Mathematical models describing the effect of overburden pressure on porosity and permeability of reservoir rocks of Upper shale member for South Rumelia and upper sandston (3 rd pay) member for Zubair oil field

Abstract

The current study is giving a new, more realistic mathematical description of the effect of stress on the amount of porosity and permeability.  In addition to that it can be used to find mathematical formulas for other petrophysical characteristics, and to find mathematical relationships between new variables such as porosity and permeability in terms of depth or between porosity and permeability itself.

The measurement of the porosity and permeability property of reservoir rocks (Core) is important in terms of reservoir studies, as they enter into petrophysical calculations such as water and oil saturation as well as calculating the amount of hydrocarbon reserves and thus give a clear picture of the productivity of the reservoir oil. One of the most important factors that affect the amount of porosity and permeability is the so-called over burden  pressure, where the reservoir rocks are under the influence of great pressure resulting from the weight of the ground layers, so when core samples are extracted from the reservoir they will expand as a result of the disappearance of the layer pressure on them, which leads to a change in the amount of porosity and permeability, Thus, laboratory results will be different from the real porosity and permeability of the reservoir, which leads to errors in reservoir calculations.

The simple non-linear regression method was used to formulate several models belonging to four families of mathematical functions (exponential function, forces function, logarithm function and polynomial function), which describe the relationship between stratified pressure and both porosity and permeability

The stable state equation (SSE) was chosen as an optimal mathematical model describing the relationship between over burden pressure and both porosity and permeability. The model's performance was evaluated using the determination coefficient (R2), as the results were highly accurate and reliable.

The study concluded that the mathematical model can be applied as a good tool in estimating the effect of over burden pressure on the petrophysical properties of sandstones rocks.