School of Mines, Gold-en, CO (1986).

3. DeMarco, M.: "Simplified Method PintJoints Injection Well Problems," World Oil (1968) 95-100.

4. Moffitt, P.D. and Menzie, D.E.: "Well Injection Tests of Non-Newtonian Fluids, " paper SPE 7177 presented at the 1978 SPE Rocky Mountain Regional Meeting, Cody, WY, May 17-19.

5. Buckley, S.E. and Leverett, M.C.: "Mechanism of Fluid Displace-ment in Sands," Trans., AIME (1942) 146, 107-16.

6. Collins, R.E.: Flow of Fluids Through Porous Marerials, Petroleum Publishing Co., Tulsa, OK (1961) 149.

7. Welge, H.J.: "Simplified Method for Computing Oil Recoveries by Gas or Water Drive," Trans., AIME (1952) 91, 195-98.

8. Buell, R.S., Kazemi, H., and Poettmann, F .H.: "Analyzing Injectivi-ty of Polymer Solutions with the Hall Plot, " paper SPE 16963 presented at the 1987 SPE Annual Technical Conference and Exhibition, Dallas, Sept. 27-30.

9. Blair, P.M. and Weinaug, C.P.: "Solution of Two-Phase Flow Prob-lems Using Implicit Difference Equations," SPEl (Dec. 1969) 417-24; Trans., AIME, 246.

10. Carreau, J.P.: "Rheological Equations from Molecular Network The-ories," PhD dissertation, U. of Wisconsin, Madison, WI (1968).

11. Vogel, P. and Pusch, G.: "Some Aspects of the Injectivity of Non-Newtonian Fluids in Porous Media," Enhanced Oil Recovery, F. John Fayers (ed.), Elsevier Science Publishers, New York City (1981) 179-96.

12. Milton, H.W. Jr., Argabright, P.A., and Gogarty, W.B.: "EOR Pros-pect Evaluation Using Field-Manufactured Polymer," paper SPE 11720 presented at the 1983 SPE California Regional Meeting, Ventura. March 23-25.

13. Savins, J.G.: "Non-Newtonian Flow Through Porous Media," Ind. & Eng. Chern. (Oct. 1969) 61, No. 10, 18-47.

51 Metric Conversion Factors bbl x 1.589 873 E-Ol

ft x 3.048* E-Ol psi x 6.894 757 E+OO

'Conversion factor is exact. SPERE

Original SPE manuscript received for review Sept. 27. 1987. Paper accepted for publica-tion Nov. 2, 1989. Revised manuscript received June 22, 1989. Paper (SPE 16963) first presented at the 1987 SPE Annual Technical Conference and Exhibition held in Dallas, Sept. 27-30.


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SPE-16963-PA (hall)