Wellbore Transmissibility from Afterflow-Dominated Pressure Buildup Data

Abstract

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.

A Method to Account for Afterflow at the Pulsing Well During Pulse Tests

“…4 Using this parameter, we can determine the afterflow vs. time profiles that would occur during the pulsing-well shut-in periods and incorporate them into a computer simulation of each pulse test. A typical pulsing well-flow profile showing afterflow during the shut-in period is illustrated in Fig.…”

From Straight Lines to Deconvolution: The Evolution of the State of the Art in Well Test Analysis

“…This was not universally understood before the development of the integrated methodology, because straight-line methods [MDH (Miller et al 1950) and Horner (1951)] and type-curve analysis-with different type curves representing the same model (Agarwal et al 1970;McKinley 1971)often gave different results.…”

“…The controversy even led to an early SPE board decision (Ramey 1992) not to include full-scale type curves in the Earlougher SPE Monograph 5 (Earlougher 1977), and it was recommended in Monograph 5 that type-curve analysis be only used in an emergency or as a checking device after "conventional" (i.e., straight-line) methods had failed. After the systematic approach to the analysis of well tests was established (Gringarten et al 1979;Gringarten 1982Gringarten , 1985aGringarten , 1986, the differences among published wellbore storage type curves (Agarwal et al 1970;McKinley 1971;Earlougher and Kersh 1974) were explained (Gringarten et al 1979), an industrystandard type curve emerged for wellbore storage and skin (Gringarten et al 1979), and the early SPE board decision was reversed.…”

“…produced by well damage or result from partial penetration (Brons and Marting 1961) or multiphase flow around the well (Kazemi 1975). Type-curve analysis (Ramey 1970;Agarwal et al 1970;McKinley 1971;Gringarten et al , 1975Cinco-Ley et al 1978;Agarwal et al 1979) was introduced by Ramey (1970) to get an insight into the meaning of the skin and therefore on the means to cure it. Particular emphasis was placed on wellbore storage (Agarwal et al 1970), highconductivity fractures (Gringarten et al 1975) and lowconductivity fractures (Cinco-Ley et al 1978).…”

New Method of Analyzing the Pressure behavior of a Well Near Multiple Boundary Systems

“…In 1968, Earlougher et al 5 applied superposition to a square system and shown that the their results are applicable to any number of wells inside the rectangle and to any type of outer boundaries such as no-flow, flow and mixed boundaries. The semilog approach was gradually replaced by type-curve matching techniques [6][7][8][9][10] in the 70's.…”