In this topic, we will apply the effective mud density formula to determine maximum ROP before fracturing formation.

**Figure 1** – Max ROP before Fracturing Formation

These two equations that will be used to determine the maximum ROP are listed below;

Effective mud density due to cuttings in the hole can be determined by the empirical equation below;

**Where;**

ρ_{eff }is effective mud density in ppg.

ρ_{m }is mud density in ppg.

Q is flow rate in gpm.

ROP is rate of penetration in fph.

d_{b }is wellbore diameter or bit diameter in inch.

**Equivalent Circulating Density (ECD) consists of three components given by the equation below;**

Equivalent Circulating Density (ECD) = ρ_{m + }ρ_{c +} ρ_{a }— Equation 2

**Where;**

ρ_{m }is mud density in ppg.

ρ_{c }is cutting density in ppg.

ρ_{a }is annular pressure loss in ppg.

**How To Apply These Two Concepts**

Formation will be fractured if the ECD while drilling is more than fracture gradient. Additionally, besides mud weight (ρ_{m}), cutting density and annular pressure loss due to hydraulic contributes to ECD.

The ECD can be described in term of effective density and annular pressure as listed below;

Equivalent Circulating Density (ECD) = ρ_{m + }ρ_{c +} ρ_{a }— Equation 2

ρ_{eff = }ρ_{m + }ρ_{c }— Equation 3

Equivalent Circulating Density (ECD) = ρ_{eff }+ ρ_{a }— Equation 4

Equivalent Circulating Density (ECD) = Fracture Gradient (FG) — Equation 5

With those relationships above, we can derive the maximum ROP into the following formulas.

**Example – **Determine the maximum ROP for this well.

**Figure 2** – Well Information

Leak off test at shoe is 12.5 ppg.

The well was drilled to 9,500’MD/9,500’TVD

Mud weight is 10.5 ppg.

Annular pressure loss is 600 psi.

Flow rate is 800 gpm.

Hole size is 12.25”.

**Solution**

ECD should not exceed the leak off test value; therefore ECD is equal to 12.5 ppg.

Annular pressure loss (ρ_{a}) = 600 ÷ (0.052 x 9,500) = 1.21 ppg

Max ROP = 647.2 fph

**Reference book =>** Formulas and Calculations for Drilling Operations