Production EngineeringHydraulic Fracturing

Mass Transfer in Acid Solutions by Fick's Law - Acidizing Formula

U_{a,y}=-D_A\frac{dc_a}{dY}

Mass Transfer in Acid Solutions by Fick's Law - Acidizing calculates diffusion flux of component a in y direction for hydraulic fracturing workflows in production engineering.

Calculate

How engineers use this formula

Use this formula when the listed inputs (D_A, dc_a_dY) 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, U_ay equals 0 mol/cm2/s.

D_Acm2/s

0.00001

dc_a_dYmol/cm4

-0.001

Inputs

D_A

cm2/s

Diffusion Coefficient of Component A

dc_a_dY

mol/cm4

Concentration Gradient in Y Direction

Outputs

U_ay

mol/cm2/s

Diffusion Flux of Component A in Y Direction

D_A

cm2/s

Diffusion Coefficient of Component A

dc_a_dY

mol/cm4

Concentration Gradient in Y Direction

Source and review

reviewed

Acidizing Fundamentals, Williams, B.B., Gidley, J.L., Schechter, R.S. (1979)

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 21.

Source