Among many techniques, the following two methods were chosen in the current study for determination the lithology of stratal units:

The neutron-density cross plot

This is considered an important and widely used technique for determining the formation lithology. This method implies plotting neutron porosity (φ_N) versus density (ρ_b) on a standard plot. The neutron log detects amount of hydrogen in formation, which is related to porosity, whereas density log enables measuring bulk density [7]. When neutron and density logs are combined, lithology can be revealed [8]. The neutron–density cross plot manifests three lithology lines pertinent to three rock types; sandstone, limestone, and dolomite. These lines are marked with porosity values, the log values for a specific depth are plotted on the cross plot to create a point. The location of each point, with respect to the lithology lines, is an indication of lithology and porosity of that point. When a point falls between two lines, this can be attributed to a mixture of the lithologies of these two lines [9].

The neutron–density cross plot of Butmah Formation (Figure 2, Figure 3) exposed dolomite, limestone with anhydrite and shale in the two wells; the porosity ranges from (0% - 15%) in wells AT-1 and SH-1B.

Cross Plot for Mineral Identification

The M-N cross plot is widely used technique that deals with formations of complex lithologies. This technique involves sonic log along with neutron and density logs. These logs are employed to calculate the lithology-dependent variables (M and N) that are independent of matrix porosity [7]. The M and N values are calculated by the following equations of [10]:

M = Δ t f − Δ t ρ b − ρ f ∗ 0.01 (1)

N = φ N f − φ N ρ b − ρ f (2)

where:

Δt_f: Interval Transit Time in the formation fluid, (189 for fresh mud and 185 for salt mud).

Δt: Interval Transit Time in the formation (from the log).

ρ_f: Density of fluid (1.0 for fresh mud and 1.1 for salt mud).

ρ_b: Bulk Density of formation (from log).

φ_N: Neutron Porosity of formation from Neutron Porosity Log.

φ_Nf: Neutron Porosity of fluid of formation (use 1.0).

M-N cross plot can determine lithology of formation, and is a good indicator of secondary porosity. It is obvious that the lithologic description is matched in both, density-neutron and M-N cross plot methods. Secondary porosity, noticed in Butmah Formation, is enhanced due to tectonic processes that creating local fractures. Figure 4 and Figure 5 represent M-N cross plot in the studied wells.

The determination of shale volume (V_sh) would follow several steps. First step is to calculate the Gamma Ray Index (GRI) from the GR log using a formula of Schlumberger (1974), as below:

GRI = GR log − GR min GR max − GR min (3)

Once GRI is calculated, it would be used in the equation of [11] to determine shale volume in older rocks [12]:

V s h = 0.33 ( 2 2 ∗ GRI − 1 ) (4)

The (V_sh) was calculated for Butmah formation, the results, shown in Figure 6, Figure 7, were dominantly < 10. To distinguish between zones of different shale content within the Butmah Formation, the standard range introduced by [13] has been used (Table 2). Consequently, Butmah Formation was found to be a clean formation in both wells.

Porosity is defined as the percentage of voids to the total volume of rock. The amount of internal voids or pores is an indicator to the amount of fluids a rock can hold [7].

Connected porosity, where pore spaces are linked, is often called effective porosity, whereas, non-effective porosity refers to isolated pores. The sum of effective

and non-effective porosity represents total porosity, which refers to all void space in a rock.

Total Porosity is determined from readings of combined neutron-density logs. This calculation can be implemented by an equation introduced by [12]:

φ t = φ N + φ D 2 (5)

where:

φ_t: Total Porosity.

φ_N: Porosity calculated from Neutron Log.

φ_D: Porosity calculated from Density Log.

Whereas effective porosity (φ_e) is calculated from the equation below:

φ e = φ t ∗ ( 1 − V s h ) (6)

where:

φ_e: Effective Porosity.

φ_t: Total Porosity.

V_sh: Shale Volume.

Secondary porosity (φ_s) is post-depositional porosity; it is commonly calculated through Secondary Porosity Index (SPI) as given by the formula:

SPI = φ t − φ s (7)

where:

SPI: Secondary Porosity Index.

φ_t: Total Porosity.

φ_s: Sonic Porosity

Figure 8 and Figure 9 display the calculated porosity types and their variation with depth in the studied wells. The total porosity of the formation is calculated using Interactive Petrophysics Program (V3.5) from neutron and density logs and have the average total porosity (8%) in well AT-1 and (7%) in well SH-1B.

The difference between the total porosity calculated from these logs and that estimated from sonic log, will give a secondary porosity index, which can be later used to calculate the effective porosity. It is obvious that porosity is varied along the wells; effective porosity decreases in lower part of Butmah Formation in well AT-1 due to shale increase (Figure 8, Figure 9).

Fluid saturation is determined from resistivity log by the Archie’s equation. The Archie’s Equation [14] is used to calculate water saturation (S_w) of uninvaded zone of a reservoir by the formula:

S w = ( a φ m ∗ R w R t ) 1 n (8)

where,

S_w: Water Saturation of the Uninvaded Zone.

R_w: Resistivity of Formation Water at formation temperature (ohm-m).

R_t: True Formation Resistivity (ohm-m).

φ: Porosity.

a: Tortuosity Factor = 1.0.

m: Cementation Exponent, ranging from 1.7 to 3.0, normally equal to 2.0.

n: Saturation Exponent, ranging from 1.8 to 4.0, normally equal to 2.0.

The Archie’s Equation can be used to calculate water saturation in flushed zone (S_xo), simply via replacing Formation Water Resistivity (R_w) with Mud Filtrate Resistivity (R_mf), and Uninvaded Zone Resistivity (R_t) with Flushed Zone Resistivity (R_xo). Calculation of (S_xo) is given by the equation:

S x o = ( a φ m ∗ R m f R x o ) 1 n (9)

Then, hydrocarbon saturation (S_h) would be calculated employing water saturation data via the equation:

S h = 1 − S w (10)

In the flushed zone, the water saturation can be used to determine the residual

oil saturation (S_or) and the movable oil saturation (S_hr) through the formula below [7]:

S o r = φ e ∗ ( 1 − S x o ) (11)

S h r = φ e ∗ ( S x o − S w ) (12)

The Butmah Formation, in well AT-1, is saturated with 37.2% water and 62.8 % with oil (residual and movable), while the average value of (S_w) in well SH-1B was 48.2%, leaving 51.8% for oil. The results of fluid saturation, for the two studied wells, are shown in Figure 10, Figure 11.

This factor represents water saturation (S_w) plus porosity (φ) of formation [8].

The BVW is calculated in the flushed and uninvaded zones by multiplying porosity by water saturation [15]:

The BVW in the Uninvaded and Flushed Zones are calculated using Equation (13) and Equation (14), respectively:

BVW = φ e ∗ S w (13)

BVW s x o = φ e ∗ S x o (14)

Figure 10 and Figure 11 describe the relationship of the variables (S_w, S_xo, S_or, S_hr, BVW, and BVW_sxo) with depth in the studied wells. Figure 10 and Figure 11 represent Computer Processed Interpretation (CPI), they show observed hydrocarbons in upper part of Butmah Formation in wells AT-1 and SH-1B. Whereas the overlying Adaiyah Formation may create a proper seal for reservoir units in Butmah due to existence of anhydrite beds at the lower part of Adaiyah Formation [6]. Movable hydrocarbon is noticed in both wells, and appears equal to the residual hydrocarbon. In some places, movable is less than residual hydrocarbons which indicate low to medium values of permeability in Butmah Formation in these wells.