Isochore

Reservoir quality maps are used to illustrate the lateral distribution of reservoir parameters such as net sand, porosity or reservoir thickness. It is important to know whether thickness values are isochore or isopach (see Figure 5.46). Isochore maps are useful if properties related to a fluid column are contoured, e.g. net oil sand. Isopach maps are used for sedimentological studies, e.g. to show the lateral thinning out of a sand body. In cases of low structural dip (<12°) isochore and isopach thickness are virtually the same. 

The isochore thickness of the total interval ( gross thickness ) "egardless of lithology. 

C) CONSTANT-TEMPERATURE CONSTANT-VOLUME (ISOTHERMAL-ISOCHORIC) PROCESSES... 

The specific heat along the critical isochore hence has the same smgularity as (5 P /5T )p for a lattice gas. 

Finally, we consider the isothennal compressibility = hi V/dp)y = d hi p/5p) j, along tlie coexistence curve. A consideration of Figure A2.5.6 shows that the compressibility is finite and positive at every point in the one-phase region except at tlie critical point. Differentiation of equation (A2.5.2) yields the compressibility along the critical isochore ... 

A more recent compilation includes tables giving temperature and PV as a function of entropies from 0.573 to 0.973 (2ero entropy at 0°C, 101 kPa (1 atm) and pressures from 5 to 140 MPa (50—1400 atm) (15). Joule-Thorns on coefficients, heat capacity differences (C —C ), and isochoric heat capacities (C) are given for temperatures from 373 to 1273 K at pressures from 5 to 140 MPa. 

Besides shear-induced phase transitions, Uquid-gas equilibria in confined phases have been extensively studied in recent years, both experimentally [149-155] and theoretically [156-163]. For example, using a volumetric technique, Thommes et al. [149,150] have measured the excess coverage T of SF in controlled pore glasses (CPG) as a function of T along subcritical isochoric paths in bulk SF. The experimental apparatus, fully described in Ref. 149, consists of a reference cell filled with pure SF and a sorption cell containing the adsorbent in thermodynamic equilibrium with bulk SF gas at a given initial temperature T,- of the fluid in both cells. The pressure P in the reference cell and the pressure difference AP between sorption and reference cell are measured. The density of (pure) SF at T, is calculated from P via an equation of state. 

This model was applied by Mukherjee et al. [20] for various natural fibers. By considering diverse mechanisms of deformation they arrived at different calculation possibilities for the stiffness of the fiber. According to Eq. (1), the calculation of Young s modulus of the fibers is based on an isochoric deformation. This equation sufficiently describes the behavior for small angles of fibrils (<45°) [19]. 

A constant-volume process is called isochoric and, for such processes, the entropy increase is written as... 

If we draw the two isochores imiii, i 2< 2, on the indicator diagram (Fig. 14), all the paths of change must lie within these limits, which fix the range or amplitude of the process. Let the initial state ( i, T) be a, and let the gas expand isothermally and reversibly to a the maximum work AT is represented by the area aa vtf i, which is shown later to be ... 

Two isotherms, isochores, adiabatics, or generally any two thermal lines of the same kind, never cut each other in a surface in space representing the states of a fluid with respect to the three variables of the characteristic equation taken as co-ordinates, for a point of intersection would imply that two identical states had some property in a different degree (e.g., two different pressures, or temperatures). Two such curves may, however,... 

The Isochoric Process Figure 2.4 shows the relationship between pcxt and V for an isochoric (constant volume) process going from state a to state b. In this process d V = 0 and tv = 0/... 

In an isothermal process, heat must be added during an expansion and removed during a compression to keep the temperature constant. We will describe this more fully as we now calculate the heat added or removed in isobaric, isochoric, and isothermal processes. 

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