Análise paramétrica da simulação composicional do processo de Drenagem Gravitacional Assistida por Gás (GAGD)

In Brazil and around the world, oil companies are looking for, and expected development of new technologies and processes that can increase the oil recovery factor in mature reservoirs, in a simple and inexpensive way. So, the latest research has developed a new process called Gas Assisted Gravity Drainage (GAGD) which was classified as a gas injection IOR. The process, which is undergoing pilot testing in the field, is being extensively studied through physical scale models and core-floods laboratory, due to high oil recoveries in relation to other gas injection IOR. This process consists of injecting gas at the top of a reservoir through horizontal or vertical injector wells and displacing the oil, taking advantage of natural gravity segregation of fluids, to a horizontal producer well placed at the bottom of the reservoir. To study this process it was modeled a homogeneous reservoir and a model of multi-component fluid with characteristics similar to light oil Brazilian fields through a compositional simulator, to optimize the operational parameters. The model of the process was simulated in GEM (CMG, 2009.10). The operational parameters studied were the gas injection rate, the type of gas injection, the location of the injector and production well. We also studied the presence of water drive in the process. The results showed that the maximum vertical spacing between the two wells, caused the maximum recovery of oil in GAGD. Also, it was found that the largest flow injection, it obtained the largest recovery factors. This parameter controls the speed of the front of the gas injected and determined if the gravitational force dominates or not the process in the recovery of oil. Natural gas had better performance than CO2 and that the presence of aquifer in the reservoir was less influential in the process. In economic analysis found that by injecting natural gas is obtained more economically beneficial than CO2

Estudo de adsorvente obtido de terras diatomáceas para remoção de metais pesados em águas produzidas: processamento, caracterização e dinâmica em leito fixo

The acceleration of industrial growth in recent decades on all continents aroused the interest of the companies to counter the impacts produced on the environment, spurred primarily by major disasters in the petroleum industry. In this context, the water produced is responsible for the largest volume of effluent from the production and extraction of oil and natural gas. This effluent has in its composition some critical components such as inorganic salts, heavy metals (Fe, Cu, Zn, Pb, Cd, ), presence of oil and chemicals added in the various production processes. In response to impact, have been triggered by research alternative adsorbent materials for water treatment and water produced, in order to removing oils and acids and heavy metals. Many surveys of diatomaceous earth (diatomite) in Brazil involve studies on the physico-chemical, mineral deposits, extraction, processing and applications. The official estimated Jazi are around 2.5 million tonnes, the main located in the states of Bahia (44%) and Rio Grande do Norte (37,4%). Moreover, these two states appear as large offshore producers, earning a prominent role in research of adsorbents such as diatomite for treatment of water produced. Its main applications are as an agent of filtration, adsorption of oils and greases, industrial load and thermal insulator. The objective of this work was the processing and characterization of diatomite diatomaceous earth obtained from the municipality of Macaíba-RN (known locally as tabatinga) as a low cost regenerative adsorbent for removal of heavy metals in the application of water produced treatment. In this work we adopted a methodology for batch processing, practiced by small businesses located in producing regions of Brazil. The characterization was made by X-ray diffraction (XRD), scanning electron microscopy (SEM) and specific surface area (BET). Research conducted showed that the improvement process used was effective for small volume production of diatomite concentrated. The diatomite obtained was treated by calcination at temperature of 900 oC for 2 hours, with and without fluxing Na2CO3 (4%), according to optimal results in the literature. Column adsorption experiments were conducted to percolation of the in nature, calcined and calcined fluxing diatomites. Effluent was used as a saline solution containing ions of Cu, Zn, Na, Ca and Mg simulating the composition of produced waters in the state of Rio Grande do Norte, Brazil. The breakthrough curves for simultaneous removal of copper ions and zinc as a result, 84.3% for calcined diatomite and diatomite with 97.3 % for fluxing. The calcined fluxing diatomite was more efficient permeability through the bed and removal of copper and zinc ions. The fresh diatomite had trouble with the permeability through the bed under the conditions tested, compared with the other obtained diatomite. The results are presented as promising for application in the petroleum industry

Caminhos e descaminhos dos municípios produtores de petróleo: o papel dos royalties no desempenho das finanças públicas municipais no estado do Rio Grande do Norte

It analyzes the magnitude, the nature and the direction of public revenues and the public expenses in oil and natural gas producing municipalities in the state of Rio Grande do Norte in the post-constituent period, and, more precisely, from the approval of Law 9.478/97, called Oil Law . It argues the fiscal federalism normative theory, the typology and the role of the intergovernamental transferences in the performance of the public finances of the local governments. Shows that the economy of Rio Grande do Norte went through deep social-economic changes in the last few decades, among which includes the discovery of the oil and the natural gas and its importance for the growth of the industrial and services sectors. It points out that the increase of the production and the international price of the oil contributed for the growth in revenues of royalties and the special participation in the beneficiary cities, what did not mean an automatic increase in the resources destined to the investment and in the quality on the provision of the goods and services come back toward the local development. On the contrary, the main conclusion of the work is that the trajectory of the oil producing municipalities is marked by paths and embezzlements in the performance of the public finances and in the provision of public goods and services. Paths, that lead to the improvement of the performance of the public finances and the quality of the public goods and services. Embezzlements, that lead to the inefficiency in the provision of goods and services and the capture of the public resources. That is, the fiscal decentralization is a necessary condition, however not enough to improve the amount and the quality of the public goods and services given by these municipalities. For that it is necessary to advance in the fiscal federalism normative theories, in search of optimum model of federalism in local governments where still predominated by patrimonialism, clientelism, fiscal illusion and the capture of the public resources in benefit of the private interests

Educação tecnológica e pré-sal: necessidades e urgências

The purpose of this dissertation is whether the demand for manpower trained in technical school for the sector of Oil and Gas (O&G) is in balance with the offer of that training in the Brazilian education system. The methodology used to obtain such information was based on School Census 2000 and 2008 where data were worked out in order to clarify the numbers of enrollments in secondary technical level demanded by the sector of O&G. The demand for manpower with that qualification as a data source was the 2010-2014 Business Plan Program for Mobilization of the National Oil and Natural Gas (PROMINP). This Program identified the future demand for manpower for the Sector of the O&G until 2014 where the occupational categories are mapped prerequisite training and experience. In order to better understand the object of this study was dome a review of the literature with regard to technical education in Brazil but also the importance of the education to economic growth and the peculiarities of the oil economy in different countries possessors of those mines, or that is, developed and underdeveloped countries. Analysis showed that enrollment in technical education in Brazil had a significant increase between the dates 2000 and 2008. It also don´t bring balance with the characteristic of the dynamics of the productive sectors of the economy mainly due to heating of the economy before the global growth especially in the Construction Industry as well as in the Oil and Natural Gas Engineering and a Naval account of the discovery of oil in the Pre-Salt. Another important aspect is that one of the major problems of qualification of manpower in Brazil is due to a bad quality of the student´s school and high school which makes difficult a good performance in office work and also this ability to learn new functions. The rapprochement between the supply of the education system and the demand for manpower with training mid-level technical support for the sector O&G showed that most technical courses demanded or had no enrollment in 2008, had few enrollment in 15 states with demand expect to occur and those enrollment were unevenly distributed among states. The analysis therefore signalize the needed of a public policy that enables the adequacy of the education system (Secondary Technical Education) to Sector of O&G in terms of enrollment and its distribution between the oil producing states and in relation to technical expertise offered

Educação tecnológica e pré-sal: necessidades e urgências

O objetivo desta dissertação de mestrado é verificar se a demanda de mão-de-obra com formação no ensino médio técnico para o setor de Petróleo e Gás (P&G) está em consonância com a oferta daquela formação no sistema educacional brasileiro. A metodologia aplicada para obter tal informação foi baseada no Censo Escolar 2000 e 2008, em que os dados foram trabalhados de maneira a explicitar o número de matrículas nos cursos de nível médio técnico, demandados pelo setor de P&G. A demanda de mão-de-obra com aquela qualificação teve como fonte de dados o Plano de Negócios 2010-2014 do Programa de Mobilização da Indústria Nacional de Petróleo e Gás Natural (PROMINP). Este Programa identificou a demanda futura de mão-de-obra para o setor de P&G até 2014, onde as categorias ocupacionais mapeadas possuem pré-requisitos de formação e experiência. Com o intuito de entender melhor o objeto deste estudo foi feita uma revisão de literatura no que diz respeito ao ensino técnico no Brasil, como também a importância da educação para o crescimento econômico e as peculiaridades da economia do petróleo nos diferentes países possuidores daquelas jazidas, ou seja, países subdesenvolvidos e desenvolvidos. As análises demonstraram que as matrículas no ensino técnico no Brasil apresentaram um significativo aumento entre as datas de 2000 a 2008. Traz também como característica a desarmonia com a dinâmica dos setores produtivos da economia, devido principalmente ao aquecimento da economia antes da crise mundial de 2008, e a retomada recente do crescimento notadamente no Setor de Construção Civil, bem como no setor de Petróleo e Gás Natural e Engenharia Naval por conta da descoberta de petróleo na camada Pré-sal. Outro aspecto relevante é que um dos grandes problemas da qualificação de mão-de-obra no Brasil se deve a má qualidade do ensino fundamental e médio, que dificulta para o futuro profissional um bom desempenho nas suas funções laborais e na capacidade de aprender novas funções. A aproximação entre a oferta no sistema educacional e a demanda de mão-de-obra com a formação de nível médio técnico para o setor de P&G, demonstraram que a maioria dos cursos técnicos demandados não apresentava matrículas em 2008, ou possuíam poucas matrículas nos 15 estados com demanda prevista, e aquelas matrículas estavam mal distribuídas entre os estados. A análise aponta para a necessidade de uma política pública que possibilite a adequação do sistema educacional (Ensino Médio Técnico) ao setor de P&G, tanto no que se refere ao número de matrículas e a sua distribuição entre os estados produtores de petróleo quanto no que se refere à especialidade técnica oferecida

Modelagem de decisão na seleção de equipamento: um estudo usando o processo analítico hierárquico na contratação de sondas de perfuração de poços de petróleo

The main goal of this dissertation is to develop a Multi Criteria Decision Aid Model to be used in Oils and Gas perforation rigs contracts choices. The developed model should permit the utilization of multiples criterions, covering problems that exist with models that mainly use the price of the contracts as its decision criterion. The AHP has been chosen because its large utilization, not only academic, but in many other areas, its simplicity of use and flexibility, and also fill all the requirements necessary to complete the task. The development of the model was conducted by interviews and surveys with one specialist in this specific area, who also acts as the main actor on the decision process. The final model consists in six criterions: Costs, mobility, automation, technical support, how fast the service could be concluded and availability to start the operations. Three rigs were chosen as possible solutions for the problem. The results reached by the utilizations of the model suggests that the utilization of AHP as a decision support system in this kind of situation is possible, allowing a simplifications of the problem, and also it s a useful tool to improve every one involved on the process s knowledge about the problem subject, and its possible solutions

Um Estudo de Politicas e Práticas do uso do GNV no transporte público urbano do Brasil

The use of Natural Gas Vehicle has had a fast increase lately. However, in order to have a continuous success this Program needs to develop converting devices of Otto-cycle engines, gasoline or alcohol, to the use of NGV (Natural Gas Vehicle) that presents low cost, maintaining the same original development of the vehicle and low level of emissions, considering the PROCONVE rules. Due to the need to diversify the matrix in order to avoid energetic dependence and due to strict pollution control, it has increased in the Brazilian market the number of vehicles converted to the use of NGV. The recent regulation of the PROCONVE, determining that the converted engines with kits should be submitted to emission testing, comes to reinforce the necessity of the proposed development. Therefore, if we can obtain kits with the characteristics already described, we can reach a major trust in the market and obtain an increase acceptance of the vehicle conversion for NGV. The use of natural gas as vehicle fuel presents several advantages in relation to liquid fuels. It is a vehicle fuel with fewer indexes of emissions when compared to diesel; their combustion gases are less harmful, with a major level of safety than liquid fuels and the market price is quite competitive. The preoccupation that emerges, and the motivation of this project, is to know which are the main justifications for such technology, well accepted in other countries, with a low index or emission, with a high level of safety, where its maintenance becomes low, reminding that for this it is necessary that this technology has to be used properly, and once available in the market will not motivate interest in the urban transportation companies in Brazil, in research centers in general. Therefore this project exists to show the society in a general way the current vision of the main governmental factors, of the national research centers and of the private companies concerning the use of natural gas vehicles in urban transport vehicles, in order to give a major reliability to the population as well as to motivate national market competitiveness with a low cost and reliable product and to enrich the national technology

Formulação e caracterização de massas de grês porcelanato preparadas a partir de matérias-primas naturais do Rio Grande do norte e com adição de chamote de telhas

Traditional ceramics have an important role in the economy of Rio Grande do Norte. The local industries manufacture over 50 million shingles a month, corresponding to 60% of their overall production. As a result of processing flaws, roughly 20% of the production must be discarded, since little or no use has been envisaged for such fired components. Therefore, the use of this kind of residue, especially in the composition of other ceramic materials, comes as an interesting option from the economical and environmental point of view. In this scenario, the objective of the present study was to assess the effect of the addition of fired shingle waste in the composition of porcelainized stoneware tiles. To that end, two porcelainized stoneware tiles compositions were initially prepared. Subsequently, contents from 10 to 30% of roofing tiles chamote were added to each one of them. All raw materials and grog were characterized by FRX, XRD, and thermal analysis. The ceramics were fired using natural gas for 30 min at different temperatures, i.e. 1150, 1200 and 1250ºC, and fully characterized. The addition of roofing tiles chamote resulted in composition with superior properties compared to additive-free compositions. Porcelainized stoneware tiles products that fulfill required standards for practical applications were achieved

Desempenho de um veículo flex em bancada dinamométrica de chassi

Flex-fuel vehicles are equipped with Otto Cycle internal combustion engines and have the capability of functioning with more than one type of fuel, mixed at the same tank and burned in the combustion chamber simultaneously. This sort of motorization is a world pattern due to the scarcity of petroleum, the trade of several types of fuels, technology advances and the restriction imposed to gas emissions to the atmosphere. In Brazil, the Flexfuel vehicles are a reality, specially the ones using fuel with 20 to 25% anhydrous alcohol mixed with gasoline and those that use natural gas or original liquid fuel (gasoline or hydrated ethanol). The Brazilian model Fiat Siena, the object of this present scientific investigation, is equipped with a unique electronic central capable of managing the liquid or gaseous fuels. The purpose of this research was to perform a comparative analysis in terms of performance (in terms of both potency and consumption) of a tetra-fuel vehicle - using a chassis dynamometer, operating with different fuels: common gasoline, premium gasoline, Podium gasoline, ethanol or natural gas. It became necessary to develop a bench of tests and trials procedures, as well as to know the functioning of the electronic management of the vehicle under analysis. The experiments were performed at the automotive laboratory in CTGAS-ER (Center of Gas Technologies and Renewable energies) at the light of Brazilian standard ABNT, NBR 7024: Light on-road vehicles - measurement of fuel consumption. The essay results on specific fuel consumption using common gasoline, premium gasoline and Podium gasoline have shown similar results, both for urban and road driving cycles

Remoção conjugada de metais e óleo de água produzida

Petroleum can be associated or not with natural gas, but in both cases water is always present in its formation. The presence of water causes several problems, such as the difficulty of removing the petroleum from the reservoir rock and the formation of waterin-oil and oil-in-water emulsions. The produced water causes environmental problems, which should be solved to reduce the effect of petroleum industry in the environment. The main objective of this work is to remove simultaneously from the produced water the dispersed petroleum and dissolved metals. The process is made possible through the use of anionic surfactants that with its hydrophilic heads interacts with ionized metals and with its lipophilic tails interacts with the oil. The studied metals were: calcium, magnesium, barium, and cadmium. The surfactants used in this research were derived from: soy oil, sunflower oil, coconut oil, and a soap obtained from a mixture of 5wt.% coconut oil and 95wt.% animal fat. It was used a sample of produced water from Terminal de São Sebastião, São Paulo. As the concentration of the studied metals in produced water presented values close to 300 mg/L, it was decided to use this concentration as reference for the development of this research. Molecular absorption and atomic absorption spectroscopy were used to determine petroleum and metals concentrations in the water sample, respectively. A constant pressure filtration system was used to promote the separation of solid and liquid phases. To represent the behavior of the studied systems it was developed an equilibrium model and a mathematical one. The obtained results showed that all used surfactants presented similar behavior with relation to metals extraction, being selected the surfactant derived from soy oil for this purpose. The values of the partition coefficients between the solid and liquid phases " D " for the studied metals varied from 0.2 to 1.1, while the coefficients for equilibrium model " K " varied from 0.0002 and 0.0009. The removal percentile for oil with all metals associated was near 100%, showing the efficiency of the process

Desenvolvimento de sistemas de pastas leves para aplicação em cimentação de poços petrolíferos com baixo gradiente de fratura

All around the world, naturally occurring hydrocarbon deposits, consisting of oil and gas contained within rocks called reservoir rocks , generally sandstone or carbonate exists. These deposits are in varying conditions of pressure and depth from a few hundred to several thousand meters. In general, shallow reservoirs have greater tendency to fracture, since they have low fracture gradient, ie fractures are formed even with relatively low hydrostatic columns of fluid. These low fracture gradient areas are particularly common in onshore areas, like the Rio Grande do Norte basin. During a well drilling, one of the most favorable phases for the occurrence of fractures is during cementing, since the cement slurry used can have greater densities than the maximum allowed by the rock structure. Furthermore, in areas which are already naturally fractured, the use of regular cement slurries causes fluid loss into the formation, which may give rise to failures cementations and formation damages. Commercially, there are alternatives to the development of lightweight cement slurries, but these fail either because of their enormous cost, or because the cement properties were not good enough for most general applications, being restricted to each transaction for which the cement paste was made, or both reasons. In this work a statistical design was made to determine the influence of three variables, defined as the calcium chloride concentration, vermiculite concentration and nanosilica concentration in the various properties of the cement. The use of vermiculite, a low density ore present in large amounts in northeastern Brazil, as extensor for cementing slurries, enabled the production of stable cements, with high water/cement ratio, excellent rheological properties and low densities, which were set at 12.5 lb / gal, despite the fact that lower densities could be achieved. It is also seen that the calcium chloride is very useful as gelling and thickening agent, and their use in combination with nanosilica has a great effect on gel strength of the cement. Hydrothermal Stability studies showed that the pastes were stable in these conditions, and mechanical resistance tests showed values of the order of up to 10 MPa

Síntese de Fischer-Tropsch sobre perovskitas LayCu0,4Fe0,6O3

The current natural gas production of 52 Mm3d-1 and the large projects for its expansion has been setting new boundaries for the Brazilian industry of oil and gas. So far, one of the biggest challenges regards to the logistics for gas transportation from offshore fields. Therefore, the transformation of natural gas into gasoline, diesel and/or olefins via Fischer-Tropsch synthesis would be an alternative to this matter. In this work, the production of hydrocarbons by Fischer-Tropsch synthesis in a slurry reactor was investigated and a perovskite-type catalyst (LayCu0,4Fe0,6O3 ± d) was used with y varying from 0 to 1 on a molar basis. In addition, Nb2O5 support was also applied in order to observe the selectivity of the produced hydrocarbons by the Fischer-Tropsch process. It is shown that the hydrogen conversion was influenced by the support as well as the different phases of the samples. The kinetic results for the CO2 production suffered great influence with the introduction of the Nb2O5 support throughout the series of samples studied. The catalysts allowed obtaining welldefined cuts of hydrocarbons in the range of C1-C6 and C17-C28, and these results were clearly influenced by the support and the lanthanum content. The higher olefin/paraffin ratio obtained was 1.8 when using a non-supported perovskite with y equal to 0.8. This would indicate the suitability of using this material for the production of olefins

Estudo da circulação hidrodinâmica e da dispersão de óleo na zona costeira entre Macau e Galinhos RN

This paper presents a study on coastal hydrodynamics and the spread of an oil spill in waters off Macau and Galinhos, on the east coast of the state of Rio Grande do Norte in Northeast Brazil. This area has a very marked coastal dynamic owing to the complexity of its geomorphological features, developed in a regime of semidiurnal mesotides involving reefs, spits, estuaries, mangroves, lakes and dunes. The region also plays an important role in the socioeconomic development of the state, given that the production of oil, natural gas, salt and shrimp is concentrated there. The series of oil platforms is interconnected by a pipeline system that carries oil to the local terminal. This pipeline could leak at any moment, causing immense ecological damage. To gauge the risks of an oil leak and resulting contamination of the coastal region, two hydrodynamic scenarios were simulated. The results obtained were used to implement a contaminant transport model with the creation of various oil leak scenarios modeled at different volumes (from small to large) and intensities (sporadic and continuous), at points considered critical for the model (on two platforms and at two pipeline intersections), under different wind (summer and winter) and tidal (high and low at new, full and quarter moon phases) conditions. The use of hydrodynamic circulation computer models as a tool for representing a real project design has been increasingly frequent in recent years, given that they enable the realistic simulation of the hydrodynamic circulation pattern in bodies of water and an analysis of the impacts caused by contaminants released into the water. This study used the computer models contained in SisBAHIA®, in continuous development in the area of Coastal Engineering and Oceanography at COPPE/UFRJ

Avaliação da estabilidade térmica e oxidativa dos biodieseis de algodão, girassol, dendê e sebo bovino

The search for new sources of environmentally friendly energy is growing every day. Among these alternative energies, biodiesel is a biofuel that has had prominence in world production. In Brazil, law 11.097, determine that all diesel sold in the country must be made by mixing diesel/biodiesel. The latter called BX, , where X represents the percent volume of biodiesel in the diesel oil, as specified by the ANP. In order to guarantee the quality of biodiesel and its mixtures, the main properties which should be controlled are the thermal and oxidative stability. These properties depend mainly of the chemical composition on the raw materials used to prepare the biodiesel. This dissertation aims to study the overall thermal and oxidative stability of biodiesel derived from cotton seed oil, sunflower oil, palm oil and beef tallow, as well as analyze the properties of the blends made from mineral oil and biodiesel in proportion B10. The main physical-chemical properties of oils and animal fat, their respective B100 and blends were determined. The samples were characterized by infrared and gas chromatography (GC). The study of thermal and oxidative stability were performed by thermogravimetry (TG), pressure differential scanning calorimeter (PDSC) and Rancimat. The obtained biodiesel samples are within the specifications established by ANP Resolution number 7/2008. In addition, all the blends and mineral diesel analyzed presented in conformed withthe ANP Regularion specifications number 15/2006. The obtained results from TG curves data indicated that the cotton biodiesel is the more stable combustible. In the kinetic study, we obtained the following order of apparent activation energy for the samples: biodiesel from palm oil > sunflower biodiesel > tallow biodiesel > cotton biodiesel. In terms of the oxidative stability, the two methods studied showed that biodiesel from palm oil is more stable then the tallow. Within the B100 samples studied only the latter were tound to be within the standard required by ANP resolution N° 7. Testing was carried out according to the EN14112. This higher stability its chemical composition

Matrizes poliméricas puras e modificadas para adsorção do gás sulfeto de hidrogênio

The underground natural gas found associated or not with oil is characterized by a mixture of hydrocarbons and residual components such as carbon dioxide (CO2), nitrogen gas (N2) and hydrogen sulfide (H2S), called contaminants. The H2S especially promotes itself as a contaminant of natural gas to be associated with corrosion of pipelines, to human toxicity and final applications of Natural Gas (NG). The sulfur present in the GN must be fully or partially removed in order to meet the market specifications, security, transport or further processing. There are distinct and varied methods of desulfurization of natural gas processing units used in Natural Gas (UPGN). In order to solve these problems have for example the caustic washing, absorption, the use of membranes and adsorption processes is costly and great expenditure of energy. Arises on such findings, the need for research to active processes of economic feasibility and efficiency. This work promoted the study of the adsorption of sulfide gas in polymer matrices hydrogen pure and modified. The substrates of Poly(vinyl chloride) (PVC), poly(methyl methacrylate) (PMMA) and sodium alginate (NaALG) were coated with vanadyl phosphate compounds (VOPO4.2H2O), vanadium pentoxide (V2O5), rhodamine B (C28H31N2O3Cl) and ions Co2+ and Cu2+, aiming to the adsorption of hydrogen sulfide gas (H2S). The adsorption tests were through a continuous flow of H2S in a column system (fixed bed reactor) adsorption on a laboratory scale. The techniques used to characterize the adsorbents were Infrared spectroscopy (FTIR), thermogravimetry analysis (TGA), X-ray fluorescence (XRF), the X-ray diffraction (XRD) electron microscopy (SEM). Such work indicates, the results obtained, the adsorbents modified PMMA, PVC and NaALG have a significant adsorptive capacity. The matrix that stood out and had the best adsorption capacity, was to ALG modified Co2+ with a score of 12.79 mg H2S / g matrix