## 1.2 History of Reservoir Engineering

Crude oil, natural gas, and water are the substances that are of chief concern to petroleum engineers. Although these substances can occur as solids or semisolids such as paraffin, asphaltine, or gas-hydrate, usually at lower temperatures and pressures, in the reservoir and in the wells, they occur mainly as *fluids*, either in the *vapor* (gaseous) or in the *liquid* phase or, quite commonly, both. Even where solid materials are used, as in drilling, cementing, and fracturing, they are handled as fluids or slurries. The separation of well or reservoir fluid into liquid and gas (vapor) phases depends mainly on temperature, pressure, and the fluid composition. The state or phase of a fluid in the reservoir usually changes with decreasing pressure as the reservoir fluid is being produced. The temperature in the reservoir stays relatively constant during the production. In many cases, the state or phase in the reservoir is quite unrelated to the state of the fluid when it is produced at the surface, due to changes in both pressure and temperature as the fluid rises to the surface. The precise knowledge of the behavior of crude oil, natural gas, and water, singly or in combination, under static conditions or in motion in the reservoir rock and in pipes and under changing temperature and pressure, is the main concern of reservoir engineers.

As early as 1928, reservoir engineers were giving serious consideration to gas-energy relationships and recognized the need for more precise information concerning physical conditions in wells and underground reservoirs. Early progress in oil recovery methods made it obvious that computations made from wellhead or surface data were generally misleading. Sclater and Stephenson described the first recording bottom-hole pressure gauge and a mechanism for sampling fluids under pressure in wells.^{3} It is interesting that this reference defines bottom-hole data as measurements of pressure, temperature, gas-oil ratio, and the physical and chemical natures of the fluids. The need for accurate bottom-hole pressures was further emphasized when Millikan and Sidwell described the first precision pressure gauge and pointed out the fundamental importance of bottom-hole pressures to reservoir engineers in determining the most efficient oil recovery methods and lifting procedures.^{4} With this contribution, the engineer was able to measure the most important basic data for reservoir performance calculations: *reservoir pressure*.

The study of the properties of rocks and their relationship to the fluids they contain in both the static and flowing states is called *petrophysics.* Porosity, permeability, fluid saturations and distributions, electrical conductivity of both the rock and the fluids, pore structure, and radioactivity are some of the more important petrophysical properties of rocks. Fancher, Lewis, and Barnes made one of the earliest petrophysical studies of reservoir rocks in 1933, and in 1934, Wycoff, Botset, Muskat, and Reed developed a method for measuring the permeability of reservoir rock samples based on the fluid flow equation discovered by Darcy in 1856.^{5,6} Wycoff and Botset made a significant advance in their studies of the simultaneous flow of oil and water and of gas and water in unconsolidated sands.^{7} This work was later extended to consolidated sands and other rocks, and in 1940 Leverett and Lewis reported research on the three-phase flow of oil, gas, and water.^{8}

It was recognized by the pioneers in reservoir engineering that before reservoir volumes of oil and gas in place could be calculated, the change in the physical properties of bottom-hole samples of the reservoir fluids with pressure would be required. Accordingly, in 1935, Schilthuis described a bottom-hole sampler and a method of measuring the physical properties of the samples obtained.^{9} These measurements included the pressure-volume-temperature relations, the saturation or bubble-point pressure, the total quantity of gas dissolved in the oil, the quantities of gas liberated under various conditions of temperature and pressure, and the shrinkage of the oil resulting from the release of its dissolved gas from solution. These data enabled the development of certain useful equations, and they also provided an essential correction to the volumetric equation for calculating oil in place.

The next significant development was the recognition and measurement of connate water saturation, which was considered indigenous to the formation and remained to occupy a part of the pore space after oil or gas accumulation.^{10,11} This development further explained the poor oil and gas recoveries in low permeability sands with high connate water saturation and introduced the concept of water, oil, and gas saturations as percentages of the total pore space. The measurement of water saturation provided another important correction to the volumetric equation by considering the hydrocarbon pore space as a fraction of the total pore volume.

Although temperature and geothermal gradients had been of interest to geologists for many years, engineers could not make use of these important data until a precision subsurface recording thermometer was developed. Millikan pointed out the significance of temperature data in applications to reservoir and well studies.^{12} From these basic data, Schilthuis was able to derive a useful equation, commonly called the Schilthuis material balance equation.^{13} A modification of an earlier equation presented by Coleman, Wilde, and Moore, the Schilthuis equation is one of the most important tools of reservoir engineers.^{14} It is a statement of the conservation of matter and is a method of accounting for the volumes and quantities of fluids initially present in, produced from, injected into, and remaining in a reservoir at any stage of depletion. Odeh and Havlena have shown how the material balance equation can be arranged into a form of a straight line and solved.^{15}

When production of oil or gas underlain by a much larger aquifer volume causes the water in the aquifer to rise or encroach into the hydrocarbon reservoir, the reservoir is said to be under water drive. In reservoirs under water drive, the volume of water encroaching into the reservoir is also included mathematically in the material balance on the fluids. Although Schilthuis proposed a method of calculating water encroachment using the material-balance equation, it remained for Hurst and, later, van Everdingen and Hurst to develop methods for calculating water encroachment independent of the material balance equation, which apply to aquifers of either limited or infinite extent, in either steady-state or unsteady-state flow.^{13,16,17} The calculations of van Everdingen and Hurst have been simplified by Fetkovich.^{18} Following these developments for calculating the quantities of oil and gas initially in place or at any stage of depletion, Tarner and Buckley and Leverett laid the basis for calculating the oil recovery to be expected for particular rock and fluid characteristics.^{19,20} Tarner and, later, Muskat^{21} presented methods for calculating recovery by the internal or solution gas drive mechanism, and Buckley and Leverett^{20} presented methods for calculating the displacement of oil by external gas cap drive and water drive. These methods not only provided means for estimating recoveries for economic studies; they also explained the cause for disappointingly low recoveries in many fields. This discovery in turn pointed the way to improved recoveries by taking advantage of the natural forces and energies, by supplying supplemental energy by gas and water injection, and by unitizing reservoirs to offset the losses that may be caused by competitive operations.

During the 1960s, the terms *reservoir simulation* and *reservoir mathematical modeling* became popular.^{22–24} These terms are synonymous and refer to the ability to use mathematical formulas to predict the performance of an oil or gas reservoir. Reservoir simulation was aided by the development of large-scale, high-speed digital computers. Sophisticated numerical methods were also developed to allow the solution of a large number of equations by finite-difference or finite-element techniques.

With the development of these techniques, concepts, and equations, reservoir engineering became a powerful and well-defined branch of petroleum engineering. *Reservoir engineering* may be defined as the application of scientific principles to the drainage problems arising during the development and production of oil and gas reservoirs. It has also been defined as “the art of developing and producing oil and gas fluids in such a manner as to obtain a high economic recovery.”^{25} The working tools of the reservoir engineer are subsurface geology, applied mathematics, and the basic laws of physics and chemistry governing the behavior of liquid and vapor phases of crude oil, natural gas, and water in reservoir rocks. Because reservoir engineering is the science of producing oil and gas, it includes a study of all the factors affecting their recovery. Clark and Wessely urged a joint application of geological and engineering data to arrive at sound field development programs.^{26} Ultimately, reservoir engineering concerns all petroleum engineers, from the drilling engineer who is planning the mud program, to the corrosion engineer who must design the tubing string for the producing life of the well.