Artificial neural networks-based correlation for evaluating the rate of penetration in a vertical carbonate formation for an entire oil field

Abstract Over the past decade, a number of drilling models have been proposed for the optimization of The rotary drilling process and the detection of abnormal pressure while drilling. These techniques have pressure while drilling. These techniques have been largely based Upon limited held and laboratory data and often yield inaccurate results. Recent developments in onsite well monitoring systems have made possible the routine determination of the best mathematical model for drilling optimization and pore pressure detection. This modeling is accomplished through a multiple regression analysis of detailed drilling data taken over short intervals. Included in the analysis are the effects of formation strength, formation depth, formation compaction, pressure differential across the hole bottom, bit diameter and bit weight, rotary speed, bit wear, and bit hydraulics.This paper presents procedures for using the regressed drilling model for selecting bit weight rotary speed, and bit hydraulics, and calculating formation pressure from drilling data. The application of the procedure is illustrated using field data. Introduction Operators engaged in the search for hydrocarbon reserves are facing much higher drilling costs as more wells are drilled in hostile environments and to greater depths. A study by Young and Tanner has indicated that the average well cost per foot drilled is increasing at approximately 7.5 percent/ year. Recently, more emphasis has been placed on the collection of detailed drilling data to aid in the selection of improved drilling practices.At present, many people are using one drilling model for optimizing bit weight and rotary speed, a different drilling model for optimizing jet bit hydraulics, and yet another model for detecting abnormal pressure from drilling data. Each model has been based on meager laboratory and field data. We have tried here to combine what is known about the rotary drilling process into a single model, develop equations for calculating formation pore pressure and optimum bit weight, rotary speed, and jet bit hydraulics that are consistent with that model, and provide a method for systematically "calibrating" the drilling model using field data. DRILLING MODEL The drilling model selected for predicting be effect of the various drilling parameters, xj, on penetration rate, dD/dt, is given by penetration rate, dD/dt, is given by(1) when Exp (z) is used to indicate the exponential function ez. The modeling of drilling behavior in a given formation type is accomplished by selecting the constants a, through a 8 in Eq. 1. Since Eq. 1 is linear, those constants can be determined from a multiple regression analysis of field data. EFFECT OF FORMATION STRENGTH The constant a, primarily represents the effect of formation strength on penetration rate. It is inversely proportional to the natural logarithm of the square proportional to the natural logarithm of the square of the drillability strength parameter discussed by Maurer. It also includes the effect on penetration rate of drilling parameters that have not yet been mathematically modeled; for example, the effect of drilled solids. EFFECT OF COMPACTION The terms a2x2 and a3x3 model the effect of compaction on penetration rate. x2 is defined by(2) and thus assumes an exponential decrease in penetration rate with depth in a normally compacted penetration rate with depth in a normally compacted formation. The exponential nature of the normal compaction trend is indicated by the published microbit and field data of Murray, and also by the field data of Combs (see Fig. 1). SPEJ P. 371

MAURER, W.C., JERSEY PRODUCTION RESEARCH CO., TULSA, OKLA. Abstract A drilling-rate formula for roller-cone bits is derived from rock cratering mechanisms. This formula holds for "perfect cleaning", which is defined as the condition where all of the rock debris is removed between tooth impacts. Under these conditions, the drilling rate of is directly proportional to the rotary speed and to the bit weight squared, and inversely proportional to the bit diameter squared and to the rock strength squared. Under imperfect cleaning conditions, such as those usually present in field drilling, regrinding of the cuttings occurs under the bit, and the drilling rates fall below those for perfect cleaning. Introduction Drilling with a roller-cone bit consists of two fundamental operations: the formation of craters under the bit teeth, and the removal of the broken rock from the craters. To delineate the mechanisms of drilling, it is first necessary to understand the mechanisms involved in the formation of individual craters and then to relate these mechanisms to the over-all drilling operation. CRATER FORMATION When a bit tooth impacts a rock, the rock is elastically deformed until the crushing strength of the rock is exceeded, at which time a wedge of crushed rock is formed below the tooth as shown in Fig. 1. As additional force is applied to the tooth, the crushed material is compressed and exerts high lateral forces on the solid material surrounding the crushed wedge. When these forces become sufficiently high, fractures are initiated below the tooth and propagate to the free surface of the rock. The trajectories of these fractures intersect the principal stresses at a constant angle, as predicted by both Mohr's and Griffith's theories of failure. It has been experimentally shown that the volume of an impact crater, Vc, varies as .........(1) where Ec is the total energy imparted to the rock during the formation of the crater, and Eo is the threshold energy required before cratering is initiated (Fig. 2). Indexing experiments have shown that, when there is a second free face to which the crater can fracture, a larger volume of material is removed and that above a transition zone there is a linear relationship between Vc and Ec, which has a slope equal to the relationship for the single crater. The beneficial effect of indexing tends to offset the threshold energy requirement to a large extent, as shown in Fig. 2, and the relationship is closely represented by ......(2) Rate-of-loading effects have been used to explain the nonproportional relationships usually obtained between drilling rate and rotary speed. The data in Fig. 3 show that the Ec/Vc parameter remained constant for craters produced with impact velocities ranging from 10 to 8,000 ft/sec. Since no rate-of-loading effects were detected over this wide range of loading rates, it seems improbable that there would, be detectable rate-of-loading effects present in the small changes in impact velocities produced by varying the rotary speed. The writer has shown (Fig. 4) that, for craters produced in rock by impacting spheres, ..............(3) where X is the depth of penetration. Simon has shown that this relationship also holds for craters produced in rock by penetrating wedge-shaped chisels. JPT P. 1270^