Threshold displacement pressures are needed to determine how much overpressure can be used in storing natural gas. An experimental technique for determining threshold pressures by displacing water with gas from samples saturated with water is presented. Threshold pressures for eight low permeability samples were measured. Threshold pressure data obtained in this work, plus data on higher permeability samples reported in the literature, are correlated with porosity, permeability, surface tension and formation resistivity factor, Mercury injection pressures also were measured and correlated with air-water threshold pressures. Threshold pressures were found to be independent of time. An aerial photograph of gas emerging from The top of a core shortly after its threshold pressure has been exceeded shows that the gas bubbles we uniformly distributed across the face of the core. Channeling will occur, however, when an increased gas phase permeability is reached. A porous medium can be resealed after its threshold pressure has been reached provided it has not been desaturated below a fixed saturation. Its new threshold pressure will be lower than when the sample is 100 percent saturated with water. Introduction The degree of overpressure in excess of the discovery pressure that a gas storage reservoir can withstand is determined by the ability of its caprock to contain gas, providing the pressure does not exceed the structural limit of the reservoir. The retention of gas in a reservoir by a caprock saturated with water is a result of the capillary forces acting at the gas water interface. Without the presence of water in a caprock, gas would leak out of the reservoir at a rate determined by the permeability of the caprock to gas. The ability of a caprock to contain gas is expressed in terms of its threshold displacement pressure, which is defined as the minimum pressure needed to initiate the displacement of a wetting phase by a nonwetting phase from a porous medium 100 percent saturated with the wetting phase. The gas industry must be able to predict how much "overpressure" a gas reservoir can withstand before leakage occurs by gas displacing water from caprock overlying the reservoir. This is of economic importance since the storage capacity of a gas reservoir is proportional to its pressure. The discovery pressure for most reservoirs is found between the upper and lower limits shown in Fig. 1. Discovery pressures in excess of their hydraulic pressure gradient are attributed to the compaction of an isolated shale formation by the overburden. The lower limit of 0.433 psi/ft corresponds to the weight of the overburden, the gradient of the rock itself. SPEJ P. 174ˆ

The nature and the limits of validity of Darcy's law as applied to the flow of natural gas through reservoirs has been considered in order to resolve some controversial aspects of the effect of turbulence on pressure drops. The equivalence between various concepts and viewpoints advanced in the past by several investigators to explain how and why a gas well does not necessarily perform according to Darcy's law is shown. Starting with generalized equations of flow of fluids through porous media, a partial differential equation has been derived which accurately represents the flow at all rates. This equation has been numerically solved using an IBM 704 digital computer. The results permit plots of unsteady radial pressure distribution curves from which specific isochronal backpressure curves may be constructed. These back-pressure curves show the effect of the fl factor on the slope of the back-pressure curve. The calculations further indicate that the drainage radius for a gas well in turbulent flow propagates at a rate dependent upon the rate of production at the wellbore. This is quite different from the case with liquid flow or natural-gas flow in laminar regime. Additionally, the effect of reservoir inhomogeneities and crossflow between layers of different permeability on the back-pressure performance of gas wells has been considered red. In light of the current numerical results the significance and limitation of the rate of flow function Y proposed by Smith has been discussed. Introduction The relationship between the pressure drop and flow rate in problems of fluid flow through porous media is known to be affected by the nature of flow through the porous matrix. It has been observed by many that, for a range of flow rates, the pressure drop remains proportional to the rate of flow. When some flow rate is reached, however, it is usually observed that the pressure drop gradually begins to increase more than proportionally to the flow rate. It is well known that this phenomenon was first observed by Osborne Reynolds in 1901 in experimenting with flow through pipes. In his classical experiments. Reynolds made visual observations on the condition of streamlines evidenced by injecting a dye into water flowing through glass tubes. In these experiments, the abrupt transition between steady, "streamline, laminar" flow and unsteady random turbulent flow was found to be a function of the dimensionless group (D / ), now known as the Reynolds number. During these experiments, in addition to observations on the nature of flow regimes, the proportionality between flow rate and pressure drop in laminar flow was contrasted with the nonlinearity between these variables in turbulent flow. Fancher and Lewis reported data on various consolidated and unconsolidated sands in 1933. Their conclusions were that ". . . the flow of fluids through these porous materials closely resembles that through pipes; that there is a condition of flow in porous systems which resembles viscous flow, another which corresponds to turbulent; that the change from one type to the other takes place at a definite and reproducible condition for each system". In 1947, Brownell and Katz published a method to predict the laminar and turbulent flow behavior from the particle size, bed porosity and the particle sphericity, employing the friction factor-Reynolds number charts for pipes. Several investigators have verified the work of Fancher, Lewis and Barnes and presented their data as friction factor-vs-Reynolds number plots. The equation which would represent the pressure gradient over the whole range of velocity must have an added term over that represented by Darcy's law. Accordingly, the pressure gradient necessary to sustain flow at the velocity (v) through a porous medium may be represented by the following equation, suggested by Forscheimer. = ..........(1) The nature and the range of validity of Darcy's law has been the subject of studies by many investigators over the past years. While everyone seemed to agree on the need for a quadratic correction term to Darcy's law to make it effective over the range of velocities, the concept of inception of turbulence and the use of the term "turbulent flow" remained controversial. JPT P. 799^

Summary Underground storage of natural gas is a mature industry vital to a gas delivery system. It developed as a subdiscipline of gas technology with certain additions. This overview treats containment of gas without migration, monitoring, inventory verification, retention of well deliverability, practice and advantages of delta pressure, aquifer behavior, and compressed air storage. Introduction Underground storage is the process which effectively balances a variable demand market with a nearly constant supply of energy provided by the pipeline system. Storage reservoirs are the warehouses to give a ready supply of gas that can serve a market with high peak demands in cold weather. The natural gas simply is injected into-underground storage reservoirs when market demand falls below the supply available from the pipeline. It is withdrawn from the storage environment to supplement the steady supply from the pipeline when the demand exceeds the supply. Through the years, underground storage has become a mature industry.For northern climates, storage gas represents about 20% of the annual sales - on a cold day, storage gas may reach 50 to 70% of gas sold. With a superb record of providing continuous fuel service to residences, hospitals, and commercial buildings, underground gas storage has been a vital part of natural gas distribution systems. Historically, underground storage (which was practiced first in 1915) experienced a remarkable growth starting in 1950, resulting in nearly 7.5 Tcf (212 × 10 m) of storage in more than 399 pools in 26 states by 1979. Some gas storage literature covering developments over the years are listed in Refs. 1 through 12. Current Status The underground storage committee of the American Gas Assn. (AGA) compiles annual statistics for the industry. Fig. 1 shows the growth of the total quantity of gas in storage reservoirs and the quantity of working gas withdrawn in a given year. Table 1 gives AGA statistics on the reservoirs, facilities, and magnitude of certain parameters. Fig. 2 is the AGA map showing the location of storage projects. Although the annual volumes of gas distributed currently are not increasing and may even decrease in some areas as a result of conservation, the change toward a larger fraction of the gas going to spaceheating has a tendency to increase the need for storage.When the expensive synthesis gas from coal and pipeline-accessible gas from Alaska and Mexico arrive in the market, storage will become increasingly important. In the case of synthetic natural gas (SNG), storage will permit matching a variable supply to the variable demand of the markets.A brief history of the technical developments during the past 40 years is given next. Early field design procedures were adapted from natural gas production technology. A series of studies conducted during the 1950's resulted in (1) practices for more efficient use of the storage reservoir, (2) assurance that injected gas remained in the reservoir, and (3) ways to handle new problems as they arose. Some of our more recent activities are described in the following sections. Development of Underground Storage Historical records show that gas storage began by allowing depleted gas reservoirs produced in the winter to be recharged in summer by pipeline gas. As the intercontinental pipeline systems spread rapidly in the postwar period, reservoirs were selected and refurbished for full use as underground storage reservoirs. JPT P. 943^

Ilk paper represents the first effort in quantifying the "turbulence intensity" as related to deliverability fronl gas wells. A new dimensiotdess number called the Forchheimer number, NFO, has been proposed along with a generalized expression of turbulence coefficient. Applications include a new concept called "inverse productivity index, J{, " proposed as an eltemative to classical backpressure plots for characterizing gas well performance. SPE Formation Evaluation, March1987

The waterflood performance of a water-wet, stratified system yith crossflow is computed by, a finite difference procedure. The effects of five dimensionless parattteters on the oil displacement eficiency, water saturation ccmtours and crossflow rates are evaluated in the absence ' of mzvi;v forces. Crossflow due to viscous and capillary f&-;es is".shown to exert a significant efleqt on oil recovery in a field-scale madel of a two-layered, water-wet sandstone reservoir. T/te ' crossflow is qt a maximum in the vicinity of the front advuvcing in the moral permeablel ayer. Under favorable mobility ratio conditions, the computed oil recovery with crossflow always is inter-Inediate bet ween that predicted for a uniform reservoir and that for a tayered reservoir with no crossflow..