Review of flow rate estimates of the Deepwater Horizonoil spillMarcia K. McNutta,1, Rich Camillib, Timothy J. Cronec, George D. Guthried, Paul A. Hsiehe, Thomas B. Ryersonf,Omer Savasg, and Frank ShafferdaOffice of the Director, US Geological Survey, Reston, VA 20192; bDepartment of Applied Ocean Physics and Engineering, Woods HoleOceanographic Institution, Woods Hole, MA 02543; cLamont–Doherty Earth Observatory, Columbia University, Palisades, NY 10964;dNational Energy Technology Laboratory, Department of Energy, Pittsburgh, PA 15236-0940; eUS Geological Survey, Menlo Park, CA 94025;fChemical Sciences Division, National Oceanic and Atmospheric Administration Earth System Research Laboratory, Boulder, CO 80305; andgDepartment of Mechanical Engineering, University of California, Berkeley, CA 94720-1740

Edited by Jane Lubchenco, Oregon State University, Corvallis, OR, and approved October 28, 2011 (received for review July 27, 2011)

The unprecedented nature of the Deepwater Horizon oil spill required the application of research methods to estimate the rate at which oilwas escaping from the well in the deep sea, its disposition after it entered the ocean, and total reservoir depletion. Here, we review whatadvances were made in scientific understanding of quantification of flow rates during deep sea oil well blowouts. We assess the degree towhich a consensus was reached on the flow rate of the well by comparing in situ observations of the leaking well with a time-dependentflow rate model derived from pressure readings taken after the Macondo well was shut in for the well integrity test. Model simulationsalso proved valuable for predicting the effect of partial deployment of the blowout preventer rams on flow rate. Taken together, thescientific analyses support flow rates in the range of ∼50,000–70,000 barrels/d, perhaps modestly decreasing over the duration of the oilspill, for a total release of ∼5.0 million barrels of oil, not accounting for BP’s collection effort. By quantifying the amount of oil at differentlocations (wellhead, ocean surface, and atmosphere), we conclude that just over 2 million barrels of oil (after accounting for containment)and all of the released methane remained in the deep sea. By better understanding the fate of the hydrocarbons, the total discharge canbe partitioned into separate components that pose threats to deep sea vs. coastal ecosystems, allowing responders in future events toscale their actions accordingly.

oil budget | particle image velocimetry | manual feature tracking

The Deepwater Horizon oil plat-form suffered a catastrophic ex-plosion and fire off the coast ofLouisiana (Fig. 1) on April 20,

2010, and sank 2 d later. Its blowout pre-venter (BOP) failed to seal the well, set-ting off the worst marine oil spill in UShistory. There were a number of reasonsfor needing to know the flow rate for thewell. First, the optimal design, proceduresfor execution, or prospects for success ofwell interventions, such as the cofferdam or top kill, were dependent on flowrate. Second, the amount of dispersantthat should be applied by the remotelyoperated vehicles (ROVs) to minimize anoil slick and release of volatile organiccompounds on the surface, where theyposed a health hazard to hundreds ofworkers involved in well intervention, wasproportional to the flow rate. Third, theplanning for containment of oil at thesea surface while the relief wells werebeing drilled required a realistic assess-ment of how much oil needed to beaccommodated. Fourth, the rate of deple-tion of the reservoir, which therefore,determined the final shut-in pressure whenthe capping stack was closed, dependedon the total amount of oil withdrawn.Much discussion by the government sci-ence team in Houston immediately afterthe well was shut in on July 15, 2010,centered on whether the low shut-inpressure was the result of high deple-tion of the reservoir (exacerbated by

a high flow rate) or the effect of a wellthat was leaking below the sea floor. Ul-timately, the partitioning of the plume inthe water column and the impact of theoil on the environment depend on the rateat which the oil is released.Initially, on April 24, 2010, the US Coast

Guard’s Federal On-Scene Coordinator, inconsultation with BP, estimated that theflow from the well was ∼1,000 barrels/d(BPD) (1). On April 28, 2010, the NationalOceanic and Atmospheric Administration(NOAA) released the first official flowrate of 5,000 BPD (1). At the time, thisnumber was highly uncertain and based onsatellite views of the area of oil on thesurface of the ocean. After the publicrelease of videos showing the plume ofhydrocarbons escaping from the damagedriser (Fig. 2) in the deep sea on May 12,2010, many scientists suggested that theflow rate was much higher than 5,000BPD, although these early estimates fromvideo did not account for the gas to oilratio as needed to convert total hydrocar-bon (gas + oil) flux to oil flow rate.On May 14, 2010, the National IncidentCommand (NIC) asked its InteragencySolutions Group (IASG) to provide scien-tifically based information on the dischargerate of oil from the well. In response,the NIC IASG chartered the Flow RateTechnical Group (FRTG) on May 19,2010. Experts from many scientific dis-ciplines were brought together to per-form the FRTG’s two primary functions:

(i) as soon as possible, generate a pre-liminary estimate of the flow rate, and(ii) within approximately 2 mo, use multi-ple, peer-reviewed methodologies to gen-erate a final estimate of flow rate andvolume of oil released.The results of the FRTG’s work are

summarized and evaluated for their appli-cability to accurate and timely estimation offlow rate during an ongoing oil spill incidentin the work by McNutt et al. (2). Here,we review the results of flow rate analyses,including work not conducted under theauspices of the FRTG, and place the resultsin terms of the advancement in scientificknowledge in contrast to contributions toongoing spill response. We consider not justthe best estimates of flow emanating fromthe wellhead but also how quantifying flowat different locations other than the sea-floor can aid in understanding the fate of oilin the environment.

Author contributions: R.C., T.J.C., P.A.H., T.B.R., O.S., andF.S. designed research; M.K.M., R.C., T.J.C., G.D.G., P.A.H.,T.B.R., O.S., and F.S. performed research; P.A.H. contributednew reagents/analytic tools; M.K.M., R.C., T.J.C., G.D.G.,P.A.H., T.B.R., O.S., and F.S. analyzed data; and M.K.M.,P.A.H., and F.S. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail:mcnutt@usgs.gov.

This article contains supporting information online atwww.pnas.org/lookup/suppl/doi:10.1073/pnas.1112139108/-/DCSupplemental.

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Flow Rate Estimates from SurfaceCollectionThe flow rate of the Macondo well isa simple concept but surprisingly difficultto measure. The flow from the well con-sisted of oil plus natural gas, with some of

the gas reacting rapidly with seawater toform methane hydrate. Response workersand the public were primarily interested inthe oil fraction, and the charge to theFRTGwas to measure the oil discharge butto do so required understanding of how

much of the total flow was oil and howmuch was natural gas. Obvious methodsthat might be perfectly sensible for mea-suring single-phase flow, such as a spinningpaddle wheel, would fail because of icingby methane hydrates.

Fig. 1. Location of the Macondo well/Deepwater Horizon spill in the Gulf of Mexico ∼50 miles (80 km) southeast of the Mississippi Delta. (Modified from theUS Geological Survey).

Fig. 2. Schematic diagram of damaged riser at the Macondo well spill site. Most hydrocarbon release occurred in the areas highlighted by black rectangles,emanating from the kink in the riser immediately above the blowout preventer (BOP) stack and the open end of the riser/drill pipe before June 3 and throughthe lower marine riser package (LMRP) after the damaged riser was cut away.

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BP was working up until the well wasfinally capped to muster enough capacity tocontain all of the flow on surface ships,which would have provided an excellentfinal measure of flow rate (at least at thatone point in time). By mid-June, BP wascollecting 25,000 BPD of oil through twocontainment systems: a riser to the vesselDiscoverer Enterprise and the choke line tothe Q4000 semisubmersible (3). Videoshowed that a substantial amount of oilwas still discharging into the ocean, andtherefore, this rate provided only a lowerbound on the flow rate for the well.Tropical storms delayed BP’s plans todeploy additional containment systemsbefore closure of the well through thecapping stack on July 15, 2010.Even with only partial surface contain-

ment, Camilli (described in ref. 2) deviseda method using gas to oil ratios of hydro-carbons recovered to the surface for esti-mating the total flow of the well (Fig. 3).The apparent gas to oil ratio of the flowcollected at the surface (3) indicates a rel-atively larger gas component than the flowfrom the subsurface well, because the riserfrom the wellhead to the ship seemed toact as a separator, preferentially siphoningthe lighter components to the surface inthe case of incomplete capture. As thecollection approaches 100% of total flowin this extrapolation, the gas to oil ratio

must trend to the true value at the sea-floor, which was obtained with a pressur-ized sampling bottle deployed from anROV by Woods Hole Oceanographic In-stitution (WHOI). This method of esti-mating flow rate is not highly precise onaccount of both the scatter in BP’s col-lection data and the need to extrapolatethe line some distance outside the regionof the data, but it yields a flow rate of48,000–66,000 BPD (2) corresponding tothe time of sample collection on June21, 2010.

Flow Rate Estimates from in SituObservationsAt the time of the Deepwater Horizonblowout, there were no proven methodsfor directly measuring the deep sea dis-charge of hydrocarbons at the relevantpressures and temperatures. Ocean-ographers had experience in quantifyingflow rates from deep sea hydrothermalvents at midocean ridges (4, 5), butmethods developed from those environ-ments had not previously been applied tomixtures of oil, gas, and water. Thus, avariety of approaches were pursued. Table1 summarizes the flow rates that wereobtained from acoustic and video obser-vations in the deep sea, and Fig. 4 plotsthose flow rates as a function of the eventday (ED) (Table 1, ED) of the measure-

ment. Rates are given for two key flowperiods: before severing the sunken riser(Fig. 2), which had been left in place to aidin the Top Kill procedure, and after sev-ering the riser (Fig. 5). The flow geometrybefore severing the riser was more com-plex, because in addition to a large plumeemanating from the end of the riser, sev-eral jets of oil and gas were escaping fromtears in the kink in the collapsed pipe atthe top of the lower marine riser package(LMRP). After the riser was severed,all discharge flowed through the top ofthe LMRP.The majority of the flow rates from in-

dependent teams listed in Table 1 andshown in Fig. 4 relied on underwater videoof hydrocarbon plumes taken by ROVsas the primary data for assessing the flowof the Macondo well. The video data ex-amined were either opportunistic fromwork-class ROVs working in and aroundthe incident site or specifically commis-sioned by the FRTG to be collected byan ROV for flow rate analysis. In all ofthese cases, an oil volume fraction [i.e., oil/(gas + oil)] of ∼0.4 was assumed basedon early time series analysis of videoshowing alternating oil vs. gassy dischargewhen humps and cooling in the riser (Fig.2) caused the flow to separate (6).Several expert teams used a flow visu-

alization and measurement technique

Fig. 3. Daily averages of GOR as a function of oil produced. The general trend indicates that the GOR drops as a greater percentage of the total flow isproduced to the surface but with considerable scatter. If the entire flow was captured, the GOR would match the true GOR of the well. The horizontal line ata GOR of 1,600 is equivalent to the surface GOR of the IGT-8 sample taken by WHOI on June 21, which was obtained at the point of exit at the wellhead and istaken to represent the true GOR of the Macondo reservoir fluids escaping from the well. Assuming that GOR samples acquired at the surface would trendlinearly to the actual GOR (IGT-8 sample collected by WHOI at well head), then the intercept should indicate the total oil flow rate on June 21. The best-fittinglinear trend to the GOR data as a function of surface oil yield indicates that, if BP had been able to capture the total flow at a GOR of 1,600, then the oilcaptured would have been 57,000 BPD on June 21. The 1 SD uncertainty on the best-fitting line to the GOR data allows the flow rate at the GOR of 1,600 to bebetween 48,000 and 66,000 BPD. (Modified from ref. 2.)

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called particle image velocimetry (PIV) toestimate the velocity of the outer surfaceof oil leak jets. PIV was originally devel-oped as a laboratory technique to measurea 2D velocity field in a transparent gasor fluid illuminated with a thin sheet oflaser light (7). To see the motion of thetransparent gas/fluid, seed particles smallenough to follow the fluid flow (i.e., witha low Stokes number) are added to thefluid: typically 1–10 μm for gases and 1–100 μm for liquids. A digital camera withline of view normal to the laser sheet re-cords two or more consecutive images ofthe seed particles. The displacement ofparticles between consecutive frames givesa 2D velocity vector field. PIV softwarehas been developed to analyze automati-cally sequences of video frames usingcross-correlation analyses of small inter-rogation windows. In the Macondoapplication, PIV analysis software at-tempted to measure the velocity of visiblefeatures (vortices, eddies, white particlespresumed to be methane hydrates, etc.) onthe surface of the opaque oil leak jets.With assumptions for the radial jet veloc-ity profile (typically Gaussian), oil leakrates could be calculated from measuredjet surface velocities.

The National Energy Technology Lab-oratory (NETL), University of Californiaat Berkeley and University of California atSanta Barbara (UCSB) experts adoptedvarious forms of manual feature-trackingvelocimetry (FTV). Manual FTV wasperformed by visually detecting the dis-placement of easily recognizable features,such as vortices and eddies, betweenconsecutive video frames. Presumedmethane hydrates, bright white particlesagainst a dark jet background, were alsoeasily recognized and tracked. Althoughthere were some minor variations in themanual FTV technique applications(details in appendices in ref. 6), all expertsmeasured similar jet velocities. After jetvelocities were measured with manualFTV, volumetric flow rate was determinedby multiplying the measured jet velocitytimes the cross-sectional area of the jet,with appropriate corrections for the gas tooil ratio (GOR). Because measurementswere made close to the jet exit (within fivejet exit diameters), the radial profile ofaverage jet velocity could be assumed tobe uniform and constant (top hat profile).The work by Crone and Tolstoy (8) used

optical plume velocimetry (OPV), amethod that was developed and calibratedusing laboratory simulations of turbulent

buoyant jets (5). In this method, the imagevelocity field is established by cross-correlating time series values of imageintensity from pixel pairs separated bysome distance in the direction of flow. Theflow rate was then calculated from theimage velocity field using an empiricallyderived shear-layer correction factor.The PIV analyses performed by experts

A, B, C, and E (Table 1) agreed with eachother but produced flow rate estimatesthat were about one-half the magnitudeestimated by the other methods, even us-ing the same primary video observations(6). Other research teams also tried to usePIV but determined that it was not pro-ducing reliable fluid velocities in this ap-plication. For example, Crone and Tolstoy(8) cite experiments completed before theMacondo crisis (5), showing that PIVwould underestimate flow rates by abouta factor of two when applied to turbulentbuoyant jets. Savas (6) carried out a sys-tematic image velocimetry study of usingsections of video where the drifting motionof the ROV camera caused an apparentdisplacement/velocity of the riser flange.The results showed that PIV software wasable to correctly measure the motionof the riser flange only when large in-terrogation windows were used. For a widerange of interrogation window sizes, PIVsoftware erroneously yielded random val-ues of velocity. The work by Shaffer et al.(9) points out that PIV is a laboratorytechnique applied under carefully con-trolled conditions to map the motion ofparticles a few pixels in diameter ina transparent fluid. At Macondo, PIVsoftware was applied to measure the ve-locity of transient opaque features from 1to 500 pixels.The relatively poor performance of PIV

in this particular application thus hadseveral potential causes. Automatic PIVanalysis software may be confused by ro-tating flow structures, can lock on toseparated or smaller flow features that aremoving more slowly and/or not samplingdeeper parts of the flow, and can aliasturbulent flow, because correlation win-dow sizes are typically fixed, whereas flowstructure sizes are not (5, 6). All of theseissues can bias velocity estimates lowerand artificially reduce flow rate estimates.More details on how the case was madeto discount the PIV estimates in this ap-plication are provided in SI Text. Themanual FTV method overcame theproblems of PIV by using the humanbrain as an expert system to painstakinglychoose large and fast structures to track.OPV inherently avoids many of theproblems associated with spatial cross-correlation techniques. Thus, as work onthis problem progressed during the crisis,it became clear to many that, althoughPIV software can correctly analyze videos

Riser falls to seabed ~62K BPD Riser cut ~4% increase -

59.8K BPD

Stacking Cap installed ~4% decrease – 53K BPD

Cumula ve Release: ~4.9 million barrelsCumula ve Oil Collected: ~0.8 million barrels (results from BP)

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Fig. 4. Summary of flow rate estimates from Table 1. The continuous curve represents the Augustmodel for the evolution in flow rate throughout the oil spill incident obtained by extrapolating the53,000 BPD estimate from DOE at the time that the capping stack was closed (12) back to the beginningof the incident using the reservoir depletion model of Hsieh (13). In this extrapolation, a flow rate in-crease of 4% was estimated to have occurred when the riser was severed, and a decrease of 4% wasestimated when the capping stack was installed. The stippled band represents a ±10% uncertainty in theAugust flow rate model. Compared with this August model are flow rate estimates from in situ oceandata plotted as a function of the day that the data for that flow rate were collected. Flow rates weretypically reported at later dates. The postriser cut estimates all used data obtained on event day 45, butthey are slightly offset from each other in time for ease of viewing. The upper bounds of the postrise cutUCSB estimate is shown as an arrow where it goes off the chart. The PIV estimates from the varioussources are pooled together, with the thick part of the bar showing the range of the means and the thinpart showing the range of the SD.

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taken under certain conditions, it was notwell-suited for analysis of ROV videos ofuncontrolled opaque turbulent oil jets.Table 1 and Fig. 4 also include the flow

rate of a WHOI team (10) derived from

acoustic Doppler current profiler meas-urements (ADCP). They collected timeseries measurements over periods of mi-nutes using an imaging sonar to determinethe cross-sectional area of the plume at

the end of the riser and the jets at the kink(Fig. 2) and the ADCP to measure thetens of thousands of individual velocitieswithin the flow field. The flow velocity andarea estimates were then multiplied toproduce an ensemble estimate of the totalvolumetric flow rate (oil plus gas) of 0.25m3/s. This approach had the benefit ofmapping the interior of the entire hydro-carbon plume acoustically despite the factthat it is opaque to video images. On June21, 2010, the WHOI team returned tothe field with a high-pressure sample bot-tle and gathered 100 mL uncontaminateddischarge of hydrocarbons inside TopHat #4 as they exited the well. Chemicalanalysis of this sample revealed that thefluids were by mass less than 1% carbondioxide and nitrogen, 15% methane, 7%ethane through pentanes, and 77% hex-anes and higher petroleum hydrocarbons(11). This detailed understanding of thefluid composition enabled calculation ofthe volumetric oil and gas fractions undervarying temperature, pressure, and phaseconditions encountered during their initialtransport through the water column (11).This sample became the basis for the oilratio = oil/(gas + oil) = 0.41 used by thevarious experts, consistent with previousindications that a value of ∼0.4 was ap-propriate (6). Given the very dissimilarnature of the acoustic vs. video observa-tions, the different methods of analysis,and the independent sources of error, thefact that the flow rates from the WHOIacoustic measurements (Fig. 4) agree withthose rates derived from video is excep-tionally strong evidence that, in late May/early June, the flow rate of the Macondowell was ∼60,000 BPD.

Flow Rate at Well Shut inAdditional estimates of the flow rate werederived when the well was shut in for thewell integrity test on July 15, 2010. Themechanism for shutting in the well wasto close off the flow with a three-ramcapping stack that was mated with theupper flange of the LMRP on the top of theBOP. Government scientists in Houstonhad requested that the capping stack beequipped with redundant pressure gauges.When the choke valve in the capping stackwas throttled back in a series of preciselycontrolled steps to close off the well,pressure readings from the capping stacktaken at the time were analyzed by threeseparate Department of Energy (DOE)laboratories to yield very consistent resultsfor the flow rate of the well at the timeof shut in: 53,000 BPD (12). When com-bined with a US Geological Survey(USGS) model for reservoir depletion asa function of time (13), these postshut-inresults provided flow rate estimates forthe entire duration of the oil spill that canbe compared against the observations

Table 1. Flow rate estimates from in situ observations

2010 Dateevent day Method

Flow rate(1,000 BPD) Source

Preriser cut estimatesMay 13–16 ED 24–27 Large eddy tracking 30 ± 12 Berkeley (BKY) (6)May 13–16 ED 24–27 Particle image

velocimetry23 ± 9 Expert E (6)

May 13–16 ED 24–27 Particle imagevelocimetry

25 ± 8 Experts A, B, C (6)

May 13–16 ED 24–27 Feature trackingvelocimetry

55 ± 14 National Energy TechnologyLaboratory (NETL) (6)

May 14 ED 25 Optical plumevelocimetry

56 ± 12 Lamont–Doherty EarthObservatory (LDEO) (8)

May 31 ED 42 Acoustic Dopplervelocity + sonar

57 ± 10 Woods Hole OceanographicInstitution (WHOI) (11)

Postriser cut estimatesJune 3 ED 45 Large eddy tracking 46 ± 4* Berkeley (BKY) (6)June 3 ED 45 Particle image

velocimetry35 ± 5* Expert E (6)

June 3 ED 45 Particle imagevelocimetry

32 ± 8* Experts A, B, and C (6)

June 3 ED 45 Digital imagevelocimetry

62 ± 58* University of California atSanta Barbara (UCSB) (6)

June 3 ED 45 Feature trackingvelocimetry

61 ± 15* National Energy TechnologyLaboratory (NETL) (6)

June 3 ED 45 Optical plumevelocimetry

68 ± 14 Lamont–Doherty EarthObservatory (LDEO) (8)

All rates expressed in stock tank barrels (stb = 0.159 m3) at the ocean surface for consistency.*Rates from p. 15 in ref. 6. In some cases, mean and SD values were not identical to values in theappendices of ref. 6, which were finalized after official flow rates were publicly reported.

Fig. 5. Hydrocarbons (oil and natural gas) escaping from the end of the riser tube after it was severedon June 3 immediately above the Macondo well BOP stack. (Modified from BP video from ROVs.)

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taken during the ongoing incident. Addi-tional details on these calculations areprovided in SI Text. Based on this analysis,the Department of Interior and DOE re-leased, on August 2, 2010, a time-varyingflow rate for the well as a function of time(Fig. 4) that was estimated by the teamof scientists from government and acade-mia to be accurate to ±10% (12). Al-though this figure does not represent aformal statistical error estimate, it ap-proximately accounts for errors in thepressure readings (based on the two re-dundant pressure gauges) and unmodeledmultiphase effects (12). Including dis-continuities to account for changing re-sistance at the well head (i.e., removal ofriser or addition of capping stack), theflow rate was estimated to have decreasedfrom 62,000 to 53,000 BPD over the 86 dof the incident for a total release of ∼5million barrels of oil. Subtracting the∼800,000 barrels of oil that never reachedthe environment because of BP’s contain-ment efforts (3) would yield 4.2 millionbarrels of oil released to the ocean andatmosphere. We call this the Augustmodel to correspond to the release monthof the estimate and distinguish it fromearlier FRTG flow estimates. The otherobserved flow rates reported here, exceptas noted, were calculated in a blindmanner, without knowledge of the Augustmodel. The agreement between this modeland the observations of in situ flow inFig. 4 provide sound evidence that theMacondo well flowed between 70,000 and50,000 BPD.

Scientific Contributions from ModelingA number of teams were involved in res-ervoir and well modeling exercises, someconcentrating on modeling the evolutionof the producing reservoir at 18,000 ft(5,500 m) below sea surface and othersworking on the various possible flow pathsup through the well and the behavior ofthe fluids on ascent. Unlike the previousapproaches, these teams did not requireaccess to the field or new data acquisition.However, they did gain access to industryproprietary data to constrain modelparameters (for example, fluid andreservoir properties, well casings andliners, etc.).Five DOE national laboratories (Los

Alamos, Lawrence Berkeley, LawrenceLivermore, NETL, and Pacific Northwest)independently calculated the flow fromthe top of the reservoir (representing thereservoir response as a bottom hole pres-sure) to the release point at the sea floor(14). A statistical sampling method wasused with these independent estimates todevelop a set of pooled estimates of flowthat allowed detailed assessment of flowconditions as related to a variety of factorsin the reservoir and the engineered part

of the system (wellbore, BOP, riser, etc.).As shown in Table 2, there was a largespread in the 95% confidence interval intheir flow rates for two key time periods,but the best estimate was very close to theAugust model. The large range in possibleflow rates stemmed from uncertaintywhether the flow through the well wasprimarily inside the casing or in the an-nular space outside the casing (Fig. 6),with the latter flow scenario resulting insignificantly lower estimates of flow. Onerather significant contribution from mod-eling was the capacity to consider the ef-fect of restrictions in the BOP on flow rate(15). After the BOP was recoveredfrom the seafloor, a postincident in-vestigation was conducted to determinewhat could be concluded about thefunctioning of the various rams in theBOP system. One finding was that theblind shear rams had, at some point,deployed, forming at least a partial re-striction to flow through the BOP.Oldenburg et al. (15) modeled the be-havior of flow of oil and gas in thereservoir and up through the well asa function of the resistance in the BOP asparameterized by the unknown pressureat the bottom of the BOP (PBOP), whichis the top of their model reservoir–wellbore system. They found effects ofphase interference of gas and oil thatwere unanticipated such that oil flow rateis independent of the restriction in theBOP until PBOP equals about 6,600 psia(45 MPa), the pressure above whichno gas exsolves (i.e., the Macondo hy-drocarbons are single phase). Althougha PBOP larger than 6,600 psia wouldimply that flow is restricted in theBOP, estimation of the precise degreeof restriction for any assumed PBOP iscomplicated because of the strong in-terplay between pressure and gas exso-lution in the whole system (reservoir–well–BOP) (15).Three independent groups of research-

ers in the field of reservoir simulationcalculated the rate at which oil and gas canbe produced from the sands penetrated byBP’s Macondo well (16). The reservoirgeometry was prescribed by maps gener-ated from 3D seismic data interpreted bythe Bureau of Ocean Energy Management(BOEM) geophysicists. The models wereconstrained using Macondo reservoir rock

and fluid properties derived from open-hole logs, pressure transient tests, pres-sure, volume, and temperature measure-ments, and core samples as well asreservoir data from an analogous welldrilled 20 miles (32 km) away. The re-searchers populated computer modelsand determined flow rates from the tar-geted sands in the well as a function ofbottom-hole pressure. This modelingprovided an estimate of the rate at whichoil could theoretically flow into the well.Permeability assumptions significantlyimpacted the results. In addition, theparticular flow path through the well wasas important as any reservoir parameterin determining the final flow rate. Be-cause of time constraints, the modelersconcentrated on two scenarios: the max-imum flow (worst case) conditions andthe most likely flow scenario. The resultsare summarized in Table 3. Two of threegroups determined most likely flow ratesthat were excellent matches to the Au-gust flow model. Although the reservoirmodeling results were not availableearly enough to impact the oil spill re-sponse in any substantive manner, thewell did not need to be flowing to conductthe model simulations. Therefore, theo-retically, these flow rates could havebeen produced before the DeepwaterHorizon accident. Based on the successof this approach, BOEM is using reser-voir modeling to calculate worst casedischarge as part of permit conditionsbefore wells enter production, andtherefore, some estimate of flow ratewould be available should a subseablowout occur.

Apparent Flow at Ocean SurfaceTwo teams provided estimates of flow fromthe Macondo well at the ocean surfaceusing unique approaches. A USGS/Na-tional Aeronautics and Space Adminis-tration team deployed the AirborneVisible/Infrared Imaging Spectrometer(AVIRIS) from an ER-2 research aircraftto quantify both the area and thicknessof oil on the ocean surface on May 17,2010. This instrument had previously beenused in such ground-breaking applicationsas the detection of asbestos in the rubbleof the World Trade Center Towers (17).Depending on the aggressiveness withwhich the team members interpreted the

Table 2. Flow rate estimates from DOE National Laboratory models of flow throughwell

Date (2010)

95% confidenceinterval for flowrate (1,000 BPD)

Best estimate forflow rate (1,000 BPD)

August model flowrate (1,000 BPD)

April 25 to May 5 40–91 65 56–67June 1–3 35–106 70 55–65

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presence of oil in each pixel imaged on thesea surface, they estimated that theamount of oil on the sea surface on May17 was between 129,000 and 246,000 bar-rels (18). They converted these numbers toa lower-bound flow rate by accounting forthe amount that had been skimmed andburned according to the US Coast Guardtally (19). They also modeled the likelyamount that had been evaporated by as-suming that 40% of the oil consisted ofvolatile components lost to evaporation ordissolution based on available NOAA in-formation. Although a lower bound, theirestimate of the flow rate of 12,500–21,500

BPD underestimated the government’sfinal August result by a factor of three,even at the upper bound. Three factorslikely contributed to the underestimate.Within a few days of the team’s release oftheir estimate of the Macondo flow rate,the first scientific reports of a plume of oiltrapped in the deep sea were publicized.Clearly not all of the flow from theMacondo well was appearing at the oceansurface. A second problem could be acontribution from tar balls. Submerged tarballs are concentrations of oil that areeasily missed in the inventory from the air.The third problem is that the near-infrared

spectroscopy method of AVIRIS wasonly able to measure oil up to 4 mm inthickness, but patches of oil at least 2 cmin thickness were observed during the fieldcalibration of the sensor. Clark et al. (18)estimated that the surface oil could havebeen as much as 500,000 barrels on May17 on account of failure to accuratelymeasure thick oil.A NOAA team (20) analyzed airborne

atmospheric data obtained from a P3 re-search aircraft to quantify the amount ofhydrocarbons (gas plus oil) evaporatingfrom the Deepwater Horizon oil spill. Theycalculated that ∼458,000 kg/day hydro-carbons were evaporating from the oceansurface. Certain volatile organic com-pounds in the Macondo reservoir fluids,including isomers between 2,2-dime-thylbutane and n-nonane, were found inthe atmosphere in the same proportion asin the reservoir, suggesting that they wereinsoluble in seawater and fully evaporated.However, methane, ethane, benzene, tol-uene, and n-butane were absent or sub-stantially depleted in the atmosphererelative to the reservoir, indicating total topartial removal of soluble species in thewater column. Their observations alloweda precise calculation of the percentage ofevaporation (14%) and dissolution inseawater (33%) for early June comparedwith the 40% combined total of evapora-tion and dissolution assumed by Labsonet al. (19) in computing a flow estimatefrom AVIRIS data. From the insolublespecies, it was possible to derive a flowrate for how much of the Macondo oil wassurfacing on the date of the flights (June10, 2010: ∼6,200–12,400 BPD). This flowrate assumes that dissolution affected thegas fraction only, which is supported bythe data, and an oil/(oil + gas) volumefraction of 0.41. At this time, ∼17,000BPD oil were being collected through TopHat #4, such that the entire flow of thewell was not entering the ocean. Thismethod of measuring the surfacing oilavoids the problem of tar balls but again,does not measure the oil that remains inthe deep sea. This estimate of flow waspublished after the August model was re-leased and therefore, was not an entirelyblind analysis. It places only a lowerbound on flow rate, because it did notquantify oil that did not surface.The availability of apparent flow rate

estimates at the ocean surface provides anopportunity to estimate the amount of theMacondo flow that did not rise to thesurface. Given that the best estimate forfull flow of the well from in situ observa-tions on about June 10, 2010 is 59,000 ±9,000 BPD, subtracting from that flow thecollection rate of 17,000 BPD yields a netflux of 42,000 ± 9,000 BPD entering theocean. Using the upper bound on thesurface flow from the NOAA P3 data (20)

Breach atSome Point

along9-7/8” Casing

Breach in7” Casing

Breach inWellhead

SealAssembly

Flow behindCasing

A B C

Fig. 6. Schematic diagram of possible well flows modeled by the well modeling teams from the DOENational Laboratories. (A) Scenario 1: flow initiates in the annular space between liner and casing,flowing through a breach at the top (in the seal assembly) into BOP and then riser; depending on flowrestrictions in BOP, some flow may reenter the 9 7/8-in casing to flow down to enter the drill pipe. (B)Scenario 2: flow initiates in a breach of the 7-in casing, flowing up the casing. Some flow enters the drillpipe, and some continues up the casing to BOP. (C) Scenario 3: flow initiates in the annular spacebetween liner and casing, entering a breach in 9 7/8-in casing and continuing to flow up inside thecasing. Some flow enters the drill pipe, and some continues up the casing to BOP. [Modified fromGuthrie et al. (14).]

Table 3. Flow rate estimates from reservoir modeling

GroupMost likely flowrate (1,000 BPD)

Worst casedischarge (1,000 BPD)

August model flowrate (1,000 BPD)

Hughes (LouisianaState University)

63 (channel/leveecomplex)

64 (extensive sheet sands) 62 decreasingto 53

Kelkar (Universityof Tulsa)*

27–32 37–45 62 decreasingto 53

Gemini SolutionsGroup

60 decreasingto 50

102 (flow-through multiplepaths in well)†

62 decreasingto 53

*Lower Kelkar estimates result from more conservative permeability and flow path assumptions com-pared with those assumptions adopted by other modeling teams.†Larger worst case discharge for Gemini team results from considering multiple flow paths through thewell, whereas other teams considered only geologic controls on maximum flow.

20266 | www.pnas.org/cgi/doi/10.1073/pnas.1112139108 McNutt et al.

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and the lower bound on the total Ma-condo well flow-rate data (2) yields anextreme lower bound on the flux of oil intothe deep sea of 29,600 BPD. Taking theupper bound on the Macondo well flowrate and the lower bound on the P3 datayields the maximum flux to the deep sea:44,800 BPD. The most likely value is about33,000 BPD or approximately one-half ofthe total Macondo oil flux remaining inthe deep sea. The NOAA results alsoconfirm that the methane remained in thedeep sea (20). The net result, therefore, ofthis deep sea release is a very substantialfraction of the total hydrocarbon budgetbeing absorbed in the deep ocean: one-half of the oil and essentially all of themethane. These values also imply that theoil flux to the surface on May 17, beforeBP’s containment efforts, would have been∼24,000–30,000 BPD, thus explaining thelower values derived from the AVIRISmeasurements without needing to assumethat much of the oil had been missed inthe form of thick oil or tar balls.

ConclusionsThe following scientific understanding willbetter prepare scientists and the oil spillresponse community for future deepsea blowouts.

i) The method of automated PIV, used byseveral groups of experts during the spillto analyze video segments, was inappro-priate for this application and resulted inoil flow rates that were biased too low bya factor of two.

ii) Except for the PIV estimates, there isremarkable agreement for the dis-charge rate for the well, regardlessof whether the estimate was derivedfrom ROV video, acoustic Dopplerdata, pressure measurements duringwell shut in, reservoir modeling, ortrends in gas to oil ratio during sur-face collection. Flow rates fall be-tween 50,000 and 70,000 BPD.

iii) These estimates do not require but donot preclude a modest reduction in

flow rate over time, which might becaused by reservoir depletion.

iv) Modeling also proved to be an extremelyvaluable exercise in terms of providinginsight to the likely effect of the deploy-ment of the blind shear rams and suggest-ing that modeling be used as a tool thatcan assess the impact of future spills be-fore they happen.

v) Estimates of flow rate at the ocean sur-face derived from multispectral imagingof oil on the ocean surface and chemicalsensing of the hydrocarbons evaporatingoff the ocean surface coupled with thetotal flow rate from the well indicatethat ∼50% of the oil (>2 million bar-rels) and essentially all of the methanedid not reach the ocean surface.

ACKNOWLEDGMENTS. We are grateful to numer-ous experts who read and improved various versionsof this manuscript, including Don Maclay and col-leagues at the Bureau of Ocean Energy Manage-ment, Steve Hickman, Mark Sogge, Curt Oldenburg,Bill Lehr, Gregg Swayze, Art Ratzel, Vic Labson,Roger Clark, and two anonymous reviewers.

1. US Coast Guard (2011) BP Deepwater Horizon Oil Spill:Incident Specific Preparedness Review (ISPR), Final Re-port. Department of Homeland Security, WashingtonDC. Available at http://www.uscg.mil/foia/docs/DWH/BPDWH.pdf. Accessed November 29, 2011.

2. McNutt MK, et al. (2011) Assessment of Flow RateEstimates for the Deepwater Horizon/Macondo Well OilSpill. Flow Rate Technical Group Report to the NationalIncident Command Interagency Solutions Group.Availableat http://www.doi.gov/deepwaterhorizon/loader.cfm?csModule=security/getfile&PageID=237763. AccessedNovember 29, 2011.

3. United States Department of Energy (2010) CombinedTotal Amount of Oil and Gas Recovered Daily from theTop Hat and Choke Line Oil Recovery Systems. Avail-able at http://energy.gov/downloads/oil-and-gas-flow-data-top-hat-and-choke-line-xls. Accessed November29, 2011.

4. Crone TJ, Wilcock WSD, McDuff RE (2010) Flow rateperturbations in a black smoker hydrothermal ventin response to a mid-ocean ridge earthquake swarm.Geochem Geophys Geosys, 11, Q03012, doi:10.1029/2009GC002926.

5. Crone TJ, McDuff RE, WilcockWSD (2008) Optical plumevelocimetry: A new flow measurement technique foruse in seafloor hydrothermal systems. Exp Fluids 45:899–915.

6. Plume Modeling Team (2010) Deepwater Horizon Re-lease Estimate of Rate by PIV. Report to the Flow RateTechnical Group. Available at http://www.doi.gov/deepwaterhorizon/loader.cfm?csModule=security/getfile&PageID=68011. Accessed November 29,2011.

7. Adrian RJ (2005) Twenty years of particle imagevelocimetry. Exp Fluids 39:159–169.

8. Crone TJ, Tolstoy M (2010) Magnitude of the 2010Gulf of Mexico oil leak. Science 330:634.

9. Shaffer F, Weiland N, Shahnam M, Syamlal M,Richards G (2010) Estimate of Maximum Oil Leak Ratefrom the BP Deepwater Horizon by the National En-ergy Technology Laboratory, in Plume Modeling Team,Deepwater Horizon Release Estimate of Rate by PIV.Report to the Flow Rate Technical Group. Available athttp://www.doi.gov/deepwaterhorizon/loader.cfm?csModule=security/getfile&PageID=68011. AccessedNovember 29, 2011.

10. Camilli R, et al. (2012) Acoustic measurement of theDeepwater Horizon Macondo well flow rate. Proc NatlAcad Sci USA 109:20235–20239.

11. Reddy CM, et al. (2012) Composition and fate of gasand oil released to the water column during theDeepwater Horizon oil spill. Proc Natl Acad Sci USA109:20229–20234.

12. Ratzel AC, et al. (2011) DOE-NNSA Flow Analysis StudiesAssociated with the Oil Release Following the Deep-water Horizon Accident. Report of the DOE-NNSA FlowAnalysis Team; Sandia National Reports, Lawrence Liver-more National Laboratory and Los Alamos National Lab-oratory. Sandia Report SAND2011-1653, August 2011,(Department of Energy, Albuquerque, NM).

13. Hsieh PA (2010) Computer Simulation of ReservoirDepletion and Oil Flow from the Macondo Well Fol-lowing the Deepwater Horizon Blowout. USGS Open-File Report 2010-1266. Available at http://www.doi.gov/deepwaterhorizon/loader.cfm?csModule=security/getfile&pageid=237562. Accessed November 29, 2011.

14. Guthrie G, et al. (2010) Nodal Analysis Estimates of FluidFlow from the BP Macondo MC252 Well. Assessmentof Flow Rate Estimates for the Deepwater Horizon/Macondo Well Oil Spill. Flow Rate Technical Group

Report to the National Incident Command InteragencySolutions Group, Appendix F. Available at http://www.doi.gov/deepwaterhorizon/loader.cfm?csModule=security/getfile&pageid=237567. Accessed November 29, 2011.

15. Oldenburg CM, et al. (2012) Numerical simulations ofthe Macondo well blowout reveal strong control of oilflow by reservoir permeability and exsolution of gas.Proc Natl Acad Sci USA 109:20254–20259.

16. Reservoir Modeling Team (2010) Flow Rate TechnicalGroup Reservoir Modeling Team Summary Report. As-sessment of Flow Rate Estimates for the Deepwater Ho-rizon/Macondo Well Oil Spill. Flow Rate Technical GroupReport to the National Incident Command InteragencySolutions Group, Appendix E. Available at http://www.doi.gov/deepwaterhorizon/loader.cfm?csModule=security/getfile&pageid=237566. Accessed November 29, 2011.

17. Clark RN, et al. (2001) Environmental Studies of theWorld TradeCenterAreaAfter the September 11th, 2001Attack. USGS Open File Report 01-0429, (US GeologicalSurvey, Denver, CO). Available at http://pubs.usgs.gov/of/2001/ofr-01-0429/. Accessed November 29, 2011.

18. Clark RN, et al. (2010)AMethod forQuantitativeMappingof Thick Oil Spills Using Imaging Spectroscopy. USGSOpen-File Report 2010-1167. Available at http://pubs.usgs.gov/of/2010/1167/. Accessed November 29, 2011.

19. Labson VF, et al. (2010) Estimated Minimum DischargeRates of the Deepwater Horizon Spill—Interim Reportto the Flow Rate Technical Group from the MassBalance Team. USGS Open-File Report 2010-1132 (USGeological Survey, Denver, CO). Available at http://pubs.usgs.gov/of/2010/1132/. Accessed November 29, 2011.

20. Ryerson TB, et al. (2011) Atmospheric emissions fromthe Deepwater Horizon spill constrain air-waterpartitioning, hydrocarbon fate, and leak rate. GeophysRes Lett 38:L07803.

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