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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Oklahoma City Oil and Gas Symposium, April 9–10, 2019

Paper Number: SPE-195208-MS

... engineers to make smarter decisions faster in a repeatable way. artificial lift system optimization problem machine learning gas lift

**calculation**performance curve gas lift system multiobjective genetic algorithm gas injection Artificial Intelligence Upstream Oil & Gas oil production...
Abstract

Gas lift is one of the most widely used artificial lift methods, and the use of nodal analysis to generate the gas lift performance curve is well established. However, the optimal gas injection rate is often selected as the point with maximum liquid production, which neglects the cost of incremental injection gas volume. This paper investigates the determination of the optimal operational point using a multiobjective optimization technique by considering the trade-off between gas consumption and oil production. The indicator-based evolutionary algorithm transforms the multiobjective problem into a single objective one using the hypervolume metric computed in the objective space. For the gas lift problem, which is a bi-objective problem aimed at maximizing oil production while minimizing gas injection rate, the hypervolume metrics are identically equivalent to geometric hyperareas under the trade-off curve. The optimization is only applied to the monotonically increasing portion of the gas lift performance curve; thus, all trivial sub-optimal conditions are excluded. The optimal operational point of gas injection rate is determined by finding the maximum rectangular hyperarea under the performance curve. The proper determination of the optimal injection gas rate could not only improve the efficiency of the gas lift itself, but also reduce the burden on the maintenance of surface facilities. The method is also applied to the multi-well scenario where a novel multi-well gas lift performance curve is generated using multiobjective Genetic Algorithm, which could help determine the optimal gas allocation/distribution scenario. The described process is incorporated in an integrated workflow which further leads to fast delivery of analysis/results that enable production engineers to make smarter decisions faster in a repeatable way.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–26, 2013

Paper Number: SPE-164478-MS

... Abstract Conventional reservoir

**calculations**using resistivity and density/neutron porosity have been the industry standard for defining reservoir characteristics. The**calculation**of water saturation from these measurements is used in every reservoir situation. Many reservoirs are not easily...
Abstract

Conventional reservoir calculations using resistivity and density/neutron porosity have been the industry standard for defining reservoir characteristics. The calculation of water saturation from these measurements is used in every reservoir situation. Many reservoirs are not easily analyzed; therefore, various and complicated analysis techniques have been developed. In some cases, years were spent in characterization before these log measurements could be applied with confidence. This time and expenditure of resources drained capital from exploration to research processes and produced many inefficient completion attempts in reservoirs that were incorrectly characterized as productive. The great hope with the introduction of NMR tools to the industry was that reservoir parameters could be established and applied in an uncomplicated manner. Advances in technology of NMR responses have produced the ability to capture polarization time and relaxation time in a single pass through the reservoir. Nuclear magnetic polarization time has been demonstrated to have a relationship to the fluid type in the reservoir. The relaxation time (T 2 ) has been used to characterize permeability with an excellent relationship to production. The Bray-Smith permeability equation was developed from this observation. This equation incorporates relaxation time and calculates permeability. No alterations to the equation for rock type or texture changes were needed. This paper presents examples of logs in three different and difficult-to-evaluate reservoirs. A reservoir with lenticular sand, another with a thinly-bedded sand and shale sequence, and a conglomerate/mudstone reservoir are each evaluated for fluid type and permeability. Effective porosity, fluid type, and permeability are all resolved accurately by the NMR. Comparisons to production results are presented.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 27–29, 2011

Paper Number: SPE-142303-MS

... . Once the latter is determined, the fracture dimensions, i.e., fracture length and width, are set. If one assumes the fracture height is known and constant then the

**calculation**is simple and a 2D fracture propagation model can be used. However, fracture height is not constant throughout the fracture...
Abstract

In 2002 we introduced the concept of Unified Fracture Design (UFD) as a coherent way to size the fracture geometry for the expressed purpose to physically optimize the well performance. We used the Proppant Number as a correlating parameter, which in turn provided the maximum dimensionless productivity index ( J D ) which corresponds to the optimum dimensionless fracture conductivity, C fD . Once the latter is determined, the fracture dimensions, i.e., fracture length and width, are set. If one assumes the fracture height is known and constant then the calculation is simple and a 2D fracture propagation model can be used. However, fracture height is not constant throughout the fracture and it cannot be considered constant during execution, depending greatly on the net pressure and vice versa. We are presenting here an iterative procedure where the fracture height is related to the net pressure. In the procedure, for any assumed net pressure, the fracture height, along with the mass of proppant and the permeabilities of the reservoir and the proppant, lead to the Proppant Number which in turn determines the desired length and width. A fracture propagation model, such as the PKN geometry for lateral growth, coupled with a changing fracture height, leads to the calculation of the net pressure which is compared with the one assumed. Convergence of the assumed and calculated net pressure is what is sought. The design procedure presented here is for both oil and gas wells. The design also includes the calculation of required treating pressure and finally it incorporates economics for production enhancement optimization beyond the physical optimization using UFD. Comparison of the 2D to the p-3D results points to the need and importance of the p-3D in a large array of reservoirs.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 27–29, 2011

Paper Number: SPE-141055-MS

... was 0.027 inches. The required

**calculated**stem travel for a fully open 1/4-inch ID port based on the surface area of the frustum of a right circular cone exceeds 0.10 inch. Although this valve would appear "OK" in the set opening pressure tester, the valve could pass only a very small total volume of...
Abstract

The tester set initial opening pressure of a gas-lift valve (GLV) and port size are no indication of its injection-gas passage at a given injection-gas pressure for unloading and/or gas lifting a well. The initial test rack opening pressure (P tro ) of a GLV creates an opening force that slightly exceeds the valve’s closing force. The importance of the required injection-gas throughput performance of a GLV for unloading and gas lifting a well increases for very high daily liquid production rate wells and for wells that the workovers are very costly. A test procedure that allows individual injection-gas throughput rate testing of every GLV and check valve prior to being installed in a well is described in this paper. The method includes GLVs with cross-over seats that prevent stem travel probe test measurements. The test requires very little gas volume and is based on a rapid pressure decline (blow-down). Recent computer electronics as National Instruments LabVIEW software and 4 channel data acquisition instrument control hardware can record up to 12,500 pressure readings per second per channel. Test procedures are now possible to dynamically test the gas throughput performance of a GLV in a fraction of a second. GLV replacement can be very costly – even by wireline in wells with subsea wellheads. After setting the P tro and aging (stabilizing) this set opening pressure, the dynamic blow-down test can be performed on each GLV with check valve. If the GLV passes this test, the valve will have the injection-gas throughput required to unload and/or gas lift the well. Every supplier of gas-lift valves should offer this testing option to the producer.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 27–29, 2011

Paper Number: SPE-141416-MS

... complex reservoir resource in place estimate adsorption model estimates of resource in place sorbed phase density fraction 0 upstream oil & gas

**calculation**composition storage capacity adsorption layer effect fraction phase mole fraction hydrocarbon el isotherm shale gas...
Abstract

Recent studies have shown that shale gas industry is incorrectly determining gas-in-place volumes in reservoirs with a large sorbed-gas by not properly accounting for the volumes occupied by the sorbed and free gas phases. Scanning electron microscopy (SEM) has discovered nanopores in organic-rich shale with sizes typically in 3-100 nm range, although pores less than 3 nm cannot be captured with current SEM technology. At that scale the adsorption layer thickness is not infinitesimally small. Thus a portion of the total pore volume would be occupied by a finite-size adsorption layer and not available for the free gas molecules. In SPE 131772, we proposed a volumetric method which accounts for the volumes taken up by the free gas and by the adsorption layer. The study was based on a single-component Langmuir adsorption model, however. This paper extends the discussions on the adsorption layer effect for multi-component natural gases with a sorption model also known as extended-Langmuir. We combine the extended-Langmuir adsorption isotherm with volumetrics and free gas composition to formulate a new gasin-place equation accounting for the pore space taken up by a multi-component sorbed phase. The method yields total gas-inplace predictions, which suggest that an adjustment is necessary in volume calculations, especially for gas shales with high C 2 + composition and high in total organic content. Using typical values for the parameters, calculations show a 20% decrease in total gas storage capacity compared to that using the conventional approach. The adjustments need to be done on the free gas volume is 18% more than the value using single-component (methane) case. The role of multi-component adsorption is more important than previously thought. The new methodology is therefore recommended for shale gas-inplace calculations.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 27–29, 2011

Paper Number: SPE-141525-MS

... an apparent viscosity for use in the Reynolds number

**calculation**by comparing the laminar flow equations for Newtonian and power law fluids. This concept was applied for the**calculation**of frictional pressure loss. The effect of proppant on fluid friction has received attention since prediction...
Abstract

The interpretation of hydraulic fracturing pressure was initiated by Nolte and Smith in the 1980s and remains qualitative. An accurate interpretation of hydraulic fracturing pressures, during injection and after shut-in, is critical to understand and improve the fracture treatment in low-permeability gas formations such as tight sand and gas shale. It would provide additional information about the wellbore and better understanding of the reservoir. In this paper, new models for the accurate calculation of bottomhole treating pressure based on surface treating pressure were first developed. This calculation was determined by incorporating hydraulic pressure, fluid friction pressure, fracture fluid property changes along the wellbore, proppant effect, perforation effect, tortuosity, effect of casing, rock toughness, thermal effect, and pore pressure effect on in-situ stress. New methods were then developed for more accurate interpretation of the net pressure and fracture propagation. The models and results were finally validated with field data from tight gas and shale gas reservoirs.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, April 4–8, 2009

Paper Number: SPE-120625-MS

... Abstract Critical velocity

**calculations**in the form of charts or simple equations are frequently used by field personnel to evaluate a gas well's flowing conditions to determine if the well is experiencing liquid loading problems. Literature detailing the critical velocity necessary to keep a...
Abstract

Abstract Critical velocity calculations in the form of charts or simple equations are frequently used by field personnel to evaluate a gas well's flowing conditions to determine if the well is experiencing liquid loading problems. Literature detailing the critical velocity necessary to keep a gas well unloaded suggests using the conditions at the top of the well as an evaluation point. This is convenient for personnel conducting the evaluation as wellhead pressure and temperature data are readily available. A number of situations exist where the use of the wellhead as the evaluation point can lead to erroneous conclusions. The most obvious situation occurs with a change in geometry downhole when a tapered tubing string is run in a well or when the tubing is set above the perforations. In these instances a more robust evaluation results from using conditions at the bottom of the well and the downhole tubing geometry. Other conditions exist where the use of downhole conditions provide a better evaluation point. The assumptions used in the development of the standard, simplified form of the critical velocity equations and charts may not be appropriate for downhole application. In these cases the fundamental equations must be used. The calculation of critical velocity requires knowledge of pressure, temperature, produced fluids and PVT properties. The determination of critical rate requires the same properties with the addition of pipe diameter. The required PVT properties including surface tension and density for both the gas and liquid phases are reviewed. Correlations to calculate water-gas surface tension were found to have excessive error so a new, more accurate method is presented. This paper provides recommendations when the use of a surface or downhole evaluation point is more appropriate in the determination of the minimum critical gas velocity for a well. Background The calculation of critical velocity is frequently used by the operators of natural gas wells to determine the gas production rate required to prevent liquids from accumulating in the well. Turner 24,25 developed a method for calculating critical velocity which has gained wide acceptance and use within the industry. In order to efficiently lift water to the surface, gas wells should produce in the mist flow region where liquid exists as a film on the wall of the pipe or as droplets within the flow stream. The basis for Turner's method is the determination of the gas rate necessary to overcome the terminal fall velocity of a liquid droplet which Turner determined to be the phenomena controlling liquid accumulation in a well. For liquid droplets that are roughly spheroidally shaped, Turner presented the following equation for calculating the terminal fall velocity of the droplet. The required gas flow velocity to keep the well unloaded then equates to this terminal fall velocity.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, April 4–8, 2009

Paper Number: SPE-120280-MS

... and Beggs, 1991). Eaton-Flanigan uses Eaton correlation with elevation term neglected, Dukler-Flanigan uses Dukler correlation with elevation term neglected, and Dukler-Eaton-Flanigan uses Dukler correlation for friction

**calculation**, Eaton correlation for liquid holdup**calculation**and elevation term...
Abstract

Abstract In this study, commonly used two-phase flow pressure prediction correlations and mechanistic models for pipelines in petroleum industry are used to simulate fluid flow in a hilly terrain pipeline. Simulation results are evaluated against experimental data. The experimental data were obtained from a published paper. Hilly terrain pipelines are often encountered in oil and gas transportation. During pipeline design and simulation, experimental data are usually unavailable to calibrate against correlations or mechanistic models. In this situation, it is difficult to determine which correlation or model to use in predicting pressure drop in hilly terrain pipes due to the complexity of flow, since in a hilly terrain pipeline, fluid flow can be uphill, downhill and horizontal. Pressure, temperature and rate measurements as well as fluid properties were given for a 2.8 mile long hilly terrain pipeline with 12-inch and 16-inch diameters. Pressure drops obtained from correlations and mechanistic models were compared with pressure measurements. Correlations and mechanistic models evaluated in this study include Beggs-Brill, Dukler, Dukler- Eaton-Flanigan, Dukler-Flanigan, Eaton, Eaton-Flanigan and Xiao and Ansari mechanistic models. The results of this study can be used as guidelines for choosing two-phase flow pressure prediction correlations and mechanistic models in designing and analyzing hilly terrain pipelines. Introduction Two-phase flow in hilly terrain pipeline is a common occurrence in oil and gas transportation. Although there are many pipeline correlations and mechanistic models around, during pipeline design and simulation, it is often difficult to determine which correlation or mechanistic model to use. Correlations and mechanistic models evaluated in this study include Beggs-Brill (BB), Dukler-Eaton-Flanigan (DEF), Dukler-Flanigan (DF), Dukler (D), Eaton (E), Eaton-Flanigan (EF), and Xiao and Ansari mechanistic models (MM). Below is a brief description of the correlations, Xiao Mechanistic model (Yuan and Zhou, 2008) and Ansari mechanistic model. The Beggs-Brill correlation was developed from experimental data obtained in a small scale test facility. The facility consisted of 1-inch and 1.5-inch sections of acrylic pipe 90 ft long. Fluids used were air and water. The correlations were developed from 584 measured tests for all inclination angles (Brill and Beggs, 1991). The Eaton correlation was developed from experimental data obtained from a flow system consisting of 2-inch and 4-inch horizontal lines. Correlations were for liquid holdup and two-phase friction factor (Brill and Beggs, 1991). The Dukler correlation was based on similarity analysis and the friction factor and liquid hold up correlations were developed from field data (Brill and Beggs, 1991). The Eaton-Flanigan, Dukler-Flanigan and Dukler-Eaton-Flanigan correlations used the Flanigan corrected correlation, where elevation term in the total pressure gradient is neglected for down hill flow (Brill and Beggs, 1991). Eaton-Flanigan uses Eaton correlation with elevation term neglected, Dukler-Flanigan uses Dukler correlation with elevation term neglected, and Dukler-Eaton-Flanigan uses Dukler correlation for friction calculation, Eaton correlation for liquid holdup calculation and elevation term is neglected (Pipesoft-2TM Manual 2, 2007). The Xiao model is a comprehensive mechanistic model developed for gas-liquid two-phase flow in horizontal and near horizontal pipelines. It has been evaluated against a data bank that includes field data culled from the A. G. A. database, and laboratory data published in the literature (Xiao et al., 1990).

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, April 4–8, 2009

Paper Number: SPE-120114-MS

... any gas well, not only because it leads to stimulation but it also reduces turbulence effects. This can be seen from Figure 1 (Marongiu-Porcu et al., 2008). Figure 1 shows

**calculated**folds of increase (FOI) between fractured and non-fractured wells for both oil and gas reservoirs within a...
Abstract

Abstract Hydraulic fracturing is particularly suited for natural gas wells. For low permeability reservoirs the need is obvious: it is the only means to monetize a huge number of gas wells. In addition, in recent years horizontal wells with multiple transverse fractures have emerged as the configuration of choice for many low permeability or unconventional reservoirs such as shale gas. However, because of increasing demand in the world economy, previously stranded gas of much higher permeability is rapidly becoming target for new field developments. Fracturing, which for similar-permeability oil reservoirs may be abandoned in favor of horizontal or complex well architecture, is a must for higher permeability gas wells because of considerably enhanced turbulence effects. But turbulence in the fracture itself creates the need for design adjustments because of substantial reduction in the effective proppant-pack permeability. We present a physical optimization scheme for fracturing natural gas wells and extend it to the fracturing of multiple treatments in horizontal wells. The latter, because of enhanced turbulence effects in the fracture, has an upper limit of application, about 0.5 md. For higher permeability, the multiple fractured horizontal well has an unacceptable reduction in well performance, and vertical wells with fractures are indicated instead. In this paper, physical optimization is complemented by economic optimization by comparing vertical wells with and without fractures and horizontal wells with multiple fractures in a range of permeabilities. Of importance are the geographic location (e.g., North America vs international) and the markedly different costs associated with them. For lower permeability reservoirs, economic considerations that would make multiple fractured horizontal wells attractive in e.g., North America, render them uneconomic in many other parts of the world. This, along with the physical constraint outlined above, creates a narrow range of permeability where the configuration is applicable. Introduction Several recent publications have addressed the application of hydraulic fracturing in gas wells to reduce turbulence and maximize productivity (Economides et al., 2002; Wang and Economides, 2004; Economides and Martin, 2007; Marongiu- Porcu et al., 2008). The conclusion is that hydraulic fracturing should be adopted as standard completion for virtually any gas well, not only because it leads to stimulation but it also reduces turbulence effects. This can be seen from Figure 1 (Marongiu-Porcu et al., 2008). Figure 1 shows calculated folds of increase (FOI) between fractured and non-fractured wells for both oil and gas reservoirs within a permeability range between 0.05 to 100 md. Figure 1 represents the results of physical optimization of hydraulic fracture treatments using the Unified Fracture Design (UFD) approach (Economides and Valkó, 2002). As the reservoir permeability increases, the FOI for oil wells declines relatively smoothly (from over 10 at 0.05 md to about 2 at 100 md). For natural gas wells the behavior of the FOI trends at low reservoir permeability mimics that of oil wells but as the permeability increases, the trend diverges: a fractured gas well starts to perform far better than a non-fractured high-permeability well because of the considerable reduction in turbulence effects that adversely affect well performance and dominate radial flow.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Production and Operations Symposium, March 31–April 3, 2007

Paper Number: SPE-106642-MS

... find out which models could be used for

**calculating**the relative permeability from capillary pressure realizing a best fit matches with the relative permeability obtained from resistivity measurements. In addition, to determine the types of wettability from resistivity measurements. Results and...
Abstract

Abstract Relative permeability and Capillary pressure characteristics of reservoir rocks are usually determined using core analysis. In the absence of representative core sample, resistivity log-derived water saturation in the transition zone may be used to depict capillary pressure curve and, in turn to determine relative permeability characteristics from petrophysical correlations. Most of reported research works have investigated the relative permeability from a steady state and unsteady-state techniques. The technique of measuring relative permeability using resistivity measurements almost absent from the reported works. Hence, the main objective of this work is to determine the relative permeability from the resistivity measurements and compare it with those obtained from capillary pressure data using the same cores. Also, it is intended to find out which models could be used for calculating the relative permeability from capillary pressure realizing a best fit matches with the relative permeability obtained from resistivity measurements. In addition, to determine the types of wettability from resistivity measurements. Results and analysis indicate that the capillary pressure and resistivity measurements result in significant different irreducible water saturation values. This, in turn, results in substantially different relative permeability characteristic curve. Also by analogy, a semi analytical method was to be developed to infer relative permeability from resistivity index and free water saturation. In most cases, the Brook-Corey and Corey models, may be the best fit match to the relative permeabilities of wetting and nonwetting phases respectively obtained from resistivity measurements. Therefore, wettability was determined using the values of water saturation exponents, water saturation at crossover point. The results indicate that, the wettability of Berea cores was neutral-mixed wet. However the wettability of the synthetic cores compacted at 3000 psi, was strongly water wet. Introduction There are two common techniques being used for determining relative permeability. These techniques are steady - state1 and unsteady-state 1, 2 methods (dynamic displacement). In steady state method, both immiscible fluids are simultaneous injected into the core at constant flow rate or pressure, for extended durations to reach equilibrium. Pressure gradient, flow rate and saturation are measured. Effective Permabilities for each phase are obtained by using Darcy law. Conventionally, changing the ratio of the injection rates and repeating the measurements as equilibrium is attained, hence, the relative permeability saturation curves would be obtained. The disadvantage of this method is, in fact, time consuming, because the equilibrium attainment may require several hours or days to reach saturation level. The mechanism of unsteady-state technique is one of the fluids will displace another one at constant rate. The equilibrium saturation at this technique is also not realized. The production data are investigated and a set of relative permeability curves is achieved using different mathematical method. The disadvantages of this method are capillary end effect, viscous, fingering and scaling effects. Several techniques have been proposed to reduce or eliminate end effect (Hassleres technique, similar approach used in Penn state method, Haflord and dispersed feed). Recently many techniques 2 are used for determining multiphase relative permeability from unsteady-state method. Improvement and empirical relationships for calculations of multiphase relative permeability have been published. The high-speed centrifuge for relative permeability measurements is also a relative new development. Centrifuge method is faster than steady state technique. There are several papers which are related to techniques for the calculation of relative permeabilities from capillary pressure. Most of them calculate relative permeability from centrifuge method under reservoir condition3-5. Heavlside Jehn and Black, C.J.J. 6 have reported that the function of relative permeability would be influenced by numerous factors such as; rock composition, fluid ptoperties, wettability and saturation history (Drainage and imbibitions processes). Okasha, T.M.et al have 7 reported how to obtain the relative permeability and they discussed its importance. They have also mentioned that the relative permeability is a rock characteristic which describes quantitatively the simultaneously flow of two or more immiscible fluid through porous media. This property is very important for predicting fluid movement in a reservoir during various recovery processes. The relative permeability can also be obtained from the following: reservoir production data; published data on general rock types; and laboratory displacement tests using representative rock and fluid.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Production and Operations Symposium, March 31–April 3, 2007

Paper Number: SPE-106092-MS

... uses zero-cost air as power fluid. It is a space efficient package which can be used on offshore locations as well. The paper describes the individual components of the system and the

**calculations**involved therein. The economic and technical comparison of this system with the conventional methods is...
Abstract

Abstract Artificial lift systems are now being considered of extreme importance as the reserves across the globe are depleting and the wells are unable to flow naturally. Over the years a number of artificial lift techniques have evolved as a result of extensive research and ground work. All the systems have proven their worth by increasing the productivity of the field by many folds. But each of these artificial lift systems has economic and operating limitations that eliminate it from consideration under certain operating condition. However all the conventional artificial lift systems have a common feature. The energy added to the lift the fluid from the wellbore is lost in the process and cannot be utilized for some other operation. This paper describes a new technique of artificial lift which uses the concept of venturi to lift the fluid to the surface. A high velocity power fluid is used to create drawdown at the throat of a surface venturi and this pressure drawdown is transmitted downhole by pressure tappings. The drawdown lifts the fluid through the production tubular in a stepwise manner. The power fluid coming out from the other end of the venturi is used to drive a turbine which generates power as a result. This power is used to operate the inlet compressor thus the cycle being completed. After startup, effectively, no energy is used up to keep operating the system. The system is of immense economic benefit as the operating expenditures are low. Also this system uses zero-cost air as power fluid. It is a space efficient package which can be used on offshore locations as well. The paper describes the individual components of the system and the calculations involved therein. The economic and technical comparison of this system with the conventional methods is also enlisted. Introduction The venturi consist of a converging tube which is an efficient device in converting pressure head to velocity head and a diverging tube converts velocity head to pressure head. The two are combined to form a Venturi tube. As shown in fig 1, it consist of a tube with a constricted throat that produces an increasing velocity accompanied with reduction in pressure, followed by a gradual diverging portion in which the velocity is transformed back into the pressure with slight friction loss. If tapping are taken from the inlet and throat of the venturi tube and this pressure differential is applied to an entrapped fluid column, then the fluid column will rise in the conduit under the application of the pressure differential. After a certain amount of rise, the column is again trapped and the differential is now transferred across it. This causes further rise. The process continues until the fluid column reaches the surface. Meanwhile the high pressure and appreciable velocity air leaving the venturi tube drives an Air generator which produces power. This power is used to operate the inlet air compressor. Thus the cycle is completed. Thus this system achieves which no other existing artificial lift system does. Recirculates power to run itself. Equipment Description The major components of this lifting system are: Inlet Air Compressor Surface Venturi Downhole Tubular and Valves Air Turbine Inlet Air Compressor As shown in the subsequent calculations, the primary concern here is the flowrate and not the pressure. Nominal pressures are required but very high flowrate are necessary for the working of the system. As such only Centrifugal Compressors suffice the purpose. Surface Venturi As shown in fig 2, it is a metallic structure of the geometry as shown. It has a converging section, throat and a diverging section. The metal thickness should be adequate enough to bear the thermal and mechanical stresses induced because of the flow. Also it should be corrosion and erosion resistant so as to be able to bear the high velocity air passing through it. The converging and diverging angle are to be fixed to optimize the stresses developed. Ideally the converging section has an angle of 20° and diverging section has an angle of 5°. Two pressure tappings are taken from the venturi that is relayed downhole.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 16–19, 2005

Paper Number: SPE-93943-MS

... problems, etc. The rod pump control system (wellsite rod pump controllers [RPCs} and host software) provides both surface dynamometer cards and

**calculated**downhole pump cards for detailed analysis. Problems that reduce the production of a well can be seen through trends and displays of historical data as...
Abstract

Abstract Today's oilfield is data-rich-but suffers due to a lack of end-user access and analysis of the available information. Important wellhead data that historically has been gathered through daily wellsite visits by operating personnel often goes unobserved because of manpower restraints. Therefore, recognition of operating problems based on such visits or on diagnostic analysis of the available data can be delayed or even lost to the operating company. Introduction Wellsite automation hardware and host-based optimization software systems for rod pumped wells have been implemented in fields with as few as 20 wells, as well as in fields with more than 3,000 wells. The fields are both primary recovery fields and tertiary recovery fields undergoing water, CO2, or steam flooding. These principles have been applied in new fields with no automation in place and in mature fields that have been automated for over a decade. Over the history of all these installations, the benefits and rationale for implementation of these types of systems have been well documented. This paper describes the multiple benefits of implementing a comprehensive production automation optimization system for rod pumped wells. Increased Production Operators are always interested in arresting the typical oil production decline curve. Automation systems are proven tools to aid in this effort through making it possible to observe changing well behavior-increasing or decreasing well inflow, downhole mechanical problems, etc. The rod pump control system (wellsite rod pump controllers [RPCs} and host software) provides both surface dynamometer cards and calculated downhole pump cards for detailed analysis. Problems that reduce the production of a well can be seen through trends and displays of historical data as displayed by the host software used by the rod pump control system.By examining the calculated downhole card of a beam-pumped well, a user of the system can identify problems such as upstroke pump leakage, friction, unanchored tubing, and gas compression. (Fig. 1) In addition, using available optimization tools, lower operating fluid levels are often achieved, which increases total fluid production. (Fig. 2) Also, simple recognition of wells not producing at all or at reduced efficiency or wells that are "down" results in less downtime and therefore more production. The interactive usability of the central-site software analysis portion of a rod pump control system allows the user to make changes to the operational parameters of a well at any time from the operating office.Changing the pump-off set point is an example of a parameter change that can be used to fine-tune production.By monitoring the performance of each well on a daily basis, the operator can make small changes to the configuration of each wellsite RPC that can decrease the span of fluid level fluctuations. (Fig. 3–4) A well-conceived automation system results in a continuing cycle of Monitoring ? Control ? Analysis ? Design to identify sources of lost production, insure maximum production using minimum runtime, and optimize individual well producing systems.(Fig. 5) Reduced Operating Cost and Well failures Reduce Electrical Costs by Optimizing the Pumping Unit and Prime Mover. A comprehensive production automation system goes beyond a basic SCADA (Supervisory Control and Data Acquisition) system's ability to merely monitor and report on collected data from rod pumped wells. Analytical tools are built into the host software to allow a user to perform a detailed analysis of collected data and redesign the pumping system, if necessary, without moving the data into another software application. Real time analysis data can be used to "model" the design program before any design work is done. For beam pumping installations, the user can evaluate pumping unit loading/size, counterbalance, rod string design, operating cost, and prime mover size. (Fig. 6) The online design program allows the user to change over one hundred other parameters in a virtual "what-if" scenario. Rather than actually making expensive changes at a well, the optimization software provides the user with a way to compare various parameter changes so each installation can be optimized for pumping unit and motor size, correct pumping unit counterbalance and rod string design, or displacement matched to inflow. (Fig. 7–8)

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 16–19, 2005

Paper Number: SPE-94305-MS

... and after the treatment.While the measurement of sonic properties during open-hole logging operations assisted somewhat in

**calculating**relative stress differentials, its application was sporadic at best, and there was no way to check the results. Pre and post-stimulation pressure buildups required...
Abstract

Abstract Sizing of hydraulic fracturing treatments in the Southeastern New Mexico (SENM) Morrow has historically relied on a trial-and error process whereby a three-dimensional fracturing model was built and run with simple gamma ray and compensated neutron density logs.Stress tables have been built utilizing over-simplified correlations involving conversions from gamma ray readings and effective porosity.The resulting simulated fracture-half lengths have been utilized in NPV (Net Present Value) optimizations to arrive at a final sizing decision. Unfortunately, this process relies on the assumption that the initial modeling generates a propped fracture geometry simulation that is realistic.Past efforts to calibrate the 3-D models in the area focused on scattered attempts to gather sonic data that could be converted to stress differentials, and the use of conventional pressure buildups before and after the treatment.While the measurement of sonic properties during open-hole logging operations assisted somewhat in calculating relative stress differentials, its application was sporadic at best, and there was no way to check the results. Pre and post-stimulation pressure buildups required shutting the well in for a period of time and subsequently risking potential deceleration of reserve recovery. A study of a variety of existing Morrow producers was undertaken to determine whether or not flowing pressure transient analysis of existing properties could be utilized to "calibrate" three-dimensional fracturing models, so that future projects would better reflect fracture geometries that were more realistic than current practice. Results of the study are presented, and a practical, user-friendly model is demonstrated whereby flowing transient analysis may be utilized to adjust three-dimensional fracturing simulations as appropriate for optimizing stimulation NPV. Introduction The literature pertaining to stimulation of southeastern New Mexico Morrow reservoirs is extensive1,2,3,4,5,6,7,8.Observations related to stimulation process are abundant, but there is a distinct shortage of guidance pertaining to maximization of NPV by optimizing treatment sizing in this formation.Literature and industry experience has made the NPV maximization process in other areas fairly routine9,10,11, but a number of factors have contributed to its lack of use in this play: The widespread absence of accurate pressure matching, caused by the prevalence of specialty fracturing fluids (primarily foam) that make it difficult to measure or estimate bottom-hole pressures during a given treatment. Industry reluctance to perform pre- and post-treatment pressure transient buildup tests; primarily due to a body of knowledge indicating that it is not uncommon to have inordinately long production recovery periods following an extended shut-in period in a typical Eddy or Lea County Morrow producer12. Wide variation in three-dimensional fracture modeling technique; probably rooted in an inability to check the results of any particular simulation.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–25, 2003

Paper Number: SPE-80933-MS

... length, and aerial width. A fracture width vs. proppant size requirement is applied, and a simple material balance

**calculation**is performed to generate a fracture volume taking fluid leakoff into account. Fracture conductivity of a low proppant-concentration, high fluid-volume fracture is estimated to...
Abstract

Abstract The popularity of water fracs has increased in recent years. The reduction in fluid cost and overall fracture stimulation cost has in some cases revived exploration in low-permeability reservoirs like the Barnett shale in north central Texas. Water fracs have also been used effectively in reservoirs with low permeability and large net pays, which require large volumes of fluid to attain adequate fracture half-lengths to achieve commercial production. In the past, the design of water fracs has been more of an art than a science. While the term "water frac" implies that the fluid is proppant-free, in most cases some proppant is usually pumped. The amount and concentration is usually low when compared to conventional fracture treatments. Water-frac designs are further complicated by the fact that fracture geometry, conductivity, and proppant transport are not easily modeled. Despite these difficulties, the attractiveness of water fracs requires the implementation of a design methodology. This paper discusses a design procedure for water fracs from a field operation/design standpoint. Volume and rate requirements are discussed for a specific zone height, desired fracture length, and aerial width. A fracture width vs. proppant size requirement is applied, and a simple material balance calculation is performed to generate a fracture volume taking fluid leakoff into account. Fracture conductivity of a low proppant-concentration, high fluid-volume fracture is estimated to optimize proppant length and fracture conductivity ratio ( C fd ). A pump schedule is generated based on the results of the previous calculations. All design calculations are simple and require only a handheld calculator or simple spreadsheet. The design model was calibrated to a microseism-mapped Cotton Valley Lime test well. A leakoff coefficient multiplier was used to calibrate the model. The model-predicted volume was then compared to actual volume on a second Cotton Valley Sand test well and on a 10-well average Barnett shale microseism fracture-mapping data set. The overall model-predicted volume for the mapped microseism geometry is compared to actual volume pumped. Introduction Water fracs have had various names through the years. From the mid 1970s to early 1980s, "river fracs" were performed on many Hugoton wells in Kansas. Water and sand from the Cimarron River was pumped at high rates (200 to 300 bbl/min) with little more than a few gallons of friction reducer, 20 to 30 dump trucks of river sand, and an occasional frog or turtle. During the same time, "pit fracs" were pumped into the Hunton and Mississippi formation in Canadian County, Oklahoma. The term "pit" comes from the water-storage container, which was an earthen pit, sometimes lined. Frac volumes ranged from 4,000 to 38,000 bbl. Averages of 1,200 gal/ft and 0.425 lb/gal were most common. From 1986 to 1988, UPRC performed water fracs in the Austin Chalk in both vertical and horizontal wells. Typical volumes were 400 bbl of acid pumped in stages with 30,000 bbl of water and wax beads diverter. In 1997, Mitchell Energy (now DEVON) experimented with light sand fracs (LSF) in the Barnett shale. The company continued reducing polymer gel loadings to the point where little more than friction reducer and biocide were used. Average job size is 2,000 to 2,500 gal/ft or 24,000 bbl for a 400-ft section. Average proppant concentration is 0.3 lb/gal. Other terms or descriptive mnemonics used to describe water fracs, including: LSF - light sand fracs SWF - slick water fracs LPF - low proppant fracs TWF - treated water fracs MHF - massive hydraulic fracs Many rules of thumb are offered for water-frac design methods. The following "rules" are among the most common: Frac tanks per 100 ft of pay (tanks/100 ft) Barrels per ft (bbl/ft) lbm of proppant per ft (lbm/ft) Rate per ft (bpm/ft)

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations
Symposium, March 24–27, 2001

Paper Number: SPE-67237-MS

..., no reliable standards are currently available that take into account quantitatively the parameters necessary for the

**calculation**of productivity index in long horizontal well. A new approach of the specific productivity index is proposed to predict the production rate considering friction losses in...
Abstract

Abstract As the length of a horizontal well is increased, its drainage area also increases. Productivity of a long horizontal well is no longer proportional to the well length because increase in the length of horizontal production section also causes frictional losses in the wellbore. However, no reliable standards are currently available that take into account quantitatively the parameters necessary for the calculation of productivity index in long horizontal well. A new approach of the specific productivity index is proposed to predict the production rate considering friction losses in long production section under inflow conditions. This paper specifically describes model development, solution and the simulation results for the production of a long horizontal well with the specific productivity index. This specific productivity index is derived by assuming steady-state flow of a slightly compressible fluid in an anisotropic formation. The influence of wellbore damage near the horizontal wellbore is also considered in the model. The sensitivity study of the various parameters affecting productivity is performed and the results are analyzed quantitatively. The study shows that there is a critical point, where rate of friction pressure is suddenly increased and productivity index is decreased abruptly with increase in horizontal well length beyond this point. This critical point is the tangent point on which friction losses should be considered for production estimation. The model facilitates determination of the new horizontal productivity index considering friction losses in long horizontal wells. Introduction Horizontal wells have several advantages: increased productivity or injectivity; reduced water or gas coning; improved seep efficiency. A vertical sweep efficiency reduce sgas or water coning. An increase in large reservoir contact area increases the production rate of horizontal wells two to four times greater than the rates of unstimulated vertical wells. de Montigny and Combe 1 and Mauduit 2 suggested that, as horizontal well length increases, the influence of formation damage on total pressure drop becomes negligible, resulting in an additional advantage over vertical wells. However, Sparlin and Hagen 3 indicated that the damage zone may affect productivity more in horizontal wells, and that skin damage sometimes can prevent horizontal well projects from succeeding. These two opposing interpretations of the horizontal well productivity, as Renard and Duppy 4 noted, come from a lack of well-defined reservoir and well characteristics to quantify the effect of formation damage on the productivity index for horizontal wells. As the well length for horizontal drilling is increased, its drainage area is also increased. Initially, it was believed that a horizontal well should be as long as possible. Current drilling technology allows wells to be drilled several thousands of feet long. However, a factor exists that can possibly limit the useful length of a horizontal well, i.e. frictional losses in the wellbore. 5 Long horizontal wells or high flow rates result in increase in the frictional losses. This may be comparable with the drawdown at the producing end of the well. A portion of the downhole well would then be unproductive because of frictional losses. Recent experience with horizontal wells has revealed that in many circumstances the inflow performance of horizontal wells do not match with the expected productivity and that their deliverability may be affected by frictional losses along the wellbore. 6 This effect has serious implications where horizontal well section is very long because the productivity index is no longer directly proportional to the well length. The purpose of this paper is to present the effect of long horizontal wells on productivity index associated with the effects of friction pressure losses of a liquid hydrocarbon in the wellbore under inflow conditions, called as specific productivity index to distinguish the conventional productivity index. This study also demonstrates the influence of wellbore damage near the horizontal wellbore on the specific productivity index of long horizontal wells.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations
Symposium, March 24–27, 2001

Paper Number: SPE-67198-MS

... individual zones within the Granite Wash wells. porosity well 1 bill grieser granite wash gas production upstream oil & gas john brinska storage capacity zone selection water saturation britt hill prop length well logging spe 67198

**calculation**production prediction log analysis...
Abstract

Abstract Completing wells with multiple pay sections can be difficult and costly. With limited capital allocated at completion time, the geologist and the completion engineer are faced with deciding how to spend the available funds to attain the best return on investment (ROI) or net present value (NPV). A process has been developed for selecting and ranking multiple pay sections and for giving accurate post-stimulation production estimates with advanced logging technology, such as magnetic resonance imaging (MRI), in conjunction with a production reservoir simulator. This process ranks multiple pay sections by hydrocarbon storage capacity (f eff )( h ), and producing capacity ( k h ). Initial productions (IP's), Estimated Ultimate Recoveries (EUR's), or projected cumulative production is then predicted for each section with variable stimulation half-lengths ( X f ) or skin values ( S ). Output can be displayed on the log or in a tabular format. NPV, ROI, or the internal rate of return (IRR) can be estimated for each stimulation scenario. These estimations can help operators justify stimulation job size and completion cost for each section of pay selected, giving the operator an additional tool for deciding how to best spend completion dollars. The ranking process can be performed rapidly, and it provides a producing potential before setting pipe. This paper illustrates the process with six field examples from the Granite Wash formation in the Ammunition Field of Washita County, OK. Actual production is compared to predicted production for each well. Introduction Ideally, reservoir deliverability and reservoir storage should drive the completion design and procedure for a given well based on the predicted economic outcome. While this is easily stated, it is difficult to achieve. Standard log presentation gives a reasonable estimate of the reservoir's storage capacity (f h ); however, unless a good correlation between porosity (f) and permeability ( k ) exists, the reservoir deliverability ( k h ) is unknown. Fracture stimulation design is predominately driven by k h . Fracture geometry and conductivity can be selected for providing maximum production results; however, unless geometry and conductivity are coupled with a predicted cash flow, an uneconomic design might result. Operators could benefit greatly from knowing the Kh value of the reservoir before setting pipe or beginning a completion. Recent advances in logging techniques, such as nuclear magnetic resonance (NMR), have greatly improved determination of k h and ? h during this study, by accurately determining permeability, researchers were able to preview the production and storage capacity of individual zones within the Granite Wash wells.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations
Symposium, March 24–27, 2001

Paper Number: SPE-67241-MS

... Abstract A new technique has been developed for analyzing the constant bottomhole pressure (BHP) test data. The method presented in this note allows to

**calculate**the skin factor for damaged and stimulated oil wells. Advantages of the BHP test are: they do not require that well be shut in...
Abstract

Abstract A new technique has been developed for analyzing the constant bottomhole pressure (BHP) test data. The method presented in this note allows to calculate the skin factor for damaged and stimulated oil wells. Advantages of the BHP test are: they do not require that well be shut in; the fluid production can be easily controlled (at constant flow rate tests the BHP is changing with time); and wellbore storage effects on the test data are short-lived. It is assumed that the instantaneous flow rate and time data are available from a well produced against a constant bottomhole pressure. Only records of the flowing time and cumulative production data are required to compute the value of the skin factor. A semi theoretical equation is used to approximate the dimensionless flow rate. This formula is used to obtain a quadratic equation for determining the skin factor. The accuracy of the basic equation will be shown below. The paper includes an example o calculation. Dimensionless Flow Rate Let us assume that the well is producing against a constant bottomhole pressure from an infinite-acting reservoir and the effective wellbore radius concept can be used 1 . In this case the relationship between well flow rate and time for a well with a constant BHP in oil field units is 2 Equation (1) Equation (2) Equation (3) Where q D is dimensionless flow rate, and t D is the dimensionless time based on the apparent well bore radius (r wa ) concept. We should also to note that Equation 1 is widely used in petroleum industry to forecast oil flow rates. Analytical expressions for the function q D =f (t D ) are available only for asymptotic cases or for large values of t D 3,4 . The dimensionless flow rate was first calculated (in tabulated form) by Jacob and Lohman 3 . Sengul 5 computed values of q D (t D ) for a wider range of t D and with more table entries. We have found 6,7 that for any values of dimensionless production time a semi theoretical Equation 4 can be used to forecast the flow rate Equation (4) Equation (5) Equation (6) In the Table 1 values of q D * calculated after Equation 4 and the results of a numerical solution 5 (q D *) are compared. The agreement between values of q D and q D * calculated by these two methods is seen to be good.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 9–11, 1997

Paper Number: SPE-37489-MS

... pressure" or "closure stress" has been used in these papers primarily in the context of

**calculating**fracture net pressure or excess pressure. 1,2 These parameters, and others, are used in**calculating**the fracture geometry during a fracture treatment. 3,4 Accurate measurements of closure stress for...
Abstract

Abstract The effect of closure stress on fracture conductivity has been well documented by laboratory measurement. Common industry practice for estimating closure stress on proppant in the field is to subtract flowing bottomhole pressure from the estimated in-situ stress of the pay interval fractured. This paper proposes that the closure stress on proppant in a fracture can be significantly higher than common estimations due to the influence of the bounding layers and the elastic response of the formation acting on the proppant. In this paper we will review past literature on fracture propagation, fracture conductivity and proppant placement and demonstrate the impact that increased proppant stress due to bounding layers can have on fracture conductivity and ultimately production. Introduction Many papers have been written on the subject of fracture propagation. The term "closure pressure" or "closure stress" has been used in these papers primarily in the context of calculating fracture net pressure or excess pressure. 1,2 These parameters, and others, are used in calculating the fracture geometry during a fracture treatment. 3,4 Accurate measurements of closure stress for individual intervals are especially important for predicting fracture height growth and, hence, fracture geometry with fracturing models. Procedures for the measurement of closure stress are also well documented in the literature. 5,6,7 These procedures describe the pumping of fluid into a formation to create a hydraulic fracture followed by the monitoring of wellbore pressure. The shape of the pressure fall-off curve can then be used to determine the closure pressure or horizontal stress acting across the plane of the vertical fracture. This procedure is best performed with a small amount of fluid and may be used on both pay and boundary intervals. By definition, the closure pressure determined through these mini-frac corresponds to the pressure in the fracture as it closes to a width of essentially zero. During hydraulic fracturing the reservoir rock is pushed apart by a fluid at pressure. The introduction of proppant with the fracturing fluid results in the fracture being propped open to some width after the fracturing fluid pressure is released. The reservoir rock can thus only partially rebound from the maximum open state caused by the fracturing fluid. As such, the closure pressure on the proppant is higher than that exhibited in the above described test since the fracture width is greater than zero. It is this extra stress, above the closure stress of the pay interval, which increases the stress on the proppant and reduces the propped fracture conductivity below values as estimated by current methods. The elastic mechanics of the above process are described in the later " Mechanics of Closure " section. To examine the magnitude of the excess closure stress on the proppant, a parametric study of fracture width versus net pressure was performed using a pseudo three-dimensional (P3D) fracture model 8 . The model data was constructed to represent a simple three layer system with equal higher stress levels in the layers above and below a lower stressed pay interval. The effect of stress differential, between the pay and bounding intervals, the thickness of the pay interval and the Young's Modulus of the layers was investigated through numerous simulations. The P3D model was applied to this problem because it was convenient to use, though care had to be taken to consistently extract the response data (excess closure stress as a function of confining stress and modulus contrast). The results of all simulations were interpolated to allow calculation of fracture conductivity (using 20/40 Ottawa sand) for any specific pay interval configuration. The results indicate that for larger Young's modulus values (greater than 4 million psi) and smaller pay thickness (less than 60 feet) the bounding layer stresses have a significant effect on the closure stress on proppant. The combined effect of the increase in closure stress felt by the proppant translates to reductions of over 50% in estimated fracture conductivity.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 9–11, 1997

Paper Number: SPE-37440-MS

... Abstract An accurate method to predict volumetric behavior of gas mixtures, such as in the case of underground gas storage where the in-situ gas is mixed with the injected gas, is presented in this paper. This method accurately

**calculates**the compressibility (Z) factor of pure hydrocarbon, non...
Abstract

Abstract An accurate method to predict volumetric behavior of gas mixtures, such as in the case of underground gas storage where the in-situ gas is mixed with the injected gas, is presented in this paper. This method accurately calculates the compressibility (Z) factor of pure hydrocarbon, non-hydrocarbon gases and gas mixtures. These calculations are based on correction functions developed from correlation of data (Z-factor) generated by the Peng-Robinson equation of state. The correction functions are function of gas composition, pressure and temperature, so the Z-factor can be calculated explicitly from gas composition under different reservoir conditions. Several comparative examples are presented to compare the Z-factors calculated by the correction functions with those calculated by the Peng-Robinson equation of state (PR-EOS) and with measured data published in the literature. The comparison results indicated that the average absolute relative deviation (AARD) is 3% for gas mixtures, 2% for pure hydrocarbon, non-hydrocarbon gases and less than 1% for pure components (methane, nitrogen, carbon dioxide). A stable method of calculating Z-factor for gases from their composition is presented. This method is iteration free so the CPU time is minimized. Accurate values of Z-factor can be calculated which are better than those obtained by linear interpolations. The correction functions can be incorporated in any non-compositional simulator to calculate the Z-factor directly without any iterative procedures which occur in compositional simulators during the calculations of Z-factor using the equation of state. These functions also eliminate the inaccurate linear interpolations of tabulated Z-values, specially during calculations of Z-factor for gas mixtures, in non-compositional simulators. Introduction The compressibility factor is an important property for gases to calculate volume (material) of gases under given conditions (pressure, temperature). Also the Z-factor is important parameter to calculate other gas properties such as the formation volume factor and the coefficient of isothermal compressibility. It is important to calculate the Z-factor more accurately, specially for gas mixtures, in order to predict the volumetric gas behavior more reasonably. In compositional simulators the calculations of the Z-factor are accurate, but for every condition the cubic equation of state is solved for Z-factor. The solution procedure involves iterations such as in Newton Raphson method. These iterations and convergence checking procedure consumes, some times, a considerable part of CPU time for just calculating gas properties (Z-factor). The CPU time should be used more efficiently in and wisely in the simulator. On the other side in the non-compositional simulators the Z-factor values are tabulated for certain gas composition and pressures and a linear interpolation procedure is used to calculated those Z-factor values which are not listed in the table. This procedure leads to erroneous calculations of Z-factor specially for gas mixtures where the linear interpolations are no longer accurate. The calculation procedure of Z-factor using the correlation functions presented in this paper has two advantages: Obtaining an accurate value of Z-factor and saving CPU time for other more important calculations in the simulator. Background Some impurities such as nitrogen and carbon dioxide are often existed in appreciable amounts in natural gases. The Z-factor for non-hydrocarbon components of natural gas in certain corresponding states differ markedly from those of hydrocarbons. This makes the non-hydrocarbon and hydrocarbon components not quit additive. Eilerts, Muller and Carlson studied the compressibility of natural gas and nitrogen mixtures. They proposed a method to calculate the Z-factor for the gas mixture by introducing a correction factor into the additive form as shown in Eq. 1. (1) where: Zm = actual Z-factor for gas mixture, Zn = Z-factor of the nitrogen in the mixture, Zn = Z-factor of hydrocarbon gas, n = mole fraction of nitrogen in the mixture. P. 453^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 9–11, 1997

Paper Number: SPE-37492-MS

..., accomplished either by perforated and non-perforated or slotted/blank liners has merit for zonal isolation, future well management and problem remediation. Economic

**calculations**, incorporating production and well completion including zonal isolation devices show substantial attractiveness from partially...
Abstract

Optimization of the Performance of Partially Completed Horizontal Wells A. Retnanto, SPE, and M.J. Economides, SPE, Texas A&M University, C.A. Ehlig-Economides, SPE, Schlumberger, and T.P. Frick, SPE, Mining University Leoben Abstract Goode and Wilkinson (1991) have presented an analytical solution for the performance of a partially completed horizontal well. In that work they suggested that normalized well performance (compared to the idealized open-hole equivalent) can be favorably disproportional to the fraction of open well, especially if the total open length is distributed among several spaced intervals. This work, using a comprehensive multi- and single-well semi-analytical well performance model, extends the Goode and Wilkinson results examining various open lengths, reservoir thicknesses and permeability anisotropy ratios. Both transient and late-time (pseudosteady-state) results are shown. It appears that the number of segments where the normalized productivity index flattens out is about four for almost all thicknesses. For thinner reservoirs the relative impact from the number of segments is more pronounced. For example, for a thin (20 ft) isotropic reservoir, 40% of open well, of 2000 ft total length, distributed in four segments, would lead to almost 90% of the open-hole equivalent productivity index. For thicker reservoirs and/or longer wells the incremental productivity index fraction decreases. The idea of a sequence of open/close segments, accomplished either by perforated and non-perforated or slotted/blank liners has merit for zonal isolation, future well management and problem remediation. Economic calculations, incorporating production and well completion including zonal isolation devices show substantial attractiveness from partially completed, segmented horizontal wells. Introduction Open-hole completion has been the one most commonly used since the early years of horizontal wells. It is still in wide use today although several other completion options are available. The main reason for alternative well completions is that open holes do not allow flexibility for zonal isolation and future well management. Figure 1 illustrates the most common completion designs for horizontal wells. They are: – Open hole (Fig. 1a) – Slotted, perforated or pre-packed liner in an open-hole (Fig. lb) – Liner with External Casing Packers (Fig. 1c) – Cased, cemented and perforated (Fig. 1d) Substantial work has been done on how to complete horizontal wells successfully, Reiss, Lessi and Spreux and Spreux et al. have presented completion technologies, especially as applied to selective completions. The competence of the formation rock is a first consideration in deciding how to complete a horizontal well. Borehole instability and borehole collapse indicate shear failure, which in a horizontal wellbore is often severe, affected by high insitu stress anisotropy and excessive wellbore cooling. In an unconsolidated formation, sand production often becomes a problem. This is an obvious reason against open-hole completions and in favor of, at least, slotted or perforated liners, sometimes augmented by sand-control screens. However, other considerations often may render liners as unattractive as open holes. Zonal isolation for production and fluid placement during stimulation may suggest the segmentation of a horizontal well with external casing packers (ECP) or other devices. To detect the origin of problems, such as water or gas influx, blank liners may be interspersed with slotted or perforated liners, all separated by external casing packers. In the case that a problem is detected through production logs, the zone may be shut off with a variety of means. Of course in the case of the ideal cemented and perforated well, problematic zones can be shut off with remedial cementing. P. 785^