The Effect of Perforating Oil Well Productivity

Abstract

Abstract A solution has been obtained to the problem of calculatingflow into a cased and perforated well. Equations describingthe idealized system were solved by numerical analysistechniques on a high-speed digital computer. Computerexperimentation indicated that the results are within 3 percent of the exact solution. Computed results are presented as an apparent skin effect, on a series of dimensionless working curves. Productivityratios can be rapidly calculated from these data for thewide range of wellbore and reservoir properties actuallyencountered in field practice. Any reasonable verticalanisotropy ratio can be included in the computation. Productivities can be calculated for wells perforated in aregular pattern, a single horizontal plane or a vertical lineon one side of the casing. Solutions for asymmetricalperforation patterns can be easily obtained from the workingcurves. Solutions for flow into well completed with ahorizontal notch are also provided. Results show that productivity can be increased by extendingperforation penetration. This is especially true forshallow penetrations. The highest productivity is obtainedwhen perforations are arranged in horizontal planes, asopposed to a vertical line on one side of the casing. Fouror five perforations in one plane will approach themaximum productivity. The effect of perforation hole diameteris small, and is noticeable only in shallow penetrations. Introduction The perforating method of well completion has beensuccessfully and widely used in most producing areas. Inthe past, the desired perforation results were achieved bysimply shooting numerous large holes in the casing. Aperforating scheme for an area, or particular well, wasestablished by evaluating two types of experimental data: thewell flow index and the productivity ratio. The well flow index test is a means of determining therelative flow capacity of perforations in a linear system. This test also gives information on the perforation size, shape and hole damage which can be expected underwellbore conditions. However, relative flow data from this testcannot be accurately transformed into the radial wellboresystem. Thus, no true indication of the productive capacityof a perforated well can be obtained from the well flowindex test. A well productivity ratio is derived from electrolyticmodels built to simulate perforated wells. Availableproductivity ratio data are limited in that all importantvariables are not extensively evaluated. For example. data arelimited to well radii of 3 and 6 in., and to maximumperforation penetration of 1 ft. Practically no information isavailable on the pattern of flow into a perforation. Theeffect of various perforation patterns on well productivityhas not yet been determined and the effect of perforationdiameter has not been thoroughly studied. Also, it will beshown that this type of electrolytic model data is probablyin error by as much as 10 per cent or more. Modern completion techniques such as limited-entryperforating, single-plane fracturing, steam and hot airinjection and chemical consolidation of incompetent formationsall rely on injection and/or production from a limited typeof completion. These completions may consist of severalhigh-capacity perforations or a horizontal notch which isequivalent to an infinite number of perforations in oneplane. Proper design of these new completion techniquesrequires, in part, accurate estimates of a well's productivecapacity. Data on perforated and notched well productivity havebeen determined in this investigation. Results arepresented as a function of the pertinent variables. Equationsdescribing the idealized system were solved by numericalanalysis techniques on a high-speed digital computer. DESCRIPTION OF PROBLEM PRACTICAL APPLICATION The computed results can be applied to wells whichmeet several general specifications. An external drainageradius of the well must be known or assumed, but the wellneed not be drilled on a regular pattern. The well must beeased and cemented through the entire producing interval. And, the casing must be perforated with one or morehorizontal planes of perforations. The perforation patternitself must conform to three geometrical requirements.The perforations in a plane must divide the plane intoequal angular segments (Fig. 1). Four perforations perplane would be 90 degrees apart.Perforations in a plane must be directly above orbeneath perforations in adjacent planes. For two shots perplane, perforations would lie in the BB' plane (Fig. 1).Horizontal planes must have equal vertical spacingand be separated from the top and bottom of theformation by one half the spacing interval. Single planes of perforations should be in the middle of the formation. This isshown in Fig. 2 where h is the formation thickness in asingle plane completion or the spacing interval in a multipleplane completion. The spacing interval at the top and bottom of theformation may vary somewhat without causing an appreciableerror in the productivity calculation if the formation isreasonably thick and there are many horizontal planes ofperforations. JPT P. 518ˆ