Thermodynamic Analysis of Transient Two-Phase Flow in Petroleum Reservoirs
- Djebbar Tiab (U. of Oklahoma) | Anthony U. Duruewuru (U. of Oklahoma)
- Document ID
- Society of Petroleum Engineers
- SPE Production Engineering
- Publication Date
- November 1988
- Document Type
- Journal Paper
- 495 - 507
- 1988. Society of Petroleum Engineers
- 1.14 Casing and Cementing, 5.3.2 Multiphase Flow, 5.7.2 Recovery Factors, 5.2 Reservoir Fluid Dynamics, 5.3.1 Flow in Porous Media, 5.9.2 Geothermal Resources, 4.1.5 Processing Equipment, 5.8.8 Gas-condensate reservoirs, 5.2.1 Phase Behavior and PVT Measurements, 7.4.4 Energy Policy and Regulation, 5.5 Reservoir Simulation, 4.1.2 Separation and Treating, 5.2.2 Fluid Modeling, Equations of State, 4.6 Natural Gas, 1.10 Drilling Equipment
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Summary. This paper presents a new method of analyzing the performance of a flowing well. The method uses a thermodynamic property known as the "availability function." The advantage of the availability-function method of analysis is that it allows the calculation of the thermodynamic efficiency of all processes, including not only those that are large work producers or consumers but also those that do not have work production or consumption as their goal. The efficiency of a process indicates how closely the process reaches its ultimate performance. It can be used as a toot to compare various processes and to make a sound decision on where improvements are possible.
The model developed in this study is capable of handling a single-component, single-phase or two-phase flow. The fluid-flow equation provide the thermodynamic properties-energy, enthalpy, entropy, and the fluid velocity-for use in the calculations of the theoretical maximum reversible work, the useful energy used to lift the hydrocarbon fluid from the bottom of the well to the surface, and the energy lost because of irreversibilities.
Results obtained from this study show that (1) a considerable fraction of the fluid energy is lost because of irreversibilities, especially at the early stages of production, and (2) the thermodynamic efficiency of fluid production would be greatly improved by minimizing wellbore heat loss.
Reservoir fluids are associated with a large quantity of energy, the magnitude of which depends on the pressure and temperature distribution throughout the reservoir. During production, the fluid energy is converted to kinetic energy, part of which is lost during the irreversible processes that cause entropy production or generation associated with energy and momentum transport with the fluids and between the fluid and the formation matrix. As a result, part of the valuable natural energy is lost.
The problem, then, confronting a petroleum engineer becomes the development of an appropriate production strategy that would result in the efficient use of the natural reservoir energy. Improper design of a production scheme can lead to short-lived production wells and a low recovery efficiency of the reservoir resource.
To increase the efficient use of the natural reservoir energy, proper accounting of the factors affecting production is extremely important because no operation can make use of all the stored energy from the reservoir. Even the portion that is readily available is easy to lose and dissipates in forms that are economically useless. It is clear that reducing the energy losses-i.e., irreversibilities-associated with fluid production leads to effective use of all available reservoir resources. Irreversibility is a total loss to the producer.
The main irreversibilities associated with fluid production are caused by friction that results from turbulence with the fluid and from the movement of fluid relative to the interior of the pipe wall. Other irreversibilities arise out of material and energy exchanges between the systems and the environment. The overall loss of energy caused by irreversible processes depends on the way these processes occur, which, in turn. is determined by the governing flow conditions. The conditions or regimes are established by the char-acteristics of the reservoir formation, the reservoir fluid, and th production rate. Among these factors, only the production rate can be controlled externally. Therefore, production rate is the fundamental variable that needs to be selected so that the extent of the irreversible process is minimized. To account for the variations in fluid proper-ties as the hydrocarbon fluid moves from the reservoir formation into the wellbore and up to the wellhead, a model in the form of differential equations of a nonlinear form is required.
The concepts of availability and irreversibility are not new in engineering fields. Lacey and Sager and Sage and Lacey applie thermodynamic data to oil production problems. They used enthalpy, entropy, pressure, and specific volume, as well as temperature, in the analysis of the energy relations in a flowing well and indicated the usefulness of such thermodynamic properties in the estimation of the reservoir energy changes accompanying production. These authors showed how the information obtained from surface samples could be used in the prediction of the volume properties of depth-liquid samples. They observed that conduction of heat through the tubing wall to the surroundings resulted in large temperature changes during the flow process. They stated, however, that changes in the state of the fluid were not greatly affected. The authors also stated that dissipation of energy as a result of frictional effects was not a major factor in the energy changes occurring during the flow of fluid through the tubing, even at high flow rates.
Tiab et al. and Sarathi and Tiab investigated the manner of consumption of the in-situ reservoir potential energy with production in gas reservoirs. They used the first and second laws of thermodynamics and the steady-state flow principles to derive interpretive equations in the calculation of the thermodynamic values, the reversible maximum-work function. They considered three simple reservoir systems: (1) a volumetric dry-gas reservoir, (2) a dry-gas reservoir system under waterdrive conditions, and (3) a volumetric dry-gas condensate reservoir system. Material-balance relationships were used in the simulation of the reservoir pressure/production history.
The principal findings of Sarathi and Tiab's work were that the maximum work in a volumetric dry-gas reservoir is independent of production rate and maximum work in a waterdrive gas reservoir depends on production rate. For waterdrive gas reservoirs, they concluded that the natural energy is better used at lower rates than at higher rates because the reservoir pressure decreases more slowly at lower production rates than at higher production rates because of differences in the water-advancement rate at the two levels of production.
The purpose of this study is to investigate the application of thermodynamic concepts-availability and irreversibility-in than analysis of a flowing well. It also provides a comprehensive mathematical description of fluid flow and energy transport in both porous media and the wellbore.
In this study, thermodynamic principles were used to establish the thermodynamic property availability function to describe the behavior of a well with fluid production.
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