GOHFER’S Total Closure Stress Equation
Pc = closure pressure, kPa
ν = Poisson’s Ratio
Dtv = true vertical depth, m
γob = overburden stress gradient, kPa/m
γp = pore fluid gradient, kPa/m
αv = vertical Biot’s poroelastic constant
αh = horizontal Biot’s poroelastic constant
Poff = pore pressure offset, kPa
εx = regional horizontal strain, microstrains
E = Young’s Modulus, GPa
σt = regional horizontal tectonic stress, kPa
- Closure stress is calculated using GOHFER’S Total Stress equation and must be calibrated to local field conditions with a strain or stress correction factor.
- In tectonically active areas, the closure stress calculated from logs will be too low and will need to be increased.
- εx= regional horizontal strain
- σt = regional horizontal tectonic stress
- generally, the strain offset approach is favoured
- The best way to calibrate closure stress is to review fracturing work, or perform a minifrac.
- If possible, this step should be completed by the completion engineer (the person running the hydraulic frac simulation software).
- The density log should be used to calculate overburden stress.
- Before the density log can be used, a synthetic log is created to remedy abnormally low data caused by bad hole, coal, etc.
- Bad density data intervals are identified by running discriminators.
- caliper and density correction logs are typically used
- The synthetic log is calibrated to intervals containing good quality density data and then integrated from treatment depth to shallowest log reading.
- a bulk density value or density function must also be assigned from surface to shallowest log reading
- Overburden stress is an important input to the closure stress equation and will take some time and effort to calculate accurately
Pore Pressure (Barree & Associates)
- Field measured data should be used to assign pore pressure.
- Pore fluid supports part of the total stress.
- Pore pressure depletion increases net stress and leads to compaction.
- Pore pressure depletion decreases total (fracture closure) stress.
Biot’s Poroelastic Parameter (Barree & Associates)
- Barree defines Biot’s poroelastic constant as the efficiency with which internal pore pressure offsets the externally applied vertical total stress.
- As Biot decreases, net (intergranular) stress increases and pore pressure variations have less impact on net stress.
- Effective porosity from the quantitative analysis is used to calculate vertical Biot’s poroelastic parameter.
- Horizontal Biot’s poroelastic parameter is generally set equal to 1.
Closure stress base case
- no strain offset
- no stress offset
With Regional Tectonism Present
- With tectonism, the closure stress base case will not match field measured data.
- a strain offset will need to be applied
A match is achieved using a strain offset.
- Applying a strain offset can decrease the stress difference between the reservoir and non-reservoir intervals.
- fracture geometry will be affected