Petroleum Engineering Equations & Formulas Part -1

Oil density

Oil density at surface conditions is commonly quoted in °API.

       API = 141.5/γo-131.5

       Where: γo is the specific gravity of oil (relative to water = 1, measured at STP).
            

The downhole density of oil (at reservoir conditions) can be calculated from the surface density equation using:

       ρorc * Bo = ρo + Rs * ρg

       Where:

       ρorc : is oil density at reservoir conditions 

       Bo   : is the oil formation volume factor     

       ρo   : is oil density at standard conditions  

       Rs   : is the solution gas : oil ratio 

Fluid Pressure

Assuming a normal pressure regime, at a given depth below ground level, a certain pressure must exist which just balances the overburden pressure (OBP) due to the weight of rock (which forms a matrix) and fluid (which fills the matrix) overlying this point. The overburden pressure is in fact balanced by a combination of the fluid pressure in the pore space (FP) and the sress between the rock grains of the matrix (σg).

Formula:

       OBP = FP + σg

       Where:

       σg: is the stress between the rock grains of the matrix

       FP: is the fluid pressure in the pore space.

Porosity

Reservoir porosity can be measured directly from core samples or indirectly using logs. Logging is the most common method employed. The formation density log is the main tool for ensuring porosity. The tool is constructed so that medium energy gamma rays are directed from a radioactive source into the formation. These rays react with the formation by a process know as Compton scattering. Gamma rays lose energy each time they collide with an electron. The number of gamma rays reaching detectors in the tool is inversely proportional to the number of electrons in the formation which is related to the formation bulk density. A low gamma count implies a high electron (and bulk) density and therefore a low porosity

The bulk density measured by the logging tool is the weighted average of the rock matrix and fluid densities so that:
       ρb = ρflΦ + ρma(1-Φ)

       Where:

       ρb : is the formation bulk density (read from the density log)

       ρma: is the matrix density

       ρfl: is the fluid density

            

Porosity (Φ) is:
       Φ = (ρma - ρb) / (ρma - ρfl)

Hydrocarbon Saturation

       Ct = SwnΦm Cw

       Where:

       Ct: is the conductivity

       Cw: is the pore water conductivity

       Sw: is the water saturation

       n : is the saturation exponent

       m : is the cementation exponent

            

In pratice logging tools are often used to measure the resistivity of the formation rather than the conductivity and therefore the above equation is more commonly inverted and expressed as:
       Rt = Sw-nΦ-mRw

       Where:

       Rt: is the formation resistivity (ohm.m)

       Sw: is the water saturation (fraction)

       Φ : is porosity(fraction)

       Rw: is the water resistivity (ohm.m)

       m : is the cementation exponent

       n : is the saturation exponent
            

In a large ange of reservoirs the saturation and cememntation exponents can be taken as m=n=2. The remaining unknown is the water saturation and the equation can be rearranged so that:
            Sw = n√((Rw)/(ΦmRt))

                and hydrocarbon saturation (fraction)

            Sh= 1 - Sw