Volume of fluids

The collection of representative reservoir fluid samples is important in order to establish the PVT properties - phase envelope, bubble point, Rg, B, and the physical properties - composition, density, viscosity. These values are used to determine the initial volumes of fluid in place in stock tank volumes, the flow properties of the fluid both in the reservoir and through the surface facilities, and to identify any components which may require special treatment, such as sulphur compounds. 

In a reservoir at initial conditions, an equilibrium exists between buoyancy forces and capillary forces. These forces determine the initial distribution of fluids, and hence the volumes of fluid in place. An understanding of the relationship between these forces is useful in calculating volumetries, and in explaining the difference between free water level (FWL) and oil-water contact (OWC) introduced in the last section. 

Applying this directly to the reservoir, when a volume of fluid (dV) is removed from the system through production, the resulting drop in pressure (dP) will be determined by... 

Figure 8.1 shows how the expansion of fluids occurs in the reservoir to replace the volume of fluids produced to the surface during production. 

The following diagram represents underground volumes of fluid produced. The relationship between the underground volumes (measured in reservoir barrels) and the volumes at surface conditions is discussed in Section 5.2. The relationships were denoted by... 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

It Is important to know how much each well produces or injects in order to identify productivity or injectivity changes in the wells, the cause of which may then be investigated. Also, for reservoir management purposes (Section 14.0) it is necessary to understand the distribution of volumes of fluids produced from and injected into the field. This data is input to the reservoir simulation model, and is used to check whether the actual performance agrees with the prediction, and to update the historical data in the model. Where actual and predicted results do not agree, an explanation is sought, and may lead to an adjustment of the model (e.g. re-defining pressure boundaries, or volumes of fluid in place). 

The general class of free boundary flow problems can, however, be modelled using the volume of fluid (VOF) approach (Nichols et ai, 1980). The main concept in this technique is to solve, simultaneously with the governing flow equations, an additional equation that represents the unknown boundary. Three different versions of this method are described in the following sections. 

Figure 2.1 served as the basis for our initial analysis of viscosity, and we return to this representation now with the stipulation that the volume of fluid sandwiched between the two plates is a unit of volume. This unit is defined by a unit of contact area with the walls and a unit of separation between the two walls. Next we consider a shearing force acting on this cube of fluid to induce a unit velocity gradient. According to Eq. (2.6), the rate of energy dissipation per unit volume from viscous forces dW/dt is proportional to the square of the velocity gradient, with t]q (pure liquid, subscript 0) the factor of proportionality ... 

For batch or stirred tank processes, in terms of the mass of adsorbent M, (kg), extraparticle volume of fluid (m ), and volumetric flow rates F, (itt/s) in and out of a tank, the material balance on component... 

The actual shape of the curve illustrated in Fig. 12.4 can vary according to factors such as metal properties and cavitation intensity. (Cavitation intensity relates to the number of bubbles created in a unit volume of fluid and the amount of energy transferred during the col-... 

The buoyant force is proportional to the mass of fluid displaced by the particle, that is, as the particle falls through the surrounding water, it displaces a volume of fluid... 

Vp = volume of fluid in eaeh stage (-r j) = rate of reaetion per unit volume in stage i. This ehanges witli i. 

In order to adequately describe the size of a heater, the heat duty, the size of the fire tubes, the coil diameters and wall thicknesses, and the cor lengths must be specified. To determine the heat duty required, the maximum amounts of gas, water, and oil or condensate expected in the heater and the pressures and temperatures of the heater inlet and outlet must be known. Since the purpose of the heater is to prevent hydrates from forming downstream of the heater, the outlet temperature will depend on the hydrate formation temperature of the gas. The coil size of a heater depeiuLs on the volume of fluid flowing through the coil and the required heat duty. 

T = upstream absolute temperature, °R V = specific volume of fluid, cu ft/lb P] = P = upstream pressure, psi abs d = pipe inside diameter, in. 

Vo = specific volume of fluid at outlet of reboiler, fE/lb Vi = specific volume of fluid at inlet to reboiler, fE/lb log = log base 10... 

Volume of fluid required to displace top plug Displacement rate... 

This is usually a closed tank or vessels that hold the volume of fluid required supporting the system. The vessels normally provide several functions in addition to holding fluid reserves. The major functions include filtration of the fluid, heat dissipation, and water separation. 

Positive-displacement compressors, also referred to as dynamic-type compressors, confine successive volumes of fluid within a closed space. The pressure of the fluid increases as the volume of the closed space decreases. 

There are two possible kinds of force acting on a fluid cell internal stresses, by which an element of fluid is acted on by forces across its surface by the rest of the fluid, and external forces, such as gravity, that exert a force per unit volume on the entire volume of fluid. We define an ideal fluid to be a fluid such that for any motion of the fluid there exists a pressure p(x, t) such that if 5 is a surface in the fluid with unit normal vector n, the stress force that is exerted across S per unit area at x at time t is equal to —p x,t)h. An ideal fluid is therefore one for which the only forces are internal ones, and are orthogonal to 5 i.e. there are no tangential forces. ... 

Using the pressure of an ideal fluid, we see that the total force acting on a volume of fluid due to the rest of the fluid is given by — fgP dS. Applying Stokes Theorem, we then have that... 

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