# Saturations Calculations Using Saturation-

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- Saturations Calculations Using Saturation-Height Modeling on the Well Mariana, offshore Lower Congo Basin Saturation Height approachs Dario Euclides Tenente Pascoal Petroleum Geosciences Supervisor: Erik Skogen, IPT Co-supervisor: Per Atle Olsen, Statoil Department of Petroleum Engineering and Applied Geophysics Submission date: July 2015 Norwegian University of Science and Technology Saturations Calculations Using Saturation- Height Modeling on the Well Mariana, offshore Lower Congo Basin Dário Euclides Tenente Pascoal Petroleum Geosciences Submission date: July 2015 Supervisor: Erik Skogen, IPT Co-Supervisor: Per Atle Olsen, STATOIL E B-with Sandflag filter . 35 Figure 12 - Comparisons of the Sw plotted against the Height Above Free Water Level. A- Without Filter; B-with Sandflag filter . 36 Figure 13 – comparison of the final Saturations models (the highlighted track). The colors represent the reservoirs used as base for models . 37 IX Figure 14 - Examples of Curves from the Classical functions (Cuddy et al., 1993). 43 Figure 15 - Plot showing the calibration of two porosity log curves to verify the LFP_PHITT used for computation of SwH models . 45 Figure 16 - Picket plot showing the water resistivity in the zone of interest. The red marks in the picket plot represents the zone in the Layout marked likewise.14 . 46 X 5 Acronyms GIIP Gas Initial in Place HAFWL Height Above Free Water Level JF Leverett J Function Pc Capillary Pressure PHITT Total Porosity (computed by the Oil Company) STOIIP Stock Tank Oil Initial In Place SwH Water Saturation Height DNS Density-Neutron curves separation TVD True Vertical Depth TVDSS True Vertical Depth Subsea 11 6 Introduction Petrophysical analysis has as main goals to produce information that facilitate on defining the STOIIP or GIIP of reservoirs. This analysis includes mainly porosity, Saturation, Net to gross. While Net to Gross, porosity and permeability are readily mapable quantities the saturation needs special considerations to be extrapolated from the well. Mapping of water saturation away from the wellbore in for instance geo-models is the main purpose of saturation height modeling. Saturations are affected by factor as Rw or Rt values from log measurements, which are mostly affected by clay content, shoulder bed effect, salinity and wellbore stability. The m and n, cementation and saturation exponents respectively, have also great effect in the water saturations values (Walther, 1967; Hamada and Alsughayer, 2001). The Saturation also varies as function of the capillary entry pressure all over the formation, which is controlled by the wettability interfacial tension and pore geometry (Harrison and Jiang, 2001). The later has been object of many studies along the years and different approach has been performed to acquire better answers. One reason why it has been studied is the fact that has direct influence on the calculation of the amount of oil or gas in the formations or in a field to be explored (when many wells are evaluated). This means that robust SwH Functions can be used for prediction of saturation at any part of the reservoir above the free water level, usually considering rock qualities variation. Former studies show that SwH functions can be acquired through two principal categories: Core analysis data and Log analysis data. Many Literatures around these two different methods are found (Wiltgen et al. 2003; Skelt and Harrison, 1995). The purpose of this thesis relies on the application of some of these methods to a given field and to discuss conformity and disparity with the saturation model already applied to the field. 6.1 Fundamentals Concepts In reservoirs the fluids are initially in equilibrium within the porous space of the rocks. Two non- miscible fluids sharing the same porous space tend to occupy different positions depending on their density contrast. Three main forces influence in the amount of each fluid in the reservoir: gravity (buoyancy) force, an external force (flow coming from an aquifer near the reservoir, for example) and interfacial forces. The effect of the latter one on the fluid amount and interface 12 position is the one to be considered in this dissertation. Thus some main concepts are important to be described. 6.2 Capillary Pressure and Wettability The Capillary pressure may be explained by the interaction between fluid-fluid and fluids-solids causing a fluid pressure difference. Consider a rock which pore space filled with two immiscible fluids. Each fluid will interact with the pore surface (solids) and with neighbor fluid sharing the same porous space. The interaction effect will depend on the inter-molecular attraction (forces): the fluid-fluid interaction, will give place a surface tension; the solid surface area occupied by the fluids depending on their molecular affinity to the solid. The degree of affinity is defined by the angle formed between the fluids interface and the solid surface, which express the wettability of the fluid. The less the angle, the greater is the wettability of the fluid. Drainage occurs when hydrocarbon migrates into a reservoir and displaces water. In order to displace water hydrocarbon need to overcome the displacement pressure of the rock set up by the capillary pressure. 6.3 Free Water Level (FWL) and Fluid Contacts The free water level, FWL in a water wet rock, is defined as the point below fluid contact which capillary pressure is zero. It is also used as reference in many Saturation-Height modeling functions which above such the height is measured. Above the FWL where capillary pressure is different from zero hydrocarbons can displace water. In logging analysis, formation pressure data plotted against True Vertical Depth are used to predict free water level by checking the points where fluid pressure gradient lines are crossed. For the fluid contacts the inference is addressed differently as its position may vary as function of the pore size: small pore-sized rocks trend to have fluid contact a bit further above from the FWL comparatively to large pore-sized rocks. Also, it can be obscured by shale beds in a shaly sand sequence, or almost unpredictable in very thin layers. 13 6.4 Fluid Saturation The amount of fluid within the porous space of a rock defines the saturation of a reservoir. There can be found three types of fluid in a reservoir: Water, Oil and Gas. The sum of the three fluids will correspond to the total pore volume and the saturation of each fluid will indicate the individual contribution of each fluid to the total. 6.4.1 Water Saturation (Sw) Water saturation corresponds to the ratio of water volume to pore volume of a rock sample. The water fraction that cannot be displaced by capillary forces and is normally attached to the matrix of the rock is often named irreducible water saturation. There are many different approaches for calculating water saturations along the well-bore. The most common, in petrophysics field, is by the well know Archie´s Formula. (1) 6.5 Saturation-Height Functions (SwH) Several studies concerning to Saturation Height were developed through the years, which gave place to different methods to compute Sw through SwH modeling. The available literature divides them mostly into two types: those based on capillary curve averaging and those log-based methods. A third type that integrates both has being also considered. The next few lines shall describe some of them. 6.5.1 Classical Functions (Leverett Function) A paper produced by Leverett (1940) describes the Capillary behavior in porous solid. His objective was considering applications of Thermodynamic and physical principles to Static and Dynamic behavior of the fluid mixture. Differently from the empirical ones, he used rock physics properties to elaborate a dimensionless function which attempt to generate universal curve. He related the Interfacial Curvature definition and its relation with three important parameters: Capillary pressure, Height and Saturation. Leverett argued that when two fluids fill a pore they 14 form an interface, which shape is function of the tension between the fluids that result in a differential pressure across the interface. This first relationship is described by the equation: ( ) (2) Where is the Interfacial tension, Pc is the capillary pressure, ( ) correspond to the main curvature of the surface and R1 and R2 are the principal radii of the curvature. The second relationship relies on the assumption that fluids in reservoir are initially in substantial capillary equilibrium. Fluids in the reservoir occupy different individual vertical position. Their position depends, among other external factors, of the fluid density contrast. Therefore, the interface may be described as result of the difference between the densities of the fluids, the gravity and their depth position difference in the reservoir. This relationship describes the well- known capillary pressure equation shown below. This equation states equilibrium between the hydrostatic pressure and the buoyance. dPc=dPo – dPw = wogdh (3) So, assuming capillary equilibrium is the same as saying there would be no curvature at the interface or zero value on the capillary pressure. Pc= wogh= ( ) (4) This can be also written: ( ) = (5) Where wo is the density difference between water and oil, h is the vertical distance of the interface above the free liquid surface and g is the gravitational constant. Leverett made some important considerations of equation (5) from which the most relevant for this study is that it could be a direct means of estimating the maximum difference pressure that may exist in a virgin reservoir. 15 The last relationship relies on assumptions of a considerable contribution on the curvature of the oil-water interface, from the dimension of the pore space and the fraction of the fluid phase existent within the pore. He also took into consideration the minimum pressure differential enough to displace water from the water saturated sand, Displacement Pressure. A two phase experiment (drainage and imbibition) was performed and measured the resultant Sw of 2 different rocks at different capillary pressures, by letting water and air come to a capillary equilibrium. Peculiar rock parameters, permeability and porosity, were related by√ , and bounded to equation (5). The right hand side became then: √ Ibrahim A. et al (1992) made a determination of relative permeability curves in tight gas sands using log data and culminate with a useful approach using the Leverett equation: √ (6) And taking into account the wettability effects was included the contact angle, into J(Sw) √ (7) They plotted the J(Sw) calculated against Sw data in a log-log scale and realized a nearly linear fit. The best reflects the equation: (8) Where β and α, are coefficients. The capillary pressure, Pc, was related to FWL by: FWL (9) Where, hFWL indicates the height above the free water level. By rearranging the equations above and solving for : 16 √ (10) A plot of the new form of equation (5) versus Sw, results in the known J function or simply J(Sw), which is dimensionless. The solution of this function is verified, in a log-log scale, by the equation (6): (11) However, this method is dependent much of the history and flow of the system (Leverett, 1942) and as each rock has different geological history, this method gives reliable result if evaluating only a single type of rock. Fig. 1 shows typical curve produced by Leverett function. 17 Figure 1 - Example of the Leverett Curve (Leverett, 1942) 6.5.2 FOIL functions Other authors calculate the Swh based in the Bulk volume of water, which received the name FOIL functions (Wiltgen et al., 2003; Cuddy et al., 1993) The most known FOIL equation is the function produced by Cuddy et al. (1993). They created a function virtually independent of porosity and permeability based on the bulk volume of water 18 and FWL. The derivation is simpler than the classic ones. It starts by using the Ibrahim´s SwH relationship and uses the BVW definition from Sw and porosity: (12) The porosity independence of Cuddy model could be shown by assuming the Sw calculated from equation (1). However, electrical properties of the rock may always influence the model results (see explanation in the Appendix). The BVW of water can be linearly related to the HAFWL when plotted in a log-log scale. The relation can be verified by the equation below. (14) Where, A and B are coefficients. Fig. 2 shows the final FOIL curve computed by Cuddy. Figure 2 - Example of foil function (Cuddy et al., 1993) 19 6.5.3 Empirical Functions These functions are based on porosity band. This means that a branch of Swh curves were plotted as function of some porosity averages measured in the same rock. The mains weakness of these functions, as pointed by Cuddy (1993), were that even though being consistent with the capillary pressure theory, were mathematically inconsistent, the data for porosity bands were not equally distributed, the vertical offset between the Swh curves needed to be known before the Swh calculations and did not have into account physical properties of the rocks. Some examples of these functions and typical curve are shown by Cuddy’s paper (Cuddy et al., 1993). Many other approaches functions exist for computing Swh (Wiltgen and Owen, 2003). Below is shown some of them: Lambda Functions: ; ⁄ Johnson “Pseudo-Permeability”: Guthrie Polynomial: Some of these functions require data of more than 1 well or core set (Pseudo-permeability) as they are based on linear correlation of permeability with same capillary pressure values, whilst others more complex to be implemented (Guthrie). 20 7 Methodology The analysis of the parameters previously described (in the previous chapter) was applied to the well described below. The choice of which data to work with was based on the necessary elements for Saturation Height equations to be computed. These were mainly parameters that describe rock qualities (porosity and permeability - through log and core data); fluid physical properties (pressures - through pressure test data and fluid density difference assumptions) and Fluid-rock interactions (contact angle, interfacial tension, and fluid saturations). Rock quality parameters were ideally calibrated to core data, while others were simply assumed. 7.1 General well information The well Mariana was drilled within the Lower Congo Basin Ultra-deep-water province, offshore of Angola. The drilled structure is highly inclined Salt flank from Oligocene which clastics have an overlying Miocene regional seal truncated up dip against a salt diaper (Geological Report, 2004). The main objective was to verify and prove the presence of two good quality oil reserves. Previous information acquired from other wells drilled in the same zone indicated that the ta
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