U.S. Department of the Interior

Bureau of Reclamation April 2016

Technical Memorandum TM-85-833000-2014-42

Evidence for Far-field Reservoir 

Pressurization, Paradox Valley, 

Colorado

Colorado Basin Salinity Control Project,

Paradox Valley Unit, Colorado 

Upper Colorado Region
Mission Statements

The mission of the Department of the Interior is to protect and 

provide access to our Nation’s natural and cultural heritage and 

honor our trust responsibilities to Indian Tribes and our 

commitments to island communities.

The mission of the Bureau of Reclamation is to manage, develop, 

and protect water and related resources in an environmentally and 

economically sound manner in the interest of the American public.


Technical Memorandum TM-85-833000-2014-42

i

Executive Summary

The Bureau of Reclamation operates a deep injection well near Paradox Valley, Colorado, which 

injects salt brine as part of the Colorado River Basin Salinity Control Program. In recent years, 

the pressure required to inject the brine has been increasing and, prior to a decrease in the 

injection flow rate in mid-2013, was approaching the maximum allowable surface injection 

pressure as permitted by the U.S. Environmental Protection Agency (EPA).

Various solutions for reducing the surface pressure without further reductions in the volume of 

brine being disposed of each year are currently under consideration, including drilling a second 

injection well. A December 2012 Consultant Review Board (CRB) recommended that the 

pressure-flow data recorded at the wellhead be investigated to determine whether the pressure 

increase is caused by far-field reservoir pressurization or near-well flow impairment. This is an 

important issue in evaluating solutions for reducing the pressures, because if the pressure were 

caused by near-well flow impairment, it might be possible to rectify the issue with a workover of 

the existing well. Cleaning and reworking the existing wellbore would likely be a more 

economical way to reduce pressures than drilling a second injection well. This report summarizes 

the work that has been performed in response to this CRB recommendation.

Available evidence suggests that far-field pressurization is the dominant factor contributing to 

the increasing wellhead pressures, and therefore a workover at the existing wellbore is not likely 

to significantly reduce pressures. Two sources of evidence were investigated: pressure-flow 

modeling, and spatiotemporal patterns of induced seismicity. 

The pressure-flow data can be reasonably well fit using a simple radial flow model and just three 

free parameters: permeability, skin due to damage, and a wellbore storage constant. Nearwellbore flow impairment should be evident as a change in one or more of these modeled 

reservoir parameters over time. There are no strong effects in the pressure-flow modeling results 

for the last several years that indicate near-wellbore changes, and thus the observed pressure 

increase at the wellhead appears to be related to far-field reservoir pressurization. The radius of 

investigation of the pressure-flow modeling of individual injection cycles is estimated to be 1 to 

2 km. Therefore, these results suggest pore pressure increase in the target injection formations to 

a distance of at least 1-2 km from the well. The actual extent of elevated pore pressures, 

however, could be well beyond the radius of investigation.

The spatiotemporal occurrence of induced seismicity indicates that there is substantial vertical 

and lateral hydraulic connectivity in the near-well region that does not appear to have degraded 

over time as brine injection has continued. These observations suggest that the increasing depth 

of fill in the injection well and any potential precipitation and clogging of fractures within ~2-3 

km of the well are not noticeably interfering with fluid flow and pore pressure propagation. In 

addition, changes observed since 2009 in the patterns of induced seismicity occurring ≥6 km 

from the well suggest that reservoir pressures may be increasing at distances up to ~18 km from 

the injection well. However, because of the low, fracture-dominated permeability of the 
Technical Memorandum TM-85-833000-2014-42

ii

Leadville formation, elevated pore pressures may be propagated over large distances through a 

limited network of fractures, potentially leading to a strongly heterogeneous pore pressure field. 

Seismicity patterns also are not symmetric around the wellbore. Seismicity in the areas 

southwest, south, and southeast of the well has been characterized by relatively low rates and 

small magnitudes at radial distances greater than about 2.5 km, and no seismicity has occurred in 

these directions at distances > 7 km, suggesting that geologic factors may be limiting pore 

pressure increase in these areas. In summary, the induced seismicity patterns are consistent with 

reservoir pressurization around the well to a distance of 2-2.5 km and suggest pressurization to 

much larger distances (up to ~ 18 km) in some azimuthal directions. 
Technical Memorandum TM-85-833000-2014-42

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Contents

Page

Executive Summary..................................................................................................................................... i

1 Introduction ......................................................................................................................................... 1

2 Local Geology...................................................................................................................................... 3

3 Injection History .................................................................................................................................. 7

3.1 Phase I (July 22, 1996 – July 25, 1999)........................................................................................ 7

3.2 Phase II (July 26, 1999 – June 22, 2000) ..................................................................................... 9

3.3 Phase III (June 23, 2000 – January 6, 2002)................................................................................ 9

3.4 Phase IV (January 7, 2002 – April 16, 2013)................................................................................ 9

3.5 Phase V (April 17, 2013 – present).............................................................................................10

4 Pressure-Flow Modeling..................................................................................................................13

4.1 Previous Work.............................................................................................................................13

4.2 Fitting of Pressure-Flow Data to Idealized Models .....................................................................14

4.3 Results of Pressure-Flow Model Fitting ......................................................................................20

4.3.1 Changes in Model Parameters over Time ..........................................................................20

4.3.2 Model Pressure-History Plots and Type Curves .................................................................28

4.3.3 Using rinv to Investigate Changes in Permeablity ................................................................39

4.3.4 Fitting Multiple Cycles Simultaneously................................................................................43

4.4 Pressure-Flow Modeling Discussion...........................................................................................44

5 Induced Seismicity............................................................................................................................47

5.1 History of Seismicity....................................................................................................................47

5.2 Relation to Pore Pressure Diffusion............................................................................................48

5.3 Near-Well Seismicity ...................................................................................................................59

5.3.1 Vertical Seismicity Distribution and Hydraulic Connectivity ................................................59

5.3.2 Seismicity Patterns and Reservoir Permeability .................................................................63

5.4 Geographical Expansion of Seismicity........................................................................................67

5.5 Spatial Extent of Injected Brine...................................................................................................69

5.6 Induced Seismicity Discussion....................................................................................................71

6 Conclusions.......................................................................................................................................73

7 References.........................................................................................................................................75

Appendix A Models for the Spatial Extent of Injected Brine ....................................................... A-1

Appendix B Electronic Supplement of Pressure and Flow Rate Data........................................ B-1

Tables

Page

Table 2-1. Paradox Valley stratigraphy......................................................................................................... 4

Table 4-1. Permeability (k), skin due to damage (sd), and dimensionless wellbores storage constant (CD) 

fit with three free parameters, and k and CD fit with sd fixed at -4.35 for all cycles. ....................................25

Table A-1. Higher-porosity zones within the Leadville formation reported in Bremkamp and Harr (1988). 

Values were derived from the sonic-porosity well log for PVU Injection Well #1...................................... A-1

Table A-2. Higher-porosity zones within non-Leadville sub-salt formations reported in Bremkamp and Harr 

(1988). Values were derived from the sonic-porosity well log for PVU Injection Well #1. ........................ A-2

Table A-3. Scenarios used for cylindrical brine intrusion models. ............................................................ A-2
Technical Memorandum TM-85-833000-2014-42

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Table B-1. Fluid density. ........................................................................................................................... B-1

Figures

Page

Figure 1-1. Location of the deep injection well at Reclamation’s Paradox Valley Unit in western Colorado.

...................................................................................................................................................................... 1

Figure 3-1. Daily average injection flow rate (top), daily average surface injection pressure (middle), and 

daily average downhole pressure at 14,100 feet (4.3 km) depth (bottom) during PVU injection operations.

...................................................................................................................................................................... 8

Figure 4-1. Recorded (blue dots) and modeled (red line) downhole pressures, fit using (a) best-fit 

parameters and (b) manually determined parameters for an example Phase I cycle, beginning May 30, 

1998. Blue lines indicate recorded flow rate. Recorded downhole pressures are calculated by adding a 

constant value of 6822 psi to measured surface pressures. The model has difficulty fitting the data during 

periods of frequent flow rate changes, such as occurred after hour 19,600...............................................22

Figure 4-2. Effective permeability (a), dimensionless wellbore storage constant (b), and skin due to 

damage (c) versus time for pressure build-up cycles in Phases II-IV. Dashed lines indicate boundaries of 

the injection phases. ...................................................................................................................................23

Figure 4-3. Scatter-plot matrix showing pairwise correlations between modeled permeability (k), skin due 

to damage (sd), dimensionless wellbore storage constant (CD), recorded pressure increase, and average 

recorded flow rate for all pressure build-up cycles in Phases II-IV. Note the strong correlation between 

modeled permeability and skin. ..................................................................................................................24

Figure 4-4. Effective permeability (a) and dimensionless wellbore storage constant (b) versus time for all 

pressure build-up cycles during Phases II-IV, fixing the value of sd to -4.35. Dashed lines indicate 

boundaries of the injection phases. ............................................................................................................26

Figure 4-5. Scatter-plot matrix showing pairwise correlations between permeability (k), dimensionless 

wellbore storage constant (CD), pressure increase, and average flow rate for all pressure build-up cycles 

in Phases II-IV, holding sd fixed at -4.35. ....................................................................................................27

Figure 4-6. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed 

line) for an example Phase I cycle, beginning July 10, 1997, allowing all three parameters to vary (top) 

and fixing sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant value 

of 6822 psi to measured surface pressures................................................................................................29

Figure 4-7. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by 

flow rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of 

Δp/q for an example Phase I cycle, beginning July 10, 1997, allowing all three parameters to vary (top) 

and fixing sd at -4.35 (bottom).....................................................................................................................30

Figure 4-8. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed 

line) for an example Phase II cycle, beginning July 26, 1999, allowing all three parameters to vary (top) 

and fixing sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant value 

of 6822 psi to measured surface pressures................................................................................................31

Figure 4-9. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by 

flow rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of 

Δp/q for an example Phase II cycle, beginning July 26, 1999, allowing all three parameters to vary (top) 

and fixing sd at -4.35 (bottom).....................................................................................................................32

Figure 4-10. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed 

line) for an example Phase III cycle, beginning January 8, 2001, allowing all three parameters to vary 

(top) and fixing sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant 

value of 6822 psi to measured surface pressures. .....................................................................................33

Figure 4-11. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by 

flow rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of 
Technical Memorandum TM-85-833000-2014-42

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Δp/q for an example Phase III cycle, beginning January 8, 2001, allowing all three parameters to vary 

(top) and fixing sd at -4.35 (bottom). Orange lines highlight the (approximate) emergence of radial flow..34

Figure 4-12. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed 

line) for an example Phase IV cycle, beginning January 14, 2007, allowing all three parameters to vary 

(top) and fixing sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant 

value of 7133 psi to measured surface pressures. .....................................................................................35

Figure 4-13. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by 

flow rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of 

Δp/q for an example Phase IV cycle, beginning January 14, 2007, allowing all three parameters to vary 

(top) and fixing sd at -4.35 (bottom). Orange lines highlight the (approximate) emergence of radial flow..36

Figure 4-14. Recorded (blue dots) and modeled (red lines) downhole pressures and percent error 

(dashed linse) during four example falloff periods, beginning (a) May 1, 1997, (b) May 28, 2000, (c) 

December 18, 2008, and (d) March 29, 2012. Values for k and Cd were fit with sd fixed at -4.35, and are 

shown in the top left corner of each plot. ....................................................................................................39

Figure 4-15. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by 

flow rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of 

Δp/q for the first 35 days (840 hours) for the cycles beginning January 8, 2004 (a), January 6, 2005 (b), 

January 7, 2009 (c), October 19, 2011 (d), and April 16, 2012 (e). Plots a-d use high sample rate from the 

SCADA system. Plot e uses daily average data, due to a period of missing data in the SCADA system 

during that time period. ...............................................................................................................................43

Figure 4-16. Recorded (open squares) and modeled (red lines) downhole pressures for the time period 

from March 2006 to January 2013. The model uses a single set of input parameters, as shown in the 

bottom left corner. Recorded downhole pressures are calculated by adding a constant value of 7133 psi 

to measured surface pressures. .................................................................................................................44

Figure 4-17. Typecurve for change in pressure (Δp) divided by flow rate (q) (circles) and the time 

derivative of Δp/q (triangles) versus time for a reservoir with negative skin due to damage and radial 

composite permeability with higher permeability further from the well. From Fekete (2012). ....................45

Figure 5-1. Maps showing the spatial distribution of shallow seismicity recorded in the Paradox Valley 

area over time: (a) injection tests, 1991-1995; (b) continuous injection, 1996-2000; (c) continuous 

injection, 2001-2008; (d) continuous injection, 2009-2013. All detected earthquakes locating less than 8.5 

km deep (relative to the ground surface elevation at the injection wellhead) are included. .......................48

Figure 5-2. Seismicity time-distance plots for 4 injection start times: (a) start of injection test #6 (Jan. 

1994), (b) start of injection test #7 (Aug. 1994), (c) start of long-term injection (Jul. 1996), and (d) 

resumption of long-term injection after 70-day shut-in (Jul. 1997). Two seismic triggering fronts are fit to 

each cycle, using a 1-D pressure diffusion relation and two different reference times. The downhole 

pressure is included for reference...............................................................................................................51

Figure 5-3. Seismicity time-distance plots of all shallow (depth < 8.5 km) events with magnitude ≥ 0.5 

occurring in the vicinity of the PVU injection well. (a) Four seismic triggering fronts overlaid – see text for 

description of their reference times (b) Seismic triggering fronts for the first two significant injection tests 

overlaid. All triggering fronts were computed using a 1-D linear pressure diffusion model and a hydraulic 

diffusivity of 0.115 m2/s. ..............................................................................................................................54

Figure 5-4. Seismicity time-distance plots of all shallow (depth < 8.5 km) events with magnitude ≥ 0.5 

occurring in the vicinity of the PVU injection well. Seismic triggering fronts for the first two significant 

injection tests are overlaid. The triggering fronts were computed using a 1-D linear pressure diffusion 

model and a hydraulic diffusivity of 0.20 m2/s.............................................................................................56

Figure 5-5. Permeabilities computed from seismic-derived values of the hydraulic diffusivity, D. 

Permeabilities were computed for a range of porosities, two values of D, and using two different 

permeability-diffusivity relations. .................................................................................................................59

Figure 5-6. Map showing epicenters of earthquakes occurring in the near-well region of induced 

seismicity, color-coded by hypocenter elevation (center), and cross sections showing distinct vertical 

offsets of hypocenters (top and bottom). Only a-quality hypocenters from the event relative location are 

included. Two northwest-striking normal faults interpreted from the hypocenter elevation patterns are 

shown. Our interpreted base of the Paradox salt and top of the Precambrian (solid black lines) are shown 

in each cross section. A simplified geologic section at the PVU wellbore is included at upper right for 

reference. ....................................................................................................................................................61

Figure 5-7. Near-well events by year, colored by elevation. Red stars designate PVU Injection Well #1..62
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Figure 5-8. Box plot of elevations of earthquakes within 500 meters of the injection well by year, with 

boxes defined by hinges. Blue dots and lines show the location of the median. Whiskers are drawn to the 

farthest point within 1.5 times the range between the upper and lower hinges. Black dots and lines 

designate outliers. .......................................................................................................................................63

Figure 5-9. Epicenters of induced earthquakes, color-coded by magnitude. .............................................65

Figure 5-10. Annual rates of induced earthquakes within 1 km of PVU Injection Well #1 (red) and greater 

than 1 km from the well (gray): (a) number of events (b) percent of events. All shallow (depth < 8.5 km) 

seismic events with magnitude ≥ MD 0.5 are included................................................................................66

Figure 5-11. Correlation between injection flow rate (top) and shallow seismicity (< 8.5 km depth) 

recorded by PVSN (bottom)........................................................................................................................67

Figure 5-12. Maps showing the spatial distribution of shallow seismicity recorded in the Paradox Valley 

area over time: (a) 2000-2003; (b) 2004-2008; (c) 2009-2013. All detected earthquakes locating less than 

8.5 km deep (relative to the ground surface elevation at the injection wellhead) are included. .................68

Figure 5-13. Estimated radial distance from the well of the injected brine over time, based on 4 different 

cylindrical models (red and blue curves). The shallow earthquakes with M ≥ 0.5 (black dots) and a 1-D 

pore pressure diffusion curve with diffusivity = 0.115 m2/s (dashed black line) beginning at the time of the 

first significant injection test (after acid stimulation) are shown for comparison. The green square 

represents a well drilled into the Leadville formation in 2008, in which no PVU brine was encountered...70

Figure A-1. Computed radii for five cylindrical models of the injected brine, assuming 100% of the 

formation pore space is accessible........................................................................................................... A-3

Figure A-2. Computed radii for five cylindrical models of the injected brine, assuming 50% of the 

formation pore space is accessible........................................................................................................... A-4

Figure A-3. Computed radii for five cylindrical models of the injected brine, assuming 10% of the 

formation pore space is accessible........................................................................................................... A-4

Figure A-4. Computed radii for five cylindrical models of the injected brine as a function of the fraction of 

pore space that is occupied by the brine. The weighted average formation porosities shown in Table A-3 

are used for these calculations. ................................................................................................................ A-5

Figure A-5. Computed radii over time for the scenario in which the injected brine is confined to the higherporosity zones in all formations (cylinder height = 90 m; formation porosity = 5.6%). Curves are shown for 

four assumed values of the percent of pore space occupied by the injected brine.................................. A-6

Figure A-6. Computed radius over time for the scenario in which the injected brine is confined to the 

higher-porosity zones in all formations (cylinder height = 90 m; formation porosity = 5.6%). The percent of 

pore space occupied by the injected brine is 5% during the injection tests and then linearly increases 

during long-term injection from 5% (in July, 1996) to 15% (in October, 2014). ........................................ A-7
Technical Memorandum TM-85-833000-2014-42

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1 Introduction

The Bureau of Reclamation operates a deep injection well near Paradox Valley, in western 

Colorado (Figure 1-1), which is referred to in this report as PVU Injection Well #1. This well has 

been in near-continuous operation since 1996, as part of the Paradox Valley Unit (PVU), a 

component of the Colorado River Basin Salinity Control Program. Injection at PVU diverts salt 

brine that would otherwise flow into the Dolores River, a tributary of the Colorado River. The 

diverted brine is injected into a 4.8-km-deep well for long-term disposal.

In recent years, the pressure required to inject the brine has been increasing and, prior to a 

decrease in the injection flow rate in mid-2013, was approaching the maximum allowable surface 

injection pressure (MASIP), as permitted by the U.S. Environmental Protection Agency (EPA).

Figure 1-1. Location of the deep injection well at Reclamation’s Paradox Valley Unit in western Colorado.

A second injection well is under consideration as a potential means to control the surface 

injection pressure without additional reductions in the volume of brine disposed of each year. A 

Consultant Review Board (CRB) was held in December 2012 to review the information that is 

currently available for selecting the location of a potential second injection well, and to make 

recommendations for additional data that could be acquired or analyses that could be performed 

to aid in the site selection process. One recommendation made by the CRB was to analyze the 
Technical Memorandum TM-85-833000-2014-42

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pressure-flow data in order to examine the temporal evolution of reservoir parameters and 

“evaluate whether the gradual pressure build-up is indeed a far-field pressurization process, or is 

more related to near-field flow impairment processes that might be rectified more economically” 

(Dusseault et al., 2013). This analysis was identified as a priority in an Accountability Report

prepared in response to the CRB recommendations (Block, 2014). This report summarizes much 

of the work that has been performed in response to this CRB recommendation. Some of this 

work is also discussed in another Technical Memorandum (Wood et al., 2016). 

While PVU lacks any observation wells that would help directly measure the degree of far-field 

subsurface pressurization, available evidence suggests that far-field pressurization is the 

dominant factor contributing to the increasing wellhead pressures. Here two sources of evidence

are considered: results of pressure-flow modeling, and the spatiotemporal occurrence of induced 

seismicity.
Technical Memorandum TM-85-833000-2014-42

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2 Local Geology

A summary of the local geology in the vicinity of Paradox Valley is provided in this section; see 

King et al. (2014) and Block et al. (2012) for further information regarding both the local and 

regional geology.

Paradox Valley and the surrounding mesas contain rocks spanning Precambrian to midCretaceous time. The Precambrian basement rock consists of granite, schist, gneiss, and 

pegmatite. Overlying the Precambrian rock is a series of sedimentary units including sandstones, 

siltstones, shales, conglomerates, limestones, dolomites, and evaporites.

A stratigraphic column of the Paradox Valley area is presented in Table 2-1. PVU Injection Well 

#1 is sited on the Triassic-age Chinle Formation. The stratigraphy of the underlying formations 

shown in Table 2-1 is taken from the geologic well log for this borehole (Harr, 1988), which 

extends into the Precambrian basement rock. Depths of geologic units encountered in this well 

are included in the table and are relative to the local ground surface elevation of 4996 ft (1523 

m). The overlying stratigraphy, including the Triassic-age Wingate sandstone to the Cretaceousage Mancos shale, is taken from a geologic map of the Moab Quadrangle produced by the United 

States Geological Survey (Williams, 1964). Descriptions of the rock units are taken from several 

sources (see Footnote 2 in Table 2-1).

The Mississippian Leadville formation is the primary target reservoir for PVU brine injection, 

due to its sedimentary and structural characteristics. The Leadville formation consists of 

limestone and dolomite layers that are fractured, faulted, and contain karst features. The lower 

Leadville formation (Kinderhookian-age) consists of stromatolitic dolomite, lime mudstones, and 

pelletal lime mudstone deposited in intertidal to subtidal environments. The upper Leadville 

formation (Osagean-age) is separated by an unconformity and contains fossiliferous pelletal and 

oolitic limestone, and lime and dolomitic mudstone (Campbell, 1981). The upper Leadville 

underwent uplift and erosion after deposition, resulting in karst-type weathering and the 

formation of a terra rosa type regolith on the surface. Hence, not only was the thickness of the 

Leadville decreased along the structural highs, but the porosity was also reduced when solution 

cavities that formed during uplift were later filled with shales and clays. Areas of dolomitization 

directly below these weathered sections generally have the best reservoir characteristics. 

Effective porosity improves with the degree of dolomitization (Bremkamp and Harr, 1988).
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Table 2-1. Paradox Valley stratigraphy

Stratigraphic Unit Depth1 Description2

CRETACEOUS3 (145-65 Ma)

Mancos Shale Above 

elevation of 

wellhead

Dark gray to black, soft, fissile marine shale with thin 

sandstone beds at various horizons.

Dakota Sandstone Friable to quartzitic fluvial sandstone and conglomeratic 

sandstone with interbedded carbonaceous nonmarine shale.

Burro Canyon Fm. Fluvial sandstone and conglomerate interbedded with 

lacustrine siltstone, shale, and mudstone, and thin beds of 

impure limestone.

JURASSIC (205-145 Ma)

Morrison Fm. Above 

elevation of 

wellhead

Fluvial and lacustrine shale, mudstone, and sandstone; local 

thin limestone beds.

Summerville Fm. Sandy shale and mudstone of terrestrial origin.

Entrada Sandstone Fine- to medium-grained, massive, and cross-bedded eolian 

sandstone; basal few feet may consist of red siltstone and 

fine-grained sandstone and is sometimes referred to as the 

Carmel Formation.

Navajo Sandstone Fine-grained, cross-bedded eolian sandstone.

TRIASSIC (255-205 Ma)

Kayenta Fm. Above 

elevation of 

wellhead

Irregularly interbedded fluvial shale, siltstone, and fine to 

coarse-grained sandstone.

Wingate Sandstone Fine-grained, massive, thick-bedded and prominently crossbedded eolian sandstone.

Chinle Fm. 0 (at surface) Siltstone interbedded with lenses of sandstone and shale, 

limestone-pebble and shale-pellet conglomerate, with lenses 

of grit and quartz-pebble conglomerate near base. Terrestrial 

depositional environment.

Moenkopi Fm. 390 Sandy shale/silty sandstone with some conglomerate 

present. Marine and terrestrial depositional environment.

PERMIAN (298-255 Ma)

Cutler Fm. 1,140 Fluvial arkose and arkosic conglomerate, with some sandy 

shales; deposited in alluvial fans.

PENNSYLVANIAN (322-298 Ma)

Hermosa Group –

Honaker Trail Fm.: 

Upper Honaker Trail

La Sal

Lower Honaker Trail

8,313

12,006

12,082

Limestone/sandstone/siltstone; deposited in marine 

conditions.

Limestone/dolomite; some silty limestone, oolitic limestone, 

and algal limestone present.

Limestone/sandstone/siltstone; deposited in marine 

conditions.

Hermosa Group –

Paradox Fm.:

Ismay

1st Main Salt

2nd Main Salt

Base Salt – Lower 

Paradox

12,350

12,839

13,104

13,497

13,566

Resulted from intermittently closed marine environment.

Limestone, stacked algal carbonate mounds and other 

shallow-water carbonates and dolomites.

Dolomite/salt; intermittently closed marine environment.

Salt/anhydrite/shale; intermittently closed marine 

environment.

Shale/anhydrite/(minor) limestone; intermittently closed 

marine depositional environment.

Hermosa Group –

Pinkerton Trail Fm.

13,693 Shales/anhydrites/siltstone/(minor) limestones; dark colored 

shales, limestone formed by marine invasion.
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Molas Fm. 13,944 Shale/siltstone/claystone; regolith/soil (terra rosa) de-veloped 

on the karst surface of the Leadville formation after a period 

of extensive weathering and erosion.

MISSISSIPPIAN (355-322 Ma)

Leadville Fm. 13,984 Limestone/dolomite. Lower unit (Kinderhookian-age) 

stromatolitic dolomite, lime mudstones, pelletal lime 

mudstones; deposited in intertidal to subtidal environments. 

Upper unit (Osagean-age) fossiliferous pelletal and oolitic 

limestone, and lime and dolomitic mudstone.

DEVONIAN (416-355 Ma)

Ouray Fm. 14,400 Limestone—lime mudstone, pelletal lime mudstone and 

skeletal limestone that is locally dolomitized; formed in quietwater marine environment.

Elbert Fm. 14,440 Sandstone/shales/shaly dolomites.

McCracken Fm. 14,607 Sandstone with occasional interbeds of sandy dolomite; 

transgressive depositional environment.

Aneth Fm. 14,681 Dolomite/shale; dense, argillaceous sequence.

CAMBRIAN (540-488 Ma)

Lynch Fm.:

Upper Lynch Shale

Lynch Limestone

Lower Lynch Shale

14,763

14,835

14,928

Sandstone/interbedded shale, dolomite, limestone.

Limestone.

Shale.

Muav Fm. 14,988 Limestone.

Bright Angel Fm. 15,103 Shale.

Ignacio Fm. 15,246 Sandstone, sometimes referred to as quartzite; transgressive 

depositional environment.

PRECAMBRIAN (>540 Ma)

Precambrian 15,446 Described regionally as granitic rock with well-developed 

northwest and northeast orthogonal fracture systems; 

identified in PVU Injection Well #1 as moderately 

metamorphosed diorite-gabbro schist.

1Depths are taken from the geologic drill log of PVU Injection Well #1 by Harr (1988). Depths are relative 

to the ground surface elevation (4996 ft) and have been corrected for borehole deviation.

2Descriptions are taken from: Bremkamp and Harr (1988), Campbell (1981), Doelling (1988), Williams

(1964), and Nuccio and Condon (1996). 3Ages from Walker and Geissman (2009).

Porosities derived from analysis of the sonic log acquired for PVU Injection Well #1 indicate 86 

ft of 5% or greater porosity (Bremkamp and Harr, 1988). This is similar to the porosity found in 

the Conoco Scorup Somerville Wilcox #1 well, located 4.6 km north-northeast of PVU Injection 

Well #1, but significantly higher than the values in any other wells in the region. In addition, the 

hydrologic permeability within the Leadville formation at PVU Injection Well #1 is greatly 

increased by the presence of an extensive fracture field related to the Wray Mesa fault system 

(Bremkamp and Harr, 1988). The Leadville formation shows very little fracturing in the nearby 

Union Otho Ayers #1-0-30 Well (Bremkamp and Harr, 1988), consistent with the lower porosity 

measured in that well. Core data from other nearby wells are not available, but given the low 

primary porosity of the Leadville, the degree of fracturing is likely to be strongly correlated with 

the porosities derived from logging.

Other formations that were considered viable injection zones in PVU Injection Well #1 include 

the Precambrian schist, the Devonian Ouray, Elbert, and McCracken formations, and the 

Cambrian Ignacio formation. The upper 191 feet (58 m) of Precambrian schist encountered in 
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PVU Injection Well #1 was estimated to contain 30 ft (9 m) of 5% or greater porosity. The 

Devonian and Cambrian formations showed some favorable porosity and fracture characteristics,

but were considered to have low storage volume potential. 

PVU Injection Well #1 contains perforations over a 286-foot (87-meter) interval in the Leadville 

formation. Two 30-foot (9-meter) intervals without perforations were left to assist in future 

treatment of the injection interval if necessary (Subsurface Technology, 2001). Additional 

perforated intervals were created in the underlying formations and Precambrian basement, 

extending more than 1400 feet (427 meters) below the bottom of the Leadville (Subsurface 

Technology, 2001). Early flow profiles indicated that the Leadville formation accepts the 

majority of fluid (Envirocorp Services and Technology Inc., 1995).

Additional logging of PVU Injection Well #1 was performed in 2001, including a mechanical 

casing caliper survey and a differential temperature survey (Subsurface Technology, 2001). The 

caliper survey indicated that the top-of fill depth was 14,172 feet (4320 meters), at the base of 

the upper Leadville perforations, indicating that the perforations in the lower Leadville and 

underlying formations were not accepting significant amounts of fluid. In contrast, a previous 

survey in 1994 indicated that the top of fill was at 14,604 feet (4451 meters), near the base of the 

underlying Elbert Formation (Subsurface Technology, 2001).
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3 Injection History

Between 1991 and 1995, a series of 7 injection tests were conducted at PVU, in addition to an 

acid stimulation test and a reservoir integrity test (Envirocorp Services and Technology Inc., 

1995). The purpose of these tests was to qualify for a permit for long-term injection from the 

Environmental Protection Agency (EPA). Continuous injection of brine began in July 1996, after 

EPA granted the permit. Since the start of continuous injection, four major changes in injection 

operations have been instituted and maintained at PVU. Each change was made to mitigate the 

potential for unacceptable seismicity or to improve injection economics. These injection phases 

are described below. Plots of the daily average injection flow rate, surface injection pressure, and 

downhole pressure at a depth of 14,100 ft (4.3 km) throughout the history of PVU injection 

operations are shown in Figure 3-1.

3.1 Phase I (July 22, 1996 – July 25, 1999)

During this initial phase of continuous injection, injection occurred at a nominal flow rate of 345 

gpm (1306 l/min), at about 4,950 psi (34.1 MPa) average surface pressure. This corresponds to 

approximately 11,800 psi (81.4 MPa) downhole pressure at 14,100 ft (4.3 km) depth. To 

maintain this flow rate, three constant-rate pumps were used concurrently, with each operating at 

a flow rate of 115 gpm. The surface pressure increased in response to this flow, and regularly

approached the wellhead pressure safety limit of 5,000 psi. At these times one or two injection 

pumps would be shut down, reducing the injection rate and allowing the pressure to drop a few 

hundred psi, before returning to three-pump injection. These shutdowns occurred frequently and 

lasted for minutes, hours, or a few days. Maintenance shutdowns lasted for one to two weeks 

and, in mid-1997, a 71-day shutdown was needed when replacing the operations contractor. The 

shutdowns resulted in an overall average injection rate for phase I of ~300 gpm (1100 l/min). 

The injectate during Phase I consisted of 70% Paradox Valley Brine (PVB) and 30% fresh water.

Due to concerns about corrosion, the decision was made in 1997 to switch from using an O2

scavenger to a rust inhibitor, as the O2 scavenger was found to be insufficient as a corrosion 

inhibitor. While the rust inhibitor was substantially more effective at inhibiting corrosion, it also 

increased the risk of precipitation of elemental sulfur (A. Nicholas, personal communication, 

2013).
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Figure 3-1. Daily average injection flow rate (top), daily average surface injection pressure (middle), and 

daily average downhole pressure at 14,100 feet (4.3 km) depth (bottom) during PVU injection operations.
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3.2 Phase II (July 26, 1999 – June 22, 2000)

Following two local magnitude (ML) 3.5 induced earthquakes in June and July, 1999, injection 

operations were changed to include a 20-day shutdown (i.e., a “shut-in”) every six months

(Mahrer et al., 2002). Prior to these events, it was noted that the rate of seismicity in the nearwellbore region (i.e. within about a 2-km radius from the wellbore) decreased during and 

following unscheduled maintenance shutdowns, and during the shutdowns following the 

injection tests of 1991 through 1995 (Mahrer et al., 2001). It was thought that the biannual 

shutdowns might reduce the potential for inducing felt seismicity by allowing extra time for the 

injectate to diffuse from the pressurized fractures and faults into the rock matrix. When injecting 

during this phase, the injection pressure and flow rate were the same as during Phase I. 

3.3 Phase III (June 23, 2000 – January 6, 2002)

Immediately following an ML 4.3 earthquake on May 27, 2000, PVU was shut down for 28 days. 

During this shutdown period, the existing injection strategy for PVU and its relationship to 

induced seismicity were evaluated. It was decided to reduce the injection flow rate in order to 

reduce the potential for inducing felt seismicity (Mahrer et al., 2001). On June 23, 2000, PVU 

injection operations resumed using a maximum of two pumps, rather than alternating between 

two and three pumps. The biannual 20-day shutdowns were maintained. The nominal flow rate 

during Phase III, while injecting using two pumps, was 230 gpm (871 l/min). Accounting for the 

two 20-day shut-ins per year, the average injection flow rate was approximately 205 gpm (776 

l/min), a decrease of about 32% compared to Phase I. The 70:30 ratio of brine to fresh water was 

maintained.

3.4 Phase IV (January 7, 2002 – April 16, 2013)

Beginning with continuous injection operations in 1996, the injectate had been diluted to 70% 

PVB and 30% Dolores River fresh water. A geochemical study had predicted that if 100% PVB 

were injected, it would interact with connate fluids and the dolomitized Leadville limestone at 

downhole (initial) temperatures and pressures, and that PVB would then precipitate calcium 

sulfate, which in turn would lead to restricted permeability (Kharaka et al., 1997). During 

October 2001, with the decreased injection volume discussed above, the injectate concentration 

concerns were reconsidered (Mahrer et al., 2002). Temperature logging in the injection interval 

documented substantial near-wellbore cooling, indicating that a significant displacement of 

connate brine away from the wellbore had occurred by this time, reducing the potential for 100% 

PVB and connate brine to mix, and therefore that if precipitation occurred, it would not be near 

the wellbore perforations where clogging would be a concern (Subsurface Technology, 2001). 

Further discussions indicated that, if precipitation occurred, its maximum expected rate would be 

~8 tons of calcium sulfate per day (Mahrer et al., 2002). To put this amount into perspective, 

injecting at ~230 gpm, assuming a density of 9.86 lbs/gal (17% more dense than fresh water), 

results in a daily injection of ~1630 tons. The maximum expected precipitate is ~0.5% of the 

daily injection mass.
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After considering this new information, Reclamation decided to begin injecting 100% PVB, in 

order to increase the amount of salt disposed following the reduced injection rate initialized in 

Phase III. Injection of 100% PVB began on January 7, 2002, following the December-January 

20-day shutdown, and has been maintained since. The same reduced injection rate as in Phase III 

(230 gpm) and biannual 20-day shutdowns have been maintained. The only noticeable effect of 

the change to 100% PVB injectate has been increasing bottom hole pressure because of the 

increased density of 100% PVB (by about 5%) over the 70% PVB to 30% fresh water mix (Ake 

et al., 2005).

3.5 Phase V (April 17, 2013 – present)

An ML 4.4 induced earthquake occurred in the northern Paradox Valley area on

January 24, 2013 (Block et al., 2014b). In response to this earthquake, injection was halted while 

a reassessment of the seismic hazard associated with PVU injection was performed. Analyses of 

the seismic and injection data indicated that the potential for inducing large felt events could be 

reduced by decreasing the long-term average injection pressures (Block and Wood, 2009; Wood 

et al., 2016). Pressure-flow modeling indicated that reducing the flow rate would reduce 

wellhead pressures, and forward modeling was used to determine an appropriate flow rate (Wood 

et al., 2016). In addition, the pressure-flow modeling indicated that changing the injection well 

shut-in schedule to have shorter, more frequent shut-ins would result in a lower average wellhead 

pressure, compared to the biannual 20-day shut-ins previously used.

As a result of these analyses, the decision was made in April 2013 to reduce the injection flow 

rate, and to increase the frequency of injection well shut-ins while reducing their duration (Block 

et al., 2014a). Due to a delay in obtaining plungers that would allow injection at a lower flow 

rate, injection was initially resumed on April 17, 2013, maintaining the flow rate at 230 gpm and 

implementing a 36-hour shut-in every week. On June 6, 2013, following the acquisition and 

installation of the new plungers, the flow rate was reduced to 200 gpm and the shut-in duration

was reduced to 18 hours. The frequency of one shut-in per week was maintained. A shut-in 

duration of 18 hours was chosen so that the total annual shut-in time would be approximately 

equivalent to that scheduled previously with the biannual 20-day shut-ins. Hence, the nominal 

flow rate during Phase V (200 gpm) was decreased by 13% from that during Phase IV (230 

gpm), and the total duration of planned shut-ins remained the same.

Because of the frequency of the new shut-in schedule, the durations of any unplanned shut-ins 

(such as those periodically required for equipment maintenance) are tracked, and those hours are 

subtracted from the duration of the weekly scheduled 18-hour shut-in. The durations of 

unplanned shut-ins had not been tracked and subtracted from the biannual 20-day shut-ins during 

earlier injection phases, and hence the total shut-in time during previous years had sometimes 

increased substantially, depending on the number and duration of unplanned shut-ins required. 

Hence, while the nominal flow rate during Phase V was decreased by 13% from that during 

Phase IV, the effective decrease in flow rate has been less than this value due to the difference in 

total shut-in time. The average flow rate during Phase V (from April 17, 2013 to December 31, 

2013) has been 180 gpm, which is ~8% less than the average flow rate of 196 gpm during the 

previous three years (2010-2012).
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Pressure-flow modeling of Phases I-IV only is included in this analysis; pressure-flow modeling 

of Phase V is still in the beginning stages.

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4 Pressure-Flow Modeling

Pressure-flow modeling can help with understanding the reservoir behavior by focusing on a few 

basic parameters such as permeability and skin effect, and analyzing their evolution over time. 

Such modeling can be used to determine whether recorded changes in wellhead pressures are 

more likely the result of changes in the near-wellbore properties, or whether a fixed set of 

reservoir parameters are adequate to fit the recorded pressures over long time periods.

4.1 Previous Work

One of the key parameters that defines reservoir behavior is the effective permeability. Previous 

estimates of permeability have varied. Drill stem tests using a variable flow rate gave an original 

permeability of 7.97 mD (Harr, 1989). However, Horner analysis performed at the same time 

indicated a permeability between 1.3 and 1.5 mD (Harr, 1989). Additionally, analysis of core 

samples from the Conoco-Scorup well located approximately 4.6 km to the northeast yielded 

permeabilities ranging from 0.03 to 1.3 mD (Harr, 1989), which could suggest significant 

regional variations in permeability.

A series of seven injection tests were performed between 1991 and 1995. Permeabilities were 

only calculated for the first three tests, which took place between July 11, 1991 and June 18, 

1992, primarily due to equipment failures in later tests. The permeabilities for the first injection 

and falloff periods were calculated as 4-5 mD and 2 mD, respectively. The second injection and 

falloff periods yielded 7.8 mD and 2.2 mD, respectively. The third falloff period yielded a 

permeability of 1.6 mD, while the third injection period was determined to be unanalyzable due 

to numerous flow rate changes caused by equipment failure. The lower permeabilities calculated 

during falloff periods, as compared with injection periods, were assumed to indicate fracture 

closure (Envirocorp Services and Technology Inc., 1995).

An early model of the injection test data attempted to fit the data from the seventh and final 

injection test, which took place from August 14, 1994 to April 3, 1995, using a fracture network 

model with 5% porosity and a permeability of 3 mD (Envirocorp Services and Technology Inc., 

1995). While they obtained reasonable fits to the data from this injection test, their model 

predicted future pressures that were significantly lower than recorded pressures. While the 

modeled injection scenarios differ from the actual injection scenarios, preventing a direct 

comparison, their model predicted that surface pressure would not exceed 4500 psi after ten 

years of continuous injection at a flow rate of 300 gpm. In contrast, the recorded pressures 

exceeded 4500 psi after less than four months of injection at an average flow rate of 163 gpm. 

This suggests that the effective permeability-thickness and/or porosity-thickness were

overestimated in this early modeling.

In 2001, Reclamation funded USGS to perform fluid-flow modeling of the 1996-2000 pressure 

and flow data using a poroelastic model, and a draft report was received in 2009 (Roeloffs and 

Denlinger, 2009). The USGS model consisted of a radially-symmetric finite element grid with 
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twenty layers based on stratigraphy, each characterized by four parameters (shear modulus, 

Poisson ratio, Skempton’s coefficient, and hydraulic diffusivity). The model was calibrated by 

trial-and-error matching of the predicted flows and pressures with those measured at the 

wellhead. For the layer representing the Leadville formation, a porosity of 10% and a 

permeability of 28 mD were assumed for a thickness of 146 meters (479 feet), with significantly 

lower values for other layers. In contrast, Bremkamp and Harr (1988) determined a porosity in 

the Leadville of ≥10% for only 2 feet of its 416-foot thickness, using sonic logging, or 18 feet, 

using visual binocular examination of recovered core. Hydraulic diffusivity (calculated from 

permeability, formation thicknesses, porosity, and shear modulus), was found to be the parameter 

most strongly effecting pressure distribution in the model. The USGS model did not incorporate 

skin factor or wellbore storage parameters.

The USGS model provides a reasonably good fit to the flow rate data for approximately the first 

500 days, but then the modeled flow rates begin to decrease, while the measured flow rates 

remain approximately constant. Roeloffs and Denlinger (2009) suggest that formation 

permeability may have increased, or that the flow may have reached a zone of higher 

permeability away from the well.

The permeability of intact limestone and dolomite generally varies from 0.01 to 0.1 mD (Bear, 

1972). The permeability value for intact rock is known as primary, or matrix, permeability, and 

is generally only applicable to laboratory samples, as rocks over larger scales will contain at least 

some degree of fracturing. Limestones may also have increased permeability due to vugular 

porosity. The permeability due to fracturing and secondary porosity is known as secondary 

permeability and can vary by several orders of magnitude, even exceeding 105 mD in some 

highly fractured locations (Cox and others, 2000). Thus, the estimated permeabilities of a few 

mD, while higher than would be expected to be measured under laboratory conditions, are 

reasonable for a moderately fractured reservoir.

4.2 Fitting of Pressure-Flow Data to Idealized Models

It was unclear initially whether complicated numerical models were required to fit the pressureflow data at the wellhead, or instead if simple idealized models would suffice. In the absence of 

monitoring wells or other independent means of verifying predicted pressures within the 

injection reservoir at distances away from the wellbore, the use of excessively complex models 

may result in overfitting of the wellhead data, and a correspondingly poor predictive capability 

of the models for future data. We therefore tried fitting the data for individual injection and shutin cycles using several simple, idealized models commonly employed in the well-testing and 

reservoir-modeling industry. F.A.S.T. WellTest software v.7.6.0, described in Fekete (2012), was 

used for this analysis.

Biot (1941) developed a model of a fluid-filled porous material based on a conceptual model of a 

coherent solid skeleton and freely moving pore fluid (Detournay and Cheng, 1993). Under this 

model, for the case of an isotropic applied stress tensor σ , the constitutive equations are,
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11 12

21 22

a ap

a ap

ε σ

ς σ

= +

= +

(4.1)

where ς is the increment of fluid content, p is the fluid pressure, and ε is the volumetric strain 

(Wang, 2000). This model includes full coupling between the solid and fluid components. 

Substituting physically meaningful constants, the most general form of the linear constitutive 

equations for isotropic material response is:

11 1

2 69 3

3

ij

ij ij kk ij

kk

p G GK H

p

H R

σ

ε δσ δ

σ

ς

  =− − +    

= +

(4.2)

where K and G are the bulk modulus and shear modulus of the drained elastic solid, and H , 

and R are constitutive constants characterizing the coupling between the solid fluid stress and 

strain (Detournay and Cheng, 1993). 

At reservoir depths, the rock compressibility is generally small, and thus a simplifying 

assumption may be made in order to uncouple the solid and fluid components. This is a common 

simplification in reservoir modeling applications, and is used in our analysis.

For the uncoupled, incompressible rock assumption, the governing equation for radial flow in 

cylindrical coordinates is:

2

2

1 t pp p c

r rr k t

∂∂ ∂ φ μ + =

∂∂ ∂ (4.3)

where r is the radial distance from the well in centimeters, t is time in seconds, p is the 

reservoir pressure in atmospheres at distance r and time t , φ is the formation porosity as a 

fraction of bulk volume, k is the formation permeability in Darcies, μ is the fluid viscosity in 

centipoises, and t c is the total compressibility in volumes per volume per atmosphere (Horner, 

1951).

For a point source, the change in pressure resulting from an applied flow is:

2

0 Ei

4 4

t q r c

p p kh kt

μ φμ

π

  − =    

(4.4)

where 0 p is the initial reservoir pressure in atmospheres at t = 0 , q is a constant rate of 

production of the well (starting at t = 0 ) in cubic centimeters of subsurface volume per second, 

h is the layer thickness in centimeters, Ei ; 0 ( x x ) > is the exponential integral (Abramowitz 
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and Stegun, 1964), and other variables are the same as in Equation (4.3). This solution assumes 

an infinite reservoir and an infinitely small wellbore radius (Horner, 1951).

For sufficiently small x > 0 , Ei( x)may be accurately approximated by Ei log ( x x ) ≈ + γ ( ), 

where γ is Euler’s constant (Abramowitz and Stegun, 1964). Thus if the parameters of the 

model are homogeneous and constant over time, then Equation (4.4) may be approximated as:

0 2

4 log . 4 tq kt p p const

kh r c

μ

π φμ

  − =−   +

 

(4.5)

which shows that for continuous injection q < 0 , the pressure change at the wellbore radius wr is

asymptotic to log(t) , and with a slope inversely proportional to the permeability-thickness 

product kh .

Typical well-testing procedures consider a period of constant production starting at time t = 0 , 

followed by a shut-in period starting at time 0t > 0, then the well pressure during the shut-in 

period at time 0t +τ , can be obtained by superimposing two equations of the form of Equation 

4.4. Using the wellbore radius wr for r, this leads to the equation:

( )

2 2

0

0

Ei Ei

44 4

wt wt

w

q rc rc

p p kh k t k

μ φμ φμ

π ττ

      − =     −         +  

(4.6)

where w p is the pressure at the wellbore in atmospheres and wr is in centimeters. Using the 

previous approximation for Ei( x) at small x > 0 , the pressure change during the shut-in period 

described by Equation (4.6) may be approximated as:

0

0 log 4 w

q t

p p kh

μ τ

π τ

  + − =−     (4.7)

For continuous injection q < 0 , Equation (4.7) shows that the pressure fall-off at the wellbore 

radius following shut-in is asymptotic to 0 log t τ

τ

  +    , where 0t is the injection duration, τ is the 

time since shut-in, and where the slope is inversely proportional to the permeability-thickness 

product kh . Horner (1951) demonstrates that the error introduced by this approximation 

typically drops to 0.25% within seconds of closing the well.

In dimensionless variables, the governing equation equivalent to Equation (4.3) is:

2

2

1 D DD

D DD D

p pp

r rr t

∂ ∂∂

+ =

∂ ∂∂ (4.8)
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where, in arbitrary units, D w r rr = is the dimensionless radial distance from the well, D 2

w t

kt

t

r c φμ = is 

dimensionless time, and D ( 0 ) kh

p pp

qμ = − is the dimensionless pressure change on the formation 

side at distance Dr and time Dt (Agarwal et al., 1970). Using the previously defined units, the 

equations for Dr and Dt are unchanged, while the equation for D p becomes 

D 0.0689 ( 0 ) kh

p p p

qμ = − . All model properties are assumed to remain constant with time, and 

pressure is calculated based on the recorded injection rate, which varies over time.

In solving Equation (4.8) for a finite wellbore, two additional variables, the wellbore storage 

constant and skin factor, are introduced in the inner boundary conditions, in order to ensure 

continuity across the wellbore boundary. In dimensionless variables, the boundary conditions 

are: 

1

1

D

wD D

D

D D r

dp p C

dt r =

  ∂ − =   ∂  

(4.9)

and

D 1

D

wD D

D r

p p ps

r =

    ∂ = −     ∂    

(4.10)

where wD p is the dimensionless pressure drop within the wellbore, CD is the dimensionless 

wellbore storage constant, s is the dimensionless skin factor, and other parameters are the same 

as in Equation (4.8) (Agarwal et al., 1970). All fluid and rock properties are assumed to remain 

constant.

Our analysis uses the recorded injection flow rates and surface pressures recorded at the PVU

wellhead since continuous injection began in 1996. The sample rate of that data is non-uniform 

over time. Injection data prior to 2003 were recorded on an older supervisory control and data 

acquisition (SCADA) system in a format that is currently inaccessible. For this period, only daily 

average pressures and flow rates are available. Starting in 2003, data are available at much 

higher sample rates (up to 1 sample every 2 seconds) due to the installation of a newer SCADA 

system. Mixing data at the two sample rates was found to create artificial trends in the data. For 

example, a large apparent decrease in the wellbore storage constant occurred when mixing the 

daily-average with the high-frequency data. While misfits were lower using data with the higher 

sample rate, and the absolute values obtained for parameters were likely more accurate, the

trends in the parameters over time are more significant to this analysis than their particular 

values. It was therefore decided to use the daily average data over the entire well operating 

history for this analysis.
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Reservoir temperature is a significant factor affecting the modeling, primarily because of its 

effect on the fluid viscosity, as the temperature of the injectate is generally assumed to be equal 

to the undisturbed reservoir temperature. While this assumption is probably adequate for shortterm injection testing, the volume of fluid that has been injected into PVU Injection Well #1 has 

likely led to cooling of the reservoir at a significant distance from the well, and thus the reservoir 

temperature varies in both time and space. However, as the model cannot account for 

temperature variations, and as there are no data to constrain temperatures away from the well, a 

single temperature was used for the modeling. A temperature of 37.8 ̊C was used, corresponding 

to the temperature measured near the base of the Leadville formation three days into a shut-in 

that occurred in March 1994 (Subsurface Technology, 2001).

Other input parameters include a reservoir thickness of 100 feet (30.5 meters), porosity of 3%, 

and salinity of 2.60 kg/L after January 8, 2002, when injection of 100% brine began, and 1.82 

kg/L prior to this date, when the injectate was a mixture of 70% brine and 30% fresh water. The 

salinity of the fresh water was assumed to be negligible relative to the brine, and therefore a 

salinity of 70% of that for the brine was used for the mixture. The assumed thickness of 100 feet 

is approximately equal to the thickness of the perforated interval of the upper Leadville, as 

logging has indicated that the middle and lower Leadville perforations are covered with fill 

(Subsurface Technology, 2001) and thus accept a significantly lower amount of flow. It is 

unknown to what extent fluid is able to migrate vertically outside of the perforated interval in the 

vicinity of the wellbore.

Viscosity and fluid compressibility are calculated using the temperature and salinity, but 

variation of these parameters over time is not included in this analysis. The calculated viscosity 

is 1.030 cP during the injection of 70% brine and 1.348 cP during the injection of 100% brine.

The calculated fluid compressibility is 1.933×10-6 psi-1 during the injection of 70% brine and 

1.731×10-6 psi-1 during the injection of 100% brine.

While the assumed model parameters have a significant effect on the absolute values of the 

calculated permeability, the effect on the relative permeability values between cycles is minimal, 

and thus we do not expect our interpretations to be significantly affected by the choice of model 

parameters. For example, if a value of 479 feet had been used for the layer thickness, roughly 

equal to the thickness of the entire Leadville formation, the calculated permeabilities would be 

reduced by a factor of 4.79, but the ratios of permeabilities between cycles would not be 

affected. Variations in model parameters in space or time, such as a change in thickness of the 

Leadville away from the well or reservoir cooling over time, could potentially have more 

significant effects, but the model cannot account for changes in these parameters, and there are

only limited data to constrain such changes.

Downhole pressures were calculated by adding a constant value to the surface pressures, 

accounting for the weight of the brine and the frictional effect due to flow, assuming new tubing

conditions with no scale buildup inside the tubing (Mahrer et al., 2004). The friction term is 

negligible for the injection rates and tubing size used at PVU. It is possible that the friction term 

becomes more significant over time due to scale build-up, but as well logging has not been 

performed at PVU since 2001 (due to the substantial cost and risk to the wellbore that would be 
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involved in such logging), the current conditions are unknown and therefore the potential 

changes in friction have not been incorporated into the analysis. A constant pressure difference 

between the wellhead and downhole pressure of 6822 psi was used for continuous injection 

Phases I-III, and 7133 psi for injection Phase IV, when injectate density increased as a result of 

the switch to 100% brine.

After comparisons of several different models supported by the Fekete software, a radially 

symmetric model was selected. This model has no-flow boundaries in the vertical direction and 

infinite-acting boundaries in the horizontal directions. Models with no-flow or constant pressure 

boundaries in the x- and/or y-directions were also considered, as well as radial composite models 

and models incorporating fractures and anisotropic permeability. However, these models 

provided either a worse fit or an insignificant improvement in the fit to the data, so the simplest 

model that adequately fit the data was selected.

There is some evidence that a radial composite model with a decreased permeability in the nearwell area may provide an improved fit over a radial flow model, particularly from the two long 

(68-day and 83-day) falloff periods that occurred in 2005-2006 and 2013, respectively. However, 

for buildup cycles, as well as for falloff periods of standard duration (~20 days), the 

improvement in fit is insufficient to justify adding additional free parameters. Additionally, the 

decrease in permeability in the near-well area is relatively minor and does not appear to change 

significantly with time, supporting the validity of a radial flow model to adequately fit the 

pressure-flow data.

While the radially symmetric model does not incorporate individual fractures, the estimated 

downhole pressures are frequently above the fracture propagation pressures (Envirocorp Services 

and Technology Inc., 1995), and thus the near-wellbore region is expected to be so extensively 

fractured as to be adequately represented as a porous medium, particularly in recent years.

There are three free parameters in the selected model: the effective permeability, k, skin due to 

damage in the near-wellbore region, sd, and dimensionless wellbore storage constant, CD. The 

entire flow rate history is incorporated into the calculation of modeled pressures. First, the 

parameters are fit individually for each buildup period. This approach is used to assess whether 

these parameters have changed over time, and because there was no clear reason for assuming 

that a single set of parameters would be adequate to fit all the data. Second, a single set of 

parameters is used to fit multiple buildup periods. This approach is used to assess whether a 

single set of parameters adequately fits multiple injection periods.

For Phases II-IV, when two twenty-day shut-ins were scheduled every year, a cycle is defined to 

be the build-up period between two scheduled shut-ins. Unscheduled 11-day and 17-day shut-ins 

occurred in the cycles beginning July 26, 1999 and January 21, 2006, respectively, so these flow 

periods were each split into two cycles for this analysis. All cycles contain unscheduled shut-ins, 

primarily due to equipment issues, which range in duration from a few hours to ten days. In order 

to analyze the six-month cycles as a single flow period despite the short shut-ins, it is necessary 

to input a small but non-zero flow rate for the short shut-in periods. 
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For Phase I, cycles are defined as the flow periods between two unscheduled multi-day shut-ins, 

which range in duration from four to seventy days. Cycles range from 47 to 345 flow days in 

duration; build-up periods of only a few days are excluded from analysis.

Defining cycles in this matter leads to a total of 38 cycles: 7 in Phase I, 3 in Phase II, 4 in Phase 

III, and 24 in Phase IV. 

4.3 Results of Pressure-Flow Model Fitting

Using the first approach described previously, the model parameters for each injection cycle 

were fit simultaneously, using a Simplex automatic parameter estimation procedure to find a 

local minimum in the misfit between the data and the model. All parameters for each injection 

cycle were fit independently from the other injection cycles. Section 4.3.1 describes how the 

computed model parameters have evolved over the various phases of injection. Section 4.3.2

describes the quality of the model fits to the pressure-flow data. Section 4.3.3 provides further 

discussion of possible changes in permeability at significant distances from the injection well. 

Following the second approach described previously, section 4.3.4 shows the results of fitting 

multiple cycles simultaneously.

4.3.1 Changes in Model Parameters over Time

In Phase I, modeled values for k range from 9.06 to 10,200 mD, and values for sd range from -

5.82 to 2000, with a strong positive correlation between these two parameters. Values for CD

range from 6.27×105 to 1.46×106. The magnitude of variations in k and sd is believed to be an 

artifact of attempts by the modeling algorithm to fit data that include factors that the model 

cannot account for. In particular, the model seems to be unable to fit periods of frequent flow 

rate changes. Figure 4-1 demonstrates this for an example Phase I cycle, beginning May 30, 

1998. Figure 4-1a shows the best fit parameters. Note that the model is not able to capture the 

shape of the pressure curve especially well at any point during the cycle. Figure 4-1b shows the 

model with manually determined parameters that are believed to be more physically realistic. 

These parameters fit the data well during the beginning part of the curve, when the flow rate is 

nearly constant at 345 gpm. However, once the pressures begin approaching 5000 psi and the 

flow rate was frequently changed between 115, 230, and 345 gpm (as discussed in Section 3.1), 

the modeled pressures begin to deviate significantly from the measured pressures. This may be 

due to a variety of factors, including using a sample rate with a lower frequency than the flow 

rate changes. 

In Phase II, the variation in model parameters is much smaller than found in Phase I, with k

ranging from 13.6 to 21.9 mD, sd ranging from -6.05 to -3.99, and CD ranging from 8.80×105 to 

1.37×106. 

In Phases III and IV, for twenty-seven of the twenty-eight cycles in these phases, effective

permeabilities range from 10.4 to 29.2 mD, with a mean of 18.0 mD and median of 16.7 mD, and 

skin values range from -5.98 to -1.98, with a mean of -4.35 and median of -4.62. The 

permeability and skin both appear to increase somewhat during Phase III, while in Phase IV 

neither of these parameters shows any clear trends with time, as shown in Figure 4-2.
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The remaining cycle initially appeared to be a significant outlier, with a modeled permeability of 

140 mD and skin value of 26.3. This cycle, which began March 4, 2006, contained a period of 

about a month near the beginning of the cycle where the flow rate fluctuated frequently between 

115 gpm and 230 gpm. As in Phase I, these rapid flow rate changes appear to cause instability in 

the modeling algorithm. For this reason, the permeability and wellbore storage constants were refit after fixing the value of sd at the mean of the preceding and following cycles. This led to a 

permeability of 20.7, with a minimal increase in the misfit. 

Modeled dimensionless wellbore storage constants for Phases III-IV vary from 9.01×105 to 

1.74×106, which correspond to dimensional wellbore storage constants of 4.17 to 8.03 ft3/psi. 

These values are significantly larger than the value expected from considering only the actual 

wellbore volume, which is on the order of 1 ft3/psi, suggesting that the fractured area around the 

well may essentially be acting as an enlarged wellbore or an extension of the wellbore (Fekete, 

2012). The wellbore storage constants are somewhat higher prior to mid-2002, with a decrease of 

about 21% between the mean values from September 1999 to January 2002 (the beginning of 

Phase IV, when the change from injection of 70% brine to injection of 100% brine occurred) and 

the mean values beginning with June 2002 (Figure 4-2b). The magnitude of the decrease 

between the mean of the cycles in these two time periods is approximately 2.94×105

, which is 

2.6 times the standard deviation of the wellbore storage constants beginning in June 2002, 

indicating that the decrease is statistically significant. It is possible that the decrease in the 

modeled wellbore storage constant indicates a decrease in the perforated interval of the wellbore 

due to narrowing of the wellbore and/or precipitation of elemental sulfur, both of which have 

been observed in past wireline logs (Subsurface Technology, 2001). There may also be 

precipitation of anhydrite in the fractures surrounding the wellbore, which was predicted by 

Kharaka et al. (1997) as a result of geochemical analyses. However, it is not clear why 

precipitation would cause a sudden decrease in the wellbore storage constant followed by a long 

period of relatively stable values, rather than a gradual decrease. 
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Figure 4-1. Recorded (blue dots) and modeled (red line) downhole pressures, fit using (a) best-fit parameters

and (b) manually determined parameters for an example Phase I cycle, beginning May 30, 1998. Blue lines 

indicate recorded flow rate. Recorded downhole pressures are calculated by adding a constant value of 6822 

psi to measured surface pressures. The model has difficulty fitting the data during periods of frequent flow 

rate changes, such as occurred after hour 19,600.
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Figure 4-2. Effective permeability (a), dimensionless wellbore storage constant (b), and skin due to damage (c) 

versus time for pressure build-up cycles in Phases II-IV. Dashed lines indicate boundaries of the injection 

phases.

There is significant tradeoff between the model parameters, as indicated by the strong positive 

correlation between the values of k and sd shown in Figure 4-3, leading to concern that the 

resulting parameters may not be robust. In order to minimize the tradeoff, the values for k and CD

are refit after fixing sd at a value of -4.35. This value for sd corresponds to the mean of the 

calculated values for the cycles in Phases III and IV. 
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Fixing sd leads to much less variation in the values obtained for k, particularly those in Phase I 

and Phase II (Table 4-1). The values for all cycles vary from 14.02 to 27.12, with a mean of 

18.76 and median of 18.36. With the exception of an outlying cycle in 2002, the values are 

highest during Phases I and II, when the injection rate was higher, then lowest during Phase III, 

and have remained relatively constant since Phase IV began in 2002 (Figure 4-4). The outlying 

cycle coincides with the switch from 70% brine to 100% brine and is likely an artifact of that 

change, as the changes in fluid viscosity and density do not happen instantaneously as modeled.

Modeling of the injection tests performed from 1991-1995, which varied from 0% to 70% brine, 

indicate a positive correlation between salinity and permeability, suggesting that the increase in 

permeability between Phase III and Phase IV may be due to the switch to 100% brine, which 

increases the fluid density and downhole pressure and may assist in keeping fractures open. A 

comparison between the parameters with sd allowed to vary or fixed is shown in Table 4-1.

Figure 4-3. Scatter-plot matrix showing pairwise correlations between modeled permeability (k), skin due to 

damage (sd), dimensionless wellbore storage constant (CD), recorded pressure increase, and average recorded

flow rate for all pressure build-up cycles in Phases II-IV. Note the strong correlation between modeled 

permeability and skin.
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Table 4-1. Permeability (k), skin due to damage (sd), and dimensionless wellbores storage constant (CD) fit 

with three free parameters, and k and CD fit with sd fixed at -4.35 for all cycles.

sd allowed to vary sd fixed at -4.35

Phase Start Date k sd CD (x105) k CD (x105)

Phase I 07/22/1996 9.06 -5.82 6.27 14.0 7.99

09/14/1996 88.3 12.9 9.45 17.7 6.69

11/09/1996 7120 2000 6.29 16.3 4.71

07/10/1997 7620 1920 13.3 20.2 8.11

12/10/1997 10200 1910 13.5 25.1 8.72

05/30/1998 9580 1990 14.6 22.9 9.19

05/16/1999 26.1 -4.47 11.4 27.1 11.1

Phase I mean 4960 1120 10.6 20.5 8.08

Phase II 07/26/1999 19.8 -4.40 8.80 20.1 8.58

09/07/1999 21.9 -3.99 13.7 20.2 13.0

01/08/2000 13.6 -6.05 11.7 23.4 14.1

Phase II mean 18.5 -4.81 11.4 21.3 11.9

Phase III 06/23/2000 10.4 -5.68 10.2 15.7 12.2

01/08/2001 13.4 -4.75 13.2 14.9 13.4

06/25/2001 16.4 -3.96 15.8 15.0 14.9

09/13/2001 17.0 -4.11 16.7 16.0 16.5

Phase III mean 14.3 -4.63 14.0 15.4 14.3

Phase IV 01/08/2002 14.4 -5.98 17.4 24.2 18.9

06/24/2002 15.7 -4.94 10.1 18.2 10.3

01/08/2003 20.5 -4.00 11.0 18.9 10.0

06/19/2003 29.2 -1.98 11.7 18.6 10.0

01/08/2004 16.3 -4.89 12.4 18.9 12.8

06/21/2004 15.5 -4.92 12.2 18.2 12.9

01/06/2005 19.9 -4.09 10.9 18.8 10.1

06/16/2005 19.4 -4.28 11.9 18.8 11.7

01/21/2006 14.7 -4.71 9.02 16.2 9.16

03/04/2006 20.7 -3.63 12.7 17.9 8.81

07/12/2006 27.8 -2.55 11.6 18.7 10.1

01/14/2007 27.0 -2.54 11.9 18.8 10.0

07/10/2007 22.6 -3.78 10.8 19.8 10.8

01/10/2008 23.5 -3.21 12.0 18.3 11.6

07/08/2008 16.7 -4.82 11.2 19.1 10.4

01/07/2009 17.8 -4.62 10.5 18.9 10.8

04/23/2009 16.7 -4.64 10.6 17.6 13.5

10/29/2009 17.8 -4.01 14.2 16.6 10.5

04/21/2010 15.6 -4.92 10.2 18.2 10.9

10/21/2010 15.8 -4.92 10.3 18.4 11.9

04/22/2011 17.1 -4.47 9.9 17.4 12.7

10/19/2011 18.5 -4.23 10.6 18.0 10.3

04/16/2012 12.7 -5.51 10.6 18.0 12.1

10/18/2012 14.6 -5.09 10.0 17.8 10.9

Phase IV mean 18.8 -4.28 11.4 18.5 11.3
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The decrease in k between Phase II and Phase III may be an effect of fracture closure due to the 

decrease in flow rate and resultant decrease in reservoir pressure. During Phases III-IV, the 

pressures have gradually increased to the high values seen in Phase II, even surpassing these 

pressures in recent years. One would expect that the increase in pressure past the Phase II 

pressures would cause fractures to re-open and permeabilities to return to the values seen in 

Phase II. However, the permeabilities have remained lower than they were in Phase II, which

suggests that the permeability is more sensitive to flow rate than pressure, but the reason for this 

is unclear. Alternatively, it is possible that the average pore pressures within the radius of 

investigation of the pressure-flow modeling have remained lower since 2000 than before, if 

spatial pore pressure gradients have changed sufficiently (see section 4.2.3 for a discussion of the 

radius of investigation). A substantial change in spatial pore pressure gradients over time to a 

radial distance of at least 1.1 km is inferred from observed patterns of near-well induced 

seismicity (see section 5.3.2).

Figure 4-4. Effective permeability (a) and dimensionless wellbore storage constant (b) versus time for all 

pressure build-up cycles during Phases II-IV, fixing the value of sd to -4.35. Dashed lines indicate boundaries 

of the injection phases.

All of the calculated permeability values are higher than those calculated from the early injection 

tests (Envirocorp Services and Technology Inc., 1995), as discussed in section 4.1. However, a 

layer thickness of 280 feet was used in these calculations. The values of the product of kh that we 

calculated for the first few injection cycles are consistent with the values calculated for the 
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injection tests, suggesting that there was not a significant increase in permeability during the 

injection tests.

The dimensionless wellbore storage constant varies from 4.70×105 to 1.89×106

, corresponding to 

a dimensional wellbore storage constant varying from 2.18 to 8.73 ft3/psi. For Phases II- IV, the 

wellbore storage constant shows a similar trend to the values fit without fixing sd, with the 

highest values occurring prior to 2002, a 25% decrease from the mean values prior to June 2002 

and the mean values beginning in June 2002, and relatively constant values since 2003. The 

decrease in the mean wellbore storage constant between January 2002 and June 2002 is 3.1 times 

the standard deviation of the data beginning in June 2002, again indicating that the decrease 

appears to be statistically significant. 

With the skin value fixed, there do not appear to be significant pairwise correlations between the 

modeled values of permeability, wellbore storage constant, pressure increase during the cycle, 

and average flow rate (Figure 4-5). 

The degree of tradeoff between the permeability and skin value demonstrates that the values for 

both parameters cannot be uniquely resolved with the current dataset. 

Figure 4-5. Scatter-plot matrix showing pairwise correlations between permeability (k), dimensionless 

wellbore storage constant (CD), pressure increase, and average flow rate for all pressure build-up cycles in 

Phases II-IV, holding sd fixed at -4.35.
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4.3.2 Model Pressure-History Plots and Type Curves

For each injection cycle, the free parameters of the model were fit simultaneously, using 

automatic parameter estimation to find a local minimum in the misfit between the recorded and 

modeled pressure at the bottom of the well. Downhole recorded pressurs were calculated from 

the measured surface pressures by accounting for the weight of the brine in the wellbore, and for 

frictional effects of the flow (Mahrer et al., 2004). Changes in flow rate during an injection cycle, 

including short shut-ins, were handled using superposition to account for the variable injection

rate history. The results of this modeling are a series of pressure-history plots and type curves, 

one for each injection cycle, which illustrate the modeled flow regime and how well it fits the 

data. The type curves show the change in pressure divided by flow rate (Δp/q) and the time 

derivative of Δp/q versus time on a log-log plot. 

Pressure-history modeling results from a typical Phase I injection cycle are shown in Figure 4-6.

This figure includes results for the case when all three model parameters are allowed to vary 

(upper plot), and for the case when sd is held fixed (lower plot). 
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Figure 4-6. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed line) 

for an example Phase I cycle, beginning July 10, 1997, allowing all three parameters to vary (top) and fixing 

sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant value of 6822 psi to 

measured surface pressures.

The model using three free parameters fits the data significantly better than the model using two 

free parameters; however, the parameters are not independent, nor are they physically 

reasonable, as discussed in Section 4.3.1. Regardless, these plots suggest that an idealized radialflow model can provide a reasonable fit to this data, with errors of less than about 5 percent. The

corresponding type curves (pressure change and derivative) are shown in Figure 4-7 and also 

suggest that a radial-flow model fits the Phase I data reasonably well.

.
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Figure 4-7. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by flow 

rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of Δp/q for an 

example Phase I cycle, beginning July 10, 1997, allowing all three parameters to vary (top) and fixing sd at -

4.35 (bottom).

Modeling results for typical injection cycles in the remaining phases are shown as follows: Phase 

II – pressure history (Figure 4-8) and type curve (Figure 4-9); Phase III – pressure history 

(Figure 4-10) and type curve (Figure 4-11); Phase IV – pressure history (Figure 4-12) and type 

curve (Figure 4-13). For each phase, the cycle shown is representative of cycles in that phase.

Unlike the Phase I cycle, model results from the later phases do not show a significantly greater 

misfit when sd is fixed rather than allowed to vary.
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Figure 4-8. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed line) 

for an example Phase II cycle, beginning July 26, 1999, allowing all three parameters to vary (top) and fixing 

sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant value of 6822 psi to 

measured surface pressures.
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Figure 4-9. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by flow 

rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of Δp/q for 

an example Phase II cycle, beginning July 26, 1999, allowing all three parameters to vary (top) and fixing sd at 

-4.35 (bottom).
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Figure 4-10. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed line) 

for an example Phase III cycle, beginning January 8, 2001, allowing all three parameters to vary (top) and 

fixing sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant value of 6822 psi 

to measured surface pressures.
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Figure 4-11. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by flow 

rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of Δp/q for 

an example Phase III cycle, beginning January 8, 2001, allowing all three parameters to vary (top) and fixing 

sd at -4.35 (bottom). Orange lines highlight the (approximate) emergence of radial flow.
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Figure 4-12. Recorded (blue dots) and modeled (red line) downhole pressures and percent error (dashed line) 

for an example Phase IV cycle, beginning January 14, 2007, allowing all three parameters to vary (top) and 

fixing sd at -4.35 (bottom). Recorded downhole pressures are calculated by adding a constant value of 7133 psi 

to measured surface pressures.
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Figure 4-13. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by flow 

rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of Δp/q for 

an example Phase IV cycle, beginning January 14, 2007, allowing all three parameters to vary (top) and fixing 

sd at -4.35 (bottom). Orange lines highlight the (approximate) emergence of radial flow.

The fits in the later phases are generally better than in Phase I, particularly compared to the time 

prior to 1998 when there were more variations in flow rate. Whether or not sd is fixed, the 

models generally fit the data within 2% error for the buildup cycles in Phase II and within 1-2% 

error in Phases III and IV. Errors tend to be lowest in periods of continuous flow, and highest at 

the beginning of cycles and around mid-cycle shut-ins.
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While the magnitude of the pressure falloff during the shut-ins is matched relatively well, the 

shapes of the falloff curves are not well-matched in the later phases, with the pressures falling off 

more slowly than predicted. It is possible to fit the falloff curves with similar values of k and sd

as were obtained from fitting the buildup curves; however, it is necessary to use significantly 

higher values of CD, as demonstrated by the example falloff curves shown in Figure 4-14. While 

this seems counterintuitive in a porous medium model, fracture closure during falloff periods

could cause more fluid to be forced into the near-wellbore area, causing pressures to falloff more 

slowly than modeled.
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Figure 4-14. Recorded (blue dots) and modeled (red lines) downhole pressures and percent error (dashed 

linse) during four example falloff periods, beginning (a) May 1, 1997, (b) May 28, 2000, (c) December 18, 

2008, and (d) March 29, 2012. Values for k and Cd were fit with sd fixed at -4.35, and are shown in the top left 

corner of each plot.

The earlier portions of the type curves shown above appear to indicate primarily the transition 

from wellbore storage to radial flow, with radial flow (identifiable as a flat spot on the derivative 

curve) emerging around 1000 hours in Phases III and IV (Figure 4-11, Figure 4-13). The

transition is more difficult to identify in Phases I and II due to the number of changes in flow 

rate. Even in Phases III and IV, the amount of scatter in the derivative, much of which is related 

to unplanned shut-ins or other changes in flow rate, makes it difficult to resolve the precise times 

that these transitions occur. Boundary effects, which cause an increase in the derivative 

following the radial flow period, are not observed. If boundary effects exist, they would be more 

readily observed during a long flow period having no shut-ins and minimal changes in flow rate 

(or alternatively, during a long shut-in period). 

4.3.3 Using rinv to Investigate Changes in Permeablity

An important concept in well test interpretation is the radius of investigation. The radius of 

investigation is not a theoretically rigorous concept, but in general has been shown to provide an 

adequate estimate of the distance that is “sensed” by the well (Fekete, 2012). There are several 

definitions of the radius of investigation, which differ only by a constant. Here we use the 

definition from Lee (1982), that the radius of investigation is the point where the pressure 

variations are fastest, which is equivalent to the location of the pressure front. Using this 

definition, the radius of investigation can be derived from the solution to the diffusivity equation 

for an instantaneous line source in an infinite medium:

2

1 4

0

r

Dt c

pp e

t

−

− = (4.11)
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where p is pressure in psi, 0 p is initial pressure in psi, t is time in hours, r is radius in feet, D is 

hydraulic diffusivity in square feet per hour, and 1 c is a constant, related to the strength of the 

instantaneous source.

The hydraulic diffusivity, in arbitrary units, is defined as :

t

k D

φμc = (4.12)

where k is permeability, φ is fractional porosity, μ is viscosity, and ct is total compressibility. 

Converting to oilfield units, this equation becomes:

4 2.64*10

t

k D

φμc

− = (4.13)

where k is in mD, μ is in centipoises, and t c is in psi-1.

Equation (4.11) can be solved for the time, mt , when the pressure disturbance is a maximum at 

inv r by differentiating with respect to time and setting equal to 0, yielding:

2 2 2

1 1 4 4

2 3

2

0

4

4

r r

D D

inv

m

p c cr

e e

t t Dt

r

t

D

π π

− − ∂ − =+ =

∂

=

(4.14)

Substituting Equation (4.12) into Equation (4.14) yields, in arbitrary units:

2

4

t inv

m

c r

t

k

φμ

= (4.15)

In oilfield units,

2 948 t inv

m

c r

t

k

φμ = (4.16)

Equivalently,

948* inv

t

kt

r

φμc = (4.17)
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The value inv r is known as the radius of investigation. Note that inv r is independent of flow rate.

Calculating the radius of investigation for a single cycle likely leads to an underestimation, since 

the pressures are still elevated at the end of a shut-in, which is not accounted for in the 

calculation of inv r . 

There is significant scatter in the recorded Δp/q derivatives (Figure 4-7, Figure 4-9, Figure 4-11, 

Figure 4-13), primarily due to changes in the flow rate, making it difficult to resolve changes in 

the derivative later in the cycle. However, calculating the radius of investigation at a certain time 

and observing the derivative at that time can provide a minimum distance from the well to which 

there are no observable changes in the permeability.

Calculating rriiiiii using typical parameters for a Phase IV cycle results in: 

220 inv r t = (4.18)

Using this value, after 35 days (840 hours), the radius of investigation is approximately 2 km. 

There are five cycles that have no shut-ins exceeding 2 hours duration within the first 35 days. 

The time derivatives of Δp/q versus t for these five cycles are plotted in Figure 4-15, using high 

sample rate data where available to increase the resolution. While there is still some scatter in the 

derivatives, there are no trends indicating a change in permeability, providing evidence that the 

permeability does not change significantly to a distance of at least 2 km from the wellbore (and 

as discussed above, rriiiiii is likely underestimated).

In contrast to the flow model results, both seismic reflection data and the spatial distribution of 

seismicity suggest an impermeable fault located about 1.5 km to the northeast of the injection 

well (King et al., 2014; Block et al., 2012). If the assumption that this fault serves as an 

impermeable boundary is correct, the inability to resolve this fault indicates that the radial flow 

model is insensitive to such features in the actual geologic structure at this distance. In particular, 

if there are preferential flow paths due to pre-existing faults, the pressures recorded at the well 

may not be equally influenced by the reservoir characteristics in all directions. An alternative 

explanation for our inability to resolve this fault in the pressure-flow modeling is that the 

estimated radius of investigation given above is biased by trade-offs between reservoir thickness, 

permeability, and rriiiiii. For example, if the modeled reservoir thickness of 100 ft were increased 

by a factor of 4, k would be reduced by a factor of 4, and inv r would be reduced by a factor of 2 

to 1.0 km.
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Figure 4-15. Recorded (blue dots) and modeled (red line) values for change in pressure (Δp) divided by flow 

rate (q), and the recorded (red triangles) and modeled (blue lines) values for the time derivative of Δp/q for 

the first 35 days (840 hours) for the cycles beginning January 8, 2004 (a), January 6, 2005 (b), January 7, 

2009 (c), October 19, 2011 (d), and April 16, 2012 (e). Plots a-d use high sample rate from the SCADA system. 

Plot e uses daily average data, due to a period of missing data in the SCADA system during that time period.

4.3.4 Fitting Multiple Cycles Simultaneously

The rate of increase in the maximum recorded surface pressure for each cycle appears to be 

greater since 2010 than previously (Figure 3-1), which suggests the possibility that the pressures 

are being affected by a reservoir boundary or a zone of decreased permeability. To explore this 

possibility, a model was constructed that held all parameters fixed for multiple cycles. Figure 

4-16 shows actual and modeled pressures for a single set of parameters for the cycles from 

March 2006 through January 2013. These parameters were derived as by fixing sd at -4.35, the 

same value as used in Section 4.3.1, and determining best fit values for k and CD , inputting small 
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injection rates during shut-in periods in order to treat these cycles as a single cycle. While there 

is a general trend of the modeled pressures being higher than the recorded pressures from 2006-

2009 and lower than recorded pressures from 2010-2013, the mismatch between the recorded 

and modeled maximum pressures is relatively small for all cycles, suggesting that a radially 

symmetric model with infinite-acting boundaries is adequate to model the data during this time 

period. It is likely that the increase in maximum pressure in recent years is therefore related to a 

decrease in the number of unscheduled maintenance shut-ins, which has led to a decrease in the 

total shut-in time per cycle, an increase in the average injection rate, and a commensurate 

increase in the maximum pressure.

This pressure rise is not unexpected, as pressure-flow modeling theory holds that even in the 

simplest case of injecting into an infinite reservoir at a constant rate, the derivative of pressure 

increase will become constant, or equivalently, the pressure will increase at a constant rate. Thus, 

pressure rise does not by itself necessarily indicate either boundary effects or near-well effects.

Figure 4-16. Recorded (open squares) and modeled (red lines) downhole pressures for the time period from 

March 2006 to January 2013. The model uses a single set of input parameters, as shown in the bottom left 

corner. Recorded downhole pressures are calculated by adding a constant value of 7133 psi to measured 

surface pressures.

4.4 Pressure-Flow Modeling Discussion

With 18 years of pressure-flow data, Paradox Valley is a unique case study. The time scale for 

typical well test models ranges from minutes to days, rather than the hundreds of days modeled 

in this study. Additionally, it is atypical of most waste disposal projects to inject above fracture 

propagation pressures for long periods of time. Consequently, there are no clear analogs in the 

published literature for the expected behavior of wellhead pressures at Paradox Valley that may

result from various assumed reservoir characteristics. The theoretical behavior for our simple 

model should be the same over long or short time periods, but the analysis is complicated by the 
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frequent flow rate changes that have occurred over the long injection history, the likely changes 

in reservoir properties over time, and the large area experiencing pore pressure increases. 

However, the ability of this simple model to fit the data reasonably well despite these 

complicating factors, both by fitting the cycles individually and by fitting the last several cycles 

with a single set of injection parameters, provides strong evidence that there have not been

significant changes in the reservoir properties near the injection well over the last several years. 

Near-wellbore scaling should be apparent in the pressure-flow data, possibly through a decrease 

in the wellbore storage constant or an increase in the skin due to damage, both of which would 

indicate degradation of the near-wellbore conditions, or through a change in permeability. A

decrease in calculated permeabilities over the last several years, which could indicate 

precipitation over a large area, is not observed.

A radial composite permeability, with a decreased permeability in the near-wellbore region 

compared to the area further from the well, should be evident as a decrease in the derivative of 

Δp/q (change in pressure divided by flow rate) versus time, as illustrated in the typecurve shown 

in Figure 4-17.

In summary, while we recognize that a radial flow model is insufficient to fully resolve the 

complexities of the geologic structure, we do not see any effects in the pressure-flow modeling

over the last several years that would appear to indicate near-wellbore changes, and thus 

conclude that the observed pressure increase is primarily due to far-field reservoir pressurization.

Figure 4-17. Typecurve for change in pressure (Δp) divided by flow rate (q) (circles) and the time derivative 

of Δp/q (triangles) versus time for a reservoir with negative skin due to damage and radial composite 

permeability with higher permeability further from the well. From Fekete (2012).
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A Consultant Review Board (CRB) was held in January 2015 to discuss the MASIP. This CRB 

recommended supplementing our analysis using a set of analytical equations. In addition to 

allowing comparison to and verification of the results obtained using the Fekete software, this 

method allows for the calculation of pressures away from the well, which may then be compared 

to the induced seismicity data. This analysis is the subject of future work.
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5 Induced Seismicity

5.1 History of Seismicity

Seismic monitoring of the Paradox Valley area began in 1983, with installation of the first 

stations of the Paradox Valley Seismic Network (PVSN). Network installation was timed to 

provide a pre-injection baseline of naturally occurring background seismicity. The network has 

been continuously operated since 1985, and has been expanded and updated over the years to 

respond to changing seismicity patterns. The current configuration consists of a surface array of 

20 digitally recorded, broadband, 3-component sensors.

Six years of pre-injection monitoring recorded no earthquakes within 18 km of PVU Injection 

Well #1. The data recorded during this period include just one local earthquake, which occurred 

about 19 km from PVU Injection Well #1. Within days of the start of the initial injection test in 

1991, seismic events were detected in the immediate vicinity of the injection well. During 

subsequent injection tests and continuous injection operations, induced earthquakes occurred at 

progressively increasing distances from the injection well. The close correlation between 

injection operations and induced seismicity at PVU has been well established (Ake et al., 2005; 

Block et al., 2014b).

The geographical distribution of induced seismicity over time is presented in the series of maps 

shown in Figure 5-1. For reference, four seismicity areas have been delineated and named: (1) 

Near-well - By the end of the injection tests in 1995, earthquakes were occurring 3 to 4 km from 

PVU Injection Well #1 (Figure 5-1a). This area of induced seismicity immediately surrounding 

the injection well is referred to here as the “near-well” region. (2) Northwest (NW) cluster - In 

mid-1997, about a year after the start of continuous injection, earthquakes began occurring 6 to 8 

km northwest of the injection well (Figure 5-1b). This cluster of induced seismicity is called the 

“northwest (NW) cluster”. (3) Northern valley - In mid-2000, earthquakes were first detected 12 

to 14 km from the injection well, along the northern edge of Paradox Valley (Figure 5-1b). 

Several distinct clusters of earthquakes have occurred along the northern edges of the valley 

since 2000 (Figure 5-1c). The earthquakes occurring in all of these clusters are referred to as 

“northern valley events”. (4) Southeast (SE) cluster - An earthquake was first detected about 6 

km southeast of the injection well in 2004 (Figure 5-1c), but the seismicity rate in this area 

markedly increased beginning in 2010 (Figure 5-1d). This group of earthquakes is referred to as 

the “southeast (SE) cluster”. In recent years, a few isolated earthquakes have been detected in 

previously aseismic areas, including in the center of Paradox Valley (Figure 5-1d).
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Figure 5-1. Maps showing the spatial distribution of shallow seismicity recorded in the Paradox Valley area 

over time: (a) injection tests, 1991-1995; (b) continuous injection, 1996-2000; (c) continuous injection, 2001-

2008; (d) continuous injection, 2009-2013. All detected earthquakes locating less than 8.5 km deep (relative to 

the ground surface elevation at the injection wellhead) are included.

5.2 Relation to Pore Pressure Diffusion

The occurrence of seismicity is not necessarily evidence of the presence of injectate, since 

seismicity may be caused by pore-pressure increase in the in-situ fluid. While it is also possible 

that seismicity could be induced by changes in the hoop and radial stresses rather than pore 

pressure changes, pore pressure perturbation is the generally accepted primary mechanism for 

inducing seismicity from fluid injection (Healy et al., 1968; Raleigh et al., 1972; Hsieh, 1979; 

Talwani and Acree, 1984). The onset of seismicity triggered on preexisting, critically loaded 

faults by pore pressure diffusion tends to exhibit distinctive trends in space-time. To evaluate 

whether pore pressure diffusion appears to be a major triggering mechanism for the PVUinduced seismicity, we examine time-distance plots of the seismicity and compare them to the 

trends expected for seismicity triggered by pore pressure diffusion.
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Linear pore pressure diffusion in a fluid-saturated poroelastic medium is described by the lowfrequency limit of the second compressional wave of the Biot equations (Biot, 1962). For the 

simplified case of uncoupled pore pressure diffusion in an isotropic, homogeneous, poroelastic 

medium, the diffusion equation reduces to:

p 2 D p

t

∂ = ∇

∂ (5.1)

or, in cylindrical coordinates:

2

2

p pp 1 D

t r rr

∂ ∂∂  

= +   ∂ ∂∂  

(5.2)

where pp is pore pressure, tt is time, and DD is hydraulic diffusivity. The wave satisfying this 

equation is dispersive, with higher frequencies traveling faster than lower frequencies (Shapiro et 

al., 1997). However, the higher frequencies also have significantly lower amplitudes, and these 

extremely small pore pressure perturbations are not likely to trigger induced seismicity (Rothert, 

2004). Rather, it is usually assumed that induced seismicity is triggered when the lowerfrequency, higher-amplitude components arrive. 

For a point pore pressure perturbation in an infinite homogeneous medium, Shapiro et al. (1997) 

derived an estimate for the earliest arrival time at a distance rr from the source corresponding to 

the higher-energy, lower-frequency components:

2

4

r

t

π D = (5.3)

or, equivalently:

r Dt = 4π (5.4)

This relation was derived assuming a constant pore pressure perturbation persisting at the source 

location until time tt or later (see Rothert, 2004, for a more detailed description). Similar 

considerations lead to the radius of investigation of the pressure-flow modeling, Equation (4.17).

At a given time tt after introduction of a significant pore pressure perturbation, induced seismic 

events have a greater probability of occurrence at distances < rr than at distances > rr. This timedistance relation is known as the triggering front of induced seismicity. It has been applied to 

case studies of seismicity induced by deep well injection into crystalline basement rock (Shapiro 

et al., 1997; Shapiro et al., 2002; Rothert, 2004; Dinske, 2010).

Other derivations of the triggering front have been developed and applied to the study of induced 

seismicity. A simple 1-D relation of the form r Dt = 4 has been used to analyze seismicity 

induced beneath reservoirs (Talwani et al., 2007; Durá-Gómez and Talwani, 2010) and within 
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confined aquifers (Assumpcão et al., 2010). More complex triggering front relations have been 

derived for anisotropic media (Shapiro et al., 1999; Dinske, 2010), but distance remains 

proportional to t . For nonlinear pore pressure diffusion, where the hydraulic properties vary 

with pressure, Hummel and Müller (2009) derived a 1-D analytical relation with r t ∝ , while

Shapiro and Dinske (2009) derived a relation for the 3-D case with 1

3 r t ∝ for large nonlinearity.

We choose to fit space-time plots of the PVU-induced seismicity data using the simple 1-D 

triggering front relation, r Dt = 4 . Based on borehole flow measurements and patterns of 

induced seismicity, we believe that most of the injected fluid and associated rise in pore pressure 

are confined primarily to the target injection formations, especially the Leadville formation. 

Pressure diffusion through these sub-horizontal layers is likely to conform better to a 1-D 

solution than to a 3-D solution for a spherical geometry. Because both the linear 1-D and 3-D 

relations are parabolic equations, the fit to the data is the same regardless of the relation used. 

However, the value of the hydraulic diffusivity derived from the fit differs depending on the 

relation.

We found 4 injection start times for which the seismicity time-distance plots appear to be 

relatively unaffected by earlier injection operations and for which there are enough seismic 

events over a large enough radial distance to define a move-out curve. These injection start times 

are: the start of injection test #6 on January 18, 1994; the start of injection test #7 on August 1, 

1994; the start of long-term injection on July 22, 1996; and the resumption of long-term injection 

on July 10, 1997, after a 70-day injection well shut-in. For injection tests prior to test #6, there 

are few recorded seismic events over limited radial distances, and therefore trying to fit a curve 

to the seismic move-out is not robust. For injection cycles between 1997 and 2000, the injection 

well shut-ins were not sufficiently long for effects of earlier injection to dissipate. Since 2000, an 

aseismic zone has persisted around the well to a radial distance exceeding 1 km, and the 

seismicity beyond that range is not sensitive enough to the injection well shut-ins that have 

occurred to dissipate sufficiently between cycles. For each of the 4 identified time periods, we 

visually fit the 1-D pressure diffusion curve to the seismic data in two ways: using the start time 

of injection as the reference time, and using a time shortly before the onset of seismicity as the 

reference time. To reduce scatter due to event location uncertainty, we include events with 

duration magnitude 0.5 and larger, since these events tend to have better-constrained locations.

The fits are shown in Figure 5-2.
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Figure 5-2. Seismicity time-distance plots for 4 injection start times: (a) start of injection test #6 (Jan. 1994), 

(b) start of injection test #7 (Aug. 1994), (c) start of long-term injection (Jul. 1996), and (d) resumption of 

long-term injection after 70-day shut-in (Jul. 1997). Two seismic triggering fronts are fit to each cycle, using a 

1-D pressure diffusion relation and two different reference times. The downhole pressure is included for 

reference.
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Figure 5-2, continued.
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Application of seismic triggering front relations to seismic time-distance plots assumes that the 

time between the elevation of pore pressure at the source point and the occurrence of seismicity 

at a given distance from the source is due solely to the pressure diffusion time lag. These 

relations do not take into account any time lag that may occur between the start of injection and 

the increase in pore pressure to a sufficiently high level to trigger seismicity. For the 4 injection 

cycles shown in Figure 5-2, seismicity begins near the well shortly after the downhole pressures 

reach a plateau. For 3 of the 4 time periods, the difference between the start of injection and the 

subsequent pressure plateau and start of seismicity is small. The corresponding difference in the 

two pressure diffusion fits is also fairly small, although the fits using a reference time 

corresponding to the pressure plateau and start of seismicity generally conform better to the 

seismic move-outs (Figure 5-2a, b, and d). Diffusivity values obtained for these 3 cycles using 

the injection start time as a reference range from 0.08 to 0.10 m2

/s; values obtained using the 

later reference times range from 0.11 to 0.12 m2

/s. In contrast to these 3 cycles, for the start of 

long-term injection, there is a 5-month delay between the beginning of fluid injection and the 

time when pressures consistently remain high and seismicity begins (Figure 5-2c). This long 

delay is partially due to 2 multi-day injection well shut-ins that occurred during the intervening 

months; a time delay required to re-pressurize a previously-stimulated reservoir is also likely. 

Using the start of injection for the pressure diffusion reference time provides a poor fit to the 

data and an anomalously low value of diffusivity, 0.055 m2/s (Figure 5-2c). Using a reference 

start time shortly before seismicity begins results in a much better fit to the seismic move-out and 

a diffusivity value of 0.115 m2

/s, consistent with the values obtained from the other cycles. The 

fact that the seismicity that began 5 months after the start of injection occurred very close to the 

injection well (rmin = ~160 m) provides further evidence that the large seismic lag time is not 

related to pressure diffusion, and therefore using a later reference time is reasonable.

To evaluate the radial distance to which a simple 1-D pore pressure diffusion model can explain 

the onset of seismicity induced by PVU injection, we overlay seismic triggering fronts on a timedistance plot showing all shallow events recorded since the start of injection. Events with depths 

less than 8.5 km and magnitudes ≥ duration magnitude MD 0.5 are included. We compute the 

seismic triggering front for several significant start times of PVU fluid injection: the start of the 

first injection test (July, 1991); the start of the first injection test after acid stimulation (October, 

1993), the start of the first injection test where surface injection pressures exceeded 4500 psi 

(January, 1994), and the start of long-term injection (July, 1996). For these calculations, we use

the average diffusivity value obtained from the previous analysis for the later reference times, 

0.115 m2

/s. The time-distance plot is shown with the 4 triggering front curves in Figure 5-3a.
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Figure 5-3. Seismicity time-distance plots of all shallow (depth < 8.5 km) events with magnitude ≥ 0.5 

occurring in the vicinity of the PVU injection well. (a) Four seismic triggering fronts overlaid – see text for 

description of their reference times (b) Seismic triggering fronts for the first two significant injection tests 

overlaid. All triggering fronts were computed using a 1-D linear pressure diffusion model and a hydraulic 

diffusivity of 0.115 m2

/s.
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While none of the triggering fronts match the onset of induced seismicity occurring at all 

distances, the triggering fronts for the first significant injection tests – those in late 1993 after 

acid stimulation and early 1994 with pressures above 4500 psi – match the onset of seismicity to 

radial distances of ~10 km very well. The seismic data are shown with just these two fronts 

overlaid in Figure 5-3b. The events at distances of 6 to 9 km are in the NW cluster. Previous 

investigators had suggested that the onset of seismicity in the NW cluster was either related to 

pressure rise along high-permeability fault zones between the well and the NW cluster (Ake et 

al., 2005) or stress changes related to the injected fluid (Roeloffs and Denlinger, 2009). These 

inferences were made based on the onset of NW-cluster induced seismicity only 1 year after the 

start of long-term injection; the effects of the injection tests apparently were not considered. The 

analysis presented here indicates that the onset of the NW-cluster seismicity in 1997 could be 

due to pore pressure perturbations introduced in late 1993 and early 1994 during the first 

significant injection tests, and that a high-permeability pathway is not needed to explain the 

observed seismicity patterns.

Shallow seismicity that we interpret as being induced by PVU injection operations at radial 

distances greater than 10 km began earlier than is predicted with the simple 1-D linear pressure 

diffusion model presented here. Although these events occur ahead of the computed seismic 

triggering front, their move-out parallels the front and therefore suggests that their triggering is 

related to a diffusive process (Figure 5-3b). Possible explanations for the early onset of 

seismicity at these distances include heterogeneity of hydraulic diffusivity, shear slip on 

critically-loaded faults from the higher-frequency, earlier-arriving components of pore pressure 

diffusion, or variations in the rate of pore-pressure diffusion due to variations in stress and strain 

conditions (Wang, 2000).

According to Shapiro (1999), the value of D obtained from analysis of seismic triggering fronts 

reflects the value for the rock prior to stimulation and potential subsequent temporal variations in 

its hydraulic properties. However, numerical modeling performed by Bruel (2007) demonstrates 

that the value of D obtained with this method may be substantially underestimated if the 

preexisting faults are not sufficiently close to failure. Hence, the fairly low value of hydraulic 

diffusivity obtained from the PVU seismic data (0.11 – 0.12 m2

/s) could indicate either that the 

rock permeability was low prior to stimulation or that the stress states on the faults within several 

km of the well were not sufficiently close to critical conditions to fail as soon as the lowfrequency diffusion front arrived. If we assume that the faults within 10 km of the injection well 

were not sufficiently critically loaded to fail as soon as the low-frequency pore pressure diffusion 

front arrived, we can estimate a value of D by fitting the move-out of the distant seismicity

(Figure 5-4). In this case, we obtain a value for D of 0.20 m2/s.
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Figure 5-4. Seismicity time-distance plots of all shallow (depth < 8.5 km) events with magnitude ≥ 0.5 

occurring in the vicinity of the PVU injection well. Seismic triggering fronts for the first two significant 

injection tests are overlaid. The triggering fronts were computed using a 1-D linear pressure diffusion model 

and a hydraulic diffusivity of 0.20 m2

/s.

The estimates of the hydraulic diffusivity computed from this analysis, ~ 0.1 – 0.2 m2

/s, are 

similar to values derived at sites where injection occurs into low-permeability crystalline 

basement rock. For example, a hydraulic diffusivity of 0.5 m2

/s was obtained at the Continental 

Deep Drilling (KTB) site in Germany (Shapiro et al., 1997), 0.17 m2/s at the Fenton Hill Hot Dry 

Rock site in New Mexico (Shapiro et al., 2002), and 0.05 m2/s at Soultz-sous-Forets in France 

(Shapiro et al., 2002). To evaluate whether the diffusivity values obtained from analysis of the 

PVU induced seismicity data are reasonable for this site, we calculate the corresponding values 

of permeability from the diffusivity estimates. We then compare these results with permeability 

values obtained independently for PVU injection formations by early flow tests in the PVU 

wellbore. 

In hydrogeology (Freeze and Cherry, 1979), the hydraulic diffusivity DD is defined as:

S

K D

S = (5.5)
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where K is the hydraulic conductivity and S S is the specific storage. Hydraulic conductivity K

is related to the material permeability k by K kg = ρ μ/ , where ρ is the fluid density, μ is the 

fluid viscosity, and g is the gravitational constant. Specific storage S S is given by ( )f ρ φ gc c + , 

where φ is the porosity, c is the (drained) compressibility of the porous medium, and f c is the 

compressibility of the pore fluid. Substituting these values into Equation (5.5) and solving for 

permeability gives:

kDc c = + μ φ ( f ) (5.6)

Comparison to equations for linear poroelasticity given by Wang (2000) indicates that the above 

equation is valid for the condition of constant stress and the assumptions of incompressible 

grains and pores. The more general formulas relating diffusivity and permeability for the 

condition of constant stress are:

k D

S σ μ σ

= (5.7)

S cc c c σ φ =− + − ( s f ') φ ( ) (5.8)

where ' s c is the unjacketed material compressibility (corresponding to the solid-grain 

compressibility if all the grains are of the same mineral), cφ is the unjacketed pore 

compressibility, and Sσ is the unconstrained specific storage coefficient. Setting ' s c and cφ to 

zero, substituting the resulting expression for Sσ into Equation (5.7), and solving for k yields 

Equation (5.6).

Corresponding equations for the condition of constant strain are (Wang, 2000):

k D

μS ∈

∈

= (5.9)

( ) ' ' 1 s

s f

c Sc cc

c ∈ φ φ

  = −+ −     (5.10)

with SS∈ being the constrained specific storage coefficient. Assuming incompressible grains and 

pores, Equation (5.10) simplifies to f S c ∈ = φ and the relation between diffusivity and 

permeability becomes:

f kDc = μφ (5.11)

At depth, c approaches ' s c , and therefore the unconstrained storage coefficient Sσ in Equation

(5.8) also approaches f φc (assuming incompressible pores: c 0 φ = ). Hence, in rigid materials at 
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depth, the unconstrained and constrained storage coefficients approach the same limit. This

approximation and the corresponding equation relating permeability and diffusivity (Equation

(5.11)) are often used in petroleum engineering (Wang, 2000) and rock mechanics (Jaeger et al, 

2007).

We compute permeability values using both Equations (5.6) and (5.11). For these calculations, 

we use the fluid viscosity (0.00103 Pa-s) and compressibility (2.8036×10-10 Pa) determined 

previously from the temperature and salinity of the 70%:30% brine-to-fresh water mix. We 

perform the calculations using diffusivity values of 0.1 and 0.2 m2

/s, to span the range of values 

determined from the analysis of the seismic data. For porosity, we assume values ranging from 

3% to 8%, based on the PVU well log data (see Table A-1, Appendix A). For the drained 

material compressibility in Equation (5.6), we first compute the undrained bulk modulus of the 

Leadville formation using a P-wave velocity of 6350 m/s, S-wave velocity of 3387 m/s, and 

density of 2750 kg/m3 determined from PVU well log data. We subsequently compute the 

corresponding drained bulk modulus using Gassmann’s equation for fluid substitution (Russell 

and Smith, 2007) and a limestone grain bulk modulus of 6.7x1010 Pa, and then take the inverse to 

get compressibility. However, for the values of porosity examined here, the difference between 

the drained and undrained moduli is negligible.

The permeability results are shown as a function of porosity in Figure 5-5. Results using 

equation (5.6) are represented by the red symbols. These permeability values range from 2.4 to 

3.9 mD for a hydraulic diffusivity of 0.1 m2

/s and range from 4.8 to 7.7 mD for a diffusivity of 

0.2 m2/s. The permeabilities computed with Equation (5.11) (blue symbols) range from 0.9 to 

2.3 mD for D = 0.1 m2

/s and range from 1.8 to 4.7 mD for D = 0.2 m2/s. These permeabilities are 

very consistent with the values determined from early flow tests in the PVU wellbore, which 

vary from about 1 to 8 mD (see section 4.1). Hence, not only does the move-out of the induced 

seismicity match the parabolic trend predicted by pore pressure diffusion, the rate of the moveout is also consistent with reservoir properties measured independently by wellbore flow tests.

Since the occurrence of induced seismicity appears to be consistent with a simple diffusion 

model of pore pressure perturbations introduced at the injection well, it is reasonable to use 

spatiotemproal seismicity patterns to qualitatively evaluate the evolution of subsurface reservoir 

pressures and hydraulic connectivity. In the following sections, we examine spatiotemporal 

patterns of the induced seismicity to evaluate the hydraulic connectivity in the near-well area and 

whether it appears to have changed over time, to evaluate the region where reservoir properties 

have likely been altered by injection, and to determine whether the large-scale spatiotemporal 

seismicity patterns are consistent with increasing far-field reservoir pressurization in recent 

years. 
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Figure 5-5. Permeabilities computed from seismic-derived values of the hydraulic diffusivity, D. 

Permeabilities were computed for a range of porosities, two values of D, and using two different permeabilitydiffusivity relations.

5.3 Near-Well Seismicity

Below we examine the 3-D spatial patterns of seismicity induced near the injection well to 

evaluate the hydraulic connectivity in the vicinity of the well. In addition, we look for any 

changes in the seismicity patterns over time that may provide evidence of temporal variations of 

hydraulic connectivity or permeability, such as an increase in permeability due to injection or a 

potential decrease in connectivity over time due to near-wellbore precipitation and clogging of 

fractures. 

5.3.1 Vertical Seismicity Distribution and Hydraulic Connectivity

Increasing depth of fill in the bottom of the injection borehole has covered all but the uppermost 

perforations and may have led to decreased fluid flow into the deeper sections of the target 

reservoirs over time. Logging of PVU Injection Well #1 performed in 2001 indicated that the 

top-of-fill within the borehole was at a depth of 14,172 feet (4320 meters), at the base of the 

upper Leadville perforations (Subsurface Technology, 2001). In contrast, a previous survey 

conducted in 1994 indicated that the top-of-fill was at 14,604 feet (4451 meters), near the base of 

the underlying Elbert Formation. The fill has not been removed from the well, nor has the well 

been re-entered since 2001. The increased amount of fill within the borehole suggests that the 

perforations in the lower Leadville and underlying formations may have been accepting 
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significantly reduced amounts of fluid since at least 2001, as compared to earlier years. This has 

led to questions over whether injected fluid is confined to the upper Leadville Formation away 

from the well, or whether it is able to migrate vertically into other permeable zones. If the 

injection depth interval has been effectively decreased by the presence of the fill, and if there is 

little vertical migration of the fluid in the surrounding formations, the near-well seismicity 

should become progressively shallower over time as the injection interval is reduced and the 

fluid below the injection interval has time to disperse. Here we examine the vertical distribution 

of seismicity within several km of the injection well and evaluate whether this distribution has 

changed over time.

Induced seismicity within 3 km of PVU Injection Well #1 occurs over an elevation range of 

more than 2 km, as illustrated by the map and cross sections in Figure 5-6. The hypocenters 

shown in Figure 5-6 were computed by an event relative location method and have estimated 

relative horizontal errors ≤ 50 m and relative vertical errors ≤ 100 m. Most of the seismicity 

within a few hundred meters of the well occurs at elevations corresponding to the Leadville and 

other subsalt Paleozoic formations at the well (light and dark blue hypocenters, Figure 5-6). 

However, at distances greater than 1–1.5 km from the well, most earthquakes occur within 

significantly shallower (orange, red, black, and gray hypocenters) or deeper (purple hypocenters) 

seismicity clusters. The large vertical distribution of near-well seismicity suggests substantial 

vertical hydraulic connectivity in this region. We have used the spatial distribution of the 

induced seismicity to infer the locations and offsets of northwest trending normal faults, 

assuming that the seismicity is primarily occurring within or near the target injection formations

(Figure 5-6). The vertical distribution of seismicity suggests that these normal faults or other 

high-permeability zones allow vertical fluid flow and pore pressure propagation. Because there 

appears to be substantial hydraulic connectivity over a vertical extent exceeding 2 km in the 

near-well area, the ability to access permeable zones within the target injection formations is 

unlikely to be substantially degraded by potential decreased fluid flow across the deep perforated 

zones in the injection well.

The vertical hydraulic connectivity within 3 km of the injection well does not appear to have 

changed over time, as interpreted from spatiotemporal patterns of induced seismicity. While the 

spatial occurrence of seismicity varies over time, the depth range of seismicity at any particular 

location remains relatively constant over time, as shown by the time sequence maps in Figure 

5-7. An aseismic zone surrounding the injection well between radial distances of approximately 

500 and 1100 m developed after a decrease in the injection flow rate in mid-2000. As discussed 

further in the next section, we interpret the scarcity of induced seismicity in this region as 

indicating a change in reservoir characteristics and pore pressure gradients rather than an absence 

of fluid flow, as suggested by the continued occurrence of seismicity at distances greater than 

1100 m from the well over a large range of elevations (Figure 5-7Error! Reference source not 

found.). Additionally, a box plot of earthquakes within 500 m of the injection well shows no 

consistent variation with time (Figure 5-8). These observations suggest that if any precipitation 

and clogging of fractures is occurring near the injection well, it is not severe or widespread 

enough to noticeably interfere with fluid flow and pore pressure propagation.
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Figure 5-6. Map showing epicenters of earthquakes occurring in the near-well region of induced seismicity, 

color-coded by hypocenter elevation (center), and cross sections showing distinct vertical offsets of 

hypocenters (top and bottom). Only a-quality hypocenters from the event relative location are included. Two 

northwest-striking normal faults interpreted from the hypocenter elevation patterns are shown. Our 

interpreted base of the Paradox salt and top of the Precambrian (solid black lines) are shown in each cross

section. A simplified geologic section at the PVU wellbore is included at upper right for reference. 
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Figure 5-7. Near-well events by year, colored by elevation. Red stars designate PVU Injection Well #1.
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Figure 5-8. Box plot of elevations of earthquakes within 500 meters of the injection well by year, with boxes 

defined by hinges. Blue dots and lines show the location of the median. Whiskers are drawn to the farthest 

point within 1.5 times the range between the upper and lower hinges. Black dots and lines designate outliers. 

5.3.2 Seismicity Patterns and Reservoir Permeability

The aseismic zone that developed around the injection well after the decrease in flow rate in mid2000 (Figure 5-7) suggests that pore pressure gradients changed as a result of the injection tests 

and early years of long-term injection, to a radial distance of at least 1100 m. Temporal 

variations in pore pressure gradients indicate that reservoir characteristics, such as permeability, 

have changed. Reservoir permeability can be enhanced during injection by shear slip on preexisting fractures, opening of new fractures, and cooling and shrinking of the rock matrix. 

Increased permeability leads to lower spatial gradients of pore pressure, which in turn can cause 

areas of previous seismic activity to become aseismic (Baisch et al., 2009). In addition, changes 

in the extent to which permeability is dependent on pore pressure (degree of nonlinearity) can 

substantially alter pore pressure gradients (Hummel and Muller, 2009). Nonlinearity may change 

over time; for example, if the rock matrix cools sufficiently to hold fractures open, permeability 

nonlinearity should decrease. 
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As the reservoir re-pressurized following the mid-2000 decrease in flow rate, the altered spatial 

pore pressure gradients within the previously stimulated region appear to have prevented the 

local pore pressures from increasing sufficiently to exceed values experienced prior to 2000, 

between distances of about 500 and 1100 m from the well. In contrast, as injection pressures 

increased (and exceeded pre-2000 values), the areas within 500 m of the well and farther than 

~1100 m from the well appear to have experienced greater pore pressures than prior to 2000. 

Therefore, seismicity has continued in these regions. Without altered reservoir characteristics 

and corresponding changes in pore pressure gradients in the region surrounding the injection 

well, seismicity should have resumed in all areas, since downhole injection pressures have 

exceeded pre-2000 values for many years. This concept of seismic activity occurring only where 

previously experienced pore pressures are exceeded, known as the Kaiser effect, has been used to 

explain spatiotemporal induced seismic patterns, and in particular, the development of aseismic 

zones, at several other injection sites (Baisch et al., 2002; Baisch et al., 2009; Baisch et al., 

2010). 

The locations of the larger-magnitude (≥ M 3.0, or M 3.0+) induced earthquakes are consistent 

with a stimulated zone around the well extending to radial distances greater than ~1.5 km. In 

computer models of injection-induced seismicity, the larger-magnitude events occur around the 

edge of the previously stimulated region (Baisch et al., 2010). At PVU, the M 3.0+ events are 

mostly concentrated in a narrow band around the southern and western edges of the near-well 

region, at radial distances between 1.6 and 2.2 km (Figure 5-9). Of the 12 induced events in this 

magnitude range, only 2 occurred at distances greater than 2.5 km from the injection well. Both 

of these more distant M 3.0+ events occurred in the NW cluster; the second and largest of these 

occurred relatively recently, in January, 2013. Maximum earthquake magnitudes are lower in the 

other seismicity clusters (Figure 5-9). Hence, the patterns of the larger-magnitude PVU events 

are consistent with a stimulated region around the injection well (where permeabilities likely

increased prior to mid-2000) to distances of roughly 1.5 to 2 km. This is approximately equal to 

the estimated radius of investigation of the pressure-flow modeling, and therefore the modeling 

should be sensitive to changes in permeability over time within this stimulated area. 

Permeabilities computed from the pressure-flow modeling with skin factor fixed show a modest 

increase in permeability between 1996 and 1999 (Table 4-1). The NW cluster may represent a 

second zone of reservoir stimulation; however, the pressure-flow modeling is not sensitive to 

reservoir characteristics at this distance from the well. 

If precipitation near the injection well has been substantially decreasing reservoir permeability in 

recent years, we would expect pore pressures near the well to increase, which may lead to 

increased seismicity rates. An increase in rates of earthquakes occurring close to the well in 

recent years is not seen. Rather, near-well seismicity rates are low compared to historical trends 

(Figure 5-10a). In addition, a lower proportion of the induced seismicity has occurred close to 

the well in recent years than in earlier years (Figure 5-10b). Hence, there is no evidence in the 

seismicity recorded to date that the reservoir permeabilities near the injection well have 

decreased.
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Figure 5-9. Epicenters of induced earthquakes, color-coded by magnitude.
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Figure 5-10. Annual rates of induced earthquakes within 1 km of PVU Injection Well #1 (red) and greater 

than 1 km from the well (gray): (a) number of events (b) percent of events. All shallow (depth < 8.5 km) 

seismic events with magnitude ≥ MD 0.5 are included.
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5.4 Geographical Expansion of Seismicity

The geographical expansion of seismicity has varied over time. The rate of expansion was 

highest during the later injection tests (1994-1995) and the early phase of long-term injection 

(1996-2000) (Figure 5-11). However, in mid-2000, when the PVU injection flow rate was 

decreased by about one-third in response to an ML 4.3 induced earthquake, the geographical 

expansion of seismicity slowed greatly, and the spatial extent of the near-well and NW-cluster 

seismicity areas largely stabilized. While new clusters of seismicity appeared in the northernvalley area in the years following the reduction in flow rate, seismicity rates there were very low. 

There were only minor changes in the seismicity patterns between the time periods of 2000-2003 

(Figure 5-12a) and 2004-2008 (Figure 5-12b). This relatively stable period lasted for about a 

decade.

Beginning in 2009, the spatial distribution and rates of seismicity began to change again (Figure 

5-12c). A distinct group of earthquakes developed in 2010 about 6 km southeast of the injection 

well, the SE cluster. While the first detected SE cluster event occurred in 2004, with two 

additional events recorded in 2008 and 2009, beginning in 2010 the SE cluster experienced 

increasing rates of seismicity: 11 events in 2010, 17 events in 2011, and 25 events in 2012.

Seismicity rates were also markedly elevated in some of the northern-valley clusters in 2010 and 

2011: 557 northern-valley earthquakes were detected in 2010 and 113 were recorded in 2011, 

Figure 5-11. Correlation between injection flow rate (top) and shallow seismicity (< 8.5 km depth) recorded 

by PVSN (bottom).
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Figure 5-12. Maps showing the spatial distribution of shallow seismicity recorded in the Paradox Valley area 

over time: (a) 2000-2003; (b) 2004-2008; (c) 2009-2013. All detected earthquakes locating less than 8.5 km 

deep (relative to the ground surface elevation at the injection wellhead) are included.
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greatly exceeding the previous annual rates of 2 to 33 events per year. Additionally, since 2009 

seismicity has been recorded in new areas, including in the center of Paradox Valley and along 

the northwest edge of Paradox Valley. Furthermore, in January 2013, a local magnitude 4.4 

earthquake occurred more than 8 km from the injection well, almost four times farther from the 

well than any previous M 3.5+ earthquake induced at PVU. The changing seismicity patterns 

observed in recent years suggest that pore-pressure perturbations may be reaching new areas and 

that pore pressures may be increasing in already stimulated regions. These observations are 

consistent with far-field reservoir pressurization inferred from modeling of the pressure-flow 

data. 

Based on the spatial distribution of induced seismicity, the influence of PVU fluid injection on 

reservoir pore pressures does not appear to be radially symmetric. Earthquakes that we interpret 

as induced by PVU fluid injection occur at distances up to ~18 km north and northwest of the 

well (Figure 5-12c). To the southwest, south, and southeast of the well, however, induced 

seismicity is only observed to distances of 5-7 km. In addition, seismicity was first observed in 

the SE cluster, located 6 km southeast of the injection well, 7 years after seismicity had begun in 

the NW cluster, located 6-8 km northwest of the well. Differences in the geographical expansion 

of seismicity by azimuth strongly suggest that pore pressure perturbation is not radially 

symmetric about the well and that elevated pore pressures may extend to much greater distances 

in some azimuthal directions than others.

5.5 Spatial Extent of Injected Brine

Neither the pressure-flow modeling nor the induced seismicity analyses presented above yield 

estimates of the spatial extent of the injected brine. We have made some gross estimates of the 

spatial extent of the injected brine using simple volumetric analyses. Our method and results are 

included in Appendix A. Here we show some of the results to briefly examine the relationship 

between the spatial distribution of brine and the spatial distribution of seismicity and pore

pressure diffusion.

The approximate relationship between the spatial extent of the injected brine, the spatial extent 

of the induced seismicity, and a 1-D pressure diffusion model is illustrated in Figure 5-13. This 

time-distance plot shows the radial distance of the observed seismicity and models of pore 

pressure diffusion and brine intrusion as a function time. Results from 4 simple volumetric 

models of brine intrusion are included. In two of these models, we assume that the injected brine 

is confined to the higher-porosity (≥ 3%) zones in all of the sub-salt formations, as identified 

from well log data. The combined thickness of these zones is 90 m, and the weighted average 

porosity from the sonic porosity well log is 5.6% (Appendix A). In the other 2 brine intrusion 

models, we assume that the brine is confined to the higher-porosity zones in the Leadville 

formation only. The combined thickness of these zones is 50 m, and the weighted average 

porosity is 5.5%. We further sub-divide each of these two models into 2 scenarios. In one 

scenario, we assume that the injected brine displaces the in-situ fluid in only 5% of the pore 

space, in all time periods. The remaining 95% of porosity is assumed to be inaccessible to the 

injected brine, either because of restricted permeability or because the injected brine mixes with 

the in-situ fluid instead of displacing it. In the second scenario, we assume that the injected brine 

invades only 5% of the pore space during the injection tests, but that the percent of pore space 
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Figure 5-13. Estimated radial distance from the well of the injected brine over time, based on 4 different 

cylindrical models (red and blue curves). The shallow earthquakes with M ≥ 0.5 (black dots) and a 1-D pore 

pressure diffusion curve with diffusivity = 0.115 m2

/s (dashed black line) beginning at the time of the first 

significant injection test (after acid stimulation) are shown for comparison. The green square represents a 

well drilled into the Leadville formation in 2008, in which no PVU brine was encountered.

invaded by the brine linearly increases during long-term injection from 5% to 15%. Since PVU 

typically injects well above the fracture propagation pressure, fractures likely grow over time, 

increasing permeability and providing access to additional pore space. In addition, as the 

reservoir formations are intruded by the injected brine, the rock matrix will cool. This thermal 

effect should cause the rock matrix to shrink, further opening fractures and increasing porosity. 

We model potential increases in porosity and/or permeability over time by gradually increasing 

the percent of existing pore space that we assume the injected brine can occupy.

The brine intrusion models shown in Figure 5-13 illustrate that the spatial extents of the pore 

pressure front and induced seismicity grow at a substantially faster rate than the spatial extent of 

the injected brine. Hence, the induced seismicity occurs ahead of the brine front, with the 

distance gap between the two increasing over time. This is especially true for the brine intrusion 

models in which the fraction of porosity invaded by the injected brine increases over time. For 

these models, the radial expansion of the brine front greatly decreases as the brine instead 

diffuses into additional pore space near the well. The relationship between the spatial extent of 

the induced seismicity and injected brine shown in Figure 5-13 is consistent with a model of 
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seismicity being triggered by pore pressure perturbation, since pressure perturbation propagates 

through the in-situ fluids ahead of the injected brine.

The brine intrusion models presented above yield estimates for the current radial distance of 

brine intrusion of roughly 2 to 4 km. If some of the injected brine invades lower-porosity 

intervals, or the fraction of pore space occupied by the brine is greater than 0.05, then the 

estimated radial distance would be less. Conversely, if the fraction of pore space occupied by the 

brine is less than 0.05 or the porosity decreases away from the injection well, then the estimated 

distance would be greater. The sensitivity of the results to different assumptions is investigated 

further in Appendix A. The estimated distance of brine intrusion of 2-4 km shown here is 

consistent with observations made in an exploration well drilled in 2008 9.7 km northwest of 

PVU Injection Well #1, on the edge of Paradox Valley (Figure 5-12b; Figure 5-13, green 

square). That well penetrated the Leadville formation, and chemical analysis of the deep brine 

recovered from the well did not match the chemistry of the brine injected at PVU (personal 

communication, Cleary Petroleum Corp. to Reclamation, 2008). Hence, this single data point 

suggests an upper limit of ~10 km for the brine intrusion as of 2008.

5.6 Induced Seismicity Discussion

Induced seismicity patterns are consistent with the results from the pressure-flow modeling that 

indicate a lack of near-wellbore flow impairment. Near-well seismicity patterns indicate 

substantial vertical hydraulic connectivity within ~3 km of the injection well, and the hydraulic 

connectivity appears to have remained fairly constant since early in injection operations. The 

seismic data suggest that permeability may have increased in the reservoir formations to 

distances of ~1.5-2.0 km from the well during early injection operations (prior to mid-2000). 

Seismicity patterns within 2 km of the well have not changed significantly since ~2001-2002, 

suggesting that near-well permeabilities are stable. These observations are consistent with results 

of the pressure-flow modeling, which indicate fairly constant permeabilities since ~2002 within 

an estimated radius of investigation of 1 to 2 km.

The large-scale geographical expansion of induced seismicity is consistent with far-field 

reservoir pressurization. Since 2009, seismicity rates have increased in some regions, and 

induced seismicity has been detected in previously aseismic areas. These changes have been

observed at distances up to ~18 km from the injection well. Hence, while the region immediately 

surrounding the injection well to a radial distance of about 2 km has been most strongly altered 

by injection operations, the seismicity patterns indicate that pore pressures have likely increased 

over much larger distances. Because of the low, fracture-dominated permeability of the Leadville 

formation, elevated pore pressures may be propagated over large distances through a limited 

network of fractures, potentially leading to a complex pore pressure field. Areas southwest, 

south, and southeast of the well have only experienced low rates and magnitudes of seismicity at 

radial distances > ~2.5 km and have not experienced any seismicity at distances > 7 km, 

suggesting that geologic factors may be limiting pore pressure increase in these areas.

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6 Conclusions

No evidence of near-well flow impairment is observed over the last several years, either in the 

pressure-flow modeling or in the patterns of induced seismicity. Rather, both the pressure-flow 

modeling and the induced seismicity are consistent with far-field reservoir pressurization. There 

is some evidence for a decrease in the wellbore storage capacity of the near-well area in early 

years, most clearly shown by the decrease in the modeled wellbore storage constant between 

January 2002 and June 2002, but any degradation in the near-well reservoir properties does not 

appear to have progressed since that time.

These studies suggest that reservoir pressurization has occurred to at least a distance of ~2 km 

from the injection well, and that substantial elevations in pore pressure could be occurring at 

much greater distances (up to ~18 km from the well) in some azimuthal directions. 

The radius of investigation of the pressure-flow modeling of individual injection cycles is 

estimated to be 1 to 2 km. Therefore, this modeling suggests substantial pore pressure increase in 

the target injection formations to a distance of at least 1-2 km from the well. Changes in the 

patterns of induced seismicity occurring ≥6 km from the well observed since 2009 suggest that 

reservoir pressures may be increasing at distances up to ~18 km from the injection well in some 

azimuthal directions. However, seismicity patterns are strongly asymmetric around the wellbore. 

Areas southwest, south and southeast of the well, at radial distances greater than about 2–2.5 km, 

have experienced relatively low levels of seismicity, suggesting that geologic factors may be 

limiting pore pressure increase in these areas. 

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A-1

Appendix A Models for the Spatial 

Extent of Injected Brine

We use simple volumetric analyses to estimate the spatial extent of the brine injected at the PVU 

Injection well #1. For these simple calculations, we assume that the volume of rock containing 

the injected brine can be represented by one or more cylinders centered at the injection well and 

that the brine is uniformly distributed within each cylinder. The relation between injected volume 

V , cylinder height h , cylinder radius r , and effective porosity φ is then:

V 2 π r h

φ

=

Estimates of the porosity of target injection formations are provided in Bremkamp and Harr 

(1988). From the sonic porosity well log, 164 ft (50 m) of the Leadville formation were 

determined to have 3% or greater porosity (Table A-1). Using the reported porosities and 

thicknesses, we calculate a weighted average porosity of 5.5% for this 164-ft (50-m) interval.

These higher-porosity zones are reported by Bremkamp and Harr to be scattered through 18 

different depth intervals within the 416 feet of Leadville formation encountered in the well. 

Bremkamp and Harr (1988) do not report porosity values for the remaining 252 ft (77 m) of the 

Leadville, but the sonic-porosity log indicates much lower porosities for the remaining intervals.

Assuming a porosity of 0.5% for the remaining intervals yields a weighted average porosity of 

2.5% for the entire 416-ft (127-m) Leadville formation. Assuming a porosity of 1% yields a 

weighted average (2.8%) that differs only slightly, and hence the average porosity of the entire 

Leadville formation is not very sensitive to the value assumed for the low-porosity zones.

Table A-1. Higher-porosity zones within the Leadville formation reported in Bremkamp and Harr 

(1988). Values were derived from the sonic-porosity well log for PVU Injection Well #1.

Thickness (ft) Thickness (m) Porosity 

Range (%)

Median 

Porosity (%)

48 14.6 3 – 4 3.5

30 9.1 4 – 5 4.5

74 22.6 5 – 8 6.5

10 3.0 8 – 10 9

2 0.6 >10 14*

*An upper porosity limit of 18% was used for this interval, based on core-derived

porosities reported in Bremkamp and Harr (1988).
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Table A-2. Higher-porosity zones within non-Leadville sub-salt formations reported in Bremkamp 

and Harr (1988). Values were derived from the sonic-porosity well log for PVU Injection Well #1.

Lithology Thickness (ft) Thickness (m) Weighted Average 

Porosity (%)

dolomites & 

limestones

28 8.5 4

sandstones 48 14.6 5.5

Precambrian 

schist

54 16.5 7

Total 130 39.6 5.8

Bremkamp and Harr (1988) report an additional 130 ft (39.6 m) of higher-porosity zones in the 

Devonian to Precambrian units. They report weighted average sonic-derived porosities for the 

total dolomite/limestone, sandstone, and Precambrian schist lithologies, as listed in Table A-2. 

The weighted average porosity for all these zones is 5.8%. 

Considering the range of possible zones that could accommodate the injected brine, we construct 

simple cylindrical models for five scenarios: (1) injected brine is confined to the higher-porosity 

zones within the Leadville formation; (2) brine is confined to the high-porosity zones within all 

formations; (3) brine is confined to the entire Leadville formation; (4) brine is confined to the 

entire Leadville formation plus the higher-porosity zones in the other formations; and (5) brine is 

accommodated by all sub-salt Paleozoic formations and into the upper 160 ft of the Precambrian 

basement. Possible brine intrusion to a depth of 160 ft into the Precambrian basement is used 

because Bremkamp and Harr (1988) report that the Precambrian has adequate reservoir 

characteristics to that depth. Weighted average porosities for these scenarios were computed 

using the porosity values listed in Tables A-1 and A-2 and assuming a porosity of 0.5% for the 

remaining intervals. Because of the uncertainties in the porosity measurements and because 

porosity may vary with distance from the well, we consider a range of possible porosity values 

for each scenario. The range extends from one-half to twice the computed weighted averaged 

porosity. The interval thickness (corresponding to the cylinder height used in the calculations), 

weighted average porosity, and porosity range for each scenario are listed in Table A-3. 

Table A-3. Scenarios used for cylindrical brine intrusion models.

Scenario Thickness (ft) Thickness 

(m)

Weighted Average 

Porosity (%)

Porosity 

Range (%)

Higher-porosity zones in 

Leadville only

164 50 5.5 2.8 – 11.0

Entire Leadville 416 127 2.5 1.2 – 4.9

Higher-porosity zones in all 

formations only

294 90 5.6 2.8 – 11.3

Entire Leadville plus higherporosity zones in other 

formations

546 167 3.3 1.6 – 6.5

All sub-salt formations 1913 583 1.3 0.6 – 2.6
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A-3

Using the thicknesses (cylinder heights) and porosity ranges listed in Table A-3, we compute 

corresponding radii of cylinders containing the cumulative volume of brine injected through 

October, 2014 (2.12 x 109 gal, or 8.02 x 106 m3

). The results for the 5 scenarios are shown in

Figure A-1. The estimated extent of brine intrusion ranges from about 0.4 to 1.3 km from the 

injection well.

1) The results shown in Figure A-1 were computed using several simple assumptions, including 

the assumptions that all the formation porosity is accessible to the injected brine (effective 

porosity = total porosity) and that the injected brine completely displaces the in-situ fluid. If 

some of the pore space is inaccessible due to limited permeability or the injected brine mixes 

with the in-situ fluid, then the porosity available to the injected brine could be considerably 

lower than the formation porosities used in the above calculations. To evaluate how this 

could affect the results, we re-compute radii assuming that 50% of the formation pore space 

is available to the injected brine (Figure A-2). In this case, radii range from 0.6 to 1.9 km. If 

only 10% of the pore space is accessible, then the radii range from ~1.3 to 4.3 km (Figure 

A-3).

Figure A-1. Computed radii for five cylindrical models of the injected brine, assuming 100% 

of the formation pore space is accessible.
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Figure A-2. Computed radii for five cylindrical models of the injected brine, assuming 50% 

of the formation pore space is accessible.

Figure A-3. Computed radii for five cylindrical models of the injected brine, assuming 10% 

of the formation pore space is accessible.
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A-5

We further evaluate the dependence of the computed radii on the fraction of pore space 

accessible to the injected brine in Figure A-4. In this plot, we show computed radii as a function 

of the fraction of pore space occupied by the brine. For these calculations, the weighted average 

porosities of the corresponding lithologies are used for each scenario (from Table A-3). The 

results indicate that, if at least 25% of the formation pore space is accessible to the injected brine, 

then the computed extent of brine intrusion is ≤ 2 km. If 10% of the pore space is accessible, 

then the computed radii range from roughly 2 to 3 km. If only 5% of the pore space is accessible, 

then the radii range from approximately 2.5 to 4.5 km. As the fraction of available pore space 

decreases below 0.05, the computed radii greatly increase as the curves become asymptotic.

Figure A-4. Computed radii for five cylindrical models of the injected brine as a function of the 

fraction of pore space that is occupied by the brine. The weighted average formation porosities shown 

in Table A-3 are used for these calculations. 
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A-6

The rate at which the radius of injected brine grows over time is investigated in the plot 

presented in Figure A-5. This example shows the scenario in which the injected brine is confined 

to the higher-porosity zones in all formations. This corresponds to a cylinder with a height of 90 

m and porosity of 5.6%. In Figure A-5, the radius of the cylinder containing the brine is shown 

as a function of time, assuming four values for the percent of the porosity that is occupied by the 

injected brine: 100%, 30%, 10%, and 5%. As can be seen, the rate of brine intrusion predicted by 

these simple models is inversely proportional to the percent of pore space occupied by the brine. 

For the lowest assumed pore space fraction occupied by the brine (5%), the highest rate of 

growth occurs. In addition, all models show that the rate of brine intrusion has been lower since 

2000 than before; this is due to the lower flow rates that have been used since 2000.

The assumption used in the above analysis that the fraction of pore space occupied by the 

injected brine is constant over time is likely not correct. Since PVU typically injects well above 

the fracture propagation pressure, fractures likely grow over time, increasing permeability and 

providing access to additional pore space. In addition, as the reservoir formations are intruded by 

the injected brine, the rock matrix will cool. This thermal effect should cause the rock matrix to 

shrink, further opening fractures and increasing porosity. We can model potential effects of 

increasing porosity and/or permeability over time by increasing the fraction of pore space 

occupied by the injected brine over time. For example, in Figure A-6 we show the computed 

radius as a function of time for the same model as in Figure A-5, except that the percent of pore 

space occupied by the injected brine is 5% during the injection tests and then linearly increases 

Figure A-5. Computed radii over time for the scenario in which the injected brine is confined to the 

higher-porosity zones in all formations (cylinder height = 90 m; formation porosity = 5.6%). Curves 

are shown for four assumed values of the percent of pore space occupied by the injected brine.
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during long-term injection from 5% (in July,1996) to 15% (in October, 2014). As can be seen, 

increasing the amount of pore space occupied by the injected brine over time by a modest 

amount can greatly slow the geographical expansion of the brine. 

Figure A-6. Computed radius over time for the scenario in which the injected brine is confined to the 

higher-porosity zones in all formations (cylinder height = 90 m; formation porosity = 5.6%). The 

percent of pore space occupied by the injected brine is 5% during the injection tests and then linearly 

increases during long-term injection from 5% (in July, 1996) to 15% (in October, 2014). 

Technical Memorandum TM-85-833000-2014-42

B-1

Appendix B Electronic Supplement of 

Pressure and Flow Rate Data

Daily average pressure and flow rate data are included in an electronic attachment to this 

Technical Memorandum. The data encompass the injection test period and continuous injection 

Phases I-IV, from July 10, 1991, to April 16, 2013. While the injection test data are not analyzed, 

their inclusion is necessary to replicate the results of the analyses, as the pressure response of the 

reservoir is dependent on the complete flow rate history. 

The injection test data have several gaps, extending up to several months. There are periods 

where the injection rates and pressures appear to be inconsistent with one another, for example 

increasing pressures during periods of 0 flow rate. These discrepancies appear to indicate poor 

data quality. We have not attempted to correct these errors; they are presented “as-is.”

The data completeness is significantly better during the period of continuous injection, which 

began in 1996. However, there was a gap in the pressure data from June 6, 2001 to June 18, 

2001, which was filled in using interpolation. Additionally, the pressures on the following four 

days, from June 19 to June 22, 2001, were inconsistent with the shape of the fall-off curves from 

other cycles. Thus, it seems likely that these values are in error, and they were filled in using 

interpolation as well.

The pressures in the attachment are surface pressures. Downhole pressures can be calculated 

using the fluid density, which varies over time, as shown in Table B-1.

Table B-1. Fluid density.

Start Date End Date Density

(g/cm3)

07/11/1991 8/14/1991 1.000

08/15/1991 11/04/1991 1.058

11/05/1991 06/05/1993 1.115

06/06/1993 10/2/1993 1.000

10/3/1993 1/7/2002 1.122

1/8/2002 4/16/13 1.173

The earthquake catalog data used in this analysis have not been attached to this Technical 

Memorandum but are available as an electronic attachment to Wood et al. (2016).