Summary A simple method is proposed for predicting downhole shaped-charge gun performance based on the use of API RP 43, Edition 5, Sec. 1 data. API Sec. 1 has been the preferred method for assessing perforating gun system performance because of the simplicity of the test and its use of standard field guns fired at maximum shot densities and positioned as they would be in an actual well. The validity of the proposed method is demonstrated, allaying past concerns regarding the translation of data from Sec. 1 nonrock, nonstressed concrete targets to downhole conditions. The new method is based on an observed linear relationship between Edition 5, Sec. 1 and Sec. 2 penetration information. The applicability of the well-known Thompson relationship between formation compressive strength and perforator penetration to Edition 5, Sec. 2 and therefore to Sec. 1 data is shown. Incorporating necessary corrections for casing entrance hole size, downhole effective formation stress, and casing configurations different from those in the API test completes the translation of surface data to downhole conditions. Introduction Well flow performance is significantly affected by the extent of perforated hole penetration into the formation and the hole size in the casing, together with other fixed geometric parameters, such as shot density and gun phasing. Values of perforation penetration and hole size commonly available to the completion designer are provided by API RP 43, Edition 5 published data. These data are derived from tests at the surface and provide only limited simulation of subsurface conditions regarding formation physical properties and stress. Surface data can significantly vary from that to be expected downhole and must be converted to in-situ values before proceeding with well flow performance calculations. This conversion of RP 43, Edition 5 surface test performance to downhole involves consideration of the specific downhole formation physical properties, formation in-situ stress, casing properties, and the specific gun-to-casing configuration. This paper reviews the factors affecting downhole penetration and casing entrance hole size for perforating guns, discusses API data as a basis for predicting downhole performance, reviews API test results and results of tests performed specifically for this paper, and proposes a procedure for translating surface API data to downhole conditions. Factors Affecting Downhole Performance of Perforating Guns Gun-to-Casing Clearance. Clearance, the distance between the gun OD and the casing ID along the axis of the shaped-charge jet, can have a significant effect on total penetration, L, and casing entrance hole size, deh. As Fig. 1 shows, the estimated downhole L/deh of a commercial 33/8-in. gun perforating 7-in. casing varies from 14.45 in./0.35 in. to 7.65 in./0.21 in. when operated in the common eccentric running position (Fig. 1a). Values are constant when clearance is controlled (Figs. 1b and 1c), typical methods for positioning guns. The importance of the gun-to-casing arrangement is evident; it is the estimated downhole L/deh used in mathematical models to calculate well flow. Formation Strength. Compressive strength of the formation being penetrated influences perforation penetration depth. Thompson disclosed a semilog relationship between formation wet compressive strength and total penetration depth (casing thickness + cement thickness + formation penetration) for API Edition 4 Section 2 type targets. Penetration performance in unstressed sandstones and limestones of different compressive strengths is available in the literature. The high-strength end of Thompson's relationship (beyond 14,000 psi)was modified by data from Weeks' formula, resulting in the composite representation in Fig. 2. As Fig. 2 indicates, a perforating gun that provides a penetration of 11.8 in. in rock with a wet compressive strength of 7,000 psi (Point A) will penetrate less than 7 in. in a l4,000-psi formation (Point B). On the other hand, it would penetrate 15 in. in a 3,000-psi material (Point C). Use of mean wet uniaxial compressive strength, S, values is suggested in applying the above relationship. S is defined as the average of compressive strength values taken perpendicular and parallel to the bedding plane of saturated rock. It is related to the commonly used dry compressive strength measured perpendicular to the bedding plane, Sd, as follows: (1) When the value of S is unavailable, it may be approximated using formation porosity by means of Fig. 3, which is derived from the results of tests in several sandstones and limestones. These tests were performed in cores taken from surface outcrops, and results might be somewhat different in downhole formations. Data are limited below about 15% porosity for sandstones. Additional work should be done to improve the definition of the porosity/compressive strength relationship over a broader range of porosity and over a larger number of formation rocks. Nevertheless, in the range of 18% to 23% porosity, substantial and consistent data are available, providing a good curve fit. Formation Effective Stress. Formation effective stress is the overburden stress, po, minus the reservoir or pore pressure, pp: (2) where all factors are measured in psi. Stress reduces penetration (Fig. 4). Conceptually, increasing stress makes the formation appear stronger. When predicting downhole penetration performance from API test results, the effect can result in either a reduction or a gain in estimated penetration. The magnitude and nature of the effect will depend on stress in the formation compared with the stress in the RP 43, Edition 5 tests. Specifics are developed later. Hydrostatic Pressure. Although wellbore pressure tends to reduce penetration, the correlation for these hydrostatic pressure effects is included in the formation effective stress correction described above. Casing Strength. Casing grade affects perforation entrance hole diameter, deh, to a significant degree but exerts only a negligible effect on penetration across the typical API Sec. 1 test range of single casing-wall thicknesses. In single-casing completions, deh varies with the midrange Brinell hardness, H, of the particular casing grade, according to the following expression: (3) P. 171^
Leaf explants ofKalanchoe laciniata were cocultivated for different days (2, 4, 6 and 8 days) with disarmedAgrobacterium tumefaciens strains A208SE, GV3111SE and EHA101 carring a binary vector pROA93. The vector contains a cauliflower mosaic virus 35S promotor which drives the coding sequence of neomycin phosphotransferase II (NPT-II) in one direction and β-glucuronidase (GUS) in the opposite direction. Prolonged cocultivation (6 days) resulted in a marked increase of GUS gene transient expression, in terms of, the number of explants with transformed cells (up to 100%) and the percent area of transformed tissue (∼ 50%). Explants cocultivated for 6-7 days showed a dramatic increase in the frequency of stable transformation and 75-80% of the inoculated explants produced transgenic plants. Cocultivation with the nopaline strain A208SE for 7 days gave as high as 10 transgenic plants per explant.
The development of accurate digital measurement of instantaneous power during a pump stroke has made possible a very quick and detailed analysis ofthe efficiency of the pumping system. The efficiency is then used as the benchmark for determining whether a complete well performance analysis is warranted from the standpoint of making best use of personnel and economic resources to increase oil production. In addition, power measurement provides direct information about lifting cost per barrel of fluid and barrel of oil produced, electrical and mechanical loading of the prime mover, peak power demand, power factor and minimum required ratings. These results give operating personnel information regarding potential problems and give to management a complete picture of the distribution of pumping costs. The power measurements are also converted, by the software, to instantaneous torque and presented as continuous torque curves for the upstroke anddownstroke. This allows determination of the existing level of counterbalance and provides the most rapid and accurate method for counterbalance adjustment to achieve lower torque loading on the gear box and reduced energy utilization. One of the principal advantages of this balancing method is that counterbalance adjustment can be made without need for an accurate description of the pumping unit's geometry which is often unknown or inaccurate. The effect of counterweight displacement on torque and power is observed immediately by repeating the power measurement after relocating the counterweights. This paper presents a series of case studies showing the Application of power measurement to a variety of pumping systems and components, including conventional, Mark II, Rotaflex units and high efficiency motors.
The development of accurate digital measurement of instantaneous power during a pump stroke has made possible a very quick and detailed analysis of the efficiency of the pumping system. The efficiency is then used as the benchmark for determining whether a complete well performance analysis is warranted from the standpoint of making best use of personnel and economic resources to increase oil production. In addition, power measurement provides direct information about lifting cost per barrel of fluid and barrel of oil produced, electrical and mechanical loading of the prime mover, peak power demand, power factor and minimum required ratings. These results give operating personnel information regarding potential problems and give to management a complete picture of the distribution of pumping costs. The power measurements are also converted, by the software, to instantaneous torque and presented as continuous torque curves for the upstroke and downstroke. This allows determination of the existing level of counterbalance and provides the most rapid and accurate method for counterbalance adjustment to achieve lower torque loading on the gear box and reduced energy utilization. One of the principal advantages of this balancing method is that counterbalance adjustment can be made without need for an accurate description of the pumping unit's geometry which is often unknown or inaccurate. The effect of counterweight displacement on torque and power is observed immediately by repeating the power measurement after relocating the counterweights. This paper presents a series of case studies showing the application of power measurement to a variety of pumping systems and components, including conventional, Mark II, Rotaflex units and high efficiency motors. INSTANTANEOUS MOTOR POWER MEASUREMENT A system was designed and implemented to undertake quantitative measurement of instantaneous power using sensors consisting of two current probes and three voltage leads, which are connected to the three phase leads inside the units switch box. Special purpose integrated circuits process the sensors data so as to generate an analog signal which is proportional to the instantaneous power. The sensors are calibrated so as to determine the power with an accuracy better than 5% provided the probes are correctly installed. The measurement procedure must be followed closely in order to obtain data of good and repeatable quality. In general the user is interested in establishing the power use of the pumping system when it is operating under steady state conditions. In the case that the well is pumping a full barrel and then begins to pump a partial barrel of liquid, the measured power will vary and will not be representative of the normal operating conditions. Therefore it is advisable to insure that the well being tested is produced while testing at the same conditions as normal operations. This can easily be undertaken by running quick dynamo meter measurements. When power measurements are to be made with the purpose of comparing the efficiency of different motor wiring options (low, medium or high torque for example) it is important not to move the current sensors after installation so as not to change the relative position of the wire within the current sensor. Such change would cause small variations in the readings which might invalidate the conclusions of the test. The data for two successive pump cycles are acquired with a high speed, high precision A/D converter and processed by a portable PC. The software then generates graphic and tabular output screens which are saved on disk for subsequent printing. Figure 1 presents the information related to energy utilization. P. 815^
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