An analysis of the scattering of transverse elastic waves by spherical obstacles is presented. The scatterer is taken to be (a) a cavity, (b) a rigid sphere, (c) a fluid-filled cavity, and (d) to consist of an elastic material with properties different from those of the surrounding material. The problems are carried as far as possible analytically without approximations and are reported as matrix equations. The solution of these equations yields the expansion coefficients that describe the waves which are scattered outward from the obstacle and which are excited within the scatterer. A general expression for the scattering cross section offered to a transverse wave has been derived. The Rayleigh approximation is then considered in detail for three of the cases.

This paper was prepared for the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Las Vegas, Nev., Sept. 30-Oct. 3, 1973. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract In the literature on Temperature logging, relationships exist which may be used to predict the temperature responses in producing wells as a function of volumetric flow rate, time of production, fluid gravity, geothermal gradient, and various thermal coefficients. These relationships indicate that under "ideal conditions" the temperature curve recorded above a producing zone as a function of depth exponentially approaches an asymptote parallel to the natural geothermal profile. This asymptote is displaced from the geothermal profile by an amount depending on the mass flow rate and the time the well has been produced. Theoretical examples will illustrate the use of these relationships to predict the temperature responses in producing wells for cases of flow rates up to 1,000 B/D producing wells for cases of flow rates up to 1,000 B/D and for production times up to 1,000 days. With the knowledge of the predictive equations, the reverse problem is considered. Temperature logs are examined to locate intervals exhibiting this exponential behavior. A coefficient in the basic relation is adjusted to make the relation fit a given exponential segment. Then, knowing the time the well has been produced, the mass flow rate is computed. If fluid-density information is available, the volumetric flow rate is computed. This method has its greatest applicability when used in conjunction with spinner-type flowmeters to detect fluid flow in the casing annulus. For use of the method, production times should be greater than 10 days, and producing zones should be separated by at least 100 feet.

To further the scientific aspect of temperature logging procedures and interpretation methods, theoretical models describing the excba~ge of heat between &sjection fluid, borehole, surrounding formation, msd &sjection zone have been tised to study: ., , t~e 0 orehoie-fiuid tempevdtww ds&mg~%fectto?s, . . . as determined by rate, depth, and duratiom of injection, the temperature a)ong the axis of the cylindrical system as it recovers under shut-in conditions from the disturbance due to itsjection, and the establishment oj the formation-temperature disturbance due to injection of fluid. Comprehension of the beat-exchange phenomena involved has been stressed, rather than a'etaiied matchi+zg of specific logs. In general, it was sought to establish what information a temperature survey could reasonably be expected to yield under "ideal" and actual jield conditions. Printed in U.S.A. The results provide specific Asformatiom cotscertsirsg: -a criterio~for rrwming ats itsjectiofl temperature survey as a source oj flow-rate data, -the eJJects of vertical beat exchange on temper-CSture distw'bution during ;tsjectiots and shut-hs, -the relation betweets time of shut-ti and abdity to discern tbe radial extent of the jormationtemperature anomaly, and -& Artie% between. mte gad ds4vatiom 0/ i*jectiots and the radial extent of tbe formation a~omaly.A principal conclusion from this study is that a temperature survey alone should not always be expected +.-. .J.lA .ml..w.t.~~t&MV i~formation.Rather, a com-." y----.'".Z,, ".. -, bination of temperature and flowmeter or tracer surveys should be conducted. Further, when injectiofi has been goizzg on for a considerable length of time, beat exchange within the formation can cause an atsomaly of greater vertical extent than the injection zone itself. 1 .