Simulation of Production and Injection Performance of Gas Storage Caverns in Salt Formations

Abstract

Summary This paper presents a simple yet comprehensive mathematical model for simulation of injection and production performance of gas storage caverns in salt formations. The model predicts the pressure and temperature of the gas in the cavern and at the wellhead for an arbitrary sequence of production and injection cycles. The model incorporates nonideal gas properties, thermodynamic heat effects associated with gas expansion and compression in the cavern and tubing, heat exchange with the surrounding salt formation, and nonuniform initial temperatures but does not include rock-mechanical effects. The model is based on a mass and energy balance for the gas-filled cavern and on the Bernoulli equation and energy balance for flow in the wellbore. Cavern equations are solved iteratively at successive timesteps, and wellbore equations are solved within an iteration cycle of the cavern equations. Gas properties are calculated internally with generally accepted correlations and basic thermodynamic relations. Example calculations show that the initial temperature distribution has a strong effect on production performance of atypical gas storage cavern. The primary application of the model is in the design, planning, and operation of gas storage projects. Introduction Subsurface caverns in rock salt formations are being increasingly used for storage of natural gas. Gas-filled caverns provide high deliverability and secure gas sources at relatively low costs and with little environmental impact. Their primary use is supply of gas during periods with short-term(days) peak demands in gas. Of course, a large number of caverns may also be used to meet seasonal variations in gas demand. The first salt cavern for gas storage was put into operation in the early 1960's in the U.S. Since that time, many more salt caverns have been constructed in the U.S., Canada, and Europe and have become vital parts of gas distribution systems. Nowadays, a typical gas cavern in a salt formation is located between 1000and 2000 m deep and has an internal volume between 1×105 and 5×105 m3, a maximum operating pressure of 15 to 25 MPa, and a total storage capacity varying from 15 to 150×106 m3 of natural gas. The open technical literature on gas storage in salt caverns deals primarily with the engineering geologic, rock-mechanical, and solution-mining aspects of caverns. To the best of our knowledge, no detailed studies have been published on the production and injection behavior of gas caverns. In this paper, we present a mathematical model for the simulation of the production and injection performance of gas storage caverns. The model emphasis is on pressure and temperature behavior during loading and unloading of the cavern; rock-mechanical aspects are not addressed. Features that are included in the model are nonideal gas properties, thermal interaction of the cavern with the surrounding rock salt, and thermodynamic heat effects that are associated with expansion and compression of gas in both cavern and wellbore. This model may find application in the planning and operation of gas caverns by gas distribution and transmission companies. Physical Model Fig. 1 shows the physical system that we wish to model. It consists of a subsurface cavern within an infinite salt formation connected to a surface wellhead assembly by a straight, vertical, cased borehole equipped with production/injection tubing. The cavern contains a dry natural gas. We assume a uniform gas pressure and temperature in the cavern at all times. The cavern pressure and temperature changes with time as a result of gas production/injection and heat exchange with the surrounding salt formation. During production, the gas expands; this is accompanied by a decrease in gas temperature. Likewise, the gas temperature increases when gas is compressed during injection. Initially (i.e., at the start of the gas storage operation), the temperature in the rock salt in the vicinity of the cavern is lower than far away from the cavern. This is the result of the solution-mining process that is used to create a cavern. In this process, cold fresh water is injected continuously into the cavern to dissolve the rock salt. The dissolution of salt into water is an endothermic process that further reduces the water temperature. During solution mining, therefore, the salt formation is cooled down continuously by circulating cold water, giving rise to a cold zone around the cavern. In the model, this cold zone is approximated by a zone of uniform temperature that is different from the temperature farther from the cavern. The two mechanisms that govern heat exchange with the salt formation are (1) transfer of heat at the cavern wall by natural convection and (2) non-steady-state conduction of heat in the salt surrounding the cavern. The heat transfer at the wall by convection is represented by an empirical heat-transfer coefficient. Flow within the tubing is assumed to be steady state and adiabatic. Therefore, temperature variations within the wellbore owing to compression and expansion of the gas are incorporated, but heat exchange with the well environment is ignored. The latter simplification is justified because of the high flow rates of the gas in the wellbore during injection and production. The gas in the cavern is assumed to be a real gas. That is, the pressure, volume, and temperature behavior of the gas are described by the real gas law, which includes the gas deviation, or z factor. The z factor depends on the composition of the gas and is a function of pressure and temperature. The well constraints that are included in the model are a prescribed production (or injection) rate and a maximum (or minimum) wellhead pressure. To allow a realistic representation of a practical operational sequence, the well constraints are to be specified as a function of time. During a production cycle, the production rate is prescribed together with a minimum wellhead pressure, which is determined by the minimum intake pressure of the surface gas plant. If this minimum pressure is reached, the well becomes pressure constrained and produces at declining rates. During an injection cycle, the injection rate, the temperature of the injection gas at the wellhead, and a maximum injection pressure are prescribed. The last is determined by the maximum permissible pressure of the wellhead and casing assembly. Cavern Equations The pressure and temperature within the cavern are governed by the mass balance and the energy balance applied to the cavern at large. Mass Balance. The mass balance states that, at any time, the amount of gas in the cavern must be equal to the amount of gas initially present minus the amount of gas produced. P. 278^