Pore space, fluids

The pores between the rock components, e.g. the sand grains in a sandstone reservoir, will initially be filled with the pore water. The migrating hydrocarbons will displace the water and thus gradually fill the reservoir. For a reservoir to be effective, the pores need to be in communication to allow migration, and also need to allow flow towards the borehole once a well is drilled into the structure. The pore space is referred to as porosity in oil field terms. Permeability measures the ability of a rock to allow fluid flow through its pore system. A reservoir rock which has some porosity but too low a permeability to allow fluid flow is termed tight . 

Laminae of clay and clay drapes act as vertical or horizontal baffles or barriers to fluid flow and pressure communication. Dispersed days occupy pore space-which in a clean sand would be available for hydrocarbons. They may also obstruct pore throats, thus impeding fluid flow. Reservoir evaluation, is often complicated by the presence of clays. This is particularly true for the estimation of hydrocarbon saturation. 

The initial temperature of a gas condensate lies between the critical temperature and the cricondotherm. The fluid therefore exists at initial conditions in the reservoir as a gas, but on pressure depletion the dew point line is reached, at which point liquids condense in the reservoir. As can be seen from Figure 5.22, the volume percentage of liquids is low, typically insufficient for the saturation of the liquid in the pore space to reach the critical saturation beyond which the liquid phase becomes mobile. These... 

Nearly all reservoirs are water bearing prior to hydrocarbon charge. As hydrocarbons migrate into a trap they displace the water from the reservoir, but not completely. Water remains trapped in small pore throats and pore spaces. In 1942 Arch/ e developed an equation describing the relationship between the electrical conductivity of reservoir rock and the properties of its pore system and pore fluids. 

The above experiment was conducted for a single fluid only. In hydrocarbon reservoirs there is always connate water present, and commonly two fluids are competing for the same pore space (e.g. water and oil in water drive). The permeability of one of the fluids is then described by its relative permeability (k ), which is a function of the saturation of the fluid. Relative permeabilities are measured in the laboratory on reservoir rock samples using reservoir fluids. The following diagram shows an example of a relative permeability curve for oil and water. For example, at a given water saturation (SJ, the permeability... 

When water is displacing oil in the reservoir, the mobility ratio determines which of the fluids moves preferentially through the pore space. The mobility ratio or water displacing oil is defined as ... 

Subsurface Fluid Pressure (Pore Pressure Gradient). The total overburden pressure is derived from the weight of the materials and fluids that lie above any particular depth level in the earth. Of interest to the petroleum industry are the sedimentary rocks derived from deposits in water, particularly, in seawater. Such sedimentary rocks contain rock particle grains and saline water within the pore spaces. Total theoretical maximum overburden pressure, P (Ib/ft-), is... 

Basically all formations penetrated during drilling are porous and permeable to some degree. Fluids contained in pore spaces are under pressure that is overbalanced by the drilling fluid pressure in the well bore. The bore-hole pressure is equal to the hydrostatic pressure plus the friction pressure loss in the annulus. If for some reason the borehole pressure falls below the formation fluid pressure, the formation fluids can enter the well. Such an event is known as a kick. This name is associated with a rather sudden flowrate increase observed at the surface. 

Sedimentary rocks from oil reservoirs exhibit significant porosity where crude oils and water often coexist to share the pore space. The characterization of the pore structure and the fluids in situ is essential in the development of oilfields and specifically in the design of the production strategy and the facility. NMR has become an increasingly important well-logging and laboratory technique to quantify rock and fluid properties. 2D NMR has recently been introduced to the petroleum industry as a commercial well-logging service [58]. We will first review a few examples of the 2D NMR experiments on the sedimentary rocks in laboratory and well-logging applications. 

The advantages of this type of system are obvious the pore space is of sufficient complexity to represent any natural or technical pore network. As the model objects are based on computer generated clusters, the pore spaces are well defined so that point-by-point data sets describing the pore space are available. Because these data sets are known, they can be fed directly into finite element or finite volume computational fluid dynamics (CFD) programs in order to simulate transport properties [7]. The percolation model objects are taken as a transport paradigm for any pore network of major complexity. 

The situation becomes quite different in heterogeneous systems, such as a fluid filling a porous medium. Restrictions by pore walls and the pore space microstructure become relevant if the root mean squared displacement approaches the pore dimension. The fact that spatial restrictions affect the echo attenuation curves permits one to derive structural information about the pore space [18]. This was demonstrated in the form of diffraction-like patterns in samples with micrometer pores [19]. Moreover, subdiffusive mean squared displacement laws [20], (r2) oc tY with y < 1, can be expected in random percolation clusters in the so-called scaling window,... 

Figure 2.9.9(a) shows a schematic representation of a thermal convection cell in Rayleigh-Benard configuration [8]. With a downward temperature gradient one expects convection rolls that are more or less distorted by the tortuosity of the fluid filled pore space. In the absence of any flow obstacles one expects symmetrical convection rolls, such as illustrated by the numerical simulation in Figure 2.9.9(b). 

Porosity (ej>) determination with NMR is a direct measurement as the response is from the fluid(s) in the pore space of the rock. The initial amplitude (before relaxation) of the NMR response of the fluid(s) saturated rock (corrected for hydrogen index) is compared with the amplitude of the response of bulk water having the same volume as the bulk volume of the rock sample. The 2 MHz NMR... 

If the NMR response is capable of estimating the pore size distribution, then it also has the potential to estimate the fraction of the pore space that is capable of being occupied by the hydrocarbon and the remaining fraction that will only be occupied by water. The Free Fluid Index (FFI) is an estimate of the amount of potential hydrocarbons in the rock when saturated to a given capillary pressure. It is expressed as a fraction of the rock bulk volume. The Bulk Volume Irreducible (BVI) is the fraction of the rock bulk volume that will be occupied by water at the same capillary pressure. The fraction of the rock pore volume that will only be occupied by water is called the irreducible water saturation (Siwr = BVI/cj>). The amount of water that is irreducible is a function of the driving force to displace water, i.e., the capillary pressure. Usually the specified driving force is an air-water capillary pressure of 0.69 MPa (100 psi). 

Interpretation for irreducible water saturation assumes that the rock is water-wet or mixed-wet (water-wet during drainage but the pore surfaces contacted by oil becomes oil-wet upon imbibition). If a porous medium is water-wet and a nonwetting fluid displaces the water (drainage), then the non-wetting fluid will first occupy the larger pores and will enter the smaller pores only as the capillary pressure is increased. This process is similar to the accumulation of oil or gas in the pore space of a reservoir. Thus it is of interest to estimate the irreducible water saturation that is retained by capillarity after the hydrocarbon accumulates in an oil or gas reservoir. The FFI is an estimate of the amount of potential hydrocarbon in... 

NMR has proven to be a valuable tool for formation evaluation by well logging, downhole fluid analysis and laboratory rock characterization. It gives a direct measure of porosity as the response is only from the fluids in the pore space of the rock. The relaxation time distribution correlates with the pore size distribution. This correlation makes it possible to estimate permeability and irreducible water saturation. When more than one fluid is present in the rock, the fluids can be identified based on the difference in the fluid diffusivity in addition to relaxation times. Interpretation of NMR responses has been greatly advanced with the ability to display two distributions simultaneously. 

Consider a porous medium with magnetic susceptibility difference Ax between the confining solid and the permeating fluid (Figure 3.7.1). Magnetic field gradients will develop in the pore space. The spatial distribution of this internal magnetic... 

Fig. 3.7.1 Schematic of the DDIF effect in porous medium. The black areas are solid grains and the white areas are pore space. Diffusing spins in permeating fluid sample the locally variable magnetic field B(r) (solid contours sketched inside pore space) as it diffuses.

In addition, mercury intrusion porosimetry results are shown together with the pore size distribution in Figure 3.7.3(B). The overlay of the two sets of data provides a direct comparison of the two aspects of the pore geometry that are vital to fluid flow in porous media. In short, conventional mercury porosimetry measures the distribution of pore throat sizes. On the other hand, DDIF measures both the pore body and pore throat. The overlay of the two data sets immediately identify which part of the pore space is the pore body and which is the throat, thus obtaining a model of the pore space. In the case of Berea sandstone, it is clear from Figure 3.7.3(B) that the pore space consists of a large cavity of about 85 pm and they are connected via 15-pm channels or throats. 

Pore shape is a characteristic of pore geometry, which is important for fluid flow and especially multi-phase flow. It can be studied by analyzing three-dimensional images of the pore space [2, 3]. Also, long time diffusion coefficient measurements on rocks have been used to argue that the shapes of pores in many rocks are sheetlike and tube-like [16]. It has been shown in a recent study [57] that a combination of DDIF, mercury intrusion porosimetry and a simple analysis of two-dimensional thin-section images provides a characterization of pore shape (described below) from just the geometric properties. 

The relative permeability to phase i, kri(s ), is taken to be a function of fluid saturation si which is the fraction of the pore space occupied by phase i it is supposed that any associated spatial variations are largely taken into account through the permeability. For two-phase flow, fluid saturations are related by... 

The porosity can be determined by knowing locally the amount of fluid that saturates the pore space. Conventionally, an average value of the porosity is determined gravimetrically. X-ray CT scanning [3] or MRI [4] can be used to determine spatial distributions of porosity - the latter method is demonstrated in this chapter. 

This type of flood can be successful only if, as the fluid moves through the reservoir, a sufficient amount of the alkali remains in solution to react with the oil. Reaction of the flood with minerals and fluid in the reservoir, however, can consume the flood s alkali content. Worse, the reactions may precipitate minerals in the formation s pore space, decreasing permeability near the wellbore where free flow is most critical. A special problem for this type of flood is the reaction of clay minerals to form zeolites (Sydansk, 1982). 

The evolution of the fluid composition reflects a lack of significant contact between the aqueous phase and the C02 while in the pore space of the reservoir. 

Let us assume that a sphere with radius a is immersed in a liquid of finite volume, e.g., a mineral in a hydrothermal fluid. Diffusion in liquids is normally fast compared to diffusion in solids, so that the liquid can be thought of as homogeneous. Similar conditions would apply to a sphere degassing into a finite enclosure, e.g., for radiogenic argon loss in a closed pore space. Given the diffusion equation with radial flux and constant diffusion coefficient... 

---