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An Axisymmetric Coupled Flow and Deformation Model for Pore

Pressure Caused by Brine Injection in Paradox Valley, Colorado:

Implications for the Mechanisms of Induced Seismicity

Evelyn Roeloffs and Roger Denlinger

U.S. Geological Survey

Vancouver, WA

20 August 2009

This report is preliminary and has not been reviewed for publication.
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Executive Summary

1. Introduction

2. Background

3. Ways in which injection could be inducing earthquakes

4. Description of model

5. Physical properties of the geologic units

6. Model calibration and sensitivity

7. Simulated pore pressure

 7.1 Pore pressure vs. distance from well

 7.2 Development of the induced seismicity pattern

 7.3 Time relationships of pressure and seismicity at increasing distances from well

 7.4 Summary of relationship between seismicity and simulated pressure

8. Displacement and Strain near the Surface

9. Conclusions

References cited

Figure Captions

Table Caption
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Executive Summary

We describe a radially-symmetric finite-element model of injectate flow for the Paradox

Basin brine disposal well. The model simulates the time variation of the fluid-pressure

changes induced by injection as a function of depth below the surface and distance from

the wellbore.

The model was calibrated to match the observed wellhead pressure-flow relationship for

the period from July 26, 1996 through March 31, 2001. These data provide good

constraints on the hydraulic diffusivity of the Leadville injection reservoir in the vicinity

of the wellbore, and imply that permeability is 3-4 times lower than the estimate obtained

from well logging.

Although the epicenters of the induced earthquakes form linear patterns, the observed

pressure-flow behavior is consistent with a radial, rather than a channelized, flow model.

If the flow were unable to penetrate uniformly in all directions from the borehole, there

would be a much faster fall-off of flow rate with time than observed. However, the

observed pressure-flow relationship at the wellbore becomes less sensitive to changes in

the permeability structure as distance from the well increases, so a channelized flow

pattern developing a few km from the wellhead cannot be ruled out.

The simulated pressure buildup in the Precambrian perforated zone is not as extensive as

in the Leadville, but there are still pressure increments in excess of 150 psi 2-3 km from

the well in the Precambrian by the end of March, 2001.

Within 4 km of the wellbore, simulated pressure increases of at least 300 psi seem

required to induce the first earthquakes. Successive onsets of seismicity occur when the

pressure reaches or exceeds its previous maximum.

The first located earthquake more than 3.75 km from the wellhead, on July 26, 1997,

seems attributable to elastic stresses acting on a pre-existing fault, rather than to fluid

pressure increase at the earthquake’s location. The stresses are presumably caused by

expansion of the volume around the wellbore as fluid mass is pumped into it. If this

interpretation is correct, then this event 7.5 km from the wellbore does not necessarily

imply that a fault was providing a preferential flow path or storage reservoir for injectate

at that time.

Simulated pressures always decrease monotonically with distance from the well, as does

the influence of time-variations in the pumping. Further than 4.75 km from the well, the

simulated pressure continues to rise monotonically through March 2001, despite periods

during which injection ceases. An important implication, which is probably still true for

a more realistic model geometry, is that ceasing injection will not lower fluid pressures at

locations several km from the wellbore until months have elapsed.

3D modeling, as well as several geophysical field techniques, could provide independent

information to help map the evolving subsurface distribution of injectate.
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1. Introduction

We describe a radially symmetric finite element model of injectate flow for the Paradox

Basin brine disposal well. The model simulates the time and space distribution of the

fluid pressure changes induced by injection versus depth below the surface and distance

from the wellbore. We calibrated the model to reproduce the observed pressure-flow

relationship at the wellhead based on data through March 2001, and we used the

calibrated model to calculate pressure changes in the formation for that time period.

These pressure changes can be compared with the temporal and spatial patterns of

earthquakes induced by fluid injection. The purpose of this report is to describe the

calculated pressure changes and how they relate to earthquakes induced by injection

operations.

2. Background

The Paradox Valley injection project was undertaken to dispose of saline groundwater in

order to prevent it from entering the Colorado River system. The well is located in the

Paradox Valley graben, which overlies a salt-cored anticline near the Colorado/Utah

border. The anticline is believed to be controlled by major subsurface faults that displace

bedrock beneath the evaporitic Paradox Formation, and the graben is a collapse feature

formed by the dissolving of these evaporates (Widmann, 1997). The injection well is

near the graben-bounding faults southwest of the Valley (Figure 1).

During project planning, in 1984, a network of seismographs was deployed by the U.S.

Bureau of Reclamation (BOR) to establish a baseline characterization of natural

seismicity in the area prior to beginning injection.

The 4.9 -km-deep injection well was drilled in 1986-1988. It was completed with

perforations in the Leadville limestone, in several deeper sandstone units, and in two

depth intervals within the deeper Precambrian granite. The perforated zones are overlain

by several carbonate units of low permeability as well as by the Paradox salt formation,

whose permeability is believed to be negligible. All of the perforations are in the depth

range 4.3-4.9 km.

The well was acid- and fracture-stimulated in summer, 1990, and initial injection testing

began in July, 1991. The first three injection tests had successively greater maximum

flow rates of 150, 225, and 450 gallons per minute (gpm), and each was accompanied by

a burst of microseismic activity. The fourth test, at a maximum injection rate of 166

gpm, produced no earthquakes. Prior to the fifth test, the lower Leadville was acidstimulated. The injection rate during the fifth interval was 300 gpm, and 81

microearthquakes were recorded. During the sixth and seventh injection intervals, flow

rates of 300-400 gpm were imposed, and both test intervals were accompanied by bursts

of microseismicity. The seventh test interval ended on April 3, 1995.

Injection resumed on a production basis on July 22, 1996 and continued, with some

interruptions, at a typical rate of 300-350 gpm and wellhead pressures of about 5000 psi.
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Seismicity continued and spread from the immediate vicinity of the borehole. On May

27, 2000 a magnitude 4.3 (MLGs from NEIC) earthquake occurred, whose epicenter was

9 km from the wellhead, and which caused minor damage. Following that earthquake,

injection was temporarily stopped, and then resumed at a lower rate.

This study describes a radial model of injectate flow from the well for the purpose of

estimating the spatial and temporal pressure distribution caused by the fluid injection.

The simulated pressure distribution depends on the permeabilities of the various injection

and confining intervals, for which estimates are available from well logging. However,

the relationship between the pressure and flow rate at the wellbore is the main piece of

information by which to calibrate the simulation, and it will be shown that adjustments to

the logging-derived permeabilities are required to simulate the observed relationship. The

simulation allows useful statements to be made about the general geometry of the

injection zone and the time relationships between pressure changes at the wellhead and

pressure changes at the locations where the earthquakes occur.

3. Physical mechanisms by which injection could be inducing

earthquakes

There are several distinct physical mechanisms by which fluid injection could be causing

earthquakes. Distinguishing among them can be difficult because testing their

plausibility requires knowing the pre-existing in-situ state of stress.

Increased fluid pressure reducing effective normal stress across planes of weakness:

The Mohr-Coulomb criterion, which is based on laboratory observations of failure and

frictional sliding of rock samples, states that shear fracture, or frictional sliding on a preexisting plane of weakness, occurs when

τ > τ 0 + μ(σ n − p) (1)

where τ represents shear stress on the plane, τ 0 represents a shear strength or resistance

to frictional failure, μ represents the static friction coefficient (about 0.6 for most crustal

rocks) , σn is normal stress across the fracture plane (compression positive), and p is

pore fluid pressure. Equation (1) predicts that increasing pore fluid pressure can

counteract normal stress across the fault plane and lead to shear failure or to sliding. The

pore fluid pressure acts in all directions, so increasing fluid pressure destabilizes faults of

all orientations.

Hydrofracturing: Extensional cracks in rock can form and propagate when their

internal fluid pressure exceeds the normal stress across the crack. Hydrofracturing is a

potential mechanism for injection-induced seismicity, especially near the wellbore, where

pressure changes of several hundred psi are induced.
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Stresses due to pressure gradients: Where fluid pressure gradients are large, a net force

on the rock skeleton results, and because this force is spatially nonuniform, it produces

stresses. Such stresses are of great importance in the near surface, in unconsolidated

materials, but have not been demonstrated to be significant in consolidated rocks at

depths of several km.

Elastic stresses due to the increasing volume of injectate. As fluid is pumped into the

the wellbore, the surrounding formation expands to accommodate the additional mass.

This expansion imposes tensional hoop stresses in the surroundings. These stresses are

elastic and therefore can be imposed before the diffusive fluid pressure front arrives at a

particular location. Fault slip caused by this mechanism is governed by the MohrCoulomb criterion (equation 1), but changes in stress, rather than pore pressure, are the

cause of the slip.

The model calculations described here do not assume that any of these mechnisms is the

cause of the seismicity at Paradox. The model only calculates the pore pressures,

stresses, and displacements, which can then be compared with the spatio-temporal

seismicity distribution to infer which of these mechanisms explain the induced seismicity.

4. Description of Model

The model described here is a radially symmetric finite element model with fully

coupled poroelasticity (Ghaboussi and Wilson, 1973). The complete simulated domain

extends from the surface to a depth of 50 km and from the borehole to a radial distance of

50 km, with a refined mesh for depths to 10 km and distances to 20 km. The injection is

simulated by applying pressure to nodes at the model borehole wall, following the actual

recorded pressure-time history . The model can compute the time-dependent

distributions of pore pressure , displacement, stress, strain, and flow throughout the

modeled domain. Figure 2 shows a detail of the mesh in the injection interval near the

borehole.

5. Physical Properties of the Geologic Units

The model requires specified values for the following physical properties: Shear

modulus, Poisson ratio, Skempton coefficient, and hydraulic diffusivity.

The shear modulus strongly affects the size of calculated displacements due to fluid

injection; the values assumed in the current model range from 9x109 Pa (1.3x106 psi) to

2.4x1010 Pa (3.5x106 psi), with the lower values being used nearer to the surface. All

materials in the model are assumed to have a Poisson ratio of 0.25.

Skempton’s coefficient is the ratio of pore pressure change to a change of mean stress in

a volume of material from which no flow can occur. Theoretically, Skempton’s

coefficient ranges from 0 to 1. It can be calculated from the porosity and shear modulus.

The values used for the porosity and Skempton coefficient are shown in Table 1.
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Skempton’s coefficient has some effect on the magnitude of the stresses induced by fluid

injection.

The hydraulic diffusivity is the parameter that most strongly affects the distribution of

pressure in the model. Hydraulic diffusivity is the ratio of transmissivity to storage

coefficient, or, equivalently, hydraulic conductivity to storativity, and has dimensions

L2/T. For the model input, diffusivities were calculated from permeabilities, formation

thicknesses, porosities, and shear moduli obtained from the BOR and are shown in Table

1.

6. Model Calibration and Sensitivity

The main information available for calibrating the model is the relationship between

pressure and flow rate at the wellhead. This relationship in turn is primarily sensitive to

the hydraulic diffusivity of the injection interval. Hydraulic diffusivity is directly

proportional to permeability, and permeabilities were adusted to obtain the best match to

the pressure-flow relationship. However, it should be emphasized that the model

actually operates with hydraulic diffusivities, not permeabilities, and that other

combinations of permeability, porosity, etc., that yield similar hydraulic diffusivities will

produce identical results.

Each material in the injection intervals was assigned a unique hydraulic diffusivity. The

pressure-flow relationship at the wellbore is most sensitive to the hydraulic diffusivity of

the Leadville formation, because that formation is thickest and most permeable, and

therefore takes up most of the fluid. However, since the flow rate represents a total rate

into all injection intervals, other combinations of hydraulic diffusivities could fit the

observations equally well.

The information provided about the Leadville was that its permeability was “> 100 md”.

However, it was clear that to successfully reproduce the observed pressure-flow

relationship, a permeability 3-4 times lower was required. Figure 3 shows the predicted

flow rates for two model runs, together with the actual flow rate history. This figure

shows that the permeability of the Leadville is strongly constrained by the data. Overall,

the model that assumes a permeability of 28 millidarcies for the Leadville fits the

observed flow rates best. The 25% difference between the two permeabilities tested

translates to an approximately 25% difference in the simulated flow rate.

Several additional points can be noted from the actual and simulated flow-rate curves in

Figure 3:

1. The simulated flow rate gradually decreases with time, but the actual flow rate does

not. The behavior of the simulated flow rate is the expected behavior for injection

into a medium with uniform, time-independent properties in which the pressure is

increasing. The fact that the observed flow rate does not decrease could have several

explanations: There could be a zone of higher permeability at some distance from the

well; the permeability could be increasing in response to the increase of pore
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pressure; or the injectate could be leaking into the confining layers more than the

simulation currently permits.

2. The observed pressure-flow behavior is quite consistent with a radial, rather than a

channelized, flow model. If the flow were unable to penetrate uniformly in all

directions from the borehole, there would be a much faster fall-off of flow rate with

time than the simulation. Since the observed flow rate remains above the simulated

flow for the radial model, it would not be possible to fit the observations with model

in which flow is channelized into a single plane, either vertical or horizontal.

3. Prior to day 120, the simulated flow rate is much higher than the observed flow rate.

By day 180, the observed flow rate is consistent with the simulated flow rate. This

change in the relationship between the simulated and observed flow rate suggests that

the formation permeability may have increased during this time period, or that the

flow may have reached a zone of higher permeability away from the well.

4. At about day 640, there is an abrupt increase in injection rate that is not simulated by

the model. If this rate is recorded accurately, then this may also represent an episode

of fracturing.

7. Simulated Pore Pressure

7.1 Pore pressure vs. distance from well

Figure 4 shows curves of injection-induced pressure versus time at a number of distances

from the injection well. At any time, pressure decreases monotonically with distance

from the well. The influence of time-variations in the pumping rate also decreases with

distance from the well. At distances greater than 4.75 km from the well, the pressure

continues to rise monotonically despite periods during which injection ceases.

Figures 5a and 5b show the pressure distribution versus depth and distance from the

well 42 days and 1202 days from the beginning of continuous operation. The primary

purpose of these figures is to show how the pressure in the Leadville compares with that

in the Precambrian. Although the pressure buildup in the Precambrian is not as extensive

as in the Leadville, there are still pressure increments in excess of 150 psi 2-3 km from

the well in the Precambrian.

7.2 Development of the induced seismicity pattern

In this and the next section, the model-simulated pressure distribution is compared with

the time- and space-distribution of earthquakes. The earthquake dataset consists of

relative relocations obtained using a 3D velocity model (L. Block, email communication,

file “locs.713.reliable.tec.new”, July 2001). It should be noted that some induced events

are not included in this dataset because they could not be located accurately enough.

However, it seems likely that this dataset includes the larger events and the improved

locations compared with the more complete catalog clarify the relationship of the

seismicity to the simulated pressure distribution.
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Figure 6 is a map view of the earthquake epicenters color-coded by month for the period

from January through October 1997, when the induced seismicity was initially spreading

from the well. The first seismicity following the start of production pumping occurred in

January, 1997. By the end of April 1997, the induced earthquakes were all less than 1.5

km from the well. On May 5, injection was suspended. On May 5, three events occurred

in a cluster about 2.5 km southwest of the wellhead. It may be significant that these

events took place as pressure at that location was beginning to decrease following the

suspension of injection. No events were located further from the wellhead than this until

after the resumption of injection.

Injection was begun again on July 10, 1997. The first induced event after this was on

July 16, within the distance range that had remained slightly active during the shutdown.

The delay between resuming injection and the onset of seismicity is probably attributable

to the time required for the pressure in the formation to exceed its previous maximum, as

will be discussed in section 7.3.

The next event, on July 26, took place 7.5 km from the wellhead. This earthquake took

place as wellhead pressure was increasing following the resumption of injection. The

almost complete lack of any earthquakes between this event and the wellhead strongly

suggests that this earthquake was caused by elastic stresses imposed by the increasing

amount of mass around the wellbore. Under that interpretation, this earthquake was not

an indication that the fluid pressure had suddenly begun propagating more quickly.

The July 26, 1997 earthquake was followed, starting August 5, by activity in a new

cluster 2 km west of the wellhead, in which 16 events were located in 10 days. In

September, more events took place within about one km of the July 26 earthquake. The

distance range between 3 and 6 km from the wellhead remained without activity. A line

passing through the epicenters of the July 26 earthquake, the cluster that began August 5,

and the September-October activity near the July 26 epicenter is closely parallels the

N46° strike of the faults bounding the Paradox Valley graben (Widmann, 1997).

Seismicity gradually resumed in the area near the well that had previously been active.

Section 7.3 describes how the seismicity at different distances from the wellhead can be

related to the simulated pressure changes at those locations.

7.3 Time relationships of pressure and seismicity at increasing distances from well

In each of Figures 7a through 7h, the simulated pressure history at a specific distance

from the well is plotted with a timeline of seismicity within an annulus around the same

radius.

0.5-1.0 km from the well (Figure 7a). There is a clear relationship between simulated

pressure and seismicity. At this distance, every significant drop in the pumping rate

modulates the seismicity as well as the simulated pressure. The first earthquake occurs

when the simulated pressure is 780 psi. Seismicity rate decreases when the injection

pressure decreases and resumes when the simulated pressure reaches 900 psi . Based on
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the simulated pressure history, seismicity in this distance range resumes after a period

with no pumping when the simulated pressure reaches its previous maximum. As

pressure increased steadily from 1050 to 1140 psi, the seismicity rate remained high.

1-1.5 km from the well (Figure 7b). The strongest initial burst of seismicity occurs about

60 days after the first seismicity in the distance range 0.5 to 1 km, when the simulated

pressure reaches 620 psi. Seismicity stops as the pressure drops during the temporary

cessation of pumping from May 1 to July 10, 1997, and resumes when the simulated

pressure reaches 700 psi, about 50 psi above the previous maximum. The simulated

pressure then climbs with only one interruption to reach 900 psi in May 1999, and the

rate of seismicity also climbs until that maximum is reached. Then the seismicity rate

gradually decreases, with some fluctuations that track the simulated pressure. The

simulation result is that the 900 psi maximum pressure was not exceeded again before

May, 2000.

1.5-2 km from the well (Figure 7c). Seismicity initiates substantially later than the two

close intervals discussed previously. The first earthquake occurs at a simulated pressure

of about 480 psi. Seismicity ceases when the pressure is dropped, and resumes when the

simulated pressure reaches 570 psi, about 100 psi above the previous maximum. As the

simulated pressure increases to a maximum of 750 psi, seismicity continues with little

modulation by intervals of low injection pressure. At this distance from the wellhead,

temporary drops in wellhead pressure cause smaller and more gradual decreases in

simulated pressure.

2-2.5 km from the well (Figure 7d). Two events occurred when simulated pressure

reached 390 psi, and then no more activity took place until after injection resumed. The

next seismicity is the cluster of events starting August 5 (Figure 6), which begins at a

simulated pressure of about 310 psi. Unlike earlier onsets nearer the borehole, this cluster

began when the simulated pressure was 100 psi lower than the previously simulated

maximum. As will be discussed in Figure 7h, this cluster is likely related to the July 26,

1997 event 7.5 km from the wellbore. The next two onsets of seismicity follow the

pattern of occurring at, or slightly above, the previous maximum simulated pressure.

Sustained activity occurs as the simulated pressure rises to its maximum of 650 psi, and

then activity decreases and stops as the pressure is maintained below that value. As at the

closer distances to the borehole, events occur at lower simulated pressures after the M4.3

earthquake in May 1997. At this distance there is a significant delay in the response of

the simulated pressure to periods when injection is temporarily stopped.

2.5 to 3 km from the well (Figure 7e). The first seismicity occurred when the simulated

pressure was 320 psi, and subsequent onsets occur at or above the previous maximum

simulated pressure. Periods when injection is stopped cause small, gradual pressure

decreases, but these variations do still appear to influence the seismicity rate.

3-3.5 km from the well (Figure 7f). Activity does not initiate here until early 1998, but the

simulated pressure at onset (380 psi) is not very different from that for the 2.5-3 km

range (320 psi). Earthquakes occur less frequently than closer to the wellbore, and the
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simulation indicates that brief interruptions in injection produce only small changes in

pressure, so it is not clear whether the pressure variations modulate the seismicity. The

seismicity rate can be seen in Figures 7a through 7f to have decreased with increasing

distance from the wellbore, consistent with decreasing injection-induced pressures.

3.5-6 km from the well (Figure 7g). Only one earthquake occurred during the simulated

time period, at a distance of 3.75 km from the wellhead. The simulated pressure rises

almost monotonically, and the earthquake occurred at a simulated pressure of 310 psi, not

very different from the onset pressures at distances of 2.5-3.5 km. The maximum

pressure is 360 psi and it is maintained for the 10-month period from the May 27 M4.3

earthquake to the end of the figure, despite the cessation of pumping.

6-9 km from the well (Figure 7h). Activity more than 6 km from the well began with the

event on July 26, 1997 7.5 km from the wellhead. This event could be interpreted to

indicate that the fluid pressure there had increased sufficiently to induce an earthquake.

However, the pattern of response to the simulated pressure observed closer to the

wellbore does not support that interpretation. First, it is implausible that the fluid

pressure due to injection would be greater at this distance than in the 3.5-6 km distance

range, where no earthquakes occurred before 1998. Second, the event occurred when the

simulated pressure was only 60 psi, whereas pressures in excess of 300 psi were

simulated when seismicity closer to the wellhead began. Third, although this event

occurred only 16 days after injection had resumed, the simulated pressure was simply

climbing monotonically, owing to the large distance to the wellhead, and therefore

provides no obvious trigger for the event to occur.

An alternative explanation is that the earthquake 6 km away on July 26 was caused by

slip on a pre-existing fault to help accommodate the increasing volume of material being

added around the wellbore. If the pressurized material around the borehole is regarded as

cylindrical, then extensional hoop stresses intensify as more material is injected, reducing

the normal stress across pre-existing subvertical faults. Such stress increments are elastic

responses to increased pressurization near the wellbore and they are therefore imposed on

the same time scale as that pressurization. The rapidly increasing pressure near the

wellbore as injection resumed after a break (Figures 7a thru 7c) would have imposed

rapidly changing stresses on the surrounding region. It is plausible that these stresses led

to the earthquake on July 26, by causing a critical effective stress to be reached, and/or

because of the rapid nature of the change.

7.4 Summary of relationship between seismicity and simulated pressure

Although the distribution of seismicity is not radial, this radially symmetric model seems

to account for some specific features in the data.

Within 4 km of the wellbore, when the onset times of seismicity at various distances from

the borehole are compared with the simulated pressure at that distance, successive onsets

of seismicity can be seen to occur when the pressure reaches its previous maximum.
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All of the earthquakes in this dataset that occurred within 4 km of the wellbore took place

when the simulated injection-induced pressure was 300 psi or more.

During the time period of this simulation (from July 22, 1996 to March 31, 2001),

simulated pressure at the initiation of seismicity decreases with distance from the

wellbore (from 780 psi within 1 km of the wellbore, to about 300 psi at 3 km from the

wellbore). This could be explained in several ways. First, if injectate is confined to a

narrower reservoir, actual pressures would not decrease with distance as quickly, so the

lower simulated pressures further from the wellbore could be due to inappropriateness of

the radial model. Second, during the period of development and testing prior to

production, the formation near the wellbore presumably experienced higher maximum

pressures, so that the simulation period may not include the first onset of seismicity for

locations nearest the well. It is of course possible that stresses are higher, or faults are

less resistant to slip, at distances several km from the wellbore, but this hypothesis is

difficult to test.

The first located event more than 3.75 km from the wellhead, on July 26, 1997, seems

attributable to elastic stresses acting on a pre-existing fault, rather than to fluid pressure

increase at the earthquake’s location. The stresses are presumably caused by expansion

of the volume around the wellbore as fluid mass is pumped into it. This earthquake was

followed by seismic events (on August 5, 1997) closer to the wellbore along the strike of

regional faults. However, this alignment of earthquakes does not necessarily imply that a

fault was providing a preferential flow path or storage reservoir for injectate in the time

period shown here.

Figures 7a through 7h illustrate how pressure variations at the wellhead are damped out

with increasing distance from the well. An important implication is that ceasing injection

will not lower fluid pressures at locations several km from the wellbore until months have

elapsed. This general conclusion would also be true in a situation where flow is confined

to a narrow region.
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8. Suggestions for future work

Further modeling, ideally supplemented by field measurements, could provide constraints

on where the Paradox injectate is flowing in the subsurface. Because increased fluid

pressure is not necessarily the cause of the induced earthquakes more than a few km from

the wellhead, it could be misleading to identify the pressure front with the expansion of

the seismically active area. Independent means of mapping the fluid distribution are

needed.

Modeling needs to be undertaken with a 3D code that can evaluate the possibility that

flow is channelized and that can more accurately represent the geologic structure in the

area.

Seismological techniques for detecting velocity changes may help map the distribution of

subsurface pressure. Focal mechanisms for the earthquakes would help discriminate

among the various possible mechanisms for inducing seismicity at Paradox. This

preliminary study suggests that increases of pore pressure alone cause earthquakes within

a limited radius of the well, while stresses imposed by addition of so much fluid mass can

induce earthquakes on pre-existing faults further from the wellbore.

Crustal deformation measurements using leveling, tiltmeters, or borehole strainmeters

could help ascertain the influence of the injected fluid on the earth’s crust. All three

techniques would be useful within a few km of the wellhead. Borehole strainmeters

might well detect strains associated with injection at the distances of 10 km or more

where events are potentially migrating. Boreholes are also excellent low-noise

environments for seismometers that could record low-level activity outside the perimeter

of the existing network.
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References Cited

Ghaboussi, J. and E. L. Wilson, Flow of compressible fluid in a porous

elastic medium with compressible constituents, International Journal of Numerical

Methods in Engineering, 5, 419-442, 1973.

Widmann, B.L., compiler, 1997, Fault number 2286, Paradox Valley graben, in

Quaternary fault and fold database of the United States: U.S. Geological Survey website,

http://earthquakes.usgs.gov/regional/qfaults, accessed 08/19/2009 07:44 PM.
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Figure captions

Figure 1. Map showing location of the injection well and the surrounding area.

Figure 2. Cross-section diagram of the finite element mesh used for a radially symmetric

simulation of pore pressure and deformation at the Paradox Salinity Control Injection

Well. Complete mesh extends to the surface and to 50 km in the radial and depth

directions.

Figure 3. Actual injection pressure history, and model-simulated pressure histories for

two different assumed permeabilities of the Leadville formation.

Figure 4. Model-simulated injection-induced pressure as a function of time at a number

of distances from the injection well.

Figure 5. Cross-section views of the model-simulated injection-induced pressure

distribution for two elapsed times after injection resumed on a production basis on July

22, 1996. (a) 42 days after July 22, 1996. (b) 1202 days after July 22, 1996.

Figure 6. Map view of earthquake epicenters (3D locations from L. Block, email

communication) for January through October, 1997.

Figure 7. Simulated pressures and timelines of earthquakes for several distance ranges

from the injection well.

Table Caption.

Table 1. Physical properties used in the finite-element model.
 FIGURE 1
4.0

4.5

5.0

190

183 Paradox

nkerton Trail

McCracken

neth/Lynch/

uav/Bright Angel

Ignacio

Molas

Leadville

Precambrian

Ismay

Salt

Lower Paradox

dville/Ouray/Elbert

Elbert

Ignacio

pper Precambrian

Precambrian

ower Precambrian

209

235

261

287

313

339

365

391

417

443

469

495

521

547

573

599

184

210

236

262

288

314

340

366

392

418

444

470

496

522

548

574

600

185

211

237

263

289

315

341

367

393

419

445

471

497

523

549

575

601

186

212

238

264

290

316

342

368

394

420

446

472

498

524

550

576

602

187

213

239

265

291

317

343

369

395

421

447

473

499

525

551

577

603

188

214

240

266

292

318

344

370

396

422

448

474

500

526

552

578

604

189

215

241

267

293

319

345

371

397

423

449

475

501

527

553

579

605

190

216

242

268

294

320

346

372

398

424

450

476

502

528

554

580

606

191

217

243

269

295

321

347

373

399

425

451

477

503

529

555

581

607

192

218

244

270

296

322

348

374

400

426

452

478

504

530

556

582

608

217

244

271

298

325

352

379

406

433

460

487

514

541

568

595

622

191

218

245

272

299

326

353

380

407

434

461

488

515

542

569

596

623

192

219

246

273

300

327

354

381

408

435

462

489

516

543

570

597

624

193

220

247

274

301

328

355

382

409

436

463

490

517

544

571

598

625

194

221

248

275

302

329

356

383

410

437

464

491

518

545

572

599

626

195

222

249

276

304

330

357

384

411

438

465

492

519

546

573

600

627

196

223

250

277

305

331

358

385

412

439

466

493

520

547

574

601

628

197

224

251

278

306

332

359

386

413

440

467

494

521

548

575

602

629

198

225

252

279

307

333

360

387

414

441

468

495

522

549

576

603

630

199

226

253

280

308

334

361

388

415

442

469

496

523

550

577

604

631

33.8MPa

(4901 psi)

l

l

l

l

l

l

l

l

l 34.7MPa

(5031 psi)

gure 1. Detail of finite element mesh used for a radially symmetric simulation of pore pressure and deformation at the

aradox Salinity Control Injection Well. Complete mesh extends to the surface and to 50 km in the radial and depth directions. Paradox Very Small Mesh
0 100 200 300 400 500 600 700 800 900 1000

0

100

200

300

400

Actual Daily Flow Rate

Simulated, Leadville, 22 md

Simulated, Leadville, 28 md

Days since 7/22/96

Flo

w

R

ate, G

allo

n

s/min

ute

Actual and Simulated Flow Rates - Radial Model
0 100 200 300 400 500 600 700 800 900

0

100

200

300

400

500

600

700

800

900

1000

1100

r=3.25 km

r=2.25 km

r=4.75 km

r=1.25 km

Injection

Pressure/5

Days since 7/22/96

Pre

s

s

ure in

cre

m

e

nt d

u

e to inje

ctio

n, p

si

InjectionInduced Pore Pressure in Leadville

r=1.75 km

r=0.75 km

r=2.75 km

r=7.5 km

r=9.5 km
0 1000 2000 3000 4000 5000 6000 7000 8000 9000

-1000

-2000

-3000

-4000

-5000

Distance from borehole, meters

D

e

pth, m

eters

0 50 100 150 200 250

Pore Pressure Induced by Injection, psi
-1000

-2000

-3000

-4000

-5000

D

e

pth, m

eters

0 50 100 150 200 250

Pore Pressure Induced by Injection, psi
-8 -6 -4 -2 0 2 4

locs.713.tec.a kgdata

1

2

3

4

5

6

7

8

9

10

km N of wellhead

km E of wellhead

0

6

4

2

-4

-2

km N of wellhead

Month

in 1997

7/26/97

r = 6 km

r = 3 km

1 km

2 km

Earthquakes Jan through Oct 1997 Earthquakes Jan through Oct 1997
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

rmag

Injection Pressure/5

Simulated Pressure 0.75 km from wellbore

Relative Magnitude

Pressure, psi

Days after July 22, 1996

Earthquakes 0.5 to 1 km from wellbore

780 psi

900

psi

1050

psi

1140

psi

Seismicity onset 5/27/00

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

(A)
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

rmag

Injection Pressure/5

Simulated pressure 1.25 km from wellbore

Relative Magnitude

Pressure, psi

Days after July 22, 1996

620

psi

900 psi

5/27/00

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

700

psi

730

psi

Earthquakes 1 to 1.5 km from wellbore

Seismicity onset

(B)
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

Injection Pressure/5

Simulated pressure 1.75 km from wellbore

rmag

Relative Magnitude

Pressure, psi

Days after July 22, 1996

570

psi

750 psi

5/27/2000

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

480

psi

(C)

Seismicity onset

Earthquake 1.5 to 2 km from wellbore
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

Injection Pressure/5

Simulated Pressure 2.25 km from wellbore

rmag

Relative Magnitude

Pressure, psi

Days after July 22, 1996

310

psi

480

psi 560

psi

650 psi

5/27/2000

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

(D)

Earthquake 2 to 2.5 km from wellbore

Seismicity onset

390

psi
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

Injection Pressure/5

Simulated Pressure 2.75 km from wellbore

rmag

Relative Magnitude

Pressure, psi

Days after July 22, 1996

5/27/2000

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

320

psi 410

psi

480

psi

540

psi 570 psi

Earthquake 2.5 to 3 km from wellbore

(E)

Seismicity onset
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

Injection Pressure/5

Simulated Pressure 3.25 km from wellbore

rmag

Relative Magnitude

Pressure, psi

Days after July 22, 1996

5/27/2000

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

 380

psi

500 psi

(F)

Earthquake 3 to 3.5 km from wellbore

Seismicity onset
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

Injection Pressure/5

Simulated Pressure 4.75 km from wellbore

rmag

Relative Magnitude

Pressure, psi

Days after July 22, 1996

5/27/2000

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

310

psi

360 psi

(G)

Earthquake 3.5 to 6 km from wellbore

Seismicity onset
0

0.5

1

1.5

2

2.5

3

3.5

4

0

500

1000

1500

7/22/96 2/7/97 8/26/97 3/14/98 9/30/98 4/18/99 11/4/99 5/22/00 12/8/00

0 200 400 600 800 1000 1200 1400 1600

Injection Pressure/5

Simulated Pressure 7.5 km from wellbore

rmag

Relative Magnitude

Pressure, psi

Days after July 22, 1996

5/27/2000

M4.3 event 

9 km from

wellbore;

flow rate

tlowered

Event on 

July 26 

1997

60

psi

210 psi

(H)

Earthquake 6 to 9 km from wellbore

Seismicity onset
Formation Description Top (m KB) Thickness (m) Porosity K, darcies K,millidarcies, in 

simulation

Porosity Skempton's 

Coefficient

Hydraulic 

Diffusivity, 

m**2/sec

Chinle 0 347 1.00E+01 0.1 0.61 1.68E-01

Cutler 347 2192 1.00E+01 0.1 0.61 1.68E-01

Honaker Trail 2539 1236 1.00E+01 0.1 0.61 1.68E-01

Paradox

Salt and 

anhydrite 3775 149 low 1.00E-08 0.0001 1.00 4.75E-10

Ismay 3923 82 1.00E-08 0.0001 1.00 4.75E-10

Salt 4005 142 1.00E-08 0.0001 1.00 4.75E-10

Lower Paradox Carbonate 4147 38 "tight" 1.00E-06 0.001 0.98 6.82E-08

Pinkerton Trail Carbonate 4185 77 "impervious" 1.00E-06 0.001 0.98 6.82E-08

Molas

Limestone or 

shale? 4262 12 "impervious" 1.00E-06 0.001 0.98 6.82E-08

Leadville (unperf)

Limestone, 

oolitic, 

fossiliferous 4275 17 >0.1 >100 md 2.79E+01 0.1 0.39 6.56E-01

Leadville/Ouray/Elb Perf 4292 129 2.79E+01 0.1 0.39 6.56E-01

Elbert (unperf) 4414 51 2.79E-03 0.05 0.56 9.80E-05

McCracken (almost all 

perforated) Sandstone 4465 23 2.79E-03 0.05 0.56 9.80E-05

Aneth-Lynch-MuavBright AngelLimestone with 

Sandstone 4487 173 2.79E-03 0.05 0.56 9.80E-05

Ignacio (unperforated) Sandstone 4660 27 2.79E-04 0.05 0.56 9.80E-06

Ignacio (perforated) Sandstone 4687 34 0.04-0.07 no data 2.79E-04 0.05 0.56 9.80E-06

Upper Precambrian Perf 

Zone Granite 4721 58 0.03-0.09 3.2 md 8.36E-01 0.06 0.15 4.25E-02

Precambrian (unperf?) Granite 4779 21 2.79E-04 0.005 0.68 6.60E-05

Lower Precambrian Perf 

Zone Granite 4801 30 2.79E-04 0.005 0.68 6.60E-05

Precambrian 2.79E-04 0.005 0.68 6.60E-05

 Information from Fact Sheet Model Input