Reservoir evolution

Reservoir evolution inferred from the 147Sm-143Nd system... 

The common-lead method looks at the isotopic evolution of lead in systems with U/Pb and Th/Pb ratios similar to or less than the ratios in bulk solar system materials. The original formulation, by Holmes and Houtermans, is a single stage model that accounts for the isotopic composition of any sample of common lead in terms of primordial lead plus radiogenic lead produced in the source up to the time that lead was separated from uranium and thorium. Multistage models that more accurately describe the evolution of natural systems have been developed. The common-lead method is used in cosmochemistry primarily to study the time of differentiation and reservoir evolution in differentiated bodies... 

As can be seen, the isotopic shift observed in lead removed from a system at time t depends on the value of p. Discussions of reservoir evolution are often cast in terms of the p of the system. By combining Equations (8.44) and (8.45), p can be eliminated to give... 

The formation volume factor for water (B, reservoir volume per stock tank volume), is close to unity (typically between 1.00 and 1.07 rb/stb, depending on amount of dissolved gas, and reservoir conditions), and is greater than unity due to the thermal contraction and evolution of gas from reservoir to stock tank conditions. 

Figure 4. Evolution of the (N2/N1) ratio in a reservoir in the two cases of closed system evolution (as a function of t/T2, where t is the time since fractionation), or in an open-system, steady-state reservoir (the steady-state (N2/N1) ratio is plotted as a function of x/ T2, where x is the residence time of the magma in the reservoir). Initial fractionation results in an arbitrarily chosen ratio of 2, which is kept constant for the iirfluent magma in the continuously replenished reservoir. The diagram shows that radioactive equilibrium is reached sooner in a closed system evolution. It also illustrates the fact that the radioactive parent-daughter pair should be chosen such as T2 is commensmate with the residence time of the magma in the reservoir (e.g., x/ T2 between 0.1 and 10). If T2 is much longer than the residence time x, then the (N2/N1) ratio will remain close to the initial value (here 2). If T2 is much shorter than x, equilibrium will be nearly established in the reservoir.

Figure 9. A schematic and ideal model showing how the residence time of the magma in a steady-state reservoir of constant mass M, replenished with an influx O of magma and thoroughly mixed, can be calculated from disequilibrium data, in the simplifying case where crystal fractionation is neglected (Pyle 1992). The mass balance equation describing the evolution through time of the concentration [N2] (number of atoms of the daughter nuclide per unit mass of magma) in the reservoir is ...

Yamada and Kawasaki [68, 69] proposed a nonequilibrium probability distribution that is applicable to an adiabatic system. If the system were isolated from the thermal reservoir during its evolution, and if the system were Boltzmann distributed at t — x, then the probability distribution at time t would be... 

The evolution of the probability distribution over time consists of adiabatic development and stochastic transitions due to perturbations from the reservoir. As above, use a single prime to denote the adiabatic development in time A, r —> r, and a double prime to denote the final stochastic position due to the influence of the reservoir, T —> T . The conditional stochastic transition probability may be taken to be... 

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. 

Table 1.6. Evolution of MPC changes in waters of reservoirs used for hygiene and drinking [3]... 

The objective of this work is to study the possible influence of the crude oil composition on the amount of coke deposit and on its ability to undergo in-situ combustion. Thus, the results would provide valuable information not only for numerical simulation of in-situ combustion but also to define better its field of application. With this aim, five crude oils with different compositions were used in specific laboratory tests that were carried out to characterize the evolution of the crude oil composition. During tests carried out in a porous medium representative of a reservoir rock, air injection was stopped to interrupt the reactions. A preliminary investigation has been described previously (8). 

Matrix acidizing treatments are more often performed, nowadays, with sensors and data acquisition systems continuously recording the surface pressure and rate histories. According to a recently proposed methodology (15), these records can be used to compute downhole rate and pressure evolutions. The bottomhole pressure history is then compared to the theoretical response of an equivalent reservoir wherein a non-reactive fluid would have been injected according to an identical rate schedule. Following this method, the difference between both theoretical and actual pressure responses originates from the evolution of the skin of the true reservoir under the influence of the acid attack. Equation 1 is then used to derive the skin decrease from this pressure difference. 

Because of the highly unstable nature of the acid attack in most of the carbonate reservoirs (propagation of wormholes), the development of a descriptive model of the skin evolution was not possible until the recent advent of the theory of fractals. In addition, the characteristics of the damaged zone greatly affect the behavior of the skin during acid injection in any type of reservoir, but particularly in carbonate ones. 

The steady-state problem yields a system of simultaneous linear algebraic equations that can be solved by Gaussian elimination and back substitution. I shall turn now to calculating the time evolution of this system, starting from a phosphate distribution that is not in steady state. In this calculation, assume that the phosphate concentration is initially the same in all reservoirs and equal to the value in river water, 10 I 3 mole P/m3. How do the concentrations evolve from this starting value to the steady-state values just calculated ... 

Fig. 3-3. Evolution of phosphate concentrations in the dilferent oceanic reservoirs. The time step for the initial adjustment is 25 years. For the long-term evolution shown in the insert, a time step of 2500 years was used.

Fig. 5 Evolution of water reserves on the reservoirs of Llobregat-Ter system. Increasing occurrence of drought periods [12]...

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