Question

# 5. Estimate numerically the change in carbonate-rock porosity caused by a complete dolomitization of calcite, accounting...

5. Estimate numerically the change in carbonate-rock porosity caused by a complete dolomitization
of calcite, accounting to the chemical reaction, 2CaCO3+Mg2+ =CaMg(CO3)2+Ca2+, will yield a carbonate rock’s porosity of 13% .

Porosity in any material is the voidage or fraction of empty space (void) in the material

Let V denote volume

For this case of carbonate rock before dolomization

V[rock]= V[calcite] + V[void]

After dolomization

V[rock] = V[calcite] + V[dolomite] + V[void]

Since the process is complete dolomization V[calcite] is 0 here

Given after dolomization:

V[void]/V[rock] = 0.13

So V[dolomite] = 1 - V[void]/V[rock] =1- 0.13 = 0.87

V[dolomite]=0.87*V[rock]

It is evident from reaction stiochiometry that 2 moles of calcite form 1 mole of dolomite.

Assuming no difference in the molar density of dolomite and calcite

V[calcite] = 0.5*V[dolomite] = 0.5^0.87*V[rock] = 0.435*V[rock]

Thus, the initial porosity of rock

V[void]/V[rock]= 1- V[calcite]/V[rock] = 1- 0.435 = 0.565 = 56.5%

A net decrease of (56.5-13)% = 43.5% change in porosity

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