Publication Rights Reserved This paper is to be presented at the 39th Annual Fall Meeting of the Society of Petroleum Engineers on Oct. 11–14, 1964, in Houston, Tex., and is considered the property of the Society of Petroleum Engineers. Permission to publish is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of JOURNAL OF PETROLEUM TECHNOLOGY or the Executive Secretary. Such abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in JOURNAL OF PETROLEUM TECHNOLOGY or SOCIETY OF PETROLEUM ENGINEERS JOURNAL is granted on request, providing proper credit is given that publication and the original presentation of the paper. 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 considered for publication in one of the two SPE magazines with the paper. Abstract Wells with multiple producing zones can be fractured one zone at a time during continuous pumping with a high degree of probability of treating all zones by [1] perforating with charges designed to produce round, burr-free holes; [21 perforating the same low number of holes [usually eight] into each zone; [3] perforating in acid; and [4] using sealer balls between frac stages exactly matching in number the holes in each zone. During field trials of the process, recovered fluid-cut sealer balls indicated that quite often jet perforated holes had poor roundness and ragged burrs preventing good seal. It was necessary to have jet charges and guns redesigned to provide consistently round and burr-free entrance holes. Perforating the same number of holes per zone eliminates the guesswork when determining the number of ball sealers to use per stage. Experience has shown that perforating in acid reduces breakdown pressures, allowing the process to be used in areas where previous fracing indicated the method could not be applied. Using sufficient holes per zone to handle the total pumping rate at a low differential pressure prevents breaking down more than one zone at a time. High differential pressure from too few holes consumes energy and adds to the cost of the treatment. A calculation procedure is used to determine the holes required per zone based on flow rates and total cross sectional area of the perforations. Radioactive frac sand and gamma ray tracer surveys have been used in conjunction with straddle packers to determine the zones treated. Success ratios calculated as the number of zones fractured divided by the number of fractures attempted have been found quite high in 7–8 zone wells and still greater in wells with fewer zones. The method is less expensive than treating one zone at a time using isolating packers and is much surer of producing multiple fractures than simultaneously fracing generously perforated multiple zones. Continuous multistage fracturing produces maximum fracture area for a given injection rate as compared with simultaneous injection into multiple zones. The multistage technique also allows use of all the steps considered essential to good, single-stage treating. Results of field trials have consistently indicated vertical fractures. The fracture orientation has been evidenced by low treating pressure gradients and by gamma ray tracer surveys. Field work with radioactive propping agents provided a means of checking the quality of the cement job after fracturing.

This paper presents a pruning technique which can be used to reduce the number of paths searched in rule-based bag generators of the type proposed by (Poznański et al., 1995) and (Popowich, 1995). Pruning the search space in these generators is important given the computational cost of bag generation. The technique relies on a connectivity constraint between the semantic indices associated with each lexical sign in a bag. Testing the algorithm on a range of sentences shows reductions in the generation time and the number of edges constructed.