Computer Simulation of Reservoir Depletion and Oil 

Flow from the Macondo Well Following the Deepwater 

Horizon Blowout 

By Paul A. Hsieh 

Open-File Report 2010–1266 

U.S. Department of the Interior

U.S. Geological Survey 

 
U.S. Department of the Interior 

KEN SALAZAR, Secretary 

U.S. Geological Survey 

Marcia K. McNutt, Director 

U.S. Geological Survey, Reston, Virginia: 2010

For product and ordering information: 

World Wide Web: http://www.usgs.gov/pubprod 

Telephone: 1-888-ASK-USGS 

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its natural and living resources, natural hazards, and the environment: 

World Wide Web: http://www.usgs.gov 

Telephone: 1-888-ASK-USGS 

Suggested citation: 

Hsieh, Paul, 2010, Computer simulation of reservoir depletion and oil flow from the Macondo well 

following the Deepwater Horizon blowout: U.S. Geological Survey Open-File Report 2010–1266, 18 p. 

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government. 

 
Contents 

Abstract ......................................................................................................................................................... 1

Background ................................................................................................................................................... 2

Reservoir Model ............................................................................................................................................ 2

Reservoir Geometry and Conditions .......................................................................................................... 2

Mathematical Formulation.......................................................................................................................... 3

MODFLOW Implementation....................................................................................................................... 5

History Matching............................................................................................................................................ 6

Simulation Results......................................................................................................................................... 7

Reservoir Depletion ................................................................................................................................... 7

Oil Flow Rate ............................................................................................................................................. 7

Uncertainty Analysis .................................................................................................................................. 7

Conclusions ................................................................................................................................................... 8

References Cited........................................................................................................................................... 8

Tables 

Table 1. Reservoir and fluid properties used in the reservoir simulation model....................................... 9

Table 2. Model parameters that are estimated by history matching....................................................... 10

Table 3. Simulated oil flow rates and total volume of oil discharged along with 95-percent prediction 

 intervals computed by PEST predictive analysis. .................................................................... 11

Table 4. Impact of ±25-percent variation in parameter value on simulated initial flow rate, final flow 

 rate, and total volume of oil discharged. .................................................................................. 12

Figures 

Figure 1. Oblique schematic view of the M56 oil reservoir...................................................................... 13

Figure 2. Schematic vertical section showing flow of oil from M56 reservoir through the Macondo well 

 and exiting at the top of the blowout preventer. ....................................................................... 14

Figure 3. Map view of an example finite-difference grid of the oil reservoir. ........................................... 15

Figure 4. Horner plot of shut-in pressure in the capping stack of the Macondo well. .............................. 16

Figure 5. Simulated reservoir pressure at the Macondo well face. ......................................................... 17

Figure 6. Simulated volumetric flow rate of oil from the Macondo well in stock tank barrels per day 

(stb/d). ..................................................................................................................................... 18

 
 

Conversion Factors 

Oil Field Units to SI 

Multiply By To obtain 

foot (ft) 0.3048 meter (m) 

gallon (gal) 0.0037854 cubic meter (m3) 

Barrel1

 (bbl) 0.15899 cubic meter (m3) 

pound per square inch (psi) 6.8948 kilopascal (kPa) 

pound per gallon (ppg) 119.83 kilogram per cubic meter (kg/m3

) 

centipoise (cP) 0.001 pascal-second (Pa·s) 

millidarcy (mD) 9.8692 × 10-16 meter squared (m2

) 

SI to Oil Field Units 

Multiply By To obtain 

meter (m) 3.281 foot (ft) 

cubic meter (m3) 264.17 gallon (gal) 

cubic meter (m3

) 6.2898 Barrel1 (bbl) 

kilopascal (kPa) 0.14504 pound per square inch (psi) 

kilogram per cubic meter (kg/m3

) 0.0083454 pound per gallon (ppg) 

pascal-second (Pa·s) 1,000 centipoise (cP) 

meter squared (m2

) 1.01325 × 1015 millidarcy (mD) 

1

Oil volume under reservoir conditions is measured in terms of reservoir barrels. Oil volume under surface 

conditions (60°F and 14.7 psi, or 15°C and 101.325 kPa) is measured in terms of stock tank barrels. When a quantity 

of oil is brought from reservoir conditions to surface conditions, the change in temperature and pressure and the 

release of gas bubbles cause the oil volume to decrease. The ratio of the oil volume under reservoir conditions to the 

volume under surface conditions is known as the formation volume factor and is denoted by B. 

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows: 

°C=(°F-32)/1.8 
Computer Simulation of Reservoir Depletion and Oil 

Flow from the Macondo Well Following the Deepwater 

Horizon Blowout

By Paul A. Hsieh 

Abstract 

This report describes the application of a computer model to simulate reservoir depletion 

and oil flow from the Macondo well following the Deepwater Horizon blowout. Reservoir and 

fluid data used for model development are based on (1) information released in BP’s 

investigation report of the incident, (2) information provided by BP personnel during meetings in 

Houston, Texas, and (3) calibration by history matching to shut-in pressures measured in the 

capping stack during the Well Integrity Test. The model is able to closely match the measured 

shut-in pressures. In the simulation of the 86-day period from the blowout to shut in, the 

simulated reservoir pressure at the well face declines from the initial reservoir pressure of 11,850 

pounds per square inch (psi) to 9,400 psi. After shut in, the simulated reservoir pressure recovers 

to a final value of 10,300 psi. The pressure does not recover back to the initial pressure owing to 

reservoir depletion caused by 86 days of oil discharge. The simulated oil flow rate declines from 

63,600 stock tank barrels per day just after the Deepwater Horizon blowout to 52,600 stock tank 

barrels per day just prior to shut in. The simulated total volume of oil discharged is 4.92 million 

stock tank barrels. The overall uncertainty in the simulated flow rates and total volume of oil 

discharged is estimated to be ±10 percent. 
Background 

The computer simulation described in this report was undertaken to supplement the work 

of the Flow Rate Technical Group, a group of scientists and engineers led by U.S. Geological 

Survey (USGS) Director Marcia McNutt to estimate the flow of oil from the Macondo well 

following the Deepwater Horizon blowout on April 20, 2010. Much of the work of the Flow Rate 

Technical Group was carried out prior to July 15, 2010, the date when the Macondo well was 

shut in to begin the Well Integrity Test. The computer simulation described in this report was 

carried out to analyze the shut-in pressure data obtained during the Well Integrity Test in order to 

gain additional knowledge of the Macondo well and the oil reservoir. Simulation results of 

particular interest include (1) the assessment of reservoir depletion resulting from oil flow during 

the 86 days from blowout to shut in, (2) the estimate of oil flow rate from the well, and (3) the 

estimate of total volume of oil discharged. 

A significant amount of data used in the development of the reservoir model described in 

this report were provided by BP personnel at meetings in Houston, Texas, during late June to 

early August 2010. Much of these data are considered proprietary and by Government regulation 

cannot be released. Although the proprietary data were included in the draft version of this report 

for USGS technical peer review, they are not included in this final release version in accordance 

with Government regulation. 

Reservoir Model 

Reservoir Geometry and Conditions 

The Macondo well produces oil from an oil reservoir known as M56. According to the 

BP investigation report of the Deepwater Horizon blowout (BP, 2010, Appendix W, p. 17, fig. 

1.6), the M56 oil reservoir consists of three oil-producing sand layers. The top of the reservoir is 

penetrated by the Macondo well at a depth of approximately 18,000 ft below sea surface. The 

combined pay thickness of the three oil-producing sand layers is approximately 90 ft. The initial 

reservoir pressure is 11,850 pounds per square inch (psi). The reservoir temperature is 

approximately 240°F. As the bubble point of the oil in the reservoir is approximately 6,500 psi 

(BP, 2010, Appendix W, p. 11), the reservoir is believed to be under single-phase (liquid oil) 

condition. Table 1 shows the reservoir and fluid properties used in the model. However, property 

values are not given in this report owing to their proprietary nature. 

To construct the reservoir model, the bulk volume of reservoir containing the oil is 

estimated by 

)1( w

o

b S

BV V    , (1) 

where 

Vb is the bulk volume of reservoir containing the oil [L3], 

Vo is the volume of original oil in place [L3

], 

B is the formation volume factor [dimensionless], 

 - 2 - 
 is porosity [dimensionless], and 

Sw is water saturation [dimensionless]. 

The sedimentary history of the Gulf Coast in the vicinity of the Macondo well suggests 

that the oil-producing sands composing the M56 reservoir are submarine channel fills 

(Posamentier, 2003). In the model, the oil reservoir is assumed to be a long, narrow channel 

having a rectangular cross section (fig. 1). The vertical thickness (b) of the channel is 90 ft. The 

horizontal length (L) and width (W) are initially unknown and are estimated by history matching 

of the Well Integrity Test. However, because L × W × b must equal Vb, L and W are related by 

ft90

Vbb

b

V WL  . (2) 

The reservoir is assumed to be a closed system. In other words, all six faces of the 

channel are impermeable boundaries. Within the reservoir, the Macondo well location is defined 

by the coordinates (xw, yw), which are initially unknown and are estimated by history matching. 

Mathematical Formulation 

The equation of oil flow in the reservoir is given by (after Matthews and Russell, 1967, p. 

7, equation 2.12) 

t

p

k

c

y

p

x

p



  







 

2

2

2

2

, (3) 

where 

p is pressure [M/(L·T2)], 

c is the system compressibility [L·T2

/M], 

k is permeability [L2

], 

μ is oil viscosity [M/(L·T)], 

x, y are Cartesian coordinates in the horizontal plane [L], and 

t is time [T]. 

In applying equation 3 to the reservoir, the following conditions are assumed: 

1. Flow of oil is under single-phase and isothermal conditions. 

2. Reservoir properties (permeability, porosity, and compressibility) are homogeneous. 

3. Permeability and viscosity are independent of pressure. 

4. Permeability is isotropic. 

Additional assumptions are given by Matthews and Russell (1967). These are standard in the 

analysis of pressure buildup and flow tests in wells and include assumptions that the reservoir is 

 - 3 - 
horizontal, the fluid compressibility is small and constant, and that pressure gradients within the 

reservoir are sufficiently small for Darcy’s law to apply. 

The system compressibility is computed as (after Matthews and Russell, 1967, p. 135, 

note 1) 

fwwow   )1(   ccScSc , (4) 

where 

co is oil compressibility [L·T2/M], 

cw is water compressibility [L·T2

/M], and 

cf is effective formation (or pore) compressibility [L·T2

/M]. 

Except for permeability, values of reservoir and fluid properties used in the reservoir 

model are assumed to be known (table 1). Permeability is estimated by history matching. 

The volumetric flow rate of oil from the reservoir through the Macondo well and exiting 

the blowout preventer is modeled by the equation (see fig. 2) 

( ) 2   oew gHppCQ , (5) 

where 

Q is the volumetric flow rate of oil at reservoir conditions [L3/T], 

C is a coefficient of pressure loss through the well [L7

/M], 

pw is the reservoir pressure at the well face [M/(L·T2

)], 

pe is the ambient pressure at the exit point of the blowout preventer [M/(L·T2

)], 

ρo is oil density [M/L3

], 

g is gravitational acceleration [L/T2

], and 

H is the elevation difference between the M56 reservoir and the exit point at the 

blowout preventer [L]. 

Equation 5 is similar to the Darcy-Weisbach equation (De Nevers, 1970), which relates 

the head loss due to friction along a given length of pipe to the square of the flow rate through 

the pipe. The value of the coefficient C in equation 5 is initially unknown and is estimated by 

history matching. In the reservoir simulation, C is kept constant for the entire period of well 

flow. This assumes that the changes in outlet configuration, such as cutting of the riser pipe, do 

not significantly impact the oil flow rate. For the Macondo well flow calculation, the ambient 

pressure at the exit point of the blowout preventer (pe) is 2,190 psi and H is 13,000 ft. The 

volumetric flow rate of oil at surface (stock tank) conditions is computed by dividing Q by the 

formation volume factor, B. 

 - 4 - 
MODFLOW Implementation 

The U.S. Geological Survey model known as MODFLOW-2000 (Harbaugh and others, 

2000) is used to simulate oil flow in the M56 oil reservoir. Although MODFLOW-2000 was

originally designed to simulate the flow of groundwater in aquifers, it can be readily adapted for 

simulating flow of oil in reservoirs under single-phase and isothermal conditions. The fluid flow 

equation solved by MODFLOW-2000 is analogous to equation 3, and can be written as 

t

h

K

S

y

h

x

h s



  







2

2

2

2

, (6) 

where 

h is hydraulic head [L], 

K is hydraulic conductivity [L/T], and 

Ss is specific storage [1/L]. 

For simulating oil flow, the quantities h, K, and Ss are computed as 

z

g

p h

o





, (7) 



K o   gk , (8) 

cgS   os  , (9) 

where 

z is the vertical elevation above a reference datum [L]. 

A modified version of the General-Head Boundary Package is used to simulate flow 

through the Macondo well, as expressed by equation 5. In its original version, the General-Head 

Boundary Package (see McDonald and Harbaugh, 1988, chapter 11) can be used to implement 

equation 5 if the exponent of the Q term were 1 instead of 2. To implement the Q2

 term, the 

Fortran source code of the General-Head Boundary Package is modified and the program 

recompiled. 

Figure 3 is a map view of an example finite-difference grid of the oil reservoir, which is 

represented by a single 90-ft thick model layer. The cell containing the Macondo well has a 

horizontal dimension of 1 ft by 1 ft. The cell size increases away from the well to a maximum 

size of 100 ft by 100 ft. During history matching, the grid is reconstructed as the well coordinates 

(xw, yw) are varied. The simulation time step is 0.2 day. Well shut in is simulated by setting the 

coefficient C in equation 5 to zero. 

 - 5 - 
History Matching 

The parameter estimation program PEST version 10 (Doherty, 2004) is used to perform 

history matching—the adjustment of model parameters so that simulated pressures match 

measured pressures. (This procedure is also known as model calibration.) The estimated model 

parameters are shown in table 2. PEST implements a nonlinear least-squares regression method 

to estimate model parameters by minimizing the sum of squares of the differences between 

measured and simulated pressures: 





N

i

sim

i

mea

i pp

1

2 ( )

,

 (11) 

where 

N is the number of measurements [dimensionless], 

mea pi is the i

th measured pressure [M/(L·T2

)], and 

sim pi is the i

th simulated pressure [M/(L·T2

)]. 

PEST uses the Gauss-Marquardt-Levenberg method to minimize Φ. Details of this method are 

given in the PEST user’s manual (Doherty, 2004). 

The pressure data used for history matching were measured during the Well Integrity 

Test, which began on July 15, 2010. At 2:20 p.m. Central Daylight Time, the final turn on the 

choke was closed and the Macondo well was shut in. Shut-in pressure was measured 

continuously by two pressure gages installed in the capping stack. Pressure data from the PT-3K1 transducer were nearly identical to pressure data from the PT-3K-2 transducer, except the 

former gave a pressure reading that was approximately 100 psi lower than that from the latter. 

For history matching, shut-in pressures measured by the PT-3K-2 transducer are used. The 

simulated shut-in pressure in the capping stack is calculated by subtracting ρogH from the 

simulated reservoir pressure at the well face to adjust for the elevation difference between the 

M56 reservoir and the pressure gage in the capping stack. The Well Integrity Test ended on 

August 3, 2010, when heavy mud was injected into the Macondo well to initiate the “static kill” 

operation. 

Figure 4 is a Horner plot showing the simulated shut-in pressures in the capping stack. 

The horizontal axis of the Horner plot shows the quantity (tp + Δt)/Δt, where tp is the period of 

oil flow (86 days), and Δt is the elapsed time since shut in. Note that on the horizontal axis, time 

increases to the left. The simulated pressures closely match the continuously measured 

pressures—the standard error of the residuals (differences between simulated and measured 

pressures) is 2.3 psi. However, the continuously measured pressures used for history matching 

are not shown in figure 4 owing to their proprietary nature. Instead, figure 4 shows only those 

pressure readings that were announced in daily Government press releases 

(http://www.restorethegulf.gov/news/press-releases) and in BP technical briefings 

(http://www.bp.com/sectiongenericarticle.do?categoryId=9034442&contentId=7063846). 

 - 6 - 
Simulation Results 

Reservoir Depletion 

Figure 5 shows the simulated reservoir pressure at the Macondo well face. The origin of 

the time axis corresponds to April 20, 2010, the date of the Deepwater Horizon blowout. The 

initial reservoir pressure is 11,850 psi. Immediately after the blowout, the simulated pressure 

drops rapidly to approximately 11,000 psi and then follows a steady decline to 9,400 psi on day 

86, just prior to shut in. After shut in, the simulated pressure recovers and eventually stabilizes at 

10,300 psi. The pressure does not recover back to the initial pressure owing to reservoir 

depletion from 86 days of oil discharge. 

Oil Flow Rate 

Figure 6 shows the simulated volumetric flow rate of oil for surface conditions 

(expressed in stock tank barrels per day). Note that this flow rate is obtained by dividing the 

simulated flow rate under reservoir conditions, Q, by the formation volume factor, B. The 

simulated initial volumetric flow rate of oil is 63,600 stock tank barrels per day. As the reservoir 

depletes, the flow rate decreases to 52,600 stock tank barrels per day on day 86, just prior to shut 

in. The simulated total volume of oil discharged over the 86-day period from blowout to shut in 

is 4.92 million stock tank barrels. 

Uncertainty Analysis 

After history matching, the program PEST is run in “predictive analysis mode” to assess 

the predictive uncertainty of the reservoir model (see Doherty, 2004, chapter 6). In this context, a 

“prediction” is simply a model-simulated quantity that is not measured—there is no implication 

that the simulated quantity is to occur in the future. Three simulated quantities are of particular 

interest: (1) the initial oil flow rate, just after the blowout; (2) the final oil flow rate, just before 

shut in; and (3) the total volume of oil discharged. Table 3 gives the predictive uncertainty of 

these simulated quantities in terms of 95-percent prediction intervals. Note that all three intervals 

are relatively narrow—the upper or lower limits are no more than a few percent higher or lower 

than the corresponding simulated value. The narrow intervals are largely due to the close match 

between simulated and observed pressures and the low degree of nonuniqueness in the estimated 

parameters. 

The prediction intervals given in table 3, however, do not fully characterize the 

uncertainty in the simulated values. In calculating these intervals, it is assumed that the values of 

the reservoir and fluid properties given in table 1 are known. However, quantities such as 

original oil in place are, in fact, best estimates and are subject to uncertainty. To evaluate the 

impact of parameter uncertainty on the simulated flow rates and total volume of oil discharged, 

each reservoir or fluid property in table 1 is varied by ±25 percent, except for oil density, which 

is varied by ±10 percent (because a ±25-percent variation in oil density is considered too 

extreme). For each parameter variation, history matching is re-performed, and the simulation 

results are tabulated in table 4. As shown by the table, the impact of the parameter variation 

ranges from 0 (no impact) to ±25 percent of the simulated flow rates and total volume of oil 

discharged. On the basis of these results, the overall uncertainty in the simulated flow rates and 

total volume of oil discharged is estimated to be ±10 percent. 

 - 7 - 
Conclusions 

The reservoir model presented in this report simulates oil discharge from the Macondo 

well following the Deepwater Horizon blowout and pressure recovery after the well was shut in. 

During the 86-day period of oil discharge, the simulated reservoir pressure at the well face 

declines from the initial reservoir pressure of 11,850 psi to 9,400 psi. After shut in, the simulated 

reservoir pressure recovers to a final value of 10,300 psi. The pressure does not recover back to 

the initial pressure owing to reservoir depletion from the oil discharge. The simulated oil flow 

rate declines from 63,600 stock tank barrels per day just after the Deepwater Horizon blowout to 

52,600 stock tank barrels per day just prior to shut in. The simulated total volume of oil 

discharged is 4.92 million stock tank barrels. Analysis of the predictive uncertainty of the 

reservoir model suggests that the 95-percent prediction intervals of the simulated flow rates and 

total volume of oil discharged are relatively narrow—the upper or lower limits are no more than 

a few percent higher or lower than the corresponding simulated value. However, these prediction 

intervals do not fully characterize the uncertainty in the simulated values. If uncertainties in 

reservoir and fluid properties are taken into account, the overall uncertainty in the simulated flow 

rates and total volume of oil discharged is estimated to be ±10 percent. 

References Cited 

BP, 2010, Deepwater Horizon accident investigation report, September 8, 2010, accessed 

October 5, 2010 at 

http://www.bp.com/sectiongenericarticle.do?categoryId=9034902&contentId=7064891. 

De Nevers, Noel, 1970, Fluid mechanics: Reading, Pa., Addison-Wesley, 514 p. 

Doherty, John, 2004, PEST model-independent parameter estimation user manual, (5th ed.): 

Watermark Numerical Computing, variously paged, accessed October 5, 2010, at 

http://www.pesthomepage.org/Downloads.php. 

Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G., 2000, MODFLOW-2000, the 

U.S. Geological Survey modular ground-water model—user guide to modularization concepts 

and the ground-water flow process: U.S. Geological Survey Open-File Report 00–92, 121 p., 

accessed October 5, 2010, at http://water.usgs.gov/nrp/gwsoftware/modflow2000/ofr00-92.pdf. 

Matthews, C.S., and Russell, D.G., 1967, Pressure buildup and flow test in wells: New York, 

Society of Petroleum Engineers of AIME, 167 p. 

McDonald, M.G., and Harbaugh, A.W., 1988, A modular three-dimensional finite-difference 

ground-water flow model: U.S. Geological Survey Techniques of Water-Resources 

Investigations, book 6, chap. A1, 586 p., accessed October 5, 2010, at 

http://pubs.usgs.gov/twri/twri6a1/. 

Posamentier, H.W., 2003, Depositional elements associated with a basin floor channel-levee 

system—case study from the Gulf of Mexico: Marine and Petroleum Geology, v. 20, p. 677–

690. 

 - 8 - 
Table 1. Reservoir and fluid properties used in the reservoir simulation model. 

[Property values used in the reservoir model are not given in this report owing to their proprietary nature] 

Reservoir or fluid property 

Original oil in place 

Formation volume factor, B

Porosity, 

Effective formation (or pore) compressibility, cf 

Oil viscosity, μ

Oil compressibility, co

Oil density, ρo

Water saturation, Sw

Water compressibility, cw

 - 9 - 
Table 2. Model parameters that are estimated by history matching. 

[See figure 1 for definition of L, W, xw, and yw. Estimated values are not given in this report because they are derived 

from proprietary data] 

Model parameter 

Horizontal length of reservoir, L 

Horizontal width of reservoir, W

X-coordinate of Macondo well, xw 

Y-coordinate of Macondo well, yw

permeability, k

Coefficient of pressure loss in well, C

 - 10 - 
Table 3. Simulated oil flow rates and total volume of oil discharged along with 95-percent prediction 

intervals computed by PEST predictive analysis. 

Simulated quantity Simulated value 95-percent prediction interval 

 Minimum Maximum 

Initial oil flow rate (stock tank barrels/day) 63,600 62,800 64,200 

Final oil flow rate (stock tank barrels/day) 52,600 51,900 53,100 

Total volume of oil discharged (stock tank barrels) 4.92 × 106 4.85 × 106

 4.97 × 106

 - 11 - 
Table 4. Impact of ±25-percent variation in parameter value on simulated initial flow rate, final flow rate, 

and total volume of oil discharged. 

[%, percent] 

Impact of ±25% variation in parameter value on 

Parameter being varied Initial flow rate Final flow rate Total volume 

Original oil in place ±25% ±25% ±25% 

Formation volume factor, B 0 0 0 

Porosity,  0 0 0 

Effective formation (or pore) 

compressibility, cf 

±12% ±12% ±12%

Oil viscosity, μ 0 0 0 

Oil compressibility, co ±13% ±13% ±13% 

Oil density, ρo ±20%* ±20%* ±20%* 

Water saturation, Sw ±1% ±1% ±1% 

Water compressibility, cw ±0.3% ±0.3% ±0.3% 

*

Oil density varied by ±10 percent.

 - 12 - 
Figure 1. Oblique schematic view of the M56 oil reservoir. 

 - 13 - 
Figure 2. Schematic vertical section showing flow of oil from M56 reservoir through the Macondo well and 

exiting at the top of the blowout preventer. 

 - 14 - 
Figure 3. Map view of an example finite-difference grid of the oil reservoir. A, Entire grid. B, Detailed view 

of a small portion of the grid in the vicinity of the Macondo well. 

 - 15 - 
6,600

6,700

6,800

6,900

7,000

7,100

1 10 100 1,000

(t p + t)/t

Shut-in Pressure at Capping Stack (psi)

pressure reading announced at

press release

simulated pressure

August 3, 2010 July 16, 2010

Figure 4. Horner plot of shut-in pressure in the capping stack of the Macondo well. tp is the period of oil 

flow, which is 86 days. Δt is elapsed time since shut in. Note that time increases to the left on the 

horizontal axis. The solid line shows the simulated shut-in pressure in the capping stack. The simulated 

pressures closely match the continuously measured pressures, which are not given in this report owing 

to their proprietary nature. Instead, the diamond symbols show pressure readings that were announced 

in daily Government press releases and in BP technical briefings. 

 - 16 - 
9,000

10,000

11,000

12,000

-20 0 20 40 60 80 100 120 140

Time (days)

Simulated Reservoir Pressure at Well Face (psi)

initial reservoir pressure

Figure 5. Simulated reservoir pressure at the Macondo well face. The origin of the time axis (t = 0) 

corresponds to April 20, 2010, the date of the Deepwater Horizon blowout. 

 - 17 - 
 - 18 - 

40,000

50,000

60,000

70,000

0 20 40 60 80

Time (days)

Simulated Flow Rate (stb/d)

100

Figure 6. Simulated volumetric flow rate of oil from the Macondo well in stock tank barrels per day (stb/d). 

This flow rate is obtained by dividing the simulated flow rate under reservoir conditions (Q) by the 

formation volume factor (B). The origin of the time axis (t = 0) corresponds to April 20, 2010, the date of 

the Deepwater Horizon blowout.