A new technique is presented for detecting the existence of and distance to two parallel sealing boundaries surrounding a producing oil or gas well. A log-log plot of time rate of change of well pressure vs. time provides a unique behavior to detect such a condition and allows the use of type-curve matching techniques to determine the khproduct. Introduction The idea of detecting and locating a reservoir boundary from transient pressure-time data first appeared in 1951. In that year Horner1 presented the transient pressure behavior of a constant-rate well located near a linear sealing fault. He also presented a method to calculate the distance to the fault from buidup pressure data. Dolan et al.2 applied the technique to drillstem tests. Davis and Hawkins3 gave an equation to determine the distance to the fault from drawdown pressure data. Gray4 reviewed these methods and discussed their limitations. Bixel et al.5considered a more general problem: a well located close to a linear discontinuity across which hydraulic diffusivity changes. They showed a procedure to determine the distance to such a discontinuity. Evrenos and Rejda6 employed superposition techniques to simulate various combinations of linear boundaries of interest in gas storage systems and showed how a match between the actual test data with various hypothesized model conditions can be used to arrive at a probable configuration of boundary conditions. Overpeck and Holden7 considered the effect of reservoir anisotropy on fault detection and showed that the distance calculated could differ by as much as 20% with those obtained by assuming isotropic medium. They gave a procedure for imaging when the principal permeability axes are at some angle other than 0 or 90° to the fault boundary. Rodgers and McArthur8 employed a minimum in standard deviation between observed pressures and a least-squares straight-line fit to determine boundary configuration. Prasad9presented a procedure to compute transient pressures for a well between two sealing faults intersecting at any angle. Jones10 in 1961 drew attention to the possible use of rate change of well pressure with time in detecting reservoir boundaries. Van Poollen11 presented graphs of time rate of change of well pressure during drawdown for various well locations between faults intersecting at 90 and 36°. Although this approach yields interpretable drawdown behavior, it has not been used widely in the petroleum literature. Witherspoon et al.12 considered the effect of a linear no-flow or flow boundary and presented the dimensionless pressure behavior caused by a constant-rate producing well at an observation well some distance away. They discussed techniques to analyze drawdown test data.

No abstract

Very little information exists for analyzing well tests wherein a part of the drainage boundary is under pressure support from water influx or fluid injection. An idealization is the behavior of a well in the center of a square whose outer boundary remains at constant pressure. A study of this system indicated important differences from the behavior of a well in a square with a closed outer boundary, the conventional system. At infinite shut-in, the well with a constant-pressure boundary will reach the initial pressure of the system, rather than a mean pressure resulting from depletion. It is possible to compute the mean pressure in the constant-pressure case at any time during shut-in. Interpretative graphs for analyzing drawdown and buildup pressures are presented and discussed. This case is also of interest in analyzing well tests obtained from developed five-spot fluid-injection patterns. Introduction Moore at. first demonstrated the application of transient flow theory to individual well behavior in 1931. Classic studies by Muskat, Elkins, and Arps in the 1930's and 1940's set the stage for two important papers in 1950 that clearly elucidated the basics of modern well-test analysis. One paper by Horner 5 summarized methods for analyzing transient pressure data from wells in infinite reservoirs (new wells in large reservoirs), and a well in a closed, circular reservoir under depletion (fully developed fields). The second paper by Miller, Dyes, and Hutchinsons considered two cases for wells assumed to have produced a long time before shut-in for pressure buildup. One case assumed a closed circular drainage boundary, and the other case assumed a circular drainage boundary at constant pressure. The former would represent annual well tests for fully developed fields, and the latter would represent wells under full water drive in single-well reservoirs. Since 1950, several hundred papers and a monograph have developed the behavior of a constant-rate well in a closed drainage shape of almost any geometry. Key in this development was a classic study by Matthews, Brons, and Hazebroek. The constant-pressure outer-boundary drainage region problem introduced by Miller-Dyes-Hutchinson was reviewed by Perrine in 1955, discussed by Hazekoek el al. in 1958 in connection with five-spot injection patterns, and mentioned briefly by Dietz in 1965. The only other studies dealing with water-drive conditions (constant-pressure outer boundaries) appear in Ref. 7 (Page 44) and in papers by Earlougher et al., published in 1968. It is clear that this case was eitherconsidered totally unimportant, orstudiously avoided. Almost all effort was expended on studying closed outer boundary (depletion) systems.Another problem concerned the conventional assumptions involved in developing well-test analysis method. Even for the common closed (depletion) systems, field applications raised the question of the importance of assumptions. Homer method of graphing assumed the well had been produced a short time, whereas the Miller-Dyes-Hutchinson method assumed that production was long enough to reach pseudosteady state -a long time in many cases. Engineers involved in applications were further confused by differences in methods, as well as by the importance of the assumptions required for analytical solutions that established welltest methods. Recently, Ramey and Cobb showed that an empirical approach could be used to avoid assumptions (which were sufficient but unnecessary) inherent in many previous analytical studies. It was decided to apply this method to the limiting case of a well in a full-water-drive, single-well reservoir - a well in a constant-pressure square. This case is a rarity not often seen in practice. It is closely approached by either an injector or a producer in a developed fluid-injection pattern, by a single injector in an aquifer gas-injection storage test, or by some single-well reservoirs in extensive aquifers.The main point is that a well in a constant-pressure square sets a limiting condition similar to a full water drive. The more common case of a well in a partial-water-drive reservoir should lie between this behavior and that of a closed square. SPEJ P. 107^

A technique for analyzing interference test data is presented that employsthe time rate of pressure change - the pD' function. Thisfunction exhibits a maximum value of 0.736 at atD/rD2 of 0.25 for an idealline-source well. Several field examples are included to demonstrate theapplication of this technique in determining transmissibility (kh/µ) andstorage (fch) between a well pair. Introduction It has been pointed out that interference tests1 may be run withgreater ease and may take less time than pulse tests2,3 to developin-situ reservoir properties such as transmissibility (kh/µ) and storage(fch). An interference test consists of recording the transient pressureresponse at an observation well caused by a constant rate change at some sourcewell. The pressure response can help determine formation continuity, fracturesorientation, and areal average transmissibility and storage between a wellpair. Interference pressure data can be analyzed by (1) least-squares regressionanalysis coupled with a two-dimensional single-phase compressible-fluidreservoir simulator4,5 and (2) type curve matching6,7techniques. A rapid hand analysis method1 requires the recognitionof the maximum slope line on pressure response ?p vs. time curve plottedon a rectangular coordinate paper. This slope is used to determine thetransmissibility (kh/µ). The intercept of this line on the time scale isused to obtain storage (fch) between the well pair. The slope of the line gives the maximum value of the time rate of change ofpressure at the observation well. This maximum slope occurs at the inflectionpoint of the ?p vs. time curve. The time to reach this maximum slope ofinflection point is also a characteristic of the system and, therefore, can beused to determine the storage (fch) between the well pair. The examplespresented in this paper will illustrate this technique. In view of the above, it is necessary to develop the behavior ofpD' at an observation well due to a constant-rate source wellfor a proper understanding of interference test behavior. The wellbore storageeffects are assumed to be negligible at this source or active well. This ispresented in the next section in terms of dimensionless quantities forsimplicity. In later discussion, equations in oilfield units are used. It is emphasized here that the pD' function has been usedbefore in petroleum literature for water influx8–10 and wellborestorage11,12 calculations. Further, pD' behaviorhas been employed in detection of reservoir boundaries.13–15 Theseapplications will not be discussed in this report.