Rock Mechanics and Rock Engineering

, Volume 52, Issue 12, pp 5025–5045 | Cite as

Determine In-Situ Stress and Characterize Complex Fractures in Naturally Fractured Reservoirs from Diagnostic Fracture Injection Tests

  • HanYi WangEmail author
  • Mukul M. Sharma
Original Paper


Estimation of in-situ stresses has significant applications in earth sciences and subsurface engineering, such as fault zone studies, underground CO2 sequestration, nuclear waste repositories, oil and gas reservoir development, and geothermal energy exploitation. Over the past few decades, Diagnostic Fracture Injection Tests (DFIT), which have also been referred to as Injection-Falloff Tests, Fracture Calibration Tests, and Mini-Frac Tests, have evolved into a commonly used and reliable technique to obtain in-situ stress. Simplifying assumptions used in traditional methods often lead to inaccurate estimation of the in-situ stress, even for a planar fracture geometry. When a DFIT is conducted in naturally fractured reservoirs, the stimulated natural fractures can either alter the effective reservoir permeability within the distance of investigation or interact with the hydraulic fracture to form a complex fracture geometry, this further complicates stress estimation. In this study, we present a new pressure transient model for DFIT analysis in naturally fractured reservoirs. By analyzing synthetic, laboratory and field cases, we found that fracture complexity and permeability evolution can be detected from DFIT data. Most importantly, it is shown that using established methods to pick minimum in-situ stress often lead to over or underestimates, regardless of whether the reservoir is heavily fractured or sparsely fractured. Our proposed “variable compliance method” gives a much more accurate and reliable estimation of in-situ stress in both homogenous and naturally fractured reservoirs. By combining the unique pressure signatures associated with the closure of natural fractures, a lower bound on the horizontal stress anisotropy can be estimated.


Diagnostic fracture injection test (DFIT) Stress determination Hydraulic fracture Natural fracture Stress anisotropy Fracture network Closure stress 

List of Symbols


Half of the total fracture surface area (only account for one of two opposite fracture walls) (\({{\text{m}}^{\text{2}}}\))


Formation total compressibility (1/Pa)


Water compressibility (1/Pa)


Wellbore storage coefficient (m3/Pa)


Carter’s leak-off coefficient, (\({\text{m}}/\sqrt {\text{s}} \))


Fracture-wellbore system storage coefficient (m3/Pa)


Young’s modulus (\({\text{Pa}}\))

\(E^{\prime} \)

Plane strain Young’s modulus (\({\text{Pa}}\))

\(g\left( {\Delta {t_{\text{D}}}} \right)\)

Dimensionless g-function of time

\(G\left( {\Delta {t_{\text{D}}}} \right)\)

Dimensionless G-function of time


Fracture height, L (\({\text{m}}\))


Instant shut-in pressure (\({\text{Pa}}\))


Formation permeability (\({{\text{m}}^{\text{2}}}\))


Pressure (\({\text{Pa}}\))


Fracturing pressure (\({\text{Pa}}\))


Initial reservoir pressure (\({\text{Pa}}\))


Leak-off rate (\({{\text{m}}^3}/{\text{s}}\))


Fracture radius (\({\text{m}}\))


Fracture stiffness, which is the reciprocal of fracture compliance (\({\text{Pa}}/{\text{m}}\))


Fracture-wellbore system stiffness (\({\text{Pa}}/{\text{m}}\))


Generic time (\({\text{s}}\))


Dimensionless time


Pumping time (\({\text{s}}\))

\(\Delta t\)

Total shut-in time (\({\text{s}}\))

\(\Delta {t_{\text{D}}}\)

Dimensionless shut-in time (\({\text{s}}\))


Fracture half-length (\({\text{m}}\))


Fracture volume (\({{\text{m}}^3}\))


Wellbore volume (\({{\text{m}}^3}\))


Contact width (\({\text{m}}\))


Local fracture width (\({\text{m}}\))

\({\mu _{\text{f}}}\)

Fluid viscosity (Pa·s)

\(\nu \)

Poisson’s ratio

\({\sigma _{{\text{ref}}}}\)

Contact reference stress (\({\text{Pa}}\))

\(\phi \)

Formation porosity



The authors would like to thank the committee of American Rock Mechanics Association (ARMA) for inviting us to submit this article to the journal, and the financial support of the Hydraulic Fracturing and Sand Control JIP at The University of Texas of Austin. Also thanks to the editors and reviewers, whose insightful comments and suggestions significantly improved the quality and readability of this article.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Petroleum and Geosystem Engineering DepartmentThe University of Texas at AustinAustinUSA

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