In a typical problem of liquid and vapor coexistence, we are usually required to know one or more of the following:

- The phase boundaries,
- The extent of each phase,
- The quality of each phase.

The main emphasis is on the quantitative prediction of the above. These three represent the three basic types of VLE problems. A more detailed description of each of them is given below.

**Phase Boundary Determination Problem**These types of problems are either a bubble-point or a dew-point calculation. They are mathematically stated as follows:

**Bubble-point T calculation:**Given liquid composition (x_{i}) and pressure (P), determine the equilibrium temperature (T),**Bubble-point P calculation:**Given liquid composition (x_{i}) and temperature (T), determine the equilibrium pressure (P),**Dew-point T calculation:**Given vapor composition (y_{i}) and pressure (P), determine the equilibrium temperature (T),**Dew-point P calculation:**Given vapor composition (y_{i}) and temperature (T), determine the equilibrium pressure (P).

**Relative Phase Quantity Determination**In this type of problem, overall composition (z

_{i}), pressure (P), and temperature (T) are given, and the extent of the phases (molar fractions of gas and liquid) are required.**Phase Quality Determination**In this type of problem, overall composition (z

_{i}), pressure (P), and temperature (T) are given, and the composition of the liquid and vapor phases is required.

Problems of types 2 and 3 are collectively referred to as *flash calculation *problems. All three are problems that we encounter in production operations as petroleum engineers. Our focus now is on solving these sorts of problems. We want to use a predictive approach to do so. This is, we want to use mathematical models — the most economical and convenient approach — to accomplish the task.

One of the assumptions that we are making here is that of equilibrium. We assume that at all times, vapor and liquid that are coexisting together are in equilibrium. Are they really in equilibrium? No! Nevertheless, the state of current knolwedge requires us to assume equilibrium so as to be able to proceed.