Reservoir systems

Gas has a much higher compressibility than oil or water, and therefore expands by a relatively large amount for a given pressure drop. As underground fluids are withdrawn (i.e. production occurs), any free gas present expands readily to replace the voidage, with only a small drop in reservoir pressure. If only oil and water were present in the reservoir system, a much greater reduction in reservoir pressure would be experienced for the same amount of production. 

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. 

Time Scales and Single Reservoir Systems 4.2.1 Turnover Time... 

Fig. 4-6 A coupled two-reservoir system with fluxes proportional to the content of the emitting reservoirs.

As an illustration of the concept introduced above, let us consider a coupled two-reservoir system with no external forcing (Fig. 4-6). The dynamic behavior of this system is governed by the two differential equations... 

An investigation of the dynamic behavior of a coupled three-reservoir system using the techniques described above is included in the problems listed at the end of the chapter. 

It should be noted that the steady-state solution of Equation (12) is not necessarily unique. This can easily be seen in the case of the four-reservoir system shown in Fig. 4-7. In the steady state all material will end up in the two accumulating reservoirs at the bottom. However, the distribution between these two reservoirs will... 

Fig. 4-7 Example of a coupled reservoir system where the steady-state distribution of mass is not uniquely determined by the parameters describing the fluxes within the system but also by the initial conditions (see text).

Before turning to nonlinear situations, let us consider two specific examples of coupled linear systems. The first describes the dynamic behavior of a multireservoir system the second represents a steady-state situation of an open two-reservoir system. 

The performance should be evaluated in terms of drug and component physical and chemical compatibilities. Particle size and emitted dose determinations are required. Through-life performance should be evaluated as this is a multidosing reservoir system. The influence of temperature and humidity on stability and performance of the product should also be considered. 

The metering of dry powder inhalers is closely linked to the device itself and may be divided into three common systems capsules, multidosing blister packs, and reservoir systems. The consideration that goes into these metering systems include convenience to the patients, stability on storage, compatibility with product, and ease of filling. 

The hormone-releasing devices have a closer resemblance to standard methods of sustained release because they involve the release of a steroid compound by diffusion [198,199]. The Progestasert, a reservoir system, is shown in Fig. 16. Progesterone, the active ingredient, is dispersed in the inner reservoir, surrounded by an ethylene/vinyl acetate copolymer membrane. The release of progesterone from this system is maintained almost constant for 1 year. The effects of release are local, with none of the systematic side effects observed with orally administered contraceptives [200-207]. 

In the case of reservoir systems that rely on the cohesivity of the blend due to interparticle interactions, studies are required on vibrational stability in simulated storage, transport, and use tests, including determination of the effects of elevated temperature and humidity. 

The waste-reservoir system undergoes a dynamic chemical evolution in which changing environmental parameters may result in variations of Kd values by several orders of magnitude at different locations and at the same location at different times. 

The application of these equations to the marine carbon system is illustrated by program ISOT01, which adds isotopes to the three-reservoir system of atmosphere, shallow ocean, and deep ocean presented in program DGC10 in Chapter 5. In subroutine EQUATIONS, equations 6 to 8 are for the stable isotope 13C, and equations 9 to 11 describe radiocarbon. The rest of the physical system is identical to that of program DGC10. 

Navarro E, Bacardit M, Caputo L, Palau T, Armengol J (2006) Limnological characterization and flow patterns of a three-coupled reservoir system and their influence on Dreissena polymorpha populations and settlement during the stratification period. Lake Reservoir Manage 22 293-302... 

Table 7.4. Eigenvalues and characteristic times of the six-reservoir system for phosphorus.

Figure 7.12 Exchange of Na in an open two-reservoir system the flux J0(t) of Na weathered from evaporites introduces a forcing term into conservation equations.

Reservoirs can be either natural or man-made. Natural reservoirs can include lakes or other contained water bodies, while man-made reservoirs usually consist of some sort of engineered structure, such as a tank or other impoundment structure. In addition to the water containment structure itself, reservoir systems may also include associated water treatment and distribution equipment, including intakes, pumps, pump houses, piping systems, chemical treatment and chemical storage areas, and so forth. 

Equation 1.2 assumes that the concentration of C is constant throughout the ocean, i.e., that the rate of water mixing is much fester than the combined effects of any reaction rates. For chemicals that exhibit this behavior, the ocean can be treated as one well-mixed reservoir. This is generally only true for the six most abundant (major) ions in seawater. For the rest of the chemicals, the open ocean is better modeled as a two-reservoir system (surface and deep water) in which the rate of water exchange between these two boxes is explicitly accoimted for. 

Buccal dosage forms can be of the reservoir or the matrix type. Formulations of the reservoir type are surrounded by a polymeric membrane, which controls the release rate. Reservoir systems present a constant release profile provided (1) that the polymeric membrane is rate limiting, and (2) that an excess amoimt of drug is present in the reservoir. Condition (1) may be achieved with a thicker membrane (i.e., rate controlling) and lower diffusivity in which case the rate of drug release is directly proportional to the polymer solubility and membrane diffusivity, and inversely proportional to membrane thickness. Condition (2) may be achieved, if the intrinsic thermodynamic activity of the drug is very low and the device has a thick hydrodynamic diffusion layer. In this case the release rate of the drug is directly proportional to solution solubility and solution diffusivity, and inversely proportional to the thickness of the hydrodynamic diffusion layer. 

Moore, J. N. (1994). Contaminant mobilization resulting from redox pumping in a metal-contaminated river-reservoir system. In Environmental Chemistry of Lakes and Reservoirs, ed. L. A. Baker, pp. 451-71. Washington, D.C. American Chemical Society. Moore, J. N., Ficklin, W. H. Johns, C. (1988). Partitioning of arsenic and metals in reducing sulfidic sediments. Environmental Science and Technology, 22, 432-7. Morrison, G. M., Batley, G. E. Florence, T. M. (1989). Metal speciation and toxicity. Chemistry in Britain, 8, 791-5. 

A K-factor correlation based on a convergence pressure of 5000 psia can be used in separator calculations for all of these reservoir systems. Surface separators for black oils typically operate at low pressures. Convergence pressure has little effect on K-factors at low pressure. 

Contaminant Mobilization Resulting from Redox Pumping in a Metal-Contaminated River-Reservoir System... 

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