Self-consistent Reservoirs Research Articles

Scale Effects on the Application of Saturation-Height Functions to Reservoir Petrofacies Units

Summary An internally self-consistent reservoir model has been constructed to investigate the effects of scale on the numerical form and application of four saturation-height functions and on the resulting predictions of reservoir fluid saturations. The treatment uses reservoir partitioning into strongly characterized, physically distinct lithounits, or petrofacies, for purposes of petrophysical interpretation, and a separate, correlative reservoir zonation for subsequent parameter mapping and volumetrics. The context is therefore that of a deterministic reservoir model. The numerical difference between apetrofacies-specific saturation-height function calibrated at the well-log scale (< 1 m) and the same type of function generated at the reservoir zonal scale (>10 m) varies with the function used and the physical character of the particular petrofacies unit. The application of saturation-height functions established separately at these two different scales has allowed the departures introduced through scale transgression to be assessed quantitatively. This has been done by comparing the predicted zonal hydrocarbon saturations generated for reservoir mapping with benchmark values of the same parameter. For this deterministic approach to reservoir description, an extended algorithm that uses bulk volume water as predictand provides the most accurate evaluation of water saturation at the reservoir zonal scale, which must be used in volumetrics applications. In contrast, an exponential form of the saturation-height function shows relatively large errors at both scales. The significance and variability of scale effects have required the formulation of a structured approach to the optimum application of saturation-height functions in deterministic reservoir description. Through this facility, it is possible to contain the uncertainty associated with the distribution of hydrocarbon saturation at the reservoir mapping and volumetrics stages.

Stationary nonequilibrium properties of a quantum-mechanical lattice with self-consistent reservoirs

The self-consistent reservoir (SCR) model of lattice thermal conductivity is combined with the quantum Langevin equation formulation of Ford, Kac, and Mazur to obtain a quantum SCR model for lattice conductivity. Application is made to simple cubic monatomic lattices with harmonic nearest-neighbor interactions. A general expression for the thermal conductivity is obtained, and its high- and low-temperature limits examined.

Disordered harmonic chain with self-consistent reservoirs

Exact calculations of heat flows and thermal conductivities in disordered harmonic chains of up to 50 atoms have been made within the framework of the self-consistent reservoir model. Thermal conductivities, obeying Fourier's law, are given as functions of the coupling to the internal heat baths for both fixed-end and free-end boundary conditions. On the basis of these calculations, it is conjectured that an infinite disordered chain with only harmonic interactions may, indeed, retain a unique finite thermal conductivity in the limit that the internal reservoir coupling goes to zero.

Simulation of Nonharmonic Interactions in a Crystal by Self-Consistent Reservoirs

Independent heat reservoirs are postulated to interact with the atoms in a harmonic system as a substitute for real nonharmonic forces. The temperature of each reservoir is determined by the condition that it exchange no energy with the system in the steady state. An explicit solution for the covariance matrix is obtained for the case of the linear chain. The thermal conductivity is finite and inversely proportional to the coupling to the reservoirs.