Porosity and Permeability Analysis from Well Logs and Core in Fracture, Vugy and Intercrystalline Carbonate Reservoirs

The measurement of porosity is important to the petroleum engineer since the porosity determines the storage capacity of the reservoir for oil and gas. It is necessary to distinguish between the absolute porosity of a porous medium and its effective porosity. In porous rocks there will always be a number of blind or unconnected pores. Absolute porosity includes these pores as well as those open to the flow of fluids whereas the effective porosity measures only that part of the pore space that is available to fluid flow. There are several ways to measure the porosity:


Introduction
Reservoir is a body of rock that has pores to contain oil and gas, and sufficient permeability to allow fluid migration. In order to have a hydrocarbon-producing reservoir, the following conditions must exist: 1. There must be a body of rock having sufficient porosity (Φ) to contain the reservoir fluids and permeability (k) to permit their movement.
2. The rocks must contain hydrocarbons in commercial quantities.
3. There must be some natural driving force within the reservoir, usually gas or water, to allow the fluids to move to the surface.
Porosity is the ratio of the pore volume to the bulk volume of the reservoir rock on percentage basis. That is Bulk volume=the total volume of the rock Pore volume=the volume of the pores between the grains The measurement of porosity is important to the petroleum engineer since the porosity determines the storage capacity of the reservoir for oil and gas. It is necessary to distinguish between the absolute porosity of a porous medium and its effective porosity. In porous rocks there will always be a number of blind or unconnected pores. Absolute porosity includes these pores as well as those open to the flow of fluids whereas the effective porosity measures only that part of the pore space that is available to fluid flow. There are several ways to measure the porosity: 1. Laboratory measurement of porosity Bulk volume is first determined by displacement of liquid, or by accurately measuring a shaped sample and computing its volume. Then any of the following methods are used to measure either the pore volume or grain volume. Summation of Pore Fluids involves independent determination of gas, oil and pore water volumes from a fresh core sample ( Figure 1).
The pore volume is determined by adding up the three independent volumes. Washburn-Bunting method measures pore volume by vacuum extraction and collection of the gas (usually air) contained in the pores. Liquid Re saturation pores of a prepared sample are filled with a liquid of known density and the weight increase of the sample is divided by the liquid density. Boyle's Law Method involves the compression of a gas into the pores or the expansion of gas from the pores of a prepared sample. Either pore volume or grain volume may be determined depending upon the porosimeter and procedure used. Grain Density measures total porosity. After the dry weight and bulk volume of the sample are determined, the sample is reduced to grain size and the grain volume is determined and subtracted from the bulk volume.

Geological Setting
KF2 Field is one of several elongated, asymmetrical, doubly plunging anticlines that characterize the Foothills region of the Unstable Shelf Zone in eastern Iraq. The northwest-southeast trending structure measures 34 km long and 3.8 km wide. Two individual domes separated by a shallow saddle make up the KF2 structure. Kithke Dome is the larger and more prolific of the two domes. It has a significant surface expression. Daoud Dome does not have a surface expression, is smaller, and less prolific [3]. The Shahl Saddle physically separates the two domes. KF2 field occupies a stratigraphically complex area comprising multiple facies developments of a complicated diagenetic history. Abundant and variable porosity and permeability exist which, although primarily lithology dependent, are enormously enhanced by the development of intensive faults, fractures and joints, this combination of uncommonly high porosity and permeability gives rise to enormously high and continuous production. The maximum reservoir thickness generally taken as approximately 225 m comprising five main facies types:

Tidal dolostone facies
It is characterized by the occurrence of stromatolitic dolostone microfacies, which occur as thin layers punctuating the lagoonal facies and developed as marginal tidal-flat complexes of the lagoonal environment. Relics of fenestral fabric are characteristic but commonly obliterated by intensive dolomitization.

Lagoonal facies
This facies is commonly found in the western part of Kirkuk area and characterized by dolomitic limestone and dolostone of peloidal-done by point counting of pores under a microscope. Impregnation of the sample in a vacuum with dyed resin facilitates pore identification.
3. A common source of porosity data are the well logs. Porosity may be calculated from the sonic, density, and neutron logs. These three logs are usually referred to as porosity logs.
4. Porosity may also be obtained from the resistivity logs.
Carbonate porosity includes three end -member genetic categories; purely depositional pores, purely diagenetic pores, and purely fracture pores. Intermediate types exist, of course, but the point is that there are three main types of carbonate porosity that represent distinctly different geological processes. Carbonates, porosities and permeabilities are dependent on the nature of the rock developed during deposition and the diagenetic/solution processes.
Main properties of reservoir study are porosity and permeability. Porosity is the ratio of voids in a rock to the total volume of rock and reflects the fluid storage capacity of a rock thereby making it a reservoir. The porosity or percentage pore volume of reservoir rocks can be measured from well cuttings, core samples from drilling or wireline well logs. Typical generally admissible porosity values for an oil reservoir range from between 10% and 25%, with porosity values of above 25% desirable [1]. Permeability on the other hand explains how connected reservoir pores, vugs or fractures are structured and variably determines the ease of flow of fluids through the rocks. They are measured in darcy or millidarcy. Permeability and porosity of a rock are interrelated as higher porosity implies higher permeability. In addition, the grain size of a rock also determines the pore throat (narrow connections) that can exist in the reservoir rock thereby controlling the permeability rate. Coarse grained rocks such as carbonates and sandstones have bigger pore throats, thus they are highly permeable while rocks with lesser grain size as shale have smaller pore throats with little or no permeability [2]. The degree of permeability depends on the size and shape of pores, the size and shape of their interconnections, and the extent of interconnections Figure 2. The relationship between porosity and permeability for a given formation is not necessarily a close or direct one. However, high porosity is often associated with high permeability. Many investigators have attempted to correlate permeability to porosity, grain size and shape, and packing. The most frequently used relation was developed by Kozeny as follows:  miliolid packstone to grainstone. Other grains include fragments of algae and mollusks. Early cementation of this facies reduces dolomitization effects; however, selective dolomitization is frequently recognized and lagoonal dolomudstone can be found alternating with the limestone.

Orbitolina-bearing facies
This is a dark grey orbitolina-rich limestone, which is variably dolomitized. Grains are dominated by large benthic orbitolinids. Microfacies range from whole-foram grainstone to wackestone to fragmented packstone to wackestone. Other subsidiary grains include bioclasts of algae, rudists and mollusks.

Rudist bioclastic facies
It is characterized by high-energy bioclastic packstones. The majority of grains are rudist fragments intermixed with fragments of open-shelf faunas. It is highly bioturbated and interlayered with thin shaley seams.

Basinal foraminiferal argillaceous facies
This is the most eastern facies of the area. It is characterized by planktonic foraminifera intermixed sporadically with calcispheres forming bioclastic packstone to wackestone microfacies. Intermixture with open-shelf bioclasts is common. The matrix is argillaceous micrite and marl.
Most of the oil in the Kirkuk and KF2fields is contained in fabric selective porosity; non-fabric selective porosity or macrovoids comprising fissures, large vugs, fractures and caverns account for only minor amounts. Permeability and production, however, are almost entirely along these channels, a fact that been indicated quite early in the history of the field.

Methodology
The method of study based on well log (Petrophysical) data from KF2oil field in Northern Iraq. Porosity, permeability, formation resistivity and connate water resistivity values for different wells were obtained from well logging of the oil field (A1 to A2, A3, A4 and A5).
Advanced core data analyses for KF2 cores were abundant enough that a study of porosity versus the Archie cementation exponent m was conducted [4]. The data and results are plotted in Figure 3 and Table 1. Archie "m" as a function of porosity is given as:

m=1.5727 φ ∧0.467
This study showed that for the available data set, "m" decreased as porosity decreased. This "m" trend impacted the saturation calculation by producing lower water saturation values at the lower porosity values than if a constant value of the "m" parameter had been used, for example a value such as 1.85 which is appropriate for porosity values in the mid-thirties.
The net effect increased the hydrocarbon pore volume slightly in the low porosity range. This trend of decreasing "m" as porosity drops has been observed elsewhere in carbonates and was documented for carbonate reservoirs in Abu Dhabi in a 1987 paper by Borai.  This slope projects to a R w value of 0.05 ohmm at formation temperature when the line is set along the left edge of the cluster of points in the 10% to 20% porosity range, the R o line defines the resistivity response for 100% water saturation in the interpretation model. The other lines represent 50%, 25%, and 12.5% water saturation level S w .

Features of carbonate reservoir rocks
Geological features such as fractures, vugs and inter-crystalline structures all contribute hugely to the secondary porosity of carbonate reservoirs Table 2. It is important to be attentive of the particular features contributing to the porosity of a producing carbonate reservoir to be able to predict, evaluate and possibly enhance the reservoir production. Though these features of carbonate reservoir provide only a small amount of the total hydrocarbon pore space, they still enhance the reservoir to produce at economic rate [5][6][7]. The cementation exponent or lithologic exponent "m" is a major factor in defining the calculation of hydrocarbon or water saturation in heterogeneous carbonate reservoirs. Resistivity and petro-physical data solves this. It can be realized from the analysis that majority of the natural fractures that were generated during the depositional and diagenetic stage of the reservoir has suffered some form of geological changes such as leaching, dolomitization, recrystallization and cementation which probably cause of drilling and production activities. The gradient value, which implies the cementation exponent of, simply indicates an inter-crystalline enhanced porosity according to Archie's porosity classification from Archie [8] and using Pickett plot shown in Figure 7. KF2 field analyses indicate further suffering diagenetic process during further production over the years. The methods approved for oil recovery purposes would further result in leaching and dissolution of the inter-crystalline pores leading to vuggy solution porosity [9][10][11][12], which are usually more complex than either intergranular -intercrystalline or fracture porosity system. Classifying the carbonate rocks of KF2 oil field according to the Dunham classification plot (Figure 7), using effective porosity values derived from their permeability data suggests packstone lime, mudstone and some moldic grainstones. This been inferred on the plot on thus confirming the textural properties and grain size of the study area [13][14][15].     The analysis from Figure 7 shows that about 80% of the observed lithofacies in wells of KF2 oil field are packstone, with some traces of mud, clay and fine silt size carbonates. Therefore explains a gradual change in the original grainstones and packstone structure of the reservoir at the time of deposition as earlier explained by Majid and Veizer [16]. Other wells observed however indicate moldic grainstones which is a sharp deviation from the original depositional facies of the reservoir and therefore verifies the dissolution of a pre-existing constituents of the KF2carbonates through the various drilling and production activities over the years.

Carbonate formation studied
The variability and heterogeneity features of carbonate reservoir from pore to reservoir scale create a significant problem covering data acquisition, petrophysical evaluation and consequently reservoir description [9]. They further explained that the variation in properties of Carbonate facies and their pore character often control the distributions of net pay, porosity and hydrocarbon saturation. Generally, pore character rules carbonate reservoir quality, which is different in sandstone reservoir where variations in mineralogy, grainsize distribution and sorting, texture and degree of indurations governs the reservoir quality [10][11][12].
From the above stated, it is authoritative that diagenetic activities such as compaction, cementation, dolomitization, dissolution and leaching which have a significant effect on the pore structure are minimized by using efficient drilling and production techniques. However, it is important to note that diagenetic activities such as dissolution and leaching could either enhance or decrease the connectivity or permeability of the pores in a carbonate reservoir. Drilling activities such as the effect of drilling bits, reactions from the combination of drilling fluids with reservoir fluids and well completion activities could also destroy the natural micro-pores of a carbonate reservoir, dissolve the inherent fractures in the reservoir and hence reduce the connectivity of the pores or further destroy the inter-crystalline structure. All these will reduce the flow rate in the reservoir and consequently decrease the performance and production rate of the well. KF2oil field is presently suffering some form of petrophysical changes because of dissolution and leaching of the natural fractures that formed originally with the reservoir at deposition. This will consequently reduce the pore connectivity, flow rate of the hydrocarbon fluids and the production of the oil field.