Here is a noise-logging technique for finding behind-casing leaks. The leak source is located from a noise-amplitude log and the type of leak (single- or two-phase flow) is determined from a spectrum of noise at the source. Appropriate frequency cuts are then used to estimate leak rates. Introduction A noise-logging technique described in this paper has proved useful in searching for fluid movement in proved useful in searching for fluid movement in channels in the cement behind the casing of oil and gas wells. Such channels, of course, provide undesirable paths of communication between sands of different pressure. The idea of noise logging is old. In 1955, Enright qualitatively described a procedure for locating down hole, with an appropriate listening device, the peak noise associated with the point of origin of a leak. Korotaev and Babalov Used a noise detector to locate gas-producing zones in thick, open intervals. Stein et al. described the interesting procedure of listening opposite a productive zone in a flowing gas well for the "pinging" of sand grains against the producing string, thereby determining the maximum rate permitted before sand production begins. permitted before sand production begins. In spite of these applications, the general industry attitude still seems to be that a noise log is no better than or not even as useful as a temperature log - the traditional leak detector. This attitude is not entirely justified since there are instances in which noise logging has clear advantages over temperature logging. For example, it is seldom possible to flow a potential blowout well at a rate sufficient to give a definitive temperature anomaly. Likewise, a leak behind casing in a producing well might have a rate too small to detect with a routine temperature survey. We give in this paper experimental results that show that if one uses a detection sonde with good fidelity over the bottom half of the audible frequency range, the frequency structure of channel-type leaks has quite distinctive features. These features not only help distinguish single-phase flow from two-phase flow, but also provide a clue to a procedure for estimating an order-of-magnitude leak rate from peak noise. Several field examples demonstrate the routine operation of noise logging for detecting leaks and estimating rates. In particular, we present cases in which the noise log gives about the same information as a temperature log, cases in which the noise log gives additional information, and cases in which incorrect conclusions were drawn from a temperature log. Finally, we describe the potential of the noise logger as a flowmeter without moving parts. Here we rely primarily on experimental data, since our field data for such applications are quite limited. Frequency Structure of Channel-Type Leaks Details of construction and calibration of the detector are in Appendix A. We merely emphasize here -that the device, when driving 9,000 ft of armored cable, has its half-power points at 20 Hz and at 5,000 Hz. All subsequent spectra data are normalized to this frequency response (see Fig. 13). The experimental noise chamber, or leak simulator, is described in Appendix B. In using the simulator to study noise, we expand fluid across a porous plug and into a jacket packed with crushed marble. A 2 1/2-in. tubing string packed with crushed marble. A 2 1/2-in. tubing string through this jacket allows the detector to be positioned at the point of the leak. Variations on the basic theme are discussed in Appendix B. JPT P. 329

This paper shows how pressure buildup data distorted by afterflow can beanalyzed directly to give a numerical value for effective wellboretransmissibility. Because such data are directly indicative of wellbore-limitedproductivity, the method is helpful in assessing productivity, the method ishelpful in assessing the need for and the effectiveness of a well stimulation. Alternatively, it is a method for interpreting that portion of a pressurebuildup curve not subject to Horner analysis. The method does not require any estimates of formation or wellboreproperties for the analysis. The procedure consists of first plotting pressurebuildup from flowing plotting pressure buildup from flowing pressure as afunction of shut-in time on a log-log pressure as a function of shut-in time ona log-log scale and, second, matching the data points to one of a set ofparametric type curves. From this match, a numerical value is calculated forwellbore transmissibility. Finally, the shape of the buildup curve indicateseither wellbore damage or stimulation. The paper describes the generation and use of type curves with computed dataillustrating the effects of wellbore damage or stimulation. A variety of fieldexamples demonstrate the practical utility of the method. practical utility of the method Introduction Afterflow, or afterproduction, is the continued influx of fluid from aformation into a wellbore after the well is shut in. The greater the storagecapacity of the wellbore, the longer the duration of afterflow. Such afterflowprecludes a conventional analysis of a pressure buildup curve so long as theafterflow rate is greater than a few percent of the production rate prior toshut in. Consequently, production rate prior to shut in. Consequently, afterflow has generally been regarded as a nuisance. Yet, it is reasonable tosuppose that such data contains valuable information. Certainly most of thepressure change occurs during afterflow provided it is present; hence, pressuremeasurements during afterflow should pressure measurements during afterflowshould be more accurate than at later times. Also, the pressure change in thewellbore during afterflow should reflect a sort of dynamic balance between twolimiting factors:the capacity of the wellbore to store fluid andtheease with which the formation supplies fluid to the wellbore. This secondfactor, which is indicative of wellbore transmissibility, is the one oftechnical importance since it determines productivity. However, most of thepublications dealing with afterflow are concerned either with estimating itsduration or with correcting pressure buildup data taken during its pressurebuildup data taken during its duration. Gladfelter, et al. gave a method forcorrecting pressure buildup data as early as 1955. Ramey has provided equationsto estimate the duration of afterflow.

Johnson et al. have described a new well-testing technique that measures formation flow properties between wells.'The technique, called pulse-testing, requires a sequence of rate changes in the flow at one well and measurement of the resulting pressure changes at an adjacent well with a very sensitive differential pressure gauge.This paper describes an extensive application of the technique in a producing oil field. Pulse-tests on 28 of 45 possible well pairs in the field provided a picture of the areal distribution of reservoir hydraulic diffusi vi ty, transmissibility and storage. The primary objective in presenting these data is to demonstrate the potential of the method for reservoir description. A second objective is to show in three ways the qualitative and quantitative accuracy of reservoir parameters determined from pulse-tests: (1) pulsetest data show a nonuniformity in the field, closely correlating with the oil-water distribution as given by production data; (2) pulse-test values for permeability are comparable with core values; and (3) perhaps most important, the field responds to a conventional interference test in the manner in which pulse-test data predict it should.

Reservoir transmissibility and storage values can be obtained from pressure pulses induced in one well and measured at a second well. Such pulse-test values are generally calculated from pulse-test values are generally calculated from equations which assume the formation is homogeneous. This paper examines the effects of areally distributed heterogeneities on pulse-test values. An influence area is first developed for a pulse-tested well pair; only those heterogeneities pulse-tested well pair; only those heterogeneities within this area significantly affect pulse-test results. Next, for three limiting cases, the manner in which a pulse test averages heterogeneities within the influence area is described. These are the cases for which one of the three formation properties - hydraulic diffusivity, transmissibility properties - hydraulic diffusivity, transmissibility and storage - is constant throughout the influence area. Finally, a method called directional correction is developed that when applied to pulse-test values of transmissibility and storage restores some, if not most, of the true degree of heterogeneity to these values. Accuracy of the method depends upon the relative variability of the true values. Introduction The pulse-testing method of Johnson et al. uses a sequence of rate changes at one well to create a low-level pressure interference response at an adjacent well. This response is readily analyzed for reservoir properties if one assumes an infinite, homogeneous reservoir model. The field data of McKinley et al. show that, despite the use of a simple analytical model, pulse-test values are sensitive to between-well pulse-test values are sensitive to between-well formation properties. Calculated values for transmissibility and storage exhibit considerable variation with direction around a central pulsing well. These values cannot, however, reflect the exact degree of heterogeneity since flow about the pulsing well is usually nonradial. pulsing well is usually nonradial. This paper examines the effects of certain idealized types of areal heterogeneities on pulse-test values calculated from the simple model. In pulse-test values calculated from the simple model. In particular, an influence area for a pulse-tested well particular, an influence area for a pulse-tested well pair is first developed. This area is defined as that pair is first developed. This area is defined as that areal portion of the formation whose properties determine the numerical value, obtained from pulse testing the well pair. Its size depends on the length of the pulse and the hydraulic diffusivity of the formation. We then determine the type of average values yielded by a pulse test when heterogeneities are distributed randomly throughout the influence area. Results of these studies provide a simple correction scheme that restores some of the true degree of heterogeneity to pulse-test values of transmissibility and storage. Accuracy of the method depends on the relative variability of the latter two reservoir parameters. PULSE-TEST TERMINOLOGY AND ANALYSIS PULSE-TEST TERMINOLOGY AND ANALYSIS A typical rate-change sequence at the pulsing well appears at the bottom of Fig. 1. The pulse rate is q reservoir B/D and the pulse length is delta t minutes. The time between pulses is R delta t minutes. Each such pulse cycle induces at the responding well the pressure response (pulse) shown at the top of Fig. 1. According to the analysis method of Johnson et al., each pressure pulse is characterized by two quantities - a time lag, tL minutes, and a pulse amplitude, delta p psi. How these values are pulse amplitude, delta p psi. How these values are determined from the pressure response is apparent from Fig. 1. For an infinite, homogeneous formation, the time lag, tL, the R-value and the well spacing, rws, are sufficient to determine the hydraulic diffusivity, of the formation. These values, coupled with pulse amplitude, p, and pulse rate, q, determine formation transmissibility, =kh/ . Formation storage, = ch, is obtained from the ratio = / . Charts to facilitate this analysis are given by Brigham for R=1. SPEJ P. 181

This paper describes a preliminary study of the linear flow of a non-Newtonian fluid, a water solution of Dextran (a polysaccharide), in porous media. A modification of Darcy's law, which uses capillary rheology data, is developed to describe non-Newtonian flow in underground reservoirs. The generalization, in effect, replaces the porous media with a capillary of equivalent radius proportional to the square root of the ratio of permeability to porosity. The constant of proportionality a . should be independent of permeability and porosity for a given type of rock. This has been partially confirmed experimentally. In principle, a capillary rheogram and a single core test permit evaluation of ao. Then non-Newtonian flow can be predicted in this type of rock regardless of porosity, permeability, or flow rate.The flow of a Newtonian fluid (a fluid with a constant viscosity) through porous media is in good agreement with Darcy's law as expressed by Equation (1) with gravitational forces neglected.(1)where V, is the fluid superficial velocity vector, V p is the pressure gradient, f i is the fluid viscosity, and k, a property of the structure of the porous medium, is the permeability with consistent units of squared length. In the petroleum industry, it is customary to measure V, in cm./sec., f i in centipoise, and V p in atm./cm. with the resulting units of k called the darcy. The conversion is 1 darcy = 9.87 X 10-e sq. cm. This paper describes an extension of Darcy's equation (1) to the case in which the fluid does not follow Newton's law of a constant viscosity (ratio of shear stress to deformation rate); rather, the fluid belongs to a class called Stokesian fluids in the literature (1 ) . Such fluids have the property that the nonhydrostatic components of the fluid stress are unique nonlinear functions of the deformation rate components with the result that the measured "viscosity" varies with the shear stress prevailing in the viscometer. The bulk of the paper develops a one-dimensional theory and compares it with preliminary experimental results for an aqueous solution of a sugar polymer available commercially under the trade name Dextran. The model is developed by direct analogy with the results obtained for flow of the fluid through a uniform capillary and utilizes the rheogram obtained from the latter. A twodimensional analysis, not given here, showed that the dispersive or nonaxial component of the velocity enters the flow equation only as a product with an unknown normal coefficient of viscosity. It should also be pointed out that our choice of the model was guided by two restrictions:( 1 ) The model must give good predictions over a wide shear stress range, and (2) the model must be in a form suitable for routine calculations. The first restriction eliminates some of the stress-deformation rate relations proposed in the literature for Stokesian fluids such as the power law model; the second eliminates others such as the Eyring model.Finally, the flow of non-Newtonian fluids in porous media is important to th...