assessment of mud-filtrate-invasion effects on borehole … · 2014-12-11 · assessment of...

Assessment of Mud-Filtrate-InvasionEffects on Borehole Acoustic Logs and

Radial Profiling of FormationElastic Properties

Shihong Chi,* SPE, Carlos Torres-Verdín, SPE, Jianghui Wu,** SPE, and Faruk O. Alpak,† SPE,U. of Texas at Austin

SummaryDespite continued improvements in acoustic-logging technology,sonic logs processed with industry-standard methods often remainaffected by formation damage and mud-filtrate invasion. Quanti-tative understanding of the process of mud-filtrate invasion is nec-essary to identity and assess biases in the standard estimates ofin-situ compressional- and shear-wave (P- and S-wave) velocities.We describe a systematic approach to quantify the effects of mud-filtrate invasion on borehole acoustic logs and introduce a newalgorithm to estimate radial distributions of elastic properties awayfrom the borehole wall. Radial saturation distributions of mudfiltrate and connate formation fluids are obtained by simulating theprocess of mud-filtrate invasion. Subsequently, we calculate radialdistributions of the elastic properties using the Biot-Gassmannfluid-substitution model. The calculated radial distributions of for-mation elastic properties are used to simulate array sonic wave-forms. Finally, estimated P- and S-wave velocities for homoge-neous, stepwise, and multilayered formation models are comparedto quantify mud-filtrate-invasion effects on sonic measurements.

We use a nonlinear Gauss-Newton inversion algorithm to es-timate radial distributions of formation elastic parameters in thepresence of invaded zones using normalized spectral ratios of arraywaveform data. Inversion examples using synthetic and field dataindicate that physically consistent distributions of formation elasticproperties can be reconstructed from array waveform data. In turn,radial distributions of formation elastic properties can be used toconstruct more-realistic near-wellbore petrophysical models forapplications in reservoir simulation and production.

IntroductionDuring and after drilling, the near-wellbore formation is oftenaltered by stress buildup and release, mud-filtrate invasion, chemi-cal reactions, and many other factors. These alterations cause thephysical properties in the near-wellbore region to be different fromthose of the virgin rock formation. Stress concentration around awellbore may cause near-wellbore damage and induce formationanisotropy on P- and S-wave velocities. The stress-induced anisot-ropy can be identified by dispersion analysis (Plona et al. 2002).Positive radial velocity gradients focus the elastic waves propa-gating away from the wellbore back toward the borehole wall.Such a phenomenon can be identified easily from high-amplitudeacoustic arrivals. In this paper, we focus our attention on mud-filtrate-invasion effects only.

It is well known that formation properties inferred from wire-line logging measurements may not reflect true properties of virginformations. A realistic description of the invaded zone is important

for the processing and interpretation of sonic logs. A commonmodel used in the open literature assumes that a sharp interfaceexists between the altered zone and the undisturbed formation(Baker 1984). The term “stepwise” is used to describe this type ofmud-filtrate-invasion model. Linear-gradient models have beendescribed for syntheses of acoustic waveforms as well (Stephenet al. 1985). Actual radial distributions of elastic wave propertiesresulting from invasion can be complex and are dependent on thespecific petrophysical properties of the rock as well as on the staticand dynamic properties of the fluids involved. We divide the in-vaded zone into a set of concentric radial layers to represent anactual invasion profile and call it a “multilayered” model. Subse-quently, we describe a procedure for calculating the radial distri-butions of formation elastic properties with the Biot-Gassmannfluid-substitution model starting from numerically simulated radialdistributions of flow saturation.

Theoretical and experimental studies (Geertsma and Smit 1961;Biot 1956a, 1956b; Toksöz et al. 1976; Domenico 1976; Dutta andOde 1979; Murphy 1982) have shown that rocks saturated withhydrocarbons and water can be differentiated with acoustic veloc-ity measurements. Using time-lapse acoustic logging, bypassedzones can be identified, and fluid movement in rock formationscan be monitored in open and cased holes. If the invasion depth isbeyond the radial length of investigation of a logging tool, themeasured velocities will reflect those of the invaded zone, and logcorrections will be necessary to estimate virgin-formation velocities.

The current industry practice of acoustic-data processing makesuse of the slowness-time coherence (STC) method to estimatein-situ velocities of rock formations. This type of processing yieldsvalues of P- and S-wave velocities, both of which are intricatefunctions of formation and borehole properties, frequency, andnumber of time samples used in the time window of the STCalgorithm. When invasion into a formation is significant, the STCmethod still gives one P-wave velocity and/or S-wave velocity ateach depth of measurement, which may reflect only properties ofthe invaded zone. However, waveforms recorded by modernacoustic tools may contain valuable information on the radial dis-tribution of near-wellbore formation properties.

In an effort to estimate radial distributions of near-wellboreformation properties, Hornby (1993) developed a tomographic re-construction technique that yielded formation P-wave velocitiesfrom sonic travel times. The estimation was performed with aseries of linear inversions followed by ray tracing. However,travel-time tomography using ray tracing requires accurate pickingof the refracted arrivals of each wave train and the use of anaccurate high-frequency ray-trace approximation.

Few studies of seismic full-waveform inversion (Sen and Stoffa1991; Zhou et al. 1997; Pratt 1999a, 1999b) show that the use ofamplitude data can improve the resolution of 1D vertical distribu-tions of velocity and density. The amplitude and phase behavior offull-waveform data are sensitive to the petrophysical properties offormations supporting the propagation of elastic waves. Therefore,full-waveform analysis has significant potential in acoustic log-ging to estimate petrophysical properties of invaded zones andvirgin formations. The reconstruction of formation slowness away

* Currently with ConocoPhillips.** Currently with Baker Atlas.† Currently with Shell Intl. E&P.

Copyright © 2006 Society of Petroleum Engineers

This paper (SPE 90159) was first presented at the 2004 SPE Annual Technical Conferenceand Exhibition, Houston, 26–29 September, and revised for publication. Original manuscriptreceived for review 4 June 2004. Revised manuscript received 29 May 2006. Paper peerapproved 25 July 2006.

553October 2006 SPE Reservoir Evaluation & Engineering

from the borehole wall can provide valuable calibration factors formeasurements acquired with shallow-reading devices. Correctionsprovided by full-waveform inversion may be of primary impor-tance for the robust and accurate computation of synthetic seis-mograms. There is, however, one major difficulty to overcome infull-waveform inversion. In all field applications, the effectivesource wavelet; the coupling among source, borehole, and forma-tion; and the coupling between receivers and the formation dependon the in-situ borehole conditions. The practical difficulty in esti-mating the sonic-source signature is probably the reason why veryfew attempts have been made to use the information borne by thefull waveform of acoustic-logging data.

Cheng (1989) described an indirect method for determiningS-wave velocities from full-waveform acoustic logs by means ofinversion. This method makes use of the spectral ratio of theP-wave trains at two source/receiver separations and simulta-neously inverts for both S-wave velocity and P-wave attenuation.In that paper, Cheng’s approach based on spectral-ratio data wasextended to full-waveform arrays to overcome the practical diffi-culty of the unknown source-output spectrum. Lee and Kim (2003)estimated P-wave velocity distributions from synthetic seismicdata by use of a spectral-ratio method. Frazer et al. (1997) andFrazer and Sun (1998) described an inversion method for process-ing array full-waveform data. Their approach does not require anexact source function, although it is a necessary part of the inver-sion. Because of this, the chosen source function can bias theinversion results.

Our inversion approach first transforms array waveforms intothe frequency domain to construct a set of normalized array sonicdata. The normalized wavefield is independent of the spectrum ofthe source; hence, the proposed inversion method allows one tomake use of the full-waveform content of sonic data without re-quiring knowledge of the source signature. Previous studies offull-waveform borehole acoustic measurements assumed a homo-geneous and isotropic formation and a model for borehole wavepropagation without surface irregularities. In this paper, we makethe assumptions of a radially multilayered formation model and acylindrical borehole.

MethodologyNumerical Simulation of Mud-Filtrate Invasion. Mud-filtrateinvasion is regarded as a water- or oil-injection process into a gasor oil reservoir wherein two-phase immiscible fluid flow is as-sumed in the simulations. To study the effects of different types ofmud filtration on gas or oil reservoirs, the following cases areselected: (a) water-based mud invades oil and gas reservoirs pen-etrated by open holes and (b) oil-based mud invades gas reservoirspenetrated by open holes. In each of these cases, it is assumed thata vertical well penetrates horizontally layered rock formations andthat the rock formation considered does not communicate hydrau-lically with its upper and lower shoulder beds. To study the sen-sitivity of mud-filtrate invasion to formation petrophysical prop-erties, we consider a low-permeability (30 md) and low-porosity(15 p.u.) reservoir and a high-permeability (300 md) and high-porosity (30 p.u.) reservoir for Cases (a) and (b).

Details of the numerical simulation of the process of mud-filtrate invasion in open holes can be found in Wu et al. (2004,2005) and George et al. (2004). In the simulations, both the dy-namic growth of the mudcake and the dynamic decrease of themudcake permeability are coupled to formation properties. Thisresults in a dynamic monotonic decrease of flow rate into theformation. After a short initial spurt of mud-filtrate invasion, theinvasion process reaches a steady state. Cycles of mudcake ruboffand buildup can also affect the process of mud-filtrate invasion.

Fig. 1 is a schematic of the process of mud filtrate invading apermeable rock formation. The invasion front moves deeper intothe formation with time. Fig. 2 shows the time evolution of water-based mud-filtrate saturation in the radial direction of a low-porosity, low-permeability, and oil-bearing sandstone formation.The water-based mud filtrate reaches a radial distance of approxi-mately 0.8 m after 4 days of invasion. Mud-filtrate invasion isshallower for the corresponding high-porosity case. Fig. 3 shows

that mud filtrate penetrates to a radial distance of 0.5 m after 4 daysof invasion.

Because of relative permeability, in the example case consid-ered here, oil-based mud invades the gas-bearing sandstone for-mation at a much slower rate than for the case of water-basedmud-filtrate invasion. Fig. 4 shows the time evolution of oil-basedmud-filtrate saturation in the radial direction of a low-porosity (15p.u.) and low-permeability (30 md) formation. Oil-based mud fil-trate reaches a radial distance of approximately 0.2 m after 4 daysof invasion. Fig. 5 shows that mud filtrate primarily concentrateswithin a distance of 0.1 m away from the borehole wall.

Radial Distributions of Density and P- and S-Wave Velocitiesin an Invaded Zone. Once radial profiles of invasion are obtainedfrom numerical simulations, radial distributions of the elastic prop-erties of a formation can be calculated using the Biot-Gassmannfluid-substitution equations. Following the tutorial presented bySmith et al. (2003), a calculation is first performed for the basicformation and fluid properties. Subsequently, for each point in thesaturation profile we calculate (a) fluid properties, (b) saturatedbulk modulus of the rock, (c) bulk density of the rock, and (d) P-and S-wave velocities.

When computing fluid and formation properties after invasion,a careful selection of homogeneous or patchy saturation models isnecessary. Over geologic time, fluids in the pores of the rocksbecome homogeneously distributed. This is one of the important

Fig. 1—Schematic of the process of mud-filtrate invasionin rock formations penetrated by a mud-filled and overbal-anced borehole.

Fig. 2—Time evolution of mud-filtrate invasion for the case ofwater-based mud invading a 15%-porosity, oil-bearing rock for-mation. From left to right, the first curve is the water-saturationprofile 1 day after the onset of mud-filtrate invasion. The timeincrement is 1 day, and the rightmost curve describes watersaturation at the 16th day.

554 October 2006 SPE Reservoir Evaluation & Engineering

assumptions of the Biot-Gassmann fluid-substitution model. How-ever, mud-filtrate invasion in the near-wellbore region changes theconnate-fluid distribution. From the numerical-simulation resultsdescribed in this paper, it is clear that the equilibrium of fluidphases in the near-wellbore region is not established within a fewdays after the onset of the mud-filtrate-invasion process. There-fore, it is more appropriate to use a patchy saturation model tocompute the corresponding bulk modulus (Hill 1963).

Numerical Simulation of Time-Lapse Borehole Acoustic Mea-surements. On the basis of saturation-profile and fluid-substitution calculations, we obtain a discretized and concentricmultilayered rock model. The radial discretization is sufficient toensure accurate representation of the continuous radial distribu-tions in the calculation of elastic properties. A corresponding step-wise-invaded-zone model also is used for the numerical simula-tion. The waveforms simulated for the multilayered and stepwisemodels are compared, with the objective of determining when thestepwise models are adequate to represent the invaded zone.

In the synthesis of array waveforms, we assume a representa-tive source/receiver configuration. For monopole logging, the cen-tral frequency of the source is 10 kHz. The minimum source/receiver distance is 9 ft, with the receiver array consisting of eightreceivers spaced at 6-in. intervals. Dipole logging makes use of a1.5-kHz source and a minimum source/receiver separation of 11.5ft. In the lower dipole mode, the eight source/receiver offsets varyfrom 3.51 m (11.5 ft) to 4.57 m (15 ft) with a receiver spacing of0.15 m (6 in.). We simulate sonic array waveforms for a homo-geneous virgin formation as well as for a saturated formation after4 days of mud-filtrate invasion.

Processing and Interpretation of Monopole and Dipole Log-ging Data. The sensitivity of acoustic measurements to differentinvasion models and radial saturation profiles can be assessed bycomparing the synthetic waveforms for homogeneous, stepwise,and multilayered radial formation models. Arrival times and am-plitudes of P- and S- wave modes are the main waveform featuresused to assess the effect of mud-filtrate invasion on boreholeacoustic logging measurements.

We use an industry standard STC method (Kimball andMarzetta 1984) to determine the P- and S-wave velocities of arraysonic waveforms. Radial depths of investigation for sonic toolsdepend on formation elastic properties, transmitter-to-receiverspacing, wavelength and wave mode considered, and frequency,among other factors. Because we chose a typical sonic-tool con-figuration and source frequencies used by the logging industry, wecan focus our study of invasion effects on velocity measurements.After P- and S-wave velocities are determined, the depth of inves-tigation can be ascertained from the inspection of radial velo-city profiles.

When correlating seismic data with acoustic logs, it is oftenfound that synthetic seismograms do not match the measured seis-mograms. As a result, corrections to the acoustic logs by means ofBiot-Gassmann fluid substitution are common in the seismic in-dustry to eliminate mud-filtrate-invasion effects from sonic logs.In this correction procedure, it is assumed that the measured ve-locities are those of the invaded zone saturated with mud filtrate.For the case of oil-based mud, filtrate mixing with gas may haveto be considered before fluid substitution. By displacing the satu-ration fluid in the invaded zone with the connate formation fluidand by applying the Biot-Gassmann fluid-substitution equation,new velocities are obtained and taken as virgin-formation veloci-ties. We investigate the validity of this practice through severalcase studies.

Fig. 3—Time evolution of mud-filtrate invasion for the case ofwater-based mud invading a 30%-porosity, oil-bearing reser-voir. From left to right, the first curve is the water-saturationprofile 1 day after the onset of mud-filtrate invasion. The timeincrement is 1 day, and the rightmost curve describes watersaturation at the 16th day.

Fig. 4—Time evolution of mud-filtrate invasion for the case ofoil-based mud invading a 15%-porosity, gas-bearing reservoir.From left to right, the first curve is the water saturation profile 1day after the onset of mud-filtrate invasion. The time incrementis 1 day, and the rightmost curve describes oil saturation at the16th day.

Fig. 5—Time evolution of mud-filtrate invasion for the case ofoil-based mud invading a 30%-porosity, gas-bearing reservoir.From left to right, the first curve is the water saturation profile 1day after the onset of mud-filtrate invasion. The time incrementis 1 day, and the rightmost curve describes oil saturation at the16th day.


Full-Waveform Inversion. In our inversion of radial elastic prop-erties, we assume a cylindrical borehole surrounded by concentricmultilayered formations. We first transform array sonic waveformsinto the frequency domain to construct a set of normalized arraysonic spectra. The normalized wavefield is independent of thespectrum of the source; hence, the proposed inversion methodallows one to make use of the full-waveform content of sonic datawithout requiring knowledge of the source signature. The normal-ized wavefield (or spectrum) of full waveforms constitutes themeasurement data input to the full-waveform inversion algorithm.For estimation of the radial distributions of elastic properties, den-sity and P- and S-wave velocities are assigned to each concentriclayer in the near-wellbore region. Subsequently, we simulate themeasured wavefields with the assumed properties. A cost functionthat enforces the quadratic difference between the simulated andmeasured normalized wavefields is used for inversion. We makeuse of a Gauss-Newton fixed-point iteration search to determine astationary point at which the cost function attains a minimum. Thestationary point yields the radial distribution of elastic properties.Details of the full-waveform inversion are given in the Appendix.

Case StudiesSandstone Oil Reservoir Invaded With a Water-Based Mud. Inonshore drilling activities, water-based mud is still widely usedbecause of its efficiency to balance formation pressure withoutsubstantially increasing costs. Elastic properties of oil in rock for-mations are much closer to those of mud filtrate derived from awater-based mud. Compared to the case of mud filtrate invading agas reservoir, it may be more difficult to distinguish mud-filtrate-invasion effects on the measured velocities. Moreover, fluid-flowproperties of oil and gas are very different from each other. Tostudy the sensitivity of the measured velocities to porosity andpermeability, this section first considers a low-porosity (15 p.u.)and low-permeability (30 md) reservoir. Table 1 summarizes thepetrophysical and fluid properties used in the simulation of water-based mud-filtrate invasion. Subsequently, we focus our attentionto the case of a high-porosity (30 p.u.) and high-permeability (300md) reservoir. Saturation profiles of mud filtrate and oil in forma-

tions are simulated for 4 days of invasion. The latter profiles areused to calculate radial distributions of elastic properties using theBiot-Gassmann fluid-substitution model.

Fig. 2 shows the time evolution of mud-filtrate invasion for thecase of water-based mud invading the oil-bearing sandstone res-ervoir of 15% porosity. Fig. 6 shows the corresponding radialdistributions of density and P- and S-wave velocities calculatedwith the fluid-substitution parameters described in Table 2. Asshown in Fig. 6, in the invaded zones the P-wave velocity is higherthan that of the virgin formation, while the S-wave velocity be-comes lower than the original velocity. P-wave velocities esti-mated from the array waveforms (Fig. 7a) simulated for stepwiseand multilayered models are approximately 1% lower than those ofthe virgin formation. STC processing can introduce 1% uncertaintyin the estimation of P-wave velocity. Therefore, the 1% lowerP-wave velocity may result from STC processing. This impliesthat the P-wave is not sensitive to the invaded zone, which exhibitsa higher P-wave velocity. On the other hand, S-wave velocitiesobtained from STC processing of monopole and dipole waveformsare 2% lower than those of the virgin formation. This behavioragrees with the velocity decrease described in Fig. 6 and indicatesthat S-wave propagation is sensitive to the invaded zone.

Fig. 8 shows the radial distributions of density and P- andS-wave velocities for the high-porosity and high-permeability caseafter 4 days of invasion. The corresponding STC results show thatthe P-wave velocity is the same as that of the virgin formationwithin the processing error bound of 1%. This behavior indicatesthat P-wave propagation is sensitive to the radial region beyondthe invaded zone. The S-wave velocity obtained for this invadedmodel is approximately 2.6% lower than that of the virgin zone.This relatively larger reduction in S-wave velocity compared to thelow-porosity case is expected because more oil is replaced bywater-based-mud filtrate.

In summary, P-wave propagation is sensitive to the virgin zone,whereas S-wave propagation is sensitive to the invaded zone whenthe radial length of mud-filtrate invasion is approximately 0.5 to0.8 m for the two sandstone reservoirs considered in this section.

Sandstone Gas Reservoir Invaded With an Oil-Based Mud.Our study indicates that, in general, oil-based mud causes shal-lower invasion than water-based mud and, hence, less formationdamage. Because oil-based mud is also chemically less activecompared to water-based mud, it is more effective in inhibitingshale swelling. This is one of the reasons why oil-based mud iswidely used to drill expensive offshore wells.

Fig. 6—Radial distributions of density and P- and S-wave veloc-ities for the case of water-based mud invading a 15%-porosity,oil-bearing reservoir after 4 days of invasion.


We selected two synthetic cases to study mud-filtrate effects onthe measured velocities of sandstone formations exhibiting lowand high porosities and permeabilities.

Fig. 9 shows the radial distributions of density and P- andS-wave velocities for the case of a gas-bearing sandstone reservoirof 15% porosity invaded with an oil-based mud.

P-wave velocities estimated from array waveforms simulatedfor a stepwise and a multilayered model are approximately 1.0%higher than that of the true formation P-wave velocity, but ap-proximately 3.0% lower than that of an invaded zone saturatedwith 90% mud filtrate. Estimated S-wave velocities are approxi-mately 0.2% lower than that of the true formation S-wave velocity,while the S-wave velocity for the invaded zone is 1.2% lower thanthat of the true formation. Therefore, P- and S-wave velocities areslightly influenced by mud-filtrate invasion and remain primarilysensitive to the radial region beyond the invaded zone.

For the 30%-porosity case, Fig. 10 shows the radial distribu-tions of density and P- and S-wave velocities. It is observed fromthe monopole waveforms (Fig. 11) that the presence of invadedzones does not affect the P-wave arrival time, but it does delay theS-wave arrival time. On the other hand, P-wave amplitudes do notchange appreciably, whereas S-wave amplitudes increase. In thedipole waveforms, the change in S-wave arrival is negligible. Di-pole waveforms for the stepwise model are significantly differentfrom those simulated for the multilayered formation model.

P-wave velocities estimated from data for homogeneous, mul-tilayered, and stepwise models are the same. This behavior indi-

Fig. 7—Simulated (a) monopole and (b) dipole waveforms forthe homogeneous, stepwise, and multilayered formation mod-els shown in Fig. 6.

Fig. 8—Radial distributions of density and P- and S-wave veloc-ities for the case of water-based mud invading a 30%-porosity,oil-bearing rock formation after 4 days of invasion.

Fig. 9—Radial distributions of density and P- and S-wave veloc-ities for the case of oil-based mud invading a 15%-porosity,gas-bearing rock formation after 4 days of invasion.


cates that P-wave propagation is sensitive to the radial region pastthe invaded zone. S-wave velocities estimated for the stepwise andthe multilayered models are approximately 1% lower than that ofthe virgin formation. According to the Biot-Gassmann fluid-substitution model, a rock formation saturated with 90% mud fil-trate should exhibit a 4.3% S-wave velocity decrease compared tothat of the virgin formation. This indicates that the measuredS-wave velocities are primarily sensitive to the virgin formationbut remain influenced by mud filtrate in the near-wellbore re-gion. In all the cases studied in this section, both P- and S-wavesare not sensitive to the invaded zone when the oil-based mud-filtrate invasion reaches a radial length of approximately 0.3 m insandstone reservoirs.

Elastic Radial Profiles of a Fast Rock Formation. This inversioncase makes use of realistic elastic properties for a fast-formationmodel (Schmitt 1988), which consists of six radial layers, includ-ing a fluid layer in the borehole. Table 3 describes the actual fluidand formation properties and the radial discretization grid used forthe inversion. Amplitude spectra of the simulated waveforms areused in the estimation to accelerate the convergence of the inver-sion algorithm.

Fig. 12 shows radial distributions and crossplots of actual andinverted elastic properties after 26 iterations of the inversion al-gorithm. The inverted radial distributions of elastic propertiesshow a good agreement with the actual properties. Global corre-lation coefficients calculated between the inverted and the actualvalues of elastic properties indicate that all the inverted elasticproperties exhibit high global similarity with the original modelproperties (0.932, 1, and 1 for P- and S-wave velocities and den-sity, respectively).

Elastic Radial Profiles of a Slow Rock Formation. This exampleis an extension of the slow formation model in the simple boreholecases described by Cheng (1989) within the context of marinesediments. Table 4 describes the model, which consists of sixradial layers, including one fluid layer in the borehole. The tooland source configurations are the same as those discussed previ-ously for simple borehole cases. Given that the low-frequencycontent of the full waveforms is more important in soft formationsthan in fast formations, data from the frequency band 2–5 kHz areused for inversion. Inversion results from this example not onlyestimate the virgin-formation elastic properties but also give adescription of near-wellbore damage.

Inversions performed with no assumption of an increasingvalue of elastic properties away from the borehole wall convergeto local minima without exception. Fig. 13 shows the radial dis-tributions and crossplots of actual and inverted elastic propertiesafter 20 iterations for a slow formation under the assumption ofmonotonically increasing values of elastic properties. The inver-sion stops at a local minimum, as can be observed from the evo-lution of the data misfit and cost functions shown in Figs. 13a and13b, respectively. Global correlation coefficients for the invertedand actual velocities are relatively high (0.83 and 0.83 for P- andS-wave velocities, respectively). However, for bulk density, thecorrelation coefficient is −0.45. This indicates the relatively lowsensitivity of the measurements to radial variations of density in

Fig. 10—Radial distributions of density and P- and S-wave ve-locities for the case of oil-based mud invading a 30%-porosity,gas-bearing rock formation after 4 days of invasion.

Fig. 11—Simulated (a) monopole and (b) dipole waveforms forthe case of homogeneous, stepwise, and multilayered forma-tion models invaded with oil-based mud after 4 days of invasionin a 30%-porosity gas reservoir.


the 2- to 5-kHz frequency band. Overall, the inversion algorithmprovides a reliable way to estimate radial distributions of elasticproperties in soft rock formations. This is a valuable tool for de-tailed analysis of acoustic-logging data in offshore wells.

Elastic Radial Profiles From Field Data. This example assessesthe feasibility and performance of the inversion algorithm whenapplied to field data. Full-waveform acoustic data were acquired

with the Dipole Sonic Imager (DSI)* tool in the depth intervalfrom 13,000 to 13,050 ft within a well penetrating a tight-sandstone gas reservoir (Anderson Well No. 2). Core data and logmeasurements indicate that the porosity of the fine-grained sand-stone formation is below 9%. Gas saturation ranges from 80% to95%. Fig. 14a displays the array waveform data acquired at thedepth of 13,030 ft. The bottom four traces show very similarcharacteristics in the number of wave modes and in the amplitudesof each wave mode. The top four traces, however, exhibit a com-pletely different character. Fig. 14b displays the amplitude spectraof the array waveform data. The main energy of the waveforms iscontained in the frequency band from 9 to 14 kHz. Input data to theinversion algorithm are chosen to be the normalized frequencydata in the band of 11–14 kHz, given that previous examples showthat data from a narrower frequency-data band improve the con-vergence of the algorithm. The STC processing method yieldsformation P- and S-wave slowness values of 66.33 and 108.01�s/ft, respectively, which are used as the initial properties for theinversion. Likewise, the density log reads a value of 2.504 g/cm3

for bulk formation density. The mud density at this depth in the

* Mark of Schlumberger.

Fig. 12—Simultaneous inversion of radial distributions of elastic properties for a six-layer fast formation using noise-free normal-ized spectra of array waveform data. Panel (a) shows the array waveform in the time domain, and Panel (b) shows the data residualsyielded by the inversion. In Panel (c), the inverted radial distributions of elastic properties are identified with solid lines and opencircles; additional lines identify original model properties. Panel (d) shows that the correlation coefficient, r2, is the correlationcoefficient between the inverted and actual elastic properties.


borehole is 14 lbm/gal (1678 kg/m3), whereas the acoustic velocityof the mud is approximately 1186 m/s. Mud-filtrate-invasion stud-ies (Salazar et al. 2005) indicate that mud filtrate reaches a radialdistance of approximately 1.5 ft in the flow unit of interest after 24hours of drilling. Thus, we use a concentric five-radial-layer modelto describe the near-wellbore invasion zone. The inner radii of theradial formation layers are 0.07, 0.15, 0.30, 0.40, and 0.45 m,respectively, and the outmost layer is assumed to be unbounded inthe radial direction. Within each radial zone, formation elasticproperties are assumed constant.

First, normalized frequency data from Traces 1 through 4 in theband from 11 to 14 kHz are used as input data for the inversion.The data misfit decreases to 4% after 20 iterations. Fig. 14c indi-cates that the formation P- and S-wave velocities increase and bulkdensity decreases in the radial direction. It is known that formationdamage caused by drilling decreases the formation velocities andthat mud-filtrate invasion in the near-wellbore region increases thebulk density. The inverted radial distributions indicate that a dam-aged zone exists in the near-wellbore region even though the bore-hole is in excellent condition. Such a result also agrees with thehigh-amplitude P-wave components that are observed from Traces1 through 4 of the array sonic waveforms. A radial profile ofmonotonically increasing P-wave velocity focuses the elasticwaves propagating away from the wellbore back toward the bore-

hole wall and increases the P-wave amplitude (Winkler 1997;Chen et al. 1996). The radial distribution of density shows a de-creasing trend from the borehole wall into the formation. Such abehavior can be interpreted as due to mud-filtrate displacing gas inthe near-wellbore region. This exercise confirms that the inversionalgorithm is reliable to estimate radial distributions of formationelastic properties in the near-wellbore region.

ConclusionsIn the cases of water-based mud invading oil-bearing sandstonereservoirs, P-wave propagation remains sensitive to virgin zones,whereas S-wave propagation is affected by invaded zones whenthe radial length of invasion of mud filtrate is approximately 0.5 to0.8 m. In this latter situation, log corrections are not necessary forP-wave velocities, whereas detailed saturation-profile calculationsare needed to correct the measured S-wave velocities for mud-filtrate-invasion effects. For the cases of oil-based mud invadingsandstone reservoirs, both P- and S-wave propagations are insen-sitive to the presence of mud filtrate in the invaded zones.

We developed a new full-waveform inversion algorithm thatmakes use of the normalized frequency spectra of sonic wave-forms. The reliability of the inversion algorithm was tested suc-cessfully with radially multilayered 1D synthetic models. In addi-tion, we obtained petrophysically consistent results when the in-

Fig. 13—Radial distributions and crossplots of the actual and inverted elastic properties for a six-layer slow formation. Theevolution of the data misfit and cost function with iteration number is shown in Panels (a) and (b), respectively. In Plot (c), theinverted radial distributions of elastic properties are identified with open circles. Additional lines identify original model properties.Panel (d) shows the correlation coefficient, r2, between the inverted and actual elastic properties.


version algorithm was applied to field data acquired in a tightgas reservoir.

Inversion exercises performed on synthetic data indicate thatthe low-frequency content of full-waveform data is sensitive toformation elastic properties radially away from the borehole wall.Thus, high-frequency components of array sonic data may be pref-erable for estimating the radial distribution of elastic properties inthe near-wellbore region.

NomenclatureC(m) � cost functiond(m) � measurement vector numerically simulated for

specific values of mdobs � measurement vector

i � index or imaginary unitIm � imaginaryj, k � indices

J(m) � Jacobian matrixli � lower boundkf � fluid wave number

kpf� radial wave number of fluid

m � size-N vector of unknown parametersmR � size-N reference vector

M � number of frequency-domain measurementsN � number of radial layers

NFREQ � number of frequencies used for each traceNREC � number of receivers

r1 � radius of the first radial formation layerR � borehole radius

R̂(1)+− � reflectivity between the fluid and the first radial

layer of the formationRe � realSj � spectra of normalized waveforms

S(�) � effective-source-output spectrumT � transpose

T12 � transfer function between the two receiversui � upper boundVf � fluid acoustic velocityVp � P-wave velocityVs � S-wave velocity

Wd·WdT � inverse of the measurement covariance matrix

Wm·WmT � inverse of the model covariance matrix

z1, z2 � receiver locations� � prescribed value of enforced data misfit� � Lagrange multiplier or regularization parameter� � density

Fig. 14—Simultaneous inversion of radial distributions of elastic properties using array waveform data acquired in the AndersonWell No. 2 and penetrating a tight gas reservoir. Panel (a) shows the array waveforms in the time domain, and Panel (b) shows thecorresponding amplitude spectra. Panel (c) shows the homogeneous-formation model used to initialize the inversion and theinverted radial distributions of formation elastic properties.


AcknowledgmentsThe work reported in this paper was funded by the U. of Texas atAustin’s Research Consortium on Formation Evaluation, jointlysponsored by Aramco, Baker Atlas, BP, British Gas, ConocoPhil-lips, Chevron, Eni E&P, ExxonMobil, Halliburton Energy Ser-vices, Marathon, the Mexican Inst. for Petroleum, Norsk-Hydro,Occidental Petroleum Corp., Petrobras, Schlumberger, Shell Intl.E&P, Statoil, Total, and Weatherford.

ReferencesBaker, L.J. 1984. The effect of the invaded zone on full wavetrain acoustic

logging. Geophysics 49: 796–809. DOI: http://dx.doi.org/10.1190/1.1441708.

Biot, M.A. 1956a. Theory of propagation of elastic waves in a fluid satu-rated porous solid I. Low-frequency range. J. Acoust. Soc. Am. 28:168–178. DOI: http://dx.doi.org/10.1121/1.1908239.

Biot, M.A. 1956b. Theory of propagation of elastic waves in a fluid satu-rated porous solid II. Higher frequency range: J. Acoust. Soc. Am. 28:179–191. DOI: http://dx.doi.org/10.1121/1.1908241.

Chen, X., Quan, Y., and Harris, J.M. 1996. Seismogram synthesis forradially layered media using the generalized reflection/transmissioncoefficients method: Theory and applications to acoustic logging. Geo-physics 61: 1150–1159. DOI: http://dx.doi.org/10.1190/1.1444035.

Cheng, C.H. 1989. Full waveform inversion of P waves for Vs and Qp.J. of Geophys. Res. 94: 15619–15625.

Cheng, C.H., Wilkens, R.H., and Meredith, J.A. 1986. Modeling of fullwaveform acoustic logs in soft marine sediments. Paper LL presentedat the 27th SPWLA Annual Logging Symposium, Houston, 9–13 June.

Domenico, S.N. 1976. Effect of brine-gas mixture on velocity in an un-consolidated sand reservoir. Geophysics 41: 882–894. DOI: http://dx.doi.org/10.1190/1.1440670.

Dutta, N.C. and Ode, H. 1979. Attenuation and dispersion of compres-sional waves in fluid-filled rocks with partial gas saturation, Whitemodel: Part I–Biot theory. Geophysics 44: 1777–1788. DOI: http://dx.doi.org/10.1190/1.1440938.

Frazer, L.N. and Sun, X. 1998. New objective functions for waveforminversion: Geophysics 63: 213–222. DOI: http://dx.doi.org/10.1190/1.1444315.

Frazer, L.N., Sun, X., and Wilkens, R.H. 1997. Inversion of sonic wave-forms with unknown source and receiver functions. Geophys. J. Int.129: 579–586.

Geertsma, J. and Smit, D.C. 1961. Some aspects of elastic wave propaga-tion in fluid-saturated porous solids. Geophysics 26: 169–181. DOI:http://dx.doi.org/10.1190/1.1438855.

George, B.K., Torres-Verdín, C., Delshad, M., Sigal, R., Zouioueche, F.,and Anderson, B. 2004. Assessment of in-situ hydrocarbon saturationin the presence of deep invasion and highly saline connate water.Petrophysics 45 (2): 141–156.

Gill, P.E., Murray, W., and Wright, M.H. 1981. Practical Optimization.London: Academic Press.

Hill, R. 1963. Elastic properties of reinforced solids: Some theoreticalprinciples. J. Mech. Phys. Solids 11: 357–372. DOI: http://dx.doi.org/10.1016/0022-5096(63)90036-X.

Hornby, B.E. 1993. Tomographic reconstruction of near borehole slownessusing refracted borehole sonic arrivals. Geophysics 58: 1726–1738.DOI: http://dx.doi.org/10.1190/1.1443387.

Kimball, C.V. and Marzetta, T.L. 1984. Semblance processing of boreholeacoustic array data. Geophysics 49: 274–281. DOI: http://dx.doi.org/10.1190/1.1441659.

Lee, K.H. and Kim, H.J. 2003. Source-independent full waveform inver-sion of seismic data. Geophysics online (published electronically on 20May 2003). DOI: http://dx.doi.org/10.1190/1.1635054.

Murphy, W.F. III. 1982. Effects of microstructure and pore fluids on theacoustic properties of granular sedimentary materials. Ph.D. thesis,Stanford U., Stanford, California.

Plona, T., Sinha, B., Kane, M. et al. 2002. Mechanical Damage Detectionand Anisotropy Evaluation Using Dipole Sonic Dispersion Analysis.Paper F presented at the 43rd Annual SPWLA Conference, Osio, Japan,2–5 June.

Pratt, R.G. 1999a. Seismic waveform inversion in frequency domain, Part1: Theory and verification in physical scale model. Geophysics 64:888–901. DOI: http://dx.doi.org/10.1190/1.1444597.

Pratt, R.G. 1999b. Seismic waveform inversion in frequency domain, Part2: Fault delineation in sediments using crosshole data. Geophysics 64:902–914. DOI: http://dx.doi.org/10.1190/1.1444598.

Salazar, J.M., Torres-Verdín, C., and Sigal, R. 2005. Assessment of per-meability from well logs based on core calibration and simulation ofmud-filtrate invasion. Petrophysics 46 (6): 434–451.

Schmitt, D.P. 1988. Shear wave logging in elastic formations. J. Acoust.Soc. of Am. 84: 2215–2229. DOI: http://dx.doi.org/10.1121/1.397015.

Sen, M.K. and Stoffa, P.L. 1991. Nonlinear one-dimensional seismic wave-form inversion using simulated annealing. Geophysics 56: 1624–1638.DOI: http://dx.doi.org/10.1190/1.1442973.

Smith, T.M., Sondergeld, C.H., and Rai, C.S. 2003. Gassmann fluid sub-stitutions: A tutorial. Geophysics 68: 430–440. DOI: http://dx.doi.org/10.1190/1.1567211.

Stephen, R.A., Cardo-Casas, F., and Cheng, C.H. 1985. Finite differencesynthetic acoustic logs. Geophysics 50: 1588–1609. DOI: http://dx.doi.org/10.1190/1.1441849.

Toksöz. M.N., Cheng, C.H., and Timur, A. 1976. Velocities of seismicwaves in porous rocks: Geophysics 41: 621–645. DOI: http://dx.doi.org/10.1190/1.1440639.

Toksöz, M.N., Wilkens, R.H., and Cheng, C.H. 1985. Shear wave velocityand attenuation in ocean bottom sediments from acoustic log wave-forms. Geophys. Res. Lett. 12: 37–40.

Torres-Verdín, C. and Habashy, T.M. 1994. Rapid 2.5-dimensional for-ward modeling and inversion via a new nonlinear scattering approxi-mation. Radio Science 29 (4): 1051–1079. DOI: http://dx.doi.org/10.1029/94RS00974.

Winkler, K.W. 1997. Acoustic evidence of mechanical damage surround-ing stressed boreholes. Geophysics 62: 16–22. DOI: http://dx.doi.org/10.1190/1.1444116.

Wu, J., Torres-Verdín, C., Sepehrnoori, K., and Proett, M.A. 2005. Theinfluence of water-base mud properties and petrophysical parameterson mudcake growth, filtrate invasion, and formation pressure. Petro-physics 46 (1): 14–32.

Wu, J., Torres-Verdín, C., Sepehrnoori, K., and Delshad, M. 2004. Nu-merical Simulation of Mud-Filtrate Invasion in Deviated Wells.SPEREE 7 (2): 143–154. SPE-87919-PA. DOI: 10.2118/87919-PA.

Zhou, C., Schuster, G.T., Hassanzadeh, S., and Harris, J.M. 1997. Elasticwave equation travel time and wavefield inversion of crosswell data.Geophysics 62: 853–868. DOI: http://dx.doi.org/10.1190/1.1444194.

Appendix—Methodology forFull-Waveform InversionThe model of wave propagation in a borehole considered in thispaper assumes an isotropic, radially multilayered formation withno geometrical irregularities along the borehole wall. As with anyinversion procedure, the accuracy and reliability of the results willdepend on how accurately the forward model describes actualin-situ conditions. In practical field studies, irregularities on theborehole wall can be quantified with caliper measurements. Con-sequently, vertical formation intervals can be identified that areconsistent with the assumption of a smooth borehole wall. Alongthe length of the receiver spacing (6 in.), the formation can beregarded as homogeneous in the axial direction.

In practice, the effect of borehole/receiver coupling can beassumed negligibly small in comparison to source coupling. Thespectral ratio of the pressure responses at two receiver locations, z1

and z2, from a common source can be written as

T12 =

S��i �−�

�R̂+ −

�1�eikpfr1

1 − R̂+ −�1�eikp

fr1

eikz2dk +eikf z2

z2�

S��i �−�

�R̂+ −

�1�eikpfr1

1 − R̂+ −�1�eikp

fr1

eikz1dk +eikf z1

z1� , . . . . . . . . . (A-1)

where S(�) is an effective-source-output spectrum, kf is thefluid wave number, kp

fis the radial wave number of fluid, R̂+−

(1)

is related to the reflectivity between the fluid and the first ra-


dial layer of formation, and r1 is the radius of the first layer. Theratio of the two source terms in Eq. A-1 is equal to unity, resultingin a final frequency representation independent of the source spec-trum. This procedure indicates that, in principle, knowledge of thesource spectrum is not necessary for full-waveform inversionwhen spectral ratios are used as input data. We note that the termT12 in Eq. A-1 is the transfer function between the two receivers.For practical applications, the source functions are never fullyknown because of the variability of mechanical coupling caused byvertical variation of formation properties. The source-independentformulation described by Eq. A-1 summarizes the conceptual basisfor a robust and efficient algorithm that can be used as the forwardcomputational model for full-waveform inversion. The transferfunction T12 depends on both the formation and borehole proper-ties. Specifically, factors that affect the transfer function include:(a) elastic properties of the formation, (b) borehole radius R, (c)acoustic velocity Vf, (d) density �f, and (e) quality factors forformation and borehole fluid. Toksöz et al. (1985), Cheng et al.(1986), and Cheng (1989) have quantified some of these factorsusing forward-modeling techniques. Because the primary goal ofthis paper is to simultaneously invert radial distributions of densityand P- and S-wave velocities, quality factors will not be subject toquantitative consideration. The normalized wavefield (or the nor-malized spectrum) of full waveforms constitutes the measurementsentered into the full-waveform inversion algorithm. A cost func-tion that enforces the quadratic difference between the simulatedand measured normalized wavefields is used for inversion. Toappraise the robustness of the inversion algorithm, this paper alsoconsiders a sensitivity study that quantifies the influence of noise,normalization trace, and regularization parameters.

For the estimation of the radial distribution of elastic properties,density and P- and S-wave velocities are assigned a constant valuewithin each radial layer in the near-wellbore region. Let m be thesize-N vector of unknown parameters that fully describes the radialdistribution of elastic properties, and let mR be a reference vectorof the same size as m that has been determined from some a prioriinformation. The estimation (inversion) of m is undertaken byminimizing a quadratic cost function, C(m), defined as (Torres-Verdín and Habashy 1994)

2C�m� = � �Wd�d�m� − dobs� �2 − �2� + � �Wm � �m − mR��2,. . . . . . . . . . . . . . . . . . . . . . . . (A-2)

where dobs is a size-M vector that contains the noisy measure-ments, and Wd·Wd

T is the inverse of the data covariance matrix.This data-weighting matrix describes the estimated variance foreach particular measurement and the estimated correlation be-tween measurements. The parameter � denotes the prescribedvalue of the enforced quadratic data misfit. A priori estimates ofthe noise in the measurements are used to determine the magnitudeof �. In Eq. A-2, d(m) is the measurement vector numericallysimulated for specific values of m; Wm·Wm

T is the inverse of themodel covariance matrix, used to enforce both a quantitativedegree of confidence in the reference model, mR, and a prioriinformation about m; and � is a Lagrange multiplier or regular-ization parameter.

The first additive term on the right side of Eq. A-2 drives theinversion toward fitting the measurements within the desired �2

value. The sole presence of such a term in the cost function C(m)will yield multivalued solutions of the inverse problem as a resultof both noisy measurements and insufficient and imperfect datasampling. Enforcing an extremely small data misfit may result inestimated models with exceedingly large norms (Torres-Verdínand Habashy 1994). The second additive term on the right side ofEq. A-2 is used to reduce nonuniqueness and to stabilize the in-version in the presence of noisy and sparse measurements. In thiscontext, the Lagrange multiplier, �, controls the relative weight ofthe two additive terms in the cost function. The developmentsconsidered in this paper make use of a relatively large regulariza-tion parameter at the outset, which monotonically decreases ac-cording to the number of iterations and the observed reduction ofthe cost function from iteration to iteration.

Measurement and Model Vectors. In the cost function (Eq. A-2),the measurement vector dobs is constructed from the real andimaginary parts of the normalized spectra, Re(S) and Im(S), in thefollowing organized fashion:

dobs = �Re�S1�, Im�S1�, . . . Re�Sj�, Im�Sj�, . . . Re�SM�, Im�SM��T,. . . . . . . . . . . . . . . . . . . . . . . . (A-3)

where j�2, 3, . . . M.

In Eq. A-3, M is the number of actual frequency domain mea-surements, and the superscript T indicates transpose. The ampli-tude of the spectra also can be used as the measurement vector atthe expense of losing phase information. The ordering procedurethat assigns an index, j, to a given measurement is a function offrequency for the spectrum of each trace and receiver location.Real and imaginary parts of one measurement are arranged next toeach other. If the sonic tool consists of NREC receivers, the nor-malized wavefield has NREC–1 traces because one trace is used toeliminate the source effect. If the number of frequencies used foreach trace is NFREQ, the actual number of measurements used forthe inversion is 2M�2*NFREQ*(NREC–1).

Similarly, the model vector is assembled as

m = �Vp,1, Vp,2, . . . , Vp,N, Vs,1, Vs,2, . . . , Vs,N, �1, . . . , �N�T

. . . . . . . . . . . . . . . . . . . . . . . . (A-4)for the simultaneous inversion of P- and S-wave velocities anddensity for each radial layer, where Vp, Vs, and � denote P-wavevelocity, S-wave velocity, and density, respectively, in the radiallayers numbered from 1 to N. By denoting the model parameters asmi, where i�1, 2, . . . , 3N, Eq. A-4 can be written as

m = �m1, m2, . . . , m3N�T. . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-5)

Gauss-Newton Fixed-Point Iteration Search. A Gauss-Newtonfixed-point iteration search (Gill et al. 1981) is used to determinea stationary point, m, at which the cost function attains a mini-mum. This method considers only first-order variations of the costfunction in the neighborhood of a local iteration point. The corre-sponding iterated formula can be written as

mk+1 = �JT�mk� � WdT � Wd � J�mk� + �Wm

T � Wm�−1

� �JT�mk� � WdT � Wd � �d�mk� − dobs + J�mk� � mk�

+ �WmT � Wm � mR� . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-6)

subject to

li � mik+1 � ui, where i = 1, 2, . . . N. . . . . . . . . . . . . . . . . (A-7)

In these expressions, the superscript k is used as an iteration count,and J(m) is the Jacobian matrix of C(m). Upper and lower boundsenforced on mk+1 are intended to have the iterated solution yieldonly physically consistent results. The fixed-point iteration searchfor a minimum of C(m) is concluded when the measured data havebeen fit within the prescribed tolerance, �2.

Relative data misfits computed with the formula

�Wd � �d�mk� − dobs� �2

�Wd � dobs �2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-8)

are used in this paper to enforce a convergence criterion forthe inversion.

SI Metric Conversion Factorscp × 1.0* E−03 � Pa�s

cycles/sec × 1.0* E+00 � Hzft × 3.048* E−01 � m

ft3 × 2.831 685 E−02 � m3

in. × 2.54* E+00 � cmin.3 × 1.638 706 E+01 � cm3

psi × 6.894 757 E+00 � kPa

*Conversion factor is exact.


Shihong Chi joined ConocoPhillips in June 2006 as a staff petro-physicist, working on petrophysical analysis and quantitativeinterpretation of 4D seismic data with rock physics models. e-mail: [email protected]. He is interested in themodeling and interpretation of logging data in deviated wells,particularly for acoustic and resistivity anisotropy applications,as well as the integration of rock physics, seismic, and reservoirengineering in time-lapse seismic inversion and applications.Previously, Chi interned with Schlumberger in 2000 and BakerAtlas/Inteq in 2001. He also worked on borehole acoustics, seis-moelectrics, and seismic modeling for fracture characteriza-tion and nuclear explosion monitoring as a post-doctoral fel-low at the Earth Resources Laboratory, Massachusetts Inst. ofTechnology from 2004 to 2006. Chi holds a BS degree in geo-physics from the U. of Science and Technology of China, an MSdegree in exploration geophysics from the U. of Petroleum,East China, and MS and PhD degrees in petroleum engineer-ing from the U. of Texas at Austin. Carlos Torres-Verdín hasbeen an associate professor in the Dept. of Petroleum andGeosystems Engineering at the U. of Texas at Austin since 1999.He conducts research on borehole geophysics, formationevaluation, and integrated reservoir characterization. From

1991 to 1997, Torres-Verdín held the position of Research Sci-entist with Schlumberger-Doll Research; from 1997 to 1999, hewas Reservoir Specialist and Technology Champion with YPF(Buenos Aires). Torres-Verdín holds a PhD degree in engineer-ing geoscience from the U. of California, Berkeley. He serves asa Review Chair for SPEJ. Jianghui Wu is a scientist with BakerAtlas in Houston. His main research areas are analysis of wire-line formation tests and formation fluid sampling and the de-velopment of a near-wellbore simulator. Previously, he was areservoir engineer with the Research Inst. of Petroleum Explo-ration and Development, CNPC, from 1996 to 1999. Wu holdsBS and MS degrees from the China U. of Petroleum and a PhDdegree from the U. of Texas at Austin, all in petroleum engi-neering. Faruk O. Alpak is a reservoir engineer with Shell Intl.E&P in Houston. His research interests include parallel reservoir-simulation techniques, numerical methods, uncertainty-baseddynamic modeling, inverse problems, numerical optimization,and computational electromagnetics. Alpak is an author orcoauthor of more than 20 journal and conference publica-tions. He holds a BS degree in petroleum and natural gas en-gineering from the Middle East Technical U. and MS and PhDdegrees in petroleum engineering from the U. of Texas at Austin.


assessment of mud-filtrate-invasion effects on borehole … · 2014-12-11 · assessment of...

Documents