spe-52400-pa

Field Results Demonstrate EnhancedMatrix Acidizing Through Real-Time

MonitoringDing Zhu, SPE, and A.D. Hill, SPE, U. of Texas

SummaryThe use of an inverse injectivity vs. superposition time plot todiagnose the changing skin factor in a matrix acidizing treatmenthas been presented previously by Hill and Zhu.1 The model hasbeen extended to calculate skin factor as a function of injection timeor injected volume to help the operator monitor and optimize thetreatment. A Windows program based on the theory has beendeveloped to provide a pretreatment test to evaluate permeabilityand initial skin factor of the formation when they are not availablebefore the acid treatment, to calculate and plot the evolving skinduring the treatment in real time, and to evaluate treatmentsafterward. It converts surface pressure, when measured, to thebottomhole pressure for the calculation, and handles fluid densityand viscosity changes in real time. Several field examples showedthat the technique can be used conveniently to monitor skin changesand diversion effects during matrix acidizing treatments. The pro-gram is reliable and flexible in acquiring and processing data,calculating skin, and diagnosing matrix acidizing treatments.

IntroductionTo monitor changing skin during a matrix acidizing treatment, thetheory for a standard injectivity test by use of the approximate linesource solution for transient flow during injection has been adopt-ed.1,2 The pressure transient response to injection for multipleinjection rates is

pi 2 pwfqN

5 mDtsup 1 b, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

where m 5162.6Bm

kh , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

b 5 mFlogS kfmctrw2D 2 3.23 1 0.868sG, . . . . . . . . . . . . . . . (3)and the superposition time function, Dtsup, is defined as

Dtsup 5 Oj51

N~qj 2 qj21!

qNlog~tN 2 tj21!. . . . . . . . . . . . . . . . . . . (4)

According to Eq. 1, a plot of inverse injectivity, ( pi 2 pwf)/qN,vs. the superposition time function, Dtsup, will yield a straight linewith a slope of m and an intercept of b. During an acid treatment,the parameters defining the slope, m, do not change, leaving m aconstant. Among the parameters defining the intercept, b, the onlyone that changes as acid is injected is the skin factor, s. As a result,each inverse injectivity/superposition time point will lie on astraight line having a slope, m, with its intercept depending on theskin factor at that moment. Thus, a family of constant skin curvescan be calculated and plotted on a diagnostic chart of inverseinjectivity vs. superposition time function before the treatment, andthe skin change can be monitored by locating the inverse injectivityas a function of superposition time on the chart.

This method is easy to apply in the field, and the result iscomparable with other more complicated methods,3,4,5 but it re-quires the user to read from the diagnostic chart and interpolatebetween lines of constant skin to obtain the skin factor in real time.The model has been extended so that the evolving skin is calculateddirectly in real time as the treatment proceeds, allowing the operatorto monitor and optimize the treatment more conveniently.

Skin Calculation From Treatment DataAs mentioned previously, the intercept of the inverse injectivity vs.Dtsup curve, b, is a function of skin factor and changes during theacid treatment as the skin factor changes. The intercept, b, can becalculated from the measured pressure and injection rate; thus, theskin factor can be determined once the intercept is known. Solvingfor the skin factor from Eq. 3, we have

s 51

0.868Fbm 2 logS kfmctrw2D 1 3.23G. . . . . . . . . . . . . . . . . (5)The intercept, b, is obtained from Eq. 1,

b 5pi 2 pw

qN2 mDtsup , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)

and the slope, m, is determined from Eq. 2. The superposition time,Dtsup, defined by Eq. 4, is used to handle multiple flow rateinjection. It eliminates the effect of the flow rate change on thepressure response and results in a smooth curve when increasingor decreasing the rate, so that the curve represents the skinchange only.

The procedure for using the real-time monitoring method is tofirst calculate the slope, m, which is a function of the reservoirparameters and is constant during the acid treatment, before theinjection of acid (or any fluid that might change the skin factor).Then, the pressure and flow rate are measured in real time at adesired time interval during the treatment. For each rate/pressure/time data point acquired, superposition time is calculated by Eq. 4,the new intercept by Eq. 6, and finally, the skin is determined byEq. 5. The theory presented has been implemented in a Windowsprogram to apply the technique in the field, and an example ofcomputing the superposition time, the intercept, and the skin factorat a given time is shown in the Appendix.

Use of Surface Pressure. The bottomhole pressure is required toapply the real-time monitoring method, but in most acid treatmentsonly the surface pressure, either on the injection string or on anannulus, is measured. Surface pressure can be converted to bot-tomhole flowing pressure by

pwf 5 ptf 1 DpPE 2 Dpf , . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

where ptf 5 the surface pressure, pwf 5 the bottomhole flowingpressure, DpPE 5 the hydrostatic pressure drop, and Dpf 5 thefrictional pressure drop. The hydrostatic pressure drop is a functionof the fluid density and changes when a different fluid is injected.The frictional pressure drop is a function of the injection rate, fluiddensity, and fluid viscosity, which may vary during an acid treat-ment. When a different fluid is introduced to displace the old fluidin the tubing, as the new fluid is pumped down, the hydrostatic

Copyright 1998 Society of Petroleum Engineers

This paper (SPE 52400) was revised for publication from paper SPE 35197, firstpresented at the 1996 SPE Permian Basin Oil and Gas Recovery Conference heldin Midland, Texas, 2729 March. Original manuscript received for review 27 May1996. Revised manuscript received 17 March 1998. Revised manuscript approved6 August 1998.

279SPE Production & Facilities, November 1998

pressure drop changes and can be calculated by

DpPE 5gq cos u

gcA Fr2Dtnew 1 r1SALq 2 DtnewDG, . . . . . . . . . . (8)where A 5 the cross-sectional area of the tubing, q 5 the injectionrate, u 5 the average inclination of the tubing, r1 5 the density ofthe old fluid, r2 5 the density of the new fluid, L 5 the length ofthe tubing, and Dtnew 5 the time increment after start of pumpingthe new fluid. Eq. 8 reduces to

DpPE 5gr2 cos u

gc, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (9)

when Dtnew . the time required to fill the tubing with the new fluid.In a similar fashion, the frictional pressure drop is different in theportions of the tubing string containing different fluids.

The vertical depth of the well should be used in calculating thehydrostatic pressure drop, and the actual length of the well (mea-sured depth) should be used in the calculation of the frictionalpressure drop. For a deviated well, these two lengths are not thesame. When coiled tubing is used to inject the fluid, the length usedto calculate the frictional pressure drop should be the actual lengthof the coiled tubing, which may be significantly longer than theactual length of the well.

Pretreatment Test. The pretreatment test was presented by Mont-gomery et al.4 to estimate the initial skin and permeability of theformation, if they are not available before an acid treatment, and isincluded in the program. Injecting an inert fluid before the acidinjection is required to conduct a pretreatment test; however, thisis a common procedure in many matrix acidizing treatments. Fromthe measured pressure and flow rate, the permeability and initialskin are calculated by standard pressure transient analysis for aconstant rate injection. Even when the information is known fromother sources, the pretreatment test is useful to calculate the initialskin and permeability as a check against previous estimates.

Real-Time Monitoring ProgramThe program developed to execute the real-time monitoring tech-nique runs under the Windows environment on a PC. When appliedin the field, the computer running the program can be connectedeasily to either a data acquisition system or another computer,provided by the service company, that has the measured tubinghead, annulus, or bottomhole pressure, and flow rate stored througha standard RS-232 interface. The data are transferred to the com-puter in a string format and then decomposed into arrays ofnumbers. The user defines the channels containing time, pressure,and flow rate and chooses the time interval to acquire data andcalculate skin factor. The calculation executes only if a full stringis received at the user-defined time and pauses if the acquired stringdoes not have enough data. The program is flexible in acceptingdifferent formats of data, and several service companies standarddata formats have been built into the program. The inverse injec-tivity vs. superposition time, the evolving skin, and the injectionrate and bottomhole pressure as functions of time are plotted in realtime (Fig. 1). Data can be input manually, if necessary. Theprogram also can be used to review and evaluate matrix treatmentsafter the treatment is completed.

Field ExamplesExample 1. This treatment was conducted in an oil field locatedin west Texas. The treated well was a vertical oil-producing wellcompleted in the San Andres (dolomite) formation. The acidtreatment consisted of multistage injection alternating 15% HCl anddiverting stages consisting of a mixture of gelled brine and rock salt.The acid and the diverting stages were separated by brine spacers.Surface pressure and flow rate were measured from a data acqui-sition system and stored in a control computer by the servicecompany.

The data were gathered from the control computer through thecommunication port and treated by the program in real time. Theprogram converted the measured surface pressure to the bottomhole

Fig. 1Output panel for the real-time monitoring program.

280 SPE Production & Facilities, November 1998

pressure, accounting for the density and viscosity changes. The skinfactor was calculated by the theory presented in this paper, and thestimulation and diversion effects were clearly indicated from thecalculated skin factor by the monitoring program.

Table 1 lists the treatment information and test results for thefield test, Fig. 2 is the rate/pressure record from this treatment, andFig. 3 shows the skin plot generated from the program. The periodsof skin reduction indicate the formation response to the acidtreatment (stages marked 1 on Fig. 3), and the periods of increasingskin are the response to the diversion (stages marked 2). From Fig.3, it can be seen that there was a delay in the formation responseto the injection, with the skin factor increasing for a while after theacid reached the perforations and decreasing for a time after thediverter reached the perforations. This could be caused by an errorin estimating the arrival of each fluid at the perforations. The delayseen in the response to the acid, particularly during the first twostages, also could be because of the slow initiation of wormholesduring the early stages of acidizing. The formation had positiveresponses to each acid injection, and the skin was removed com-pletely by the acid treatment several times during the treatment. Thediversion was also effective, as indicated by the apparent skinincreasing after each injection of the diverting agent. Each diverterstage created an effective skin increase; however, it is also clear thatthe acid was removing the diverter, as indicated by the apparent skindropping to near zero (or even below) after the acid stages fol-lowing diverter stages. Fig. 3 shows that the skin factor decreasedto zero or even below several times during the treatment, whichsuggests that the treatment should be stopped after the third acidinjection because the rest of the treatment did not add any benefit.In this dolomite formation, if the formation is naturally fractured,a slightly negative skin of 21 or 22 is possible with completedamage removal. Because the skin factor returned nearly to thesame value after the third, fourth, and fifth stages of acid, it is likelythat the maximum matrix stimulation benefit had been achieved.The last couple of diversion injections caused a significant increasein the apparent skin effect, and the last acid injection did not lastlong enough to reduce the skin again to zero.

Example 2. This acid treatment was conducted at an offshore fieldbeing waterflooded. The treated well was a deviated water-injectionwell with a depth of 3,300 ft. The treatment was a one-stage acidinjection through coiled tubing, and the coiled tubing length was7,600 ft. The tubing pressure and annular pressure were measuredat the surface. The coiled tubing length was used to calculate thefrictional pressure drop.

Communication was established between the control board andthe computer running the program, and the data were acquired fromthe control board. The program processed the data correctly at realtime. A pretreatment test analysis was conducted to confirm theestimate of the reservoir permeability and the initial skin.

Table 2 lists the monitoring result for the example, and Fig. 4is the rate/pressure record from this treatment. Fig. 5 shows the skinplot generated from the program in real time. The skin factor was

Fig. 2Flow rate and bottomhole pressure for Example 1.

TABLE 1RESERVOIR INFORMATION AND MONITORINGRESULTS FOR EXAMPLE 1

Time(minutes)

q(bbl/min)

pwf(psi) s Fluid at Perforations

1.0 2.1 1772 11 brine3.0 2.1 2102 1 brine5.0 1.3 2153 7 brine7.0 1.0 2103 10 brine9.0 1.0 2133 11 brine

11.0 1.0 2183 13 brine15.0 0.7 1823 9 xylene21.0 0.7 1823 10 xylene27.0 0.7 1843 11 xylene29.0 0.7 2072 19 brine31.0 0.8 2070 15 brine33.0 0.9 1959 10 brine37.0 0.9 1979 11 brine41.0 0.8 1970 13 brine43.0 0.7 1942 15 brine45.0 0.6 1943 18 brine47.0 0.6 1963 19 brine51.0 0.5 1954 24 brine75.0 0.5 2053 30 acid85.0 1.4 2108 7 acid91.0 2.1 2050 2 acid97.0 1.9 2173 4 gelled rock salt

101.0 1.9 2253 5 gelled rock salt107.0 1.2 2213 10 acid113.0 0.8 2210 20 acid117.0 0.5 2183 35 acid121.0 0.4 2174 45 acid125.0 0.6 2162 28 acid129.0 0.5 2163 35 acid133.0 0.5 2136 34 acid135.0 1.6 2233 7 acid147.0 2.1 2212 3 gelled rock salt153.0 2.1 2006 0 acid155.0 0.7 2041 17 acid159.0 2.2 1932 0 acid179.0 0.5 2193 31 acid189.0 2.5 2205 2 acid191.0 2.9 2201 0 acid193.0 2.9 2051 21 acid195.0 3.0 2293 0 gelled rock salt201.0 0.3 2274 63 acid203.0 0.3 2234 62 acid207.0 0.3 2254 66 acid209.0 0.4 2254 49 acid211.0 0.4 2254 48 acid221.0 0.5 2223 37 acid229.0 3.0 2216 0 acid235.0 2.9 2520 3 gelled rock salt237.0 0.4 2294 48 acid239.0 0.3 2294 68 acid245.0 0.4 2294 52 acid251.0 3.2 2305 0 acid257.0 2.5 2512 4 gelled rock salt259.0 0.8 2485 26 gelled rock salt261.0 0.3 2284 66 acid267.0 0.3 2264 68 acid273.0 0.3 2254 69 acid281.0 0.3 2284 72 acid291.0 0.3 2304 75 acid313.0 0.3 2304 76 acid317.0 0.3 2314 77 acid319.0 0.3 2226 70 acid

Reservoir pressure 5 1229 psi, permeability 5 3.5 md, formation thickness 581 ft, porosity 5 0.18, formation factor 5 1.08, initial skin factor 5 30.


calculated with both the annular surface pressure and the tubing-head pressure. The result from the annular pressure is more reliablebecause there was no flow in the annulus; thus, no frictionalpressure drop was involved in the calculation. Obviously, theformation did not respond to the treatment as expected. The skinfactor increased as the acid was injected, and the flow in theformation was not improved by the treatment. A mixture of xyleneand 15% HCl was used in this treatment. The operator concludedthat hydrofluoric acid (HF) was needed to remove the damage inthis well.

Example 3. The third well tested was a water-disposal injectionwell treated with a 30 bbl preflush of 15 wt% HCl, followed by 60bbl of 3 wt% HF, 12 wt% HCl mud acid, and displaced with a 2wt% NH4Cl solution. No diversion methods were used (see Table 3).

Fig. 6 is the rate/pressure record from this treatment, and Fig. 7shows the skin factor response generated by the real-time moni-

toring program. The initial skin factor for this well was about 110and remained constant as the normal injection water was displacedfrom the tubing by the HCl preflush. The skin factor then decreasedgradually in response to the HCl preflush, with the decreasebeginning after about 12 bbl of HCl should have reached theformation. The response to the HF/HCl stage was more pro-nounced, but, again, with a delay from when HF first reached theformation. The mud acid stage was calculated to reach the topperforations at about 27 minutes, at which time the skin factor wasabout 86; however, the skin factor continued to decline at the samerate until about 5 minutes later (about 10 bbl of injection), afterwhich the decline rate increased sharply. Finally, the skin factorbecame constant at near zero at the end of the treatment, when the2% NH4Cl solution had displaced the mud acid from the nearwellbore vicinity.

This treatment showed an obvious, pronounced decrease in skinfactor in response to both the HCl preflush and the mud acid stages.


TABLE 2RESERVOIR INFORMATION AND MONITORING RESULTS FOR EXAMPLE 2

t(minutes)

q(bbl/min)

pwf from pa(psi)

pwffrom ptf

(psi)s from

pwfs from

ptfFluid at

Perforation

288.86 1.52 2304.7 2304.8 20 20 acid

291.85 1.48 2304.7 2249.9 21 20 acid

295.95 1.47 2314.6 2464.3 22 26 acid

298.66 1.48 2294.8 2444.5 21 25 acid

311.83 1.24 2205.8 3225.0 23 56 acid

313.46 1.30 2205.8 2936.0 22 44 acid

316.17 0.44 1929.0 2074.9 52 65 acid

316.30 0.86 1938.9 2031.3 25 29 brine

317.11 1.18 2088.4 2602.0 23 41 brine

323.78 1.36 2255.3 2425.9 22 27 brine

325.82 0.75 2275.0 2608.1 45 62 brine

328.39 1.00 2255.3 2392.5 32 38 brine

333.67 0.42 2116.9 2170.1 72 77 brine

334.35 0.44 2097.1 2094.4 67 67 brine

334.76 0.42 2077.3 2102.1 69 71 brine

335.58 0.44 2057.5 2074.9 64 65 brine

335.98 0.42 2047.7 2092.3 66 71 brine

336.12 0.43 2047.7 2083.7 65 68 brine

336.53 0.42 2037.8 2092.3 66 71 brine

336.80 0.42 2037.8 2082.6 66 70 brine

Reservoir pressure 5 1000 psi, formation factor 5 1, porosity 5 0.24, formation thickness 5 80 ft, permeability 5 100 md,initial skin factor 5 20, compressibility 5 5 3 1026 psi21, viscosity 5 1 cp.

Fig. 3The evolving skin factor during the treatment, Example 1.


The final skin factor of near zero showed that the designed acidvolume, which was only 7 gal/ft of mud acid, was sufficient toregain the natural conductivity of the nondamaged reservoir (skin 50) with a matrix acidizing treatment.

Conclusions1. A new method of real-time monitoring of the skin change

during a matrix acidizing treatment has been developed to help theoperator evaluate an acid treatment while it proceeds. The methoduses the relationship between inverse injectivity and the superpo-sition time function to calculate the evolving skin from measuredpressure and flow rate.

2. A Windows program based on the real-time monitoring theorywas designed to apply the technique in the field. It can be used forsurface pressure measurement, varying flow rate, and varyinginjected fluid density and viscosity.

3. Field examples demonstrate that the real-time monitoringtechnique shows the reservoir response to stimulation and diversionclearly and can be used to optimize matrix acidizing treatments.

NomenclatureA 5 area of the cross section of tubingb 5 intercept of inverse injectivity vs. Dtsup plot for ver-

tical wellB 5 formation volumetric factorct 5 total formation compressibility, psi21g 5 acceleration of gravity

gc 5 gravitational constanth 5 formation thickness, ftk 5 formation permeability, mdL 5 wellbore length, ftm 5 slope of inverse injectivity vs. Dtsup plot for vertical

wellN 5 number of time periodsp 5 pressure, psi

pa 5 annulus pressure, psipi 5 initial formation pressure, psiptf 5 tubing injection pressure (surface), psipwf 5 bottomhole flowing pressure, psi

q 5 flow rateqj 5 injection rate at time j, bbl/minqN 5 injection rate at time N, bbl/minrw 5 wellbore radius, fts 5 skin factort 5 time, hourtj 5 jth time periodtN 5 Nth time period

Dpf 5 friction pressure drop, psiDpPE 5 hydrostatic pressure drop, psiDtnew 5 time since a new fluid is pumped, minutesDtsup 5 superposition time function

f 5 porosityr 5 density, lbm/ft3m 5 viscosity, cpu 5 tubing inclination

AcknowledgmentsWe thank the sponsors of the Stimulation, Logging, and FormationDamage Research Program at the U. of Texas, Austin, for supportof this work. We also thank James Pappas of Fina Oil and Gas andCarl Montgomery of Arco E&P Technology for their assistancewith field-testing.

References1. Hill, A.D. and Zhu, D.: Real-Time Monitoring of Matrix Acidizing

Including the Effects of Diverting Agents, SPEPF (May 1996) 95.


TABLE 3RESERVOIR INFORMATION AND MONITORINGRESULTS FOR EXAMPLE 3

Time(minutes)

q(bbl/min)

pwf(psi) s

Fluid atPerforations

9.83 1.58 1942 110 HCl

10.83 1.61 1861 97 HCl

11.85 1.61 1953 109 HCl

12.85 1.62 2011 117 HCl

13.85 1.62 1906 102 HCl

14.85 1.62 1997 115 HCl

15.87 1.62 1901 102 HCl

16.87 1.63 1873 97 HCl

17.38 1.63 1928 105 HCl

18.38 1.63 1873 97 HCl

19.90 1.64 1835 91 HCl

20.90 1.64 1853 94 HCl

21.40 1.64 1812 88 HCl

22.43 1.64 1803 87 HCl

23.43 1.64 803 87 HCl

25.43 1.64 1798 86 HCl

27.45 1.65 1802 86 HF/HCl

28.97 1.65 1793 85 HF/HCl

30.48 1.65 1743 78 HF/HCl

31.48 1.66 1673 69 HF/HCl

33.00 2.28 1671 49 HF/HCl

34.00 2.32 1638 44 HF/HCl

35.52 2.34 1493 30 HF/HCl

36.53 2.35 1422 23 HF/HCl

38.03 3.14 1458 18 HF/HCl

39.03 3.16 1444 17 HF/HCl

40.03 3.16 1403 14 HF/HCl

41.55 3.18 1367 12 HF/HCl

45.05 3.22 1367 11 HF/HCl

46.05 3.23 1374 12 HF/HCl

47.05 3.29 1325 8 HF/HCl

48.05 3.30 1304 7 HF/HCl

49.57 3.31 1269 4 HF/HCl

50.57 3.33 1242 2 NH4CL

51.58 3.33 1224 1 NH4CL

53.10 3.35 1201 0 NH4CL

54.60 3.33 1229 1 NH4CL

Reservoir pressure 5 1100 psi, formation factor 5 1, porosity 5 0.19, formationthickness 5 360 ft, permeability 5 85 md, initial skin factor 5 100,compressibility 5 3.5 3 1026 psi21, viscosity 5 0.68 cp.


2. Earlougher, R.C. Jr.: Advances in Well Test Analysis, Monograph Series,SPE, Richardson, Texas (1977) 5.

3. Prouvost, L.P. and Economides, M.J.: Applications of Real-Time MatrixAcidizing Evaluation Methods, SPEPE (November 1989) 401; Trans.,AIME, 287.

4. Montgomery, C.T., Jan, Y.-M., and Niemeyer, B.L.: Development of aMatrix Acidizing Stimulation Treatment Evaluation and Recording Sys-tem, SPEPF (November 1995) 219.

5. Behenna, F.R.: Interpretation of Matrix Acidizing Treatment Using aContinuously Monitored Skin Factor, paper SPE 27401 presented at the1994 SPE Formation Damage Control Symposium, Lafayette, Louisiana,710 February.

6. Economides, M., Hill, A.D., and Ehlig-Economides, C.: PetroleumProduction System, Prentice-Hall, Englewood Cliffs, New Jersey (1994)133150.

AppendixAn Example of Calculating Skin FactorThis example will calculate the skin factor at Point 4 in Table 2. Theinformation for the reservoir and the treatment are listed in Table 2.

From Eq. 2, the slope of the inverse injectivity vs. Dtsup, m, is

m 5162.2 3 1 3 1

80 3 100 5 0.0203, . . . . . . . . . . . . . . . . . . . . . (A-1)

and the superposition time from Eq. 4 is

Dtsup 51.48 2 1.52

1.48 logS298.66 2 288.8660 D1

1.47 2 1.481.48 logS298.66 2 291.8560 D

11.48 2 1.47

1.48 logS298.66 2 295.9560 D5 0.0186; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-2)

thus, from Eq. 6, the intercept at that point is

b 52294.8 2 10001.48 3 1440 2 ~0.0203 3 0.0186!

5 0.608 2 0.0004

5 0.607, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-3)and the skin factor at the point, by Eq. 5, is

s 51

0.868F 0.6070.0203 2 logS 1000.24 3 1 3 5 3 1026 3 0.52D1 3.23G5 25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-4)

SI Metric Conversion Factorsbbl 3 1.589 873 E201 5m3cp 3 1.0* E203 5Pazsft 3 3.048* E201 5m

ft3 3 2.831 685 E202 5m3gal 3 3.785 412 E203 5m3psi 3 6.894 757 E100 5kPa

*Conversion factors are exact. SPEPF

Ding Zhu is a research associate in the Petroleum Engineeringand Geosystems Dept. at U. of Texas, Austin. She holds a BSdegree in mechanical engineering from Beijing U. of Scienceand Technology and MS and PhD degrees in petroleum engi-neering from the U. of Texas, Austin. A. Daniel Hill is the B.J.Lancaster Professor of Petroleum Engineering in the PetroleumEngineering and Geosystems Dept. at the U. of Texas, Austin.e-mail: [email protected]. He holds a BS degree fromTexas A&M U. and MS and PhD degrees from the U. of Texas,Austin, all in chemical engineering. Hill, author of the SPE Mono-graph Production Logging: Theoretical and Interpretive Ele-ments and a 198889 Distinguished Lecturer, was 199495member and 199597 chairman of the Books Committee,199293 member and 199395 chairman of the Symbols andMetrication Committee, and a 198085 and 199597 memberof the Editorial Review Committee. He was the founding chair-man of the Austin Section in 198687 and U. of Texas StudentChapter faculty sponsor during 198384 and 198788.




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