Characterizing Mechanical and Flow 

Properties using Injection Falloff Tests

Presented by 

Dave Cramer / March 28, 2011

EPA Hydraulic Fracturing Technical Workshop #3

Fate and Transport
2

Agenda

• Review the basics of fracture injection / fall-off tests.

• Describe fracture closure analysis for determining in-situ 

stress and non-ideal fracture closure mechanisms.

• Describe after-closure analysis for determining reservoir 

flow behavior, reservoir flow capacity (kh/u) and initial 

reservoir pressure (pi). 

• Discuss integration of this information for enhanced 

control of hydraulic fracturing.
3

Injection Fall-off Diagnostics

The process starts with the creation of a small hydraulic fracture,

typically requiring less than 5 barrels for a shale gas interval.
4

Hydraulic Fractures Open Normal to the 

Least Principal Stress

This stress regime is typical for deeply buried reservoir rock.

S1

S3

S2
Parameters driving hydraulic fracture pressure response at the wellbore (from Nolte) 5

Drivers of Bottomhole Pressure Behavior

Initially, rock mechanical properties and in-situ stress influence 

the pressure fall-off response. Later, pressure fall-off behavior is 

dominated by reservoir flow properties and pore fluid pressure. 

From Nolte
6

Fracture Closure

initial late time

Asperities on opposing fracture faces touch in the initial stages of fracture

closure. The adjacent void space imparts residual fracture conductivity.

Proportional to normalized fracture width

MWX Test Site Project
7

Flow Regimes in Hydraulically Fractured 

Wells with Residual Fracture Conductivity

Achieved in the afterclosure period.

Radial flow solutions 

can be used to derive 

far-field kh/u.

During the pseudo-radial flow period, the area of 

investigation is well beyond the region of the fracture. 

From Cinco-Ley
8

Assumed Case for Modeling Purposes: FractureEnhanced Wellbore in Cylindrical Reservoir

Hydraulic Diffusivity

=k / ø μ cT

=fluid mobility / fluid storativity

Hydraulic diffusivity determines the speed that pressure changes induced by 

production or injection are transmitted through the reservoir. 

0.01

0.1

1

10

100

0.001 0.01 0.1 1 10 100 1000 10000

tD = 0.000264 k t / ø μ c xF

2

pD = (kh / 1424qT) (m(p)i - m(p)WF)

Xe/Xf=10 Xe/Xf=infinity Xe/Xf=1 Xe/Xf=1.5 Xe/Xf=2 Xe/Xf=3 Xe/Xf=5 Xe/Xf=7 Xe/Xf=15

unit slope

half slope

Well centered in square reservoir

1 1.5 2 3 5 7 10 15

8

xE/xF =

SPE 4051

Approximate start of semi-log straight line

(pseudoradial flow period) k / ø μ cT 1/xF

2

p

Q (rate)

Fractured-Well Type Curve

tD = 0.000264kt/φμcTxF

2

Start of pseudo-radial flow tD>1
9

Pressure Memory Gauge

To facilitate doing long-duration tests, memory gauges are used to monitor 

and record the pressure fall-off downhole or more commonly at the wellhead.
10

4300

4740

5180

5620

6060

6500

1080 1100 1120 1140 1160 1180 1200

Elapsed Test Time (min) Calc. Bottomhole Pressure (psi) .

31

471

911

1351

1791

2231 Wellhead Pressure (psi) .

perforating event

wireline and perforating gun 

removed from the well 

ready to start 

DFIT

pressure loss: 9 psi in ~33 minutes

increase pressure in the

wellbore prior to perforating

Pre-job estimate of 

reservoir pore pressure

Overbalanced Perforating

Maintaining the wellbore pressure above reservoir pressure prevents gas influx 

into the wellbore and enables closed-chamber analysis under certain conditions.
11

Propagating a Hydraulic Fracture

Compressing the wellbore fluid

Injection rate (bbl/d)

Calc. Bottomhole 

Pressure (psi)

1 bbl/min injection rate;

1 bbl of fluid injected 

following fracture initiation.

Fracture initiation event

Stop injection. 

Start shut-in period

Injection time and volume are kept short to minimize fracture 

dimensions and satisfy the conditions of an impulse event.
12

Lebien 1 Silurian DFIT

Fracture Penetration (m)

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

1.07 min

2915

m

TVD

2920

2925

2930

2935

Stress (psi)

6475 7025 Silty Silty Silty Silty Silty

0.000

0.008

0.016

0.024

0.032

0.040

0.048

0.056

0.064

0.072

0.080 Width - Total in

Modeled Fracture Geometry

Even with a small injection, reservoir investigation is significant.
13

Pressure Fall-off History

Hydrostatic pressure is added to the observed wellhead 

pressure value to compute bottomhole pressure. 

14+ days of data

Hydrostatic pressure is added to the observed wellhead 

pressure value to compute bottomhole pressure. 
14

Diagnostic Log-Log Plot of Pressure Fall-Off

Derivative plot is used for identification of fracture closure behavior 

and after-closure reservoir flow regimes.
15

Log-Log Graph Characteristic Slopes

Primary derivative (dp/dt or dΨ From Barree (SPE 107877) /ta)

Semi-log derivative (t dp/dt or ta dΨ/ta)

Impulse derivative (t2 dp/dt or ta

2 dΨ/ta

)

Diagnostic slopes depend on the derivative type used.
16

G Function Plots for Fracture Closure 

Identification

The semilog derivative is the primary plot for identifying fracture closure.
17

G-Time Functions for Analyzing a Closing 

Fracture

ΔtD = (t – tp) / tp

g(ΔtD) = 4/3 ((1+Δtp)

1.5 - Δ tp1.5)

G(ΔtD) = 4/π (g(Δtp) - g0

where,

t = total test time (pumping and shut-in)

tp = pumping time

G(ΔtD) = G-Function time in previous slide

G(ΔtD)C = G-Function time at fracture closure

η = fluid efficiency (i.e., fluid remaining in 

fracture total fluid injection, at shut-in)

η = [G(ΔtD)C] [2 + G(ΔtD)C]

The G-Time Function linearizes the pressure response 

of a closing fracture under ideal conditions.
18

Square Root of Time Plots for Fracture 

Closure Identification

The 1st derivative plot is a secondary method for confirming fracture closure. 
19

P P r r 1

h v v h t

Where,

σv = overburden stress, psi = 10,752 psi (1.12 psi/ft; bulk density log)

ν = Poisson’s ratio = 0.23 (from dipole sonic log computation)

αv = vertical Biot’s parameter = 1.0

αh = horizontal Biot’s parameter = 1.0

Pr = reservoir pore pressure, 4693 psi (0.49 psi/ft; DFIT)

σt = external (tectonic) stress, psi = 0 psi (assumed)

σh = minimum horizontal stress, psi = 6503 psi (predicted from above)

σh = minimum horizontal stress, psi = 7269 psi (observed from DFIT)

Poroelastic Equation for Estimating In-Situ 

Horizontal Stress

The fracture closure method for deriving minimum in-situ stress can be

used to evaluate and adjust the values derived from predictive equations.
20

After-Closure Flow Regime Type Curve

Pseudo-radial flow is indicated by 1.) the -1 slope trend in both ΔP & semilog 

derivative plots and 2.) equivalency of ΔP and semilog derivative values . 

Pseudo-radial flow period
21

After-Closure Flow Regimes Plot Time Function

linear flow time function = 

FL

2

linear flow time function

FL

2 =

where,

t = total test time (including injection time)

tc = time to fracture closure (including injection time)

Note: In gas reservoirs, the pseudo-time function (ta) is 

used to adjust time. 

It’s the linear flow time function squared, 

which is a function of total test time and fracture closure time.
22

After-Closure Radial Flow Plot 

24 70.6 i

R

kh V

M

The solution derived with the Radial Flow specialty plot

shows good agreement with the Type Curve plot.

MR=63,300 psi

kh/u = 24x70.6 [1.06 (63,300)]

=0.028 md-ft/cp; kh=0.000732 md-ft:

k=0.000045 md or 45 nanodarcies

μ=0.0258 cp

Vi: bbls

k: md

MR: psi/cycle

h: ft

μ: cp

a

1

t or t , hr

FR

t = injection time + shut-in time
23

ACA Regimes Plot-MCM Shale,Int3,Cyc4 dP/dP' 0.20 0.50 1.0 2.0 5.0 dP = (P-Pi) and dP' 100 200 500 1000

1/F-L^2

1.0 2.0 5.0 10 20

dP

dP/dP'

dP'

290.0

Less Smoothing More Smoothing

PRes

(psi)

Cycle 5

After-Closure Flow Regime Plot: Linear Flow

Ratio plot

ΔP

dΔP

Pseudo-linear flow indicator: when pressure change and 

derivative both lie on the half-slope trend line & pressure 

change is 2x the value of the derivative. This test meets the 

criteria for pseudolinear flow. Reservoir pressure can be 

inferred from this analysis.

half slope

trend lines

Radial flow signature 

is absent

Nolte method

2x

Certain types of naturally fractured reservoirs exhibit long-term linear flow.

2

1

FL

2

1

FL
24

Summary

 Injection Fall-off Testing is an efficient way to derive in-situ information on 

most rock types. 

• A modest-size hydraulic fracture is created and pressure fall-off during shut in period is 

analyzed for fracture closure and after-closure radial flow period.

• Injection rate and volume are tailored for interval thickness and leak-off characteristics. 

 Identification of fracture closure provides information on rock stress.

• A combination of derivative-based diagnostic plots are used. 

• Non-ideal fracture propagation (e.g., fracture height growth, fissure opening, multiple fracture 

closures) can be identified and evaluated.

 After-closure analysis is used to derive rock transmissibility (kh/u) and pore 

fluid pressure. 

• Radial flow is identified and evaluated by type curves and specialty plots.

• Computations are based on well testing theory.

 The resulting information is employed to assist in controlling the hydraulic 

fracturing process.

• The information is used in hydraulic fracture modeling to predict fracture geometry, proppant 

placement, fracture conductivity, etc.

• Treatment design is modified as necessary to achieve treatment objectives.