Production EngineeringHydraulic Fracturing

Young Modulus from Sonic Travel Time (Acidizing) Formula

E=2.16\times10^8\frac{[\rho_{ma}(1-\phi)+\rho_{fl}\phi](1-2\nu)(1+\nu)}{(1-\nu)t_s^2}

Young Modulus from Sonic Travel Time (Acidizing) calculates young modulus for hydraulic fracturing workflows in production engineering.

Calculate

How engineers use this formula

Use this formula when the listed inputs (t_s, phi, nu, rho_ma, rho_fl) are known and the assumptions behind the cited hydraulic fracturing relationship match the engineering case being checked.

Assumptions

Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
The declared units match the field-unit constants used in the formula.
The cited formula applies to the selected petroleum engineering workflow.

Limitations

The calculation does not replace a full engineering model or operating procedure.
Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

Mixing unit systems without converting the inputs.
Using default example values as field recommendations.
Applying the formula outside the source assumptions.

Default example

Using the default inputs, E equals 4,063,500 psi.

t_smicrosecond/ft

phifraction

0.2

nudimensionless

0.25

rho_malb/ft3

165

rho_fllb/ft3

62.4

Inputs

t_s

microsecond/ft

Sonic Travel Time

phi

fraction

Porosity

nu

dimensionless

Poisson Ratio

rho_ma

lb/ft3

Formation Matrix Density

rho_fl

lb/ft3

Formation Fluid Density

Outputs

E

psi

Young Modulus

t_s

microsecond/ft

Sonic Travel Time

rho_ma

lb/ft3

Formation Matrix Density

rho_fl

lb/ft3

Formation Fluid Density

Source and review

reviewed

Williams, B.B., Gidley, J.L. and Schechter, R.S. 1979. Acidizing Fundamentals. Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers of AIME, Page 56.

Source