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Proceedings Papers

Publisher: Offshore Mediterranean Conference

Paper presented at the OMC Med Energy Conference and Exhibition, September 28–30, 2021

Paper Number: OMC-2021-206

... FOR THE COMMERCIALIZATION OF THERMONUCLEAR FUSION POWER Boris Paladino, Fabio Di Fonzo, Center for Nano Science and Technology - CNST@PoliMi, Serena Bassini, Marco Utili, ENEA-

**FSN**-ING Division, C.R. Brasimone. This paper was presented at the 15th OMC Med Energy Conference and Exhibition in Ravenna, Italy, September 28-30...
Abstract

Abstract After decades of scientific research, nuclear fusion is on the verge of maturing into a sustainable and safe power generating technology. The most consolidated designs of power plants envisioned have in common the deuterium-tritium fusion reaction, which implies the production of the latter from Li, in a breeding blanket (BB), the technological cornerstone for a self-sustaining power plant. Whatever the specific design of the BB, two issues are omnipresent: T permeation from the breeding zone and corrosion of the structural materials by the Li compounds used. Here we present the summary of our work on ductile amorphous ceramic coatings (DACs) deposited by Pulsed Laser Deposition, to overcome these challenges, aiming at simplifying the BB and the T2 management subsystems. This new class of ceramic coatings have unique properties: high strength and ductility and a high density amorphous structure. The mechanical properties assure the reliability of coated steel parts under the most extreme thermal cycles and the isotropic, homogeneous structure impermeability to gases (H2, D2, O2) even at high temperature. The key engineering performances are: a permeation reduction factor (PRF) higher than 10 5 (T>450 °C) for coated EUROFER with respect to an uncoated reference; corrosion protection of the EUROFER in contact with Pb-16Li both in static and dynamic conditions; a high resistivity capable to drastically reduce Magneto Hydrodynamic Effects. In recognition of the key enabling potential of DAC in fusion, the European Commission awarded us the 2020 SOFT Innovation Prize. Even if more validation is needed and scale-up of the coating technologies used to produce DACs are in progress, they hold the promise to minimize the time and the cost to transition fusion from a plasma physics experiment to a safe and unlimited power generating technology. Introduction Nuclear fusion energy is the holy grail of scientists and engineers working to find a sustainable way to produce electricity abundantly and at low cost. The International Thermonuclear Experimental Reactor (ITER) will be the last multinational science-driven experiment to study plasma physics and fusion ignition. After, fusion will enter the pre-commercialization stage, with the development of demonstrative fusion power plants designed to harvest the fusion energy and generate net power. The European DEMOnstration power plant (DEMO) is the archetypal of these demonstrative plants. Lately, this transition is speeding up, with the "nationalization" of the programs and the emergence of start-ups (among others General Fusion (CA), Commonwealth Fusion Systems (USA), Tokamak Energy (UK)). Most of these demonstrative power plants have in common the deuterium-tritium fusion reaction, which implies the production of the latter from Li (while D is extracted from the sea), in a breeding device, which in DEMO is called breeding blanket (BB). In the case of DEMO, it consists of a set of D-shaped segments surrounding the reactor's main vessel having a threefold purpose: host the heat extraction system, shield from the radiation field incoming from the main reaction core and finally produce tritium in situ, thus guaranteeing the self- sufficiency of the power plant. Currently, two different breeding blanket concepts are investigated for DEMO: the water-cooled lithium-lead (WCLL) and the helium-cooled pebble bed (HCPB). Also to mention two alternative solutions investigated for the future: the dual coolant lithium-lead (DCLL) andthe helium-cooled lithium-lead (HCLL). The WCLL, HCLL and DCLL foresee a liquid eutectic alloy of lithium and lead (Pb-16Li) as the breeding media [1-5], while the HCPB solid LiSiO4 pebbles. For all designs, the major issue is T permeation. In fact, whilst the BB is designed to produce a large amount of tritium, EUROFER, a reduced activation ferritic-martensitic steel chosen as structural material for DEMO, is highly permeable to all hydrogen isotopes, and hence to T, at the working temperature of the BB, 450 °C. This phenomenon is of particular concern since the Pressurised Heat Transfer System (PHTS) is directly interfaced with the BB and hence T could escape the nuclear island of the plant, with a possible radioactive hazard for the workers and the public, being tritium a radioactive gas. To face this issue, a tritium recovery system from the PHTS would be then necessary, thus complicating the overall engineering. Two secondary issues are instead strictly linked to Pb-16Li: corrosion and magnetohydrodynamic (MHD) effects. Even if corrosion is not a major issue in WCLL due to the low speed of the Pb-16Li, it could cause the dispersion of activated corrosion products in the breeding medium, which could eventually accumulate in the cold segments of the circuit. MHD originates from the interaction between the flowing Pb-16Li and the steel structures under the intense magnetic field of the plasma confinement, causing high pressure drops and unsafe loadings on the structures [6-14]. Since traditional structural materials employed in the nuclear industry are not able to withstand these strict conditions, innovative solutions have been actively investigated during the years. Towards this goal, IIT and ENEA, in the framework of EUROFUSION, developed multifunctional DAC coatings designed to solve all the three issues above mentioned at once. In the present paper, we summarize the main results obtained so far in the development of multifunctional DAC coatings produced by pulsed laser deposition (PLD) and their testing in fusion relevant experiments.

Proceedings Papers

Publisher: Offshore Mediterranean Conference

Paper presented at the OMC Med Energy Conference and Exhibition, September 28–30, 2021

Paper Number: OMC-2021-017

... facility reaction fusion engineering divertor module port module configuration plasma DIVERTOR TOKAMAK TESTING FACILITY (DTT): A TEST FACILITY FOR THE FUSION POWER PLANT Gian Mario Polli, ENEA

**FSN**department & DTT S.C.a r.l., with the support of the DTT community. This paper was presented...
Abstract

Abstract In the European Fusion Roadmap for the realisation of fusion energy within 2050, one of the main mission is the identification of a reliable solution for the heat exhaust in the reactor. Indeed, the power released by the nuclear fusion reactions of deuterium and tritium in the plasma will be in part spread over the so-called blanket that surrounds the plasma, in part, a fifth of the total, will be directed to the so-called divertor. This second flux of energy is constituted primarily by the ashes of the reactions (alpha particles), that would rapidly choke the plasma reactions if not extracted continuously. A "standard" divertor, operating in a plasma fully detached condition, i.e. no contact between plasma and first wall of the vessel, will be tested in ITER. Nonetheless, the baseline strategy implemented in ITER could not be extrapolated to DEMO and future power plants since the amount of fusion power density released in a reactor would exceed the limits available in ITER and a modification of the ITER divertor would be too long and expensive. Then the problem of thermal loads on the divertor may remain particularly critical in the road to the realization of a reactor. For this reason, a dedicated facility, where a number of scaled experiments could be tested, fully integrated with the expected physical parameters and engineering solutions to be used in DEMO, is of paramount importance. DTT, Divertor Tokamk Test facility, has been designed and it is under construction in ENEA Frascati Research Center with the aim to test different divertor magnetic configurations in an integrated way. It will be a high field superconducting tokamak device (6 T) carrying plasma current up to 5.5 MA in pulses with length up to about 100s and with 45 MW of additional heating power, needed to reproduce the energy flux expected in a reactor by the sole fusion reactions in the plasma. To easy the management and the operation of the machine, DTT will indeed operate only with deuterium plasmas. This paper describes the status of the design and construction activities of DTT, highlighting especially the constraints imposed by the divertor system in the integration design activities.

Proceedings Papers

Luis C.B. Bianco, Paulo A. Barata, Fabio S.N. Rosa, Átila F.L. Aragão, Paulo S. Batista Santos, Alejandro T. Stepkowski

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, September 26–29, 2004

Paper Number: SPE-90155-MS

Abstract

Abstract The BARBI Concept was a result of an integrated project targeted to drilling and production operations in deep and ultradeep waters, with the main goal of reducing the well construction costs and enhancing productivity. Based on the new available technologies for drilling and completion, improvements on the well design were made. Time reduction on the execution was attained by the decrease on the number of drilling phases, speeding up well construction by the extensive use of rotary steerable tool, use of expandable sand screens and synthetic base mud for the drilling and completion phases, and simplification on the operational procedures. The increase in well productivity was a result of the lower formation damage due to the design fluid and the use of larger screens ID that led to a more uniform oil influx, which potentially delays the water breakthrough. Substantial cost reduction on the CAPEX was achieved and this paper discusses the application of the new concept in horizontal well construction that is being applied in Campos Basin. Introduction Wells at the Campos Basin, offshore area Southeastern Brazil, have been designed and drilled following an evolving process along the last 31 years of exploitation. Since the discovery of the Garoupa Field in 1973, Petrobras has been moving to deeper waters. Subsea engineering and well technologies have been developed and applied to overcome the environmental restrictions. Today more than 60% of Brazil's oil production comes from fields located offshore in water depths over 1,000 m. The challenge for developing offshore deepwater oil fields has led to a paradigm changing in the early 80's technology, mostly centered in closely-spaced vertical and deviated wells. The new scenarios required a reduced number of largely spaced horizontal wells. Additionally, some of the internal heterogeneities of turbidite reservoirs were poorly understood. Facies were well described from cores, but scarce information was available from inter-well areas. The well design evolution was driven mainly by the exploration campaign in the decades of 80's and 90's following the geological structures that leads to a huge subsee structures in deep and ultradeep waters. Since then, reserves were added, but so were new challenges. The extensive use of 3D seismics as a reservoir characterization tool allowed the reduction of risks and the optimization of well locations. However, the increase in water depth led to high currents, which need long and heavier risers. Small moored rigs gave place to a large, sophisticated and expensive dynamic position drilling rigs. An important characteristics throughout the eastern Brazilian margin is that deeper the water depth, shallow the burial sediments. This leads to reservoirs with low fracture gradients and very tight operational window. Because of the poor cementation sand control is mandatory and horizontal open-hole gravel-packs and selective frack-packs have been used to improve productivity, avoiding sand production. The extensive use of the slender well architecture 1 , associated with new technologies for drill bits and drilling fluids, helped to reduce rig time, cut costs and raise oil production. The time spent to construct a well was gradually decreased. However, further improvements are needed and dependent on new developments in drilling and completion technologies.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE/IADC Drilling Conference, February 19–21, 2003

Paper Number: SPE-79791-MS

Abstract

Abstract The Marlim Sul Field, located in Campos Basin, southeast Brazil, is the one of the largest oil fields in the country. The water depth ranges from 1000 to 1900 meters and has been developed by horizontal wells with potential productivity up to 5000 m3/d. Due to the presence of unconsolidated sandstones, sand control is mandatory and open-hole gravel-pack has been used to avoid sand production. The regular casing program consist of a 30" conductor casing, a 13 3/8" surface casing, a 9 5/8" production casing and a 5 1/2" base pipe screen gravel packed in the 8 1/2" horizontal section. The application of new technologies such as rotary steerable tool, expandable screens and synthetic oil base drilling and completion fluids allowed a new well design, eliminating one phase in the well. This new design used a 30" conductor casing, 10 3/4" production casing and a combination of conventional 7" liner and a 5 1/2" expandable screens inside of the 8 1/2"well. The liner and the expandable screens are deployed in one trip. After screen expansion, a cementing job is performed through a stage collar in order to isolate the formation above the pay zone. Besides the overall cost reduction, an increment in well productivity is expected. Simulations showed that compared to 5 1/2" base pipe screen, the increased internal diameter achieved by the expandable screens, increases the PI and establishes a better production distribution along the horizontal section 1 . Therefore, a delay in the water production is expected. This paper is focused in the criteria used for the new well design and the operational procedures used for well construction. Introduction The Marlin Sul Field, discovered in October 1987, is located in the Northeast portion of the Campos Basin, in the coastline of the Rio de Janeiro State, at a distance of about 110 Km from the continent (fig.1). It occupies an area of about 600 Km2, in deep water and the field development is divided into four modules. The reservoir consists of Oligomiocene and Eocene sandstones, unconsolidated, with porosities around 32 %, permeability around 2000 mD and predominantly 24 API oil. Wells were projected and drilled following an evolving process along the field development and a standard design was achieved. The time spent to construct a horizontal well was gradually decreased up to 102 days. Further improvements on the well design were limited on the necessity of open-hole sand control, low fracture gradients and large well extension. Based on the new technologies available, improvements on the well design can be done in order to reduce more the rig time. Substantial cost reduction is expected and this paper discusses a new concept in horizontal well construct that is about to be applied in the Campos Basin. Brief Well Design Review The drilling design for offshore wells at the Campos Basin evolved in time as larger depths of water were explored and the concept of horizontal wells were accepted for field exploitation. At the beginning, due to the unknowledge about the conditions of the shallow sediments, it was necessary to be conservative and the large number of deployed casings reflected the concern about wellhead stability and well instability at the high inclination sections. As the challenges were growth, new drilling fluids formulations were designed to allow high inclination wells and horizontal wells being drilled. Due to the unconsolidated nature of the reservoir sandstones, gravel-pack techniques were also improved, allowing drill and complete wells up to 1100 m long. The well design evolution is showed on figure 2. The first significant change for the directional well design was the exclusion of the 7" liner with extension of the 9 5/8" casing through the reservoir, allowing a cased gravel-pack with 5 1/2" base pipe screens. Following, studies demonstrated that the 42" surface casing could be eliminated because the 30" casing as a conductor was sufficient support capacity to support the loads developed at the wellhead.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the IADC/SPE Asia Pacific Drilling Technology, September 7–9, 1998

Paper Number: SPE-47802-MS

Abstract

Abstract This paper describes the project and execution of a well using Underbalance Drilling (UBD) technique in South Brazil. Due to very hard formation in the intermediary section of the well and a very damage-sensitive reservoir, the use of UBD was considered mandatory for this field. New equipment were specially designed for use in the well including a liquid-gas separator and a new manifold. Since nitrogenated fluid was used as drilling fluid, a membrane was used to on-site generation of nitrogen. The article gives field data obtained in the well and also shows comparison between the results obtained with UBD and conventional drilling. A description of the advantages, problems and shortcomings of the technique also is included in the paper. P. 213

Journal Articles

Journal:
SPE Formation Evaluation

Publisher: Society of Petroleum Engineers (SPE)

*SPE Form Eval*6 (04): 505–512.

Paper Number: SPE-19602-PA

Published: 01 December 1991

... resolution of a log curve. Data analysis from these wells indicates that both the vertical resolution and repeatability of individual capture and inelastic curves differ. We found that the H-yield and capture curves have the highest vertical resolution 0.3 m) and the best signal/noise ratios (

**FSN**=30: 1...
Abstract

Summary Induced gamma ray spectroscopy (IGRS) logs from two cyclic-steam-stimulation observation wells in Cold Lake were analyzed to determine the vertical resolution and repeatability of data derived from gamma rays of inelastic and capture neutron reactions. Time-series analysis, a technique that uses the Fourier representation of the log data, was used to quantify the vertical resolution and the signal/noise characteristics of various IGRS log curves and to compute the coherence vs. spatial frequency of data collected on multiple IGRS passes. The coherence function ranges from 1.0 for perfect repeatability to 0.0 for incoherent noise. Because no real variations in the measured data were expected for the 12- to 24-hour data-collection period, any deviation of the coherence function from 1.0 is attributed to incoherent noise. Generally, coherence is high at low frequencies (large vertical scales) and low at high frequencies (small vertical scales). By noting the frequency at which the coherence level decreases to the expected value of random noise, we can quantify the vertical resolution of a log curve. Data analysis from these wells indicates that both the vertical resolution and repeatability of individual capture and inelastic curves differ. We found that the H-yield and capture curves have the highest vertical resolution (˜0.3 m) and the best signal/noise ratios ( F SN ˜ 30:1). In contrast, the capture Ca and Si yields are of significantly lower quality ( F SN ˜ 2 : 1). Only a small difference exists between the vertical resolution of the inelastic C (1.0 m) and 0 (1.3 m) yields, but the F SN of the 0 yield is only one-half that of the C yield. Fortunately, the vertical resolution and the repeatability of the C/O ratio, F CO are determined primarily by the quality of the inelastic C data. Specific to our application of monitoring heavy-oil saturations during cyclic-steam stimulation in a relatively uniform, high-porosity unconsolidated sand, we developed a simplified F CO interpretation that does not rely on the elemental yields from capture data. This linear model permits us to assess the uncertainties in computed saturations from the statistical noise in the inelastic F CO data. Introduction IGRS logs are used routinely in Cold Lake to monitor bitumen saturations on observation wells and occasionally to evaluate new wells. Esso Resources Canada Ltd. uses cyclic-steam stimulation to recover bitumen from the Cretaceous unconsolidated Clearwater formation. Throughout the commercial operations, bitumen is produced from directional wells drilled from a central pad location. 1 These wells generally are logged before being cased; however, sometimes a key well cannot be logged before casing, so IGRS logs may be run to quantify bitumen saturations and to provide data for reservoir description. Reservoir descriptions are derived primarily from capture gamma ray data (i.e., Si, Ca, Fe, H, S, and Cl yields and the capture cross section, S), and bitumen saturations are obtained from the inelastic F CO data. Besides large commercial operations, Esso also operates several pilots 1–4 to test various production scenarios and to study the physics of cyclic-steam stimulation. 5 Observation wells playa key role in the pilots, and much has been learned from temperature observations. 4 To monitor changes in bitumen saturations at the observation wells, we rely primarily on the inelastic F CO data from IGRS logs. Two observation wells located 15 m apart on one pad have been logged 10 times with IGRS logs during various phases of cyclic-steam stimulation. An 8D-m interval in the Clearwater formation and a 30-m interval in the shallower Grand Rapids formation are logged routinely to monitor tool performance and stability. A specially made 3-m casing joint that carries 22.5 kg of graphite was installed on one of the wells below the Clearwater sands to provide an in-situ, stable, high-carbon F CO calibration facility. Calibration and the statistical precision of the IGRS data must be understood. Porosities are very high (f˜33%) in the unconsolidated Clearwater sands, making it feasible to collect continuous IGRS data by logging slowly. Generally, we make four inelastic passes at 0.5 m/min and four capture passes at 2 m/min. These data are averaged to obtain a single continuous F CO curve. To decrease the statistical noise inherent in the F CO data further, we average the data from multiple vertical levels. We use time-series analysis 7 to quantify the statistical noise in the inelastic and capture data and to determine the optimal vertical averaging. Fig. 1 demonstrates the statistical nature of the IGRS data with eight F CO passes across several heavy-oil sands of varying thicknesses in the Grand Rapids. Pass-to-pass variability is large, but the median-filtered data compare well with the openhole shallow resistivity data (Fig. 2). Because the Grand Rapids sands are not being produced in Cold Lake, data from two different runs (eight passes and five vertical levels, separated by 15.24 cm) were pooled and sorted for median filtering. The median value chosen from these data was used to represent the F CO value. The correspondence of the median-filtered F CO and the shallow resistivity data suggests that the vertical resolution of the averaged F CO data is 1 or 2 m. The comparison of the averaged F CO with openhole shallow resistivity data also illustrates that the shallow depth of investigation of the IGRS measurements 8 is not necessarily a problem at Cold Lake. Cold Lake bitumen is extremely viscous (100 Pa·s) and the oil sands do not invade. Furthermore, both wells were drilled with a 311-mm [12.25-in.] bit and cased with 178-mm [7-in.] casing, which results in a 50-mm-thick cement sheath and reduces the formation volume that the tool can investigate. Fig. 3 shows four passes of inelastic and capture IGRS data from one run. The top (429 m) and base (480 m) of the Clearwater formation are evident on the C, O, F CO , S, and Fe- and Si-yield data. The S data exhibit good pass-to-pass repeatability; the S and Cl yields appear to consist mainly of statistical noise. An Fe-rich carbonate-cemented tight streak: (siderite) at 467 m is evident in the Ca, H, Si, and Fe yields. A radioactive tag is at 447 m, and the graphite calibrator is between 480 and 483 m. Fig. 4 shows the calibrator and data from eight repeat logs run across it.

Proceedings Papers

Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, July 23–25, 2018

Paper Number: URTEC-2882814-MS

... in hydraulic- fracture system. 4 Solution Methodology A semi-analytical method is used to solve the well test model of the horizontal well with continuum and discrete fracture networks. First, we discretize the natural fractures and hydraulic fractures into

**fsn**segments and**Fsn**segments, respectively...
Abstract

Abstract This paper develops a well testing model for horizontal wells with continuum and discrete fracture networks. The proposed model has the capability to analyze the pressure behavior by considering complex fracture networks and natural fractures efficiently. The proposed model includes three domains: matrix, natural fracture networks, and discrete hydraulic fracture networks. The pressure transient solution of these diffusivity equation is obtained by using Laplace transforms and superposition principle. It is found that there are some interesting flow behaviors in shale reservoirs like bilinear flow, "V-shape" caused by fracture supply, pseudo boundary-dominated flow, impact of natural fractures, etc. The pseudo boundary-dominated flow provides us the information about how large the area covered by hydraulic fracture networks. This work provides a throughout understanding of transient pressure behaviors in shale reservoirs and guidelines for the producer optimize field development and well economics 1 Introduction Because of geological activities, high fluid pressure, thermal loading, etc, natural fractures are commonly seen in some shale reservoirs (Kuchuk and Biryukov, 2015). Meanwhile, lots of large-scale hydraulic fracturing treatments are implemented to ensure commercial production rate. Thus, it is very common that shale reservoirs comprise a huge number of natural and hydraulic fractures. However, it is neither practical nor advantageous to use numerical models to analyze the pressure transient behaviors. First, how to address the natural fractures is the primary work to investigate the transient behaviors in those reservoirs. Huge amount of literatures have reported the pressure transient analysis in naturally fractured reservoirs (Barenblatt et al., 1960; Warren and Root, 1963; Kazimi, 1969; de Swaan, 1976; Teimoori et al., 2003; Dershowitz et al., 2000; Araujo et al., 2004). Unfortunately, the explicitly of natural fractures cannot be reflected clearly. With the gridding approaches (Palagi and Aziz, 1994; Karimi-Fard et al., 2003; Xu et al., 2017), fracture flow, matrix flow, and matrix-fracture flow are comprehensively captured. Although more accurate results can be obtained, the application of gridding approaches is time-consuming, expensive, and site-specific. Therefore, modelling thousands of fractures in numerical DFM is unpractical.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, October 9–12, 2005

Paper Number: SPE-96785-MS

Abstract

Abstract A new refracture-candidate diagnostic test is presented that requires a brief injection at a pressure exceeding the fracture initiation and propagation pressure followed by an extended shut-in period with the pressure falloff recorded. Provided the time of injection is short relative to the reservoir response, the pressure falloff can be analyzed as a slug test by transforming and plotting the falloff data on a variable-storage, constant-rate drawdown type curve for a well producing from single or multiple finite- or infinite-conductivity vertical fractures in an infinite-acting reservoir. Characteristic variable storage behavior is used to diagnose a pre-existing fracture retaining residual width and to determine if a pre-existing fracture is damaged. Using the proposed model and analysis methodology, a quantitative type-curve/model match can be used to estimate reservoir properties. In addidtion to the new fracture diagnostic solution, a new single-phase fracture-injection/falloff dimensionless pressure solution is also provided along with new pressure-transient solutions for a well producing from multiple arbitrarily-oriented finite- or infinite-conductivity fractures. Introduction Oil and gas wells often contain potentially productive layers bypassed either intentionally or inadvertently during an original completion.Subsequent refracturing programs designed to identify underperforming wells and recomplete bypassed layers have sometimes been unsuccessful in part because the programs tend to focus on commingled well performance and well restimulation potential without thoroughly investigating individual layer properties and the refracturing potential of individual layers. Perhaps the most significant impediment to investigating layer properties is a lack of representative and cost-effective diagnostics that can be used to determine layer permeability, reservoir pressure, and to quantify the effectiveness of previous stimulation treatments. Post-frac production logs,[1–2] near-wellbore hydraulic fracture imaging with radioactive tracers,[3–4] and far-field microseismic fracture imaging[5] all suggest 10% to 40% of the layers targeted for completion during primary fracturing operations using limited-entry fracture treatment designs are bypassed or ineffectively stimulated. Quantifying bypassed layers has proved difficult because imaged wells represent a very small percentage of all wells completed. Consequently, bypassed or ineffectively stimulated layers may not be easily identified, and must be inferred from analysis of the commingled well stream, production logs, or conventional pressure-transient tests of individual layers. A refracture-candidate diagnostic used prior to a refracture treatment should complete the following objectives.[6] To determine if: A pre-existing fracture exists. A pre-existing fracture is damaged. To estimate: Effective fracture half-length of a pre-existing fracture. Fracture conductivity of a pre-existing fracture. Reservoir transmissibility. Average reservoir pressure. When the diagnostic test objectives are achieved, the benefits of refracturing can be easily evaluated, and the incremental production from a refracture treatment can be predicted. Quantitative conventional pressure-transient testing, which includes drawdown, drawdown/buildup, or injection/falloff tests at a pressure less than the fracture propagation pressure, can be used to achieve the objectives of a refracture-candidate diagnostic test. However, conventional pressure-transient tests are best suited for evaluating a single layer. For wells producing from multiple layers, multilayer pressure-transient tests have been published,[7] but in practice, determining layer flow rates for test interpretation from multiple layers is problematic—especially with upwards of 20 layers producing.[8] In general, a cost-effective quantitative diagnostic test does not exist for wells producing from multiple layers. Diagnostic testing in low permeability multilayer wells has been attempted, and Hopkins et al.[9] describe several diagnostic techniques used in a Devonian shale well to diagnose the existence of a pre-existing fracture(s) in multiple targeted layers over a 727 ft interval. The diagnostic tests included isolation flow tests, wellbore communication tests, nitrogen injection/falloff tests, and conventional drawdown/buildup tests. The post-frac diagnostic program described by Hopkins et al.[9] is thorough and addresses the objectives of a refracture-candidate diagnostic. However, the diagnostic program is also expensive and time consuming - even for a relatively simple four layer case. Many refracture candidates in low permeability gas wells contain stacked lenticular sands with between 20 to 40 layers which need to be evaluated in a timely and cost effective manner.

Journal Articles

*Int. J. Offshore Polar Eng.*16 (02).

Paper Number: ISOPE-06-16-2-138

Published: 01 June 2006

... are obtained from superimposition of the normal force and bending moment capacities of the concrete and reinforcement presented above. They are stated as: Nu hx =Ncu hx +Asfsn hx Mu hx =Mcu hx +Asqs hx (8a) in which As is the cross-sectional area of the reinforcement and the functions,

**fsn**hx and qs hx...
Abstract

In this paper, a general formulation of the section capacities of a circular RC tubular cross-section is first presented assuming that the strain-stress relation of the concrete in the compression zone is simply modelled as a bilinear function with ultimate values given in Eurocode 2. It is also assumed that the concrete works only in the compression zone. In the cross-section, tension stresses are carried by the reinforcement. Having presented a general formulation of the extreme bending moment and normal force of an RC monopod offshore tower subjected to wave loading, uncertainties in both section capacities and loading terms are presented. Then, a reliability calculation of the cross-section is performed to find out the reliability index. In this calculation, the balance of the normal force is used to determine the concrete compression zone during the reliability iteration, and the failure function is defined on the basis of the section capacity and applied bending moments on the cross-section. Variation of the reliability index with various parameters is investigated, and most sensitive uncertainty variables are determined. INTRODUCTION Reinforced concrete (RC) structures have been alternatively used at early stages of offshore structural engineering in moderately deep-water environments (Watt, 1978; Huslid et al., 1982) and may still be used for gas and oil production, and perhaps for observation purposes. Even for deep-water environments, RC structural components or systems are an alternative solution for a stable structural configuration, such as a floating concrete platform's hulls and pontoons (Haug and Fjeld, 1996), in harsh weather conditions. The concept of a mobile offshore base (Rognaas et al., 2001) is another application of RC in offshore environments. Beyond these uses, concrete piles have also been commonly used as foundation elements to support offshore structures such as bridges, oil rigs and floating airports (Eicher et al., 2003).

Journal Articles

Journal:
Marine Technology and SNAME News

*Mar Technol SNAME N*41 (04): 141–160.

Paper Number: SNAME-MTSN-2004-41-4-141

Published: 01 October 2004

... that their direc- tional stability is much reduced and excessive speed can lead to violent behaviour in yaw and associated roll. A Table 1 Trim and stability: condition 1, grain cargo leaving Port Germein Item Weight (tons) KGF Vertical Moment LCG About Aft Moment Forward Moment

**FSN**T/F Deep tank 970 6.7 6,499...
Abstract

As the era of the deep-water commercial sailing ships was coming to its close, several steamship companies with concern for their deck officer requirements decided to train their future officers as cadets in training ships under their own house flags. These were in the form of square-rigged vessels fitted to accommodate several cadets. They were classified as cargo-cum-cadet ships, and for the purpose existing ships were purchased. The cadets were given instruction in seamanship, navigation, cargo stowage, sailmaking, boatwork, and ship's business, all with the object that on graduation and so qualified they would be posted to company steamships as deck officers.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2001 SEG Annual Meeting, September 9–14, 2001

Paper Number: SEG-2001-0690

... ] S8S #W° ffs_u fSfGUfGpVfQr4n9pqfSmSr<oOfGp_gsqh oWx<pqgMª xzsqgMr4n hV¡gsq| gMnysq| f(hkfSgMhkjlgimpqfD0

**fSn**mSgMfSh x4n uff¡giuffsq| T0gMnyrzsq| fGp rzpu hf~Mr0rWhkfpqfShkr4~i ffsqgMrWnxzhfS~M~ x4hVgMnr4pqj£x<sqgir4nyx rW ffsVsq| f ~MrDpqfD0**fSn**mG£skpqfSnvu < BW ¹ B ½E...
Abstract

ABSTRACT Seismic inversion consists in finding an earth model that best fits the data. For this purpose, we have to minimize a least square function that measures the amplitude of the misfits according to norm to be chosen in the date space. In general the chosen norm is Euclidean or L2. Unfortunately, such a norm is not adapted to data corrupted by a high amplitude correlated noise : the noise is, in this case, inverted as a part of the signal, and the inversion results are unacceptable. Our paper is a quest for some norms in the data space that allow to reject a high amplitude correlated noise in the residuals so that the model does not match the data but matches the signal instead.

Journal Articles

Journal:
Journal of Ship Research

*J Ship Res*29 (03): 162–169.

Paper Number: SNAME-JSR-1985-29-3-162

Published: 01 September 1985

... the conditions at the bottom can be derived by studying the equilibrium of the differential e ement at the bottom end of the column shown in Fig. 8.

**Fsn**is the restoring force of the linear spring at the bottom**Fsn**= -knx(O) (29) and Msn is the restoring moment of the rotational spring at the bottom Mss = -rsO(O...
Abstract

The post-buckling behavior of heavy tubular columns following static instability under the combined action of weight, tension/compression at the top, and fluid static pressure forces in the gravity field is studied. A two-dimensional nonlinear small-strain large-deflection model of the column is derived, consisting of an integrodifferential equilibrium equation and two end rotation conditions. The equation of equilibrium is discretized using a finite-element method. An approximate solution valid in the neighborhood of the bifurcation point and an incremental solution are used to determine the secondary equilibrium path. The results of both methods are corrected by Newton-Raphson iteration. Conditions for unstable initial post-buckling behavior and existence of limit points on the secondary equilibrium path are presented. The numerical solution is applied to the problem of the elastica and is found to be in good agreement with the analytical solution. The secondary equilibrium path for a 500-m-long (1640 ft) marine drilling riser is calculated for two sets of boundary conditions and various values of the drilling mud density. The effect of the drilling mud density and the boundary conditions on the riser's post-buckling behavior is discussed.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Gas Technology Symposium, May 15–17, 2006

Paper Number: SPE-100586-MS

... = + + + + + A A A A A 1

**fsn**m = , 1,2 and , 1,2f fsi n j m n= =A , 55) where the angle, is defined in the rescaled equivalent isotropic reservoir and is related to the anisotropic reservoir by 1 0 tan tan 0 2 2 x y k k = < < = . 56) A semianalytical solution accounting for multiple...
Abstract

Abstract A new analytical pressure transient solution (constant rate) for a well containing multiple arbitrarily-oriented uniform-flux, infinite-conductivity, or finite-conductivity fractures in an infinite-slab reservoir is presented. The multiple-fracture solution is derived using a new uniform-flux solution for a single arbitrarily-oriented fracture in an anisotropic reservoir. The variables in this solution are: fracture half-length, fracture conductivity, and fracture angle of rotation for each fracture relative to the primary fracture. Example constant-rate type curves are provided for two intersecting fractures - cruciform or oblique - and three intersecting fractures - trifracture. Introduction Fracture imaging has changed the concept of a well producing from an infinite-slab through a single planar fracture. Microseismic fracture imaging strongly suggests complex fracture patterns can develop during primary fracture treatments,[1–2] and fracture imaging during subsequent refracturing treatments demonstrates that secondary fractures are oriented in a plane(s) other than the primary fracture.[3] An analytical solution for a well producing from an infinite-slab reservoir through multiple arbitrarily-oriented finite- or infinite-conductivity fractures is presented that was developed as part of a new pressure-transient test for refracture-candidate assessment.[4] Obviously, this solution is also applicable when interpreting conventional pressure transient tests in reservoirs with multiple arbitrarily-oriented fractures. The purpose of this paper is to derive the new analytical solution; evaluate a pressure-averaging infinite-conductivity solution versus a semianalytical solution; illustrate the solutions by generating type curves for typical configurations of two intersecting - cruciform or oblique - fractures and three intersecting - star-shaped - tri-fractures; and present a model and type curves for a pressure-transient test in a formation exhibiting complex fracturing patterns.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, October 11–16, 2020

Paper Number: SEG-2020-3399306

..., provided that the subsequent estimation of <X> is reasonably attainable. Furthermore, the use of all mentioned strategies in a combined way further contributes to reducing the operational effort. We describe blended, sparsely-sampled and narrowband data, called incomplete data, as: P ' .fd nd

**fsns**' f...
Abstract

Acquisition of incomplete data, i.e., blended, sparsely-sampled and narrowband data, is an attractive strategy, provided that the recovery of complete data, i.e., deblended, well-sampled and broadband data, is attainable. In this paper, we propose a machine-learning (ML) based scheme that simultaneously performs suppression of blending interference, reconstruction of missing traces and extrapolation of low frequencies. We train a neural network using a set of incomplete and complete data. Incomplete data, which are never used for training, are subsequently fed into the trained network to predict complete data. We demonstrate the applicability of the proposed method using both synthetic and field data examples. Although blending, spatial-sampling and band-limitation schemes applied in this study lead to a significant reduction of the size of incomplete data in the frequency-space domain, both numerical and field data examples clearly show that the ML based scheme effectively deals with deblending, trace reconstruction and low-frequency extrapolation in a simultaneous fashion. It is noteworthy that no discernible difference in prediction errors between extrapolated frequencies and preexisting frequencies is observed. Presentation Date: Tuesday, October 13, 2020 Session Start Time: 8:30 AM Presentation Time: 11:25 AM Location: 362A Presentation Type: Oral

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*40 (12): 1609–1616.

Paper Number: SPE-16622-PA

Published: 01 December 1988

... Fj contains the internal and external force components (1) segment tension F u(t), (2) shear forces caused by bending rigidity

**Fsn**0 (t), (3) fluid forces F1 (t), (4) seafloor reac- tive forces Fr(t), (5) buoyancy and weight Fw, (6) buoy forces FB(t), and (7) tether forces Fuit). Because...
Abstract

Summary. Recent research indicates that dynamic amplification of tension in lines and risers can be of the same order of magnitude as the so-called quasistatic values. Also, dynamic effects in the mooring system can affect low-frequency motions of the structure by increasing virtual stiffness and damping. This paper presents three-dimensional (3D) computational procedures that describe the motion, tension, and bending moment along a flexible pipe or mooring line. The paper also discusses correlations with model test data. Introduction The increasing number of mooring concepts for offshore structures and trends toward cheaper technology because of low oil prices put high demands on the design of the mooring arrangement. Important parameters are the large displacement of the structure, deep and hostile waters, and the need for year-round workability. The wide variety of mooring systems may be illustrated by the existence of shallow and deepwater single-point moorings with temporarily or permanently moored tankers. clump weight systems used for guyed towers, and wire moorings for semisubmersible crane vessels. The current design procedures include mainly a dynamic motion analysis of the moored object. This provides extreme positions of the structure. The mooring line tensions at these extreme positions can be found from the static-load excursion characteristics of the mooring system. In this quasistatic mooring analysis, all other phenomena that affect the maximum line load are taken into account in an overall safety factor. as required by certifying authorities. Typical values are three for operational and two for survival conditions. Experimental and theoretical research has shown that high-frequency oscillations (in the wave-frequency range) of the upper end of a mooring line can generate significant dynamic amplification of line loads. These dynamic effects depend on frequency of oscillation, amplitude of oscillation, specific line mass. pretension, and hydromechanic line properties. From a systematic series of forced oscillation model tests, van Sluijs and Blok found that the ratios of maximum dynamic tension and maximum quasistatic tension strongly depend on the frequency of oscillation. This ratio is enhanced by increasing oscillation amplitude, increasing pre-tension, and reduction of line mass. Knowing the importance of dynamics for mooring systems, a similar behavior is expected for related "line-type" configurations such as flexible risers, pipe bundles, etc. The additional parameters concerning dynamic effects in these cases are the direct wave force and the bending stiffness. The traditional theoretical approach to solve the dynamic behavior of cable/riser systems is based on semi-analytical techniques. Geometrical nonlinearities are neglected to reduce the equations to differential equations that can be solved. Perturbation techniques are applied with success. but are restricted to certain areas. A more general approach to the problem is discretization techniques. The line is assumed to be composed of a limited number of discrete elements. These elements can have physical properties of their own. Thus, the formed system of partial differential equations describing the variables along the line can be replaced by equations of motion in an earth-bound system of coordinates. The most successful methods are widely known as the lumped mass method (LMM) and the finite-element method. This paper presents an LMM technique and the resultant algorithm (applied in the DYNFLX computer program). This approach was validated with results of an extensive study conducted by the Maritime Research Inst, Netherlands (MARIN) on behalf of the Netherlands Marine Technological Research (MATS) program (Fig. 1). Theory Basic Approach. The mathematical model for simulation of 3D behavior of flexible lines is an extension of the LMM technique used for mooring chains and wires. The spacewise discretization of the line is obtained by lumping the mass and all forces to a finite number of nodes. To derive the governing equations of motions for the jth lumped mass, Newton's law is written in global coordinates (Fig. 2): {[Mj] + [mj(t)]} ..........................(1) The added inertia matrix can be derived from the normal and tangential fluid inertia coefficients by directional transformations. [mj(t)]=nnj ...........................(2) where anj and ayj represent the normal and tangential added masses, respectively. anj=p(kIn-1), atj=p(KIt-1) and [ nj], [ tj]=directional transformation matrices. The nodal force vector ->F j contains the internal and external force components segment tension F sigma(t), shear forces caused by bending rigidity Fsno(t), fluid forces Ff (t), seafloor reactive forces Fr(t), buoyancy and weight Fw, buoy forces FB(t), and tether forces F sigma T(t). Because the tangential stiffness of the line (represented by its modulus of elasticity, EA) is an order of magnitude higher than the stiffness in normal direction, the tension is taken into account in the solution procedure. The tension vector on the jth node results from the tension and orientation of the adjacent line segments. ,............(3) where JPT P. 1609^

Proceedings Papers

Paper presented at the The 28th International Ocean and Polar Engineering Conference, June 10–15, 2018

Paper Number: ISOPE-I-18-086

... equation: (M + m)x¨(t) + t k(t )x (t) d . +C0 x (t) = FF K+ FD + Fw + Fc +

**Fsn**(t) + Fm(t) + Fconnector(t) (1) Where x¨(t) is the acceleration vector, x (t) is the velocity vector, x(t) is the displacement vector, M and m represent mass matrix and additional mass matrix, respectively. t k(t...
Abstract

ABSTRACT To figure out the effects of the connector on a multi-module VLFS for further connector design, a set of different stiffness and damping connectors is selected for analyzing their effects on constraining the modules relative motions and their own bearing load. The numerical model is developed based on Orcaflex and validated against model test results. It is found that the connector with very large stiffness although can provide strong constraints between modules for suppressing the relative motions, the connector load is incredibly large as expected. So the connector stiffness should be explicitly determined. Furthermore, the damping model should provide a high damping ratio in the frequency range where the incident wave dominates. INTRODUCTION Multi-module very large floating structure (VLFS) has recently attracted many researches for its many advantages compared to single large module, e.g., flexibility for future extensions, lower weight and capability of quick transportation and installation (Tajali and Shafieefar, 2011). To fulfill the functionality of the VLFS for floating airport or other activities (Derstine and Brown, 2000), the multiple modules are usually connected by connectors. Researches on the stiffness and damping of connectors for using by VLFS are encouraged to improve VLFS motion response performance and provide an engineering solution for its future actual construction. A flexible connected semi-submersible VLFS conceptual design was proposed in 1999 (Zueck et al., 2000). Since then, VLFS characteristics (i.e., mooring system, hydroelastic problem and connector design) have been widely investigated. Some succeeding investigations (e.g., Mark and Richard, 1999; Haney, 1999) revealed some characters of the flexible connectors' load. Flexible connectors stiffness in the directions of six degrees of freedom (DOFs) can be adjusted freely according to the environmental conditions, which allows the relative motion of VLFS modules (usually relative roll, pitch, and yaw motions), and may reduce connector loads. Wang et al. (1991) calculated the hydrodynamic and wave load of a VLFS using three dimensional hydroelastic theory, and found that the maximum impact on the VLFS module motion and the connector load was the connector stiffness. Riggs and Ertekin (1999) analyzed the stiffness of a flexible connector under various sea conditions, and the response rules were analyzed. They found that there would be a great resonance response of the connector under some sea conditions. Riggs et al. (1999) analyzed the impact of connector damping on the VLFS motion, and explained why different damping connectors have various effects on the VLFS motion response. Karperaki et al. (2016) simulated a connector using a simple spring-damper model in shallow water, and analyzed the impact of water depths and submarine topography on the connector performance. Some researchers found the stiffness of connectors is the key factor affecting the modules hydrodynamic response and connectors constraint force (Gao et al., 2013; Kim et al., 2007; Shu et al., 2002; Yu et al., 2004; Ding et al., 2005). Linjian et al. (2016) used the simplified algorithm to studying the effect of connectors stiffness on dynamic constraint forces. The results showed a linear increase trend with the increase of the connector stiffness.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 18–21, 1992

Paper Number: SPE-24378-MS

..." .0 MI. -10 ~IRI -1.2

**Fsn**-"100 0.1 M" -100 om 0.001 0.01 0.1 10 100 1000 Fig. II: Effect of F SJ2 on Canesian slope response for an infinitely large, three-region composite reservoir with CD = 0, MJ2 = 10, MJ3 = 100, FSJ3 = 100, and R21RJ 1.2. 100 I 598 _0 :a 0 ~ 0.. "0 ~ -< .E' "0 0 ~ 0. ~ spt. 2437...
Abstract

SPE Members Abstract Usually, well tests from enhanced oil recovery projects, such as steam injection, in-situ combustion, and CO2 flooding projects, are analyzed using a radial, two-region composite reservoir model. However, a three-region model may be more appropriate in may cases. An analytical solution for the transient pressure response of a well in a radial, three-region reservoir is available. But a detailed study of the transient pressure an-or pressure derivative response of a well in a three-region reservoir has not been presented in the literature. Using a analytical solution, this study establishes the ratio of the intermediate region radius to the inner region radius as a correlating parameter for the transient pressure derivative responses for a three-region reservoir. Additional four parameters are related to the mobilities and the storativities of different regions. This study shows that the deviation time method would result in a estimate for the inner region radius, if the effects of the mobilities ad the storativities of the inner ad the intermediate regions are not balanced in a way to produce a incorrect deviation time. Analytical expressions for the effective porosity-compressibility pressure and mobility are developed for the analysis of pressure transient data by the pseudosteady state (PSS) method. The PSS method would result in an estimate of the combined volume of the inner and the intermediate regions, if an effective porosity-compressibility value is used to analyze the pseudosteady data. However, at times, the development of an apparent pseudosteady state may yield an overestimated volume. An idea about the development of an apparent pseudosteady state may be obtained by calculating the effective dimensionless time corresponding to the time to start of an approximately constant Cartesian slope for the pressure transient data in question. Introduction Two-region composite reservoir models have been used to analyze pressure transient data from enhanced oil recovery projects. Three-region composite reservoir models have been used less frequently to analyze well tests from enhanced oil recovery projects. Ref. 1 presents a review of analysis methods used to interpret well-test data from enhanced recovery projects along with several design and interpretation relationships developed from a analysis of well-test response for a well located in a two-region composite reservoir. P. 589^

Journal Articles

Journal:
Journal of Ship Research

*J Ship Res*35 (04): 339–351.

Paper Number: SNAME-JSR-1991-35-4-339

Published: 01 December 1991

...) where f= -~ fZhds, 5= ~Zhds (25) JS fsfn~hds, ~=

**fsn**~hds (26) The couples (N,U) and (VAb) are related to the cross sec- tion, and (W,0) to the girder contour. The application of the couple (VAb) is suitable for the assembling of two beams with different cross-sectional width, since the influence...
Abstract

The torsional problem of a pontoon, consisting of channel middle part and rectangular tube peaks, isconsidered within the higher-order beam theory. The cross section and the contour compatibility conditions for assembling of the pontoon parts are investigated. The acceptability of the introduced assumptions is checked by three-dimensional finite-element model analysis. Some deficiencies of the classical beam theory regarding the girder stiffness are noticed. The finite-element formulation to be used for the torsional analysis of the ship's hull with large hatch openings is given.

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*13 (10): 1037–1049.

Paper Number: SPE-18-PA

Published: 01 October 1961

... applicatbns when viscosity and diameter are given. F5 and Fo again de- pend in fact on the liquid's viscosity number only (see Fig. 6); li~ewise, Fo in the expression for F reading F', =

**FsN**. + F.. (4a) The factor F8 seems to be a constant, but its value has not yet fully been established. Again, for flow...
Abstract

The paper deals with pressure gradients occurring in flowing and gas-lift wells, a knowledge of which can be applied to the determination of optimum flow-string dimensions and to the design of gas-lift installations. The study is based on a pressure-balance equation for the pressure gradient. It appears that a pressure-gradient correlation of general validity must essentially consist of two parts-one part being a correlation for liquid hold-up and the other part being one for wall friction. Dimensional analysis indicates that both liquid hold-up and wall friction are related to nine dimensionless groups. It is shown that in the field of interest only four groups are really important. On the basis of these four groups a restricted experimental program could be selected that nevertheless covered practically all conditions encountered in oil wells. This experimental program has been carried out in a laboratory installation. Three essentially different flow regimes were found. The pressure gradients in these regions are presented in the form of a set of correlations. Comparison of these correlations with a few available oilfield data showed excellent agreement. Introduction Prediction of the pressure drop in the flow string of a well is a widely known problem in oilfield practice. Accurate data on the pressure gradient of a simultaneous flow of gas and liquid in a vertical pipe are especially useful for the determination of optimum flowstring dimensions. It is well known that with moderate gas and liquid flows such a vertical string acts as a "negative restriction". The pressure drop decreases when the throughput through a given pipe increases, and when at a given throughput the cross-sectional area is decreased. The reason is that, with increasing velocities, the flow becomes more agitated so that the gas slips relatively more slowly through the liquid. With the resulting increase in gas content in the string, the static head decreases. When the area becomes very small, however, the high velocities entail great wall friction, which causes an increase in pressure drop. For a given flow, therefore, minimal pressure drop is obtained by using a certain cross section. This means that, in principle, each well can be provided with an optimum flow string for minimum pressure drop and, hence, maximum possible production rate. The procedure for the selection of the optimum string has been discussed by Gilbert. A necessary tool in the procedure, however, is accurate knowledge of the pressure gradient to be expected for various values of the governing variables. Another application of pressure-gradient data lies in the field of gas-lift practice: they provide a means of determining the optimum gas-injection rate, optimum injection pressure and optimum injection depth. Much work has already been done in the study of the pressure gradient of vertical gas-liquid flow. Poettmann and Carpenter presented a pressure-gradient correlation based on measurements in wells. This correlation has been found to provide accurate predictions in high-pressure wells and in high-production wells for flow through both tubing and annuli. However, when their method is checked on low pressure-low production wells or on wells with viscous crudes, serious discrepancies are found. As we shall see in the next section, this is due to the fact that their correlation factor, representing all irreversible energy losses, is given as a function of only one correlation group. Some important variables, such as gas-liquid ratio and liquid viscosity, are not incorporated in this group so that their specific effects are not accounted for. To study also the mechanism of vertical gas-liquid flow outside the ranges covered by the Poettmann-Carpenter publication and extensions, a laboratory investigation has been carried out. This study is founded on a pressure-gradient equation that is based on a pressure balance. To reduce the number of test runs required, a dimensional analysis has been carried out, followed by a selection of relevant dimensionless groups. These groups guided a subsequent experimental study, and with their aid the experimental program could be minimized while still covering the majority of the situations encountered in oilfield practice. In this paper the choice of a formula for the pressure gradient is discussed first. This is followed by a brief description of the experimental setup. Subsequently, the dimensional analysis is discussed and the relevant dimensionless groups are selected, resulting in the experimental program required.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2002 SEG Annual Meeting, October 6–11, 2002

Paper Number: SEG-2002-1837

...), bulk modulus increment is then equal to f s n ns K K K KK K ? )(1 1( 2 (10) Furthermore, since usually Ks >> Kf , for reservoir rocks 0.1)

**fsn**KKK )(10 (11) Therefore, fKGK (12) where G is dry frame properties called the saturation Gain function and defined as ? ?? 21( )( n f K G K K (13) Equation 12...
Abstract

Summary For isotropic, homogeneous porous materials, Gassmann’s (1951) equations are physically constrained by the Voigt and Reuss bounds and critical porosity. . These bounds provide stricter constraints on input parameters and output results of fluid saturation effects on bulk modulus. We recast the Gassmann''s relations in terms of a porositydependent normalized modulus Kn, and pore fluid sensitivity in terms of a rock gain function G. These simplified Gassmann’s relations suggest that correct input of grain bulk modulus and fluid modulus is key for accurate estimation of fluid saturation effects. We have developed new empirical relation (Han & Batzle 2000) to calculate fluid properties. Measured data on sandstone suggest that the gain function for reservoir sandstones (porosity of 20- 30%) is around 2 and increases with increasing clay content. We also empirically estimate grain bulk modulus for clean and shaly sandstone based on measured velocities.

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