PetroCalcHubFree
Browse
90 indexed pages

Geomechanics and Fracturing Equations

Browse 90 geomechanics and fracturing petroleum engineering equations with variables, units, source references, and calculator links.

Geomechanics and fracturing calculations support stress, fracture-gradient, rock-mechanics, and naturally fractured reservoir screening.

90
Formulas
Free
No sign-in
Sources
Reviewable
Geomechanics and FracturingNaturally Fractured Reservoirs

Areal Fracture Intensity from Trace Length

P21=LtAsP_{21}=\frac{L_t}{A_s}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Average Fracture Spacing from Linear Intensity

Sf=1P10S_f=\frac{1}{P_{10}}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Lame Constant and Poisson Ratio

K=λ(1+ν)3νK=\frac{\lambda(1+\nu)}{3\nu}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Lame Constant and Shear Modulus

K=λ+2G3K=\lambda+\frac{2G}{3}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Pressure and Volume Strain

K=pΔV/VK=\frac{p}{\Delta V/V}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Shear Modulus and Poisson Ratio

K=2G(1+ν)3(1−2ν)K=\frac{2G(1+\nu)}{3(1-2\nu)}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Young's Modulus and Poisson Ratio

K=E3(1−2ν)K = \frac{E}{3(1 - 2\nu)}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Classic Breakdown Pressure for a Vertical Wellbore

Pb=3Shmin−SHmax−Pp+ToP_b=3S_{hmin}-S_{Hmax}-P_p+T_o
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Compressional and Shear Wave Velocities from Elastic Moduli

Vp=K+4G/3ρV_p=\sqrt{\frac{K+4G/3}{\rho}}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Cubic Matrix Block Interporosity Flow Coefficient

λ=60Lm2rw2kmkf\lambda=\frac{60}{L_m^2}r_w^2\frac{k_m}{k_f}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Drilling-Induced Tensile Fracture Margin

MT=σθθ+TsM_T=\sigma_{\theta\theta}+T_s
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Minimum Horizontal Stress Fracture Pressure

Shmin=ν1−ν(Sv−Pp)+PpS_{hmin}=\frac{\nu}{1-\nu}(S_v-P_p)+P_p
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Pore Pressure Gradient from Corrected D-Exponent

Gpp=Gob−(Gob−Gnp)(dcodcn)1.2G_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{d_{co}}{d_{cn}}\right)^{1.2}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Pore Pressure Gradient from Resistivity Ratio

Gpp=Gob−(Gob−Gnp)(RoRn)1.2G_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{R_o}{R_n}\right)^{1.2}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Pore Pressure Gradient from Sonic Transit Time

Gpp=Gob−(Gob−Gnp)(ΔtnΔto)3G_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{\Delta t_n}{\Delta t_o}\right)^3
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Effect of Pore Pressure on Stress

S=λξoδ+2Gξ−αδPS = \lambda \xi_o \delta + 2G\xi - \alpha\delta P
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Effective Stress on Individual Grains

σg=S−Pp\sigma_g = S - P_p
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Failure Criteria - Mohr-Coulomb Stress Components

τ=0.5(σa−σb)sin⁡(2β)\tau=0.5(\sigma_a-\sigma_b)\sin(2\beta)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Formation Compressibility from Hydrofrac Data

β=1VsdVsdP\beta=\frac{1}{V_s}\frac{dV_s}{dP}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Fracture Gradient - Zoback and Healy

Shmin=(1+μf2+μf)−2(Sv−Pp)+PpS_{hmin} = (\sqrt{1 + \mu_f^2} + \mu_f)^{-2}(S_v - P_p) + P_p
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Fracture Permeability from Hydraulic Aperture Cubic Law

kf=bh212k_f=\frac{b_h^2}{12}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Fracture Porosity from Aperture and Volumetric Intensity

ϕf=bfP32\phi_f=b_fP_{32}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Fracture Pressure - Hubbert and Willis

Shmin=0.3(Sv−Pp)+PpS_{hmin}=0.3(S_v-P_p)+P_p
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Fracture Storativity

ω=ϕfhfctfϕfhfctf+ϕmhmctm\omega = \frac{\phi_f h_f c_{tf}}{\phi_f h_f c_{tf} + \phi_m h_m c_{tm}}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Hoek and Brown Criteria for Principal Stress Failure

σa=σc+Comσc/Co+s\sigma_a=\sigma_c+C_o\sqrt{m\sigma_c/C_o+s}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Horizontal Effective Stress - Lorenz and Teufel

Shor=ν1−νSv+αP(1−ν1−ν)S_{hor}=\frac{\nu}{1-\nu}S_v+\alpha P\left(1-\frac{\nu}{1-\nu}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Horizontal Maximum Stress - Bredehoeft

Shmax=3Shmin−Pb−PpS_{hmax}=3S_{hmin}-P_b-P_p
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Induced Fracture Dip

Dip=tan⁡−1(hd)\mathrm{Dip}=\tan^{-1}\left(\frac{h}{d}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Initial Effective Horizontal Stress

σh=ν1−ν(ρbH144−αPp)\sigma_h=\frac{\nu}{1-\nu}\left(\frac{\rho_bH}{144}-\alpha P_p\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Isothermal Compressibility of Limestones - Newman Correlation

Ct=97.32×10−6(1+55.8721ϕ)1.42869C_t=\frac{97.32\times10^{-6}}{(1+55.8721\phi)^{1.42869}}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Kazemi Rectangular Matrix-Block Shape Factor

α=4(1Lmx2+1Lmy2+1Lmz2)\alpha=4\left(\frac{1}{L_{mx}^2}+\frac{1}{L_{my}^2}+\frac{1}{L_{mz}^2}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Least Principal Stress - Matthews and Kelly

Shmin=Ki(Sv−Pp)+PpS_{hmin}=K_i(S_v-P_p)+P_p
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Lim-Aziz Anisotropic Rectangular Matrix-Block Shape Factor

α=π2kmg(kxLmx2+kyLmy2+kzLmz2)\alpha=\frac{\pi^2}{k_{mg}}\left(\frac{k_x}{L_{mx}^2}+\frac{k_y}{L_{my}^2}+\frac{k_z}{L_{mz}^2}\right)
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Linear Fracture Intensity from Scanline Count

P10=NfLsP_{10}=\frac{N_f}{L_s}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Linearized Mohr Failure Line

τ=So+σnμi\tau=S_o+\sigma_n\mu_i
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Linearized Mohr-Coulomb Criteria

σ1=Co+(μ2+1+μ)2σc\sigma_1=C_o+(\sqrt{\mu^2+1}+\mu)^2\sigma_c
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

M Modulus from Shear and Bulk Modulus

M=K+4G3M=K+\frac{4G}{3}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

M Modulus from Young's Modulus and Poisson Ratio

M=E1−ν(1+ν)(1−2ν)M=E\frac{1-\nu}{(1+\nu)(1-2\nu)}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Matrix Block Shape Factor from Surface Area

α=AVmx\alpha=\frac{A}{V_mx}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Matrix-Block Shape Factor from Dimensionless Constant

α=σDLm2\alpha=\frac{\sigma_D}{L_m^2}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Matthews-Kelly Fracture Gradient from Stress Ratio

Shmin=(σminσv)(Sv−Pp)+PpS_{hmin}=\left(\frac{\sigma_{min}}{\sigma_v}\right)(S_v-P_p)+P_p
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Hoop Stress at the Wellbore Wall

σθ,max=3Shmax−Shmin−2Po−ΔP−Sdt\sigma_{\theta,max}=3S_{hmax}-S_{hmin}-2P_o-\Delta P-S_{dt}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Horizontal Stress from Wellbore Breakout Width

Shmax=Co+2Pp+P+σt−Shmin(1+2cos⁡θb)1−2cos⁡θb,θb=(π−wb)/2S_{hmax}=\frac{C_o+2P_p+P+\sigma_t-S_{hmin}(1+2\cos\theta_b)}{1-2\cos\theta_b},\quad \theta_b=(\pi-w_b)/2
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Principal Stress in Normal Faulting

σmax=σc(Sv−Pp)Shmin−Pp\sigma_{max}=\frac{\sigma_c(S_v-P_p)}{S_{hmin}-P_p}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Principal Stress in Reverse Faulting

σmax=σc(Shmax−Pp)Sv−Pp\sigma_{max}=\frac{\sigma_c(S_{hmax}-P_p)}{S_v-P_p}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Principal Stress in Strike-Slip Faulting

σmax=σc(Shmax−Pp)Shmin−Pp\sigma_{max}=\frac{\sigma_c(S_{hmax}-P_p)}{S_{hmin}-P_p}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Axial Stress at a Vertical Wellbore

σminaxial=3Shmin−Shmax−2Po−P−σt\sigma_{minaxial}=3S_{hmin}-S_{hmax}-2P_o-P-\sigma_t
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Hoop Stress at the Wellbore Wall

σθ,min=3Shmin−Shmax−2Po−ΔP−Sdt\sigma_{\theta,min}=3S_{hmin}-S_{hmax}-2P_o-\Delta P-S_{dt}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Mud Pressure to Avoid Wellbore Breakout

PWshear=Pp+3σHmax−σhmin−UCS1+qP_{Wshear}=P_p+\frac{3\sigma_{Hmax}-\sigma_{hmin}-UCS}{1+q}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Mode I Fracture Stress Intensity

KI=(Pf−Sc)πL0.5K_I=(P_f-S_c)\pi L^{0.5}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Modified Eaton Pore Pressure Gradient from Specific Energy

Gpp=Gob−(Gob−Gnp)(SPEoSPEn)mG_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{SPE_o}{SPE_n}\right)^m
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Modified Lade Failure Criterion

η=(I13I3−27)(I1Pa)m\eta=\left(\frac{I_1^3}{I_3}-27\right)\left(\frac{I_1}{P_a}\right)^m
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Mody-Hale Osmotic Pore-Pressure Increase from Molar Volume

ΔP=Em(RψLTVw)ln⁡(ApAm)\Delta P=E_m\left(\frac{R_{\psi L}T}{V_w}\right)\ln\left(\frac{A_p}{A_m}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Mud Pressure for Target Breakout Width

PWBO=Pp+(σHmax+σhmin)−2(σHmax−σhmin)cos⁡(π−wBO)−UCS1+qP_{WBO}=P_p+\frac{(\sigma_{Hmax}+\sigma_{hmin})-2(\sigma_{Hmax}-\sigma_{hmin})\cos(\pi-w_{BO})-UCS}{1+q}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Hoop Stress at the Wellbore Wall

σθ=Shmax+Shmin−2(Shmax−Shmin)cos⁡(2θ)−2Po−ΔP−Sdt\sigma_\theta=S_{hmax}+S_{hmin}-2(S_{hmax}-S_{hmin})\cos(2\theta)-2P_o-\Delta P-S_{dt}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Radial Stress Near a Wellbore

σrr=12(Shmax+Shmin−2Po)(1−R2r2)+12(Shmax−Shmin)(1−4R2r2+3R4r4)cos⁡(2θ)+PoR2r2\sigma_{rr}=\frac{1}{2}(S_{hmax}+S_{hmin}-2P_o)\left(1-\frac{R^2}{r^2}\right)+\frac{1}{2}(S_{hmax}-S_{hmin})\left(1-4\frac{R^2}{r^2}+3\frac{R^4}{r^4}\right)\cos(2\theta)+P_o\frac{R^2}{r^2}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Tangential Hoop Stress Near a Wellbore

Sgth=12(Shmax+Shmin−2Po)(1+R2r2)−12(Shmax−Shmin)(1+3R4r4)cos⁡(2θ)−PoR2r2−SdtSg_{th}=\frac{1}{2}(S_{hmax}+S_{hmin}-2P_o)\left(1+\frac{R^2}{r^2}\right)-\frac{1}{2}(S_{hmax}-S_{hmin})\left(1+\frac{3R^4}{r^4}\right)\cos(2\theta)-P_o\frac{R^2}{r^2}-S_{dt}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Parallel Fracture Set Permeability from Cubic Law

kset=bh312sfk_{set}=\frac{b_h^3}{12s_f}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pore Pressure Increase Due to Fluid Activity Mody and Hale

δP=Em(RTV)ln⁡(ApAm)\delta P=E_m\left(\frac{RT}{V}\right)\ln\left(\frac{A_p}{A_m}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pore Pressure of Shale Flemings

Pp=Sv−1βcln⁡(ϕoϕ)P_p=S_v-\frac{1}{\beta_c}\ln\left(\frac{\phi_o}{\phi}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pore Pressure of Shale Traugott

Ppsh=z[Svz−(Svz−Phydroz)(RoRn)1.2]P_{psh}=z\left[\frac{S_v}{z}-\left(\frac{S_v}{z}-\frac{P_{hydro}}{z}\right)\left(\frac{R_o}{R_n}\right)^{1.2}\right]
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pressure to Grow Fractures - Abe, Mura et al.

Pgrow=Sc1−(Pp/Sc)1−(cf/ci)21−1−(cf/ci)2P_{grow}=S_c\frac{1-(P_p/S_c)\sqrt{1-(c_f/c_i)^2}}{1-\sqrt{1-(c_f/c_i)^2}}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Radial Stress Around a Vertical Wellbore

σrr=0.5(Shmax+Shmin−2Po)(1−R2/r2)+0.5(Shmax−Shmin)(1+3R4/r4−4R2/r2)cos⁡(2θ)+PoR2/r2\sigma_{rr}=0.5(S_{hmax}+S_{hmin}-2P_o)(1-R^2/r^2)+0.5(S_{hmax}-S_{hmin})(1+3R^4/r^4-4R^2/r^2)\cos(2\theta)+P_oR^2/r^2
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Ratio of Pore Pressure Change to Original Due to Depletion

q=ΔPpShmax−Shminq=\frac{\Delta P_p}{S_{hmax}-S_{hmin}}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Reservoir Stress Path from Biot Coefficient and Poisson Ratio

A=α(1−2ν)1−νA=\frac{\alpha(1-2\nu)}{1-\nu}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Rotation of Maximum Principal Stress Near Wellbore

γ=12tan⁡−1(AΔPpsin⁡2θShmax−Shmin+AΔPpcos⁡2θ)\gamma=\frac{1}{2}\tan^{-1}\left(\frac{A\Delta P_p\sin 2\theta}{S_{hmax}-S_{hmin}+A\Delta P_p\cos 2\theta}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Rotation of Maximum Principal Stress Zoback Day Lewis

γ=12tan⁡−1(Aqsin⁡2Δ1+Aqcos⁡2Δ)\gamma=\frac{1}{2}\tan^{-1}\left(\frac{Aq\sin 2\Delta}{1+Aq\cos 2\Delta}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shale Compaction

ϕe=ϕe−βsσv\phi_e=\phi e^{-\beta_s\sigma_v}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shear Modulus from Force Area and Deformation Angle

G=F/AθG=\frac{F/A}{\theta}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shear Modulus from Young's Modulus and Poisson Ratio

G=E2(1+ν)G = \frac{E}{2(1 + \nu)}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shear Wave Velocity from Shear Modulus and Density

Vs=(Gρ)0.5V_s=\left(\frac{G}{\rho}\right)^{0.5}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Single-Fracture Flow Rate from Cubic Law

Q=Wbh3Δp12μLQ=\frac{Wb_h^3\Delta p}{12\mu L}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Slab Matrix Block Interporosity Flow Coefficient

λ=12hs2rw2kmkf\lambda=\frac{12}{h_s^2}r_w^2\frac{k_m}{k_f}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Spherical Matrix Block Interporosity Flow Coefficient

λ=15rm2rw2kmkf\lambda=\frac{15}{r_m^2}r_w^2\frac{k_m}{k_f}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Components in Original Coordinate System in Depletion Drive

Sx=Shmax−APp−AΔPp2(1−cos⁡2Δ)S_x=S_{hmax}-AP_p-\frac{A\Delta P_p}{2}(1-\cos 2\Delta)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Components Near Normal Faulting in Reservoir

Sx=Shmax−AdP−AdP2(1−cos⁡2θ)S_x=S_{hmax}-AdP-\frac{AdP}{2}(1-\cos 2\theta)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Path for Induced Normal Faulting

A=1−1(μ2+1+μ)2A=1-\frac{1}{(\sqrt{\mu^2+1}+\mu)^2}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Perturbation Segall and Fitzgerald

M=α(1−2ν)πH(1−ν)8RM=\alpha\frac{(1-2\nu)\pi H}{(1-\nu)8R}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Subsidence Due to Uniform Pore Pressure Reduction in Free Surfaces

uz=−cm(1−ν)DΔPpVπ(r2+D2)1.5u_z=-\frac{c_m(1-\nu)D\Delta P_pV}{\pi(r^2+D^2)^{1.5}}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Tangential Stress Extremes at a Deviated Wellbore

σtmax=12(σzz+σaa+(σzz−σaa)2+4τ2)\sigma_{tmax}=\frac{1}{2}\left(\sigma_{zz}+\sigma_{aa}+\sqrt{(\sigma_{zz}-\sigma_{aa})^2+4\tau^2}\right)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Tensile Breakdown Pressure with Thermal Stress

Pb=Pp−σHmax+3σhmin+Ts+σΔTP_b=P_p-\sigma_{Hmax}+3\sigma_{hmin}+T_s+\sigma^{\Delta T}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Thermal Hoop Stress from Wellbore Temperature Change

σΔT=αTE1−νΔT\sigma^{\Delta T}=\frac{\alpha_T E}{1-\nu}\Delta T
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Twisting Stress Around a Vertical Wellbore

τ=12(Shmax−Shmin)(1+2R2r2−3R4r4)sin⁡(2θ)\tau=\frac{1}{2}(S_{hmax}-S_{hmin})\left(1+\frac{2R^2}{r^2}-\frac{3R^4}{r^4}\right)\sin(2\theta)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Unconfined Compressive Strength of Rock

Co=2So(μ2+1+μ)C_o=2S_o(\sqrt{\mu^2+1}+\mu)
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Velocity of Bulk Compressional Waves

Vb=Eρ1−ν(1+ν)(1−2ν)V_b=\sqrt{\frac{E}{\rho}\frac{1-\nu}{(1+\nu)(1-2\nu)}}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Volumetric Fracture Intensity from Fracture Area

P32=AfVrP_{32}=\frac{A_f}{V_r}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Warren-Root Interporosity Flow Coefficient

λ=αrw2kmkf\lambda=\alpha r_w^2\frac{k_m}{k_f}
View formula
Geomechanics and FracturingNaturally Fractured Reservoirs

Warren-Root Shape Factor from Fracture Sets

α=4n(n+2)Lm2\alpha=\frac{4n(n+2)}{L_m^2}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Weak-Plane Anisotropic Failure Stress

σ=2σc(Sw+μσc)[1−μcot⁡(β)]sin⁡(2β)\sigma=\frac{2\sigma_c(S_w+\mu\sigma_c)}{[1-\mu\cot(\beta)]\sin(2\beta)}
View formula
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Wellbore Breakout Width from Mud Pressure

wBO=π−arccos⁡(σHmax+σhmin−UCS−(1+q)(PW−Pp)2(σHmax−σhmin))w_{BO}=\pi-\arccos\left(\frac{\sigma_{Hmax}+\sigma_{hmin}-UCS-(1+q)(P_W-P_p)}{2(\sigma_{Hmax}-\sigma_{hmin})}\right)
View formula