Abstract Underbalanced drilling (UBD) is one of the most widely used technologies preferred in depleted and/or low pressured formations. In order to achieve underbalanced conditions, drilling fluids are usually gasified. Major drilling fluids preferred during UBD are pure gas, gas-liquid mixtures, foams, etc. This study is focused on gas-liquid mixtures. As the gas is introduced, the behavior of the drilling fluid becomes hard to explain due to many reasons. First of all, gas is compressible and physical properties of gas are very sensitive to changes in pressure and temperature. Second, a multiphase flow phenomenon arises. When there is multiphase flow, flow patterns should be considered. It is known that, there is a difficulty to predict hydraulic behavior of gas-liquid mixtures due to this flow pattern dependence. During a drilling operation, one of the parameters that should be well considered is hole cleaning. Hole cleaning is a challenging task even for a single phase drilling fluid. Moreover, there is still a lack of information how the cuttings are transported when gas-liquid mixtures are used as drilling fluids. Flow rate optimization during UBD operations for liquid and gas phases are usually conducted based on formation pressures only. However, only considering this criteria alone as the optimization objective is misleading and may cause serious problems during the drilling operation. In this study, gas and liquid flow rates during UBD operations are conducted not only based on formation pressures, but also based on effective hole cleaning. It is assumed that liquid phase is the major contributor for cuttings transport, and gas phase is only influencing the bottom hole pressure. A mechanistic model is introduced for estimating the hydraulic behavior of gas-liquid mixture drilling fluids under different flow patterns. Based on the bottom hole pressure and effective hole cleaning point of view, an algorithm is proposed for estimation the optimum required flow rates for liquid and gas phases based on the introduced mechanistic model. Also, the model predicts the required backpressure that has to be applied. Introduction Underbalanced drilling operations are increasingly applied, especially when new wells are required at depleted reservoirs in order to conduct enhanced oil recovery techniques or secondary recovery applications. Usually, gas-liquid mixture fluids are preferred for applying underbalanced techniques. However, one of the main problems for applying underbalanced drilling techniques is te selection of proper liquid and gas volumetric flow rates. Generally, these rates are selected based on the formation pressure, i.e., at static conditions, the hydrostatic pressure of the mixture is selected to handle the formation pressure. But, in such a case, at dynamic conditions, bottomhole pressure may exceed formation pressure, and the advantages of underbalanced conditions are missed. If the dynamic conditions are considered for selecting the liquid-gas rates, this time at static conditions, bottomhole pressure may be too low when compared with formation pressure, and formation fluids may intrude into the wellbore. Therefore, it is a better option to keep the bottomhole pressure constant and equal to formation pressure for all times, i.e., static and dynamic conditions.

Abstract The annular frictional performance of non-Newtonian fluids is one of the major considerations during developing hydraulic programs for drilling operations. Proper estimation of the frictional pressure losses become more critical while determining hydraulic horsepower requirements and selection of proper mud pump systems, and foresee any serious problems that may occur regarding with hydraulics during drilling operations. Since the rheological behavior of the non- Newtonian fluids has already been challenging, it becomes even more complicated during pipe rotation, especially in eccentric wellbores. In many cases, significant differences are observed when theoretical calculations and measurements for pressure losses are compared. This study aims to develop correction factors for determining the frictional pressure losses accurately in eccentric annulus for non-Newtonian fluids including the effect of pipe rotation. Extensive experimental work has been conducted on METU-PETE Flow Loop for numerous non- Newtonian drilling fluids including KCl-polymer muds and PAC systems for different flow rates and pipe rotation speeds, and frictional pressure losses are recorded during each test. Rheological characteristics of the drilling fluids are determined using a rotational viscometer. Observations showed that, pipe rotation has a significant influence on frictional pressure loss, especially at lower flow rates. Up to a point, as the pipe rotation increases, the frictional pressure losses also increase. As the flow rates are increased, the effect of pipe rotation on frictional pressure losses diminishes. Also, after a certain pipe rotation speed, no additional contribution of pipe rotation on frictional pressure loss is observed. When the developed friction factors are used, there is a good agreement between the calculated and observed frictional pressure losses for any pipe rotation speed. Introduction Proper determination of the frictional pressure loss for a non- Newtonian fluid is a very challenging task during pipe rotation, especially in eccentric annuli. On the other hand, poor estimation of the frictional pressure loss may cause serious problems in selection of the mud pumps and determination of the hydraulic horsepower requirements. Therefore, it becomes more significant and essential to identify the frictional pressure loss of non-Newtonian fluids in an annulus with pipe rotation. A number of studies have been conducted to investigate the influence of pipe rotation on frictional pressure loss in eccentric and concentric annulus over the years. Delwiche et al. 1 and Marken et al. 2 investigated using real wells pipe rotation effects on pressure loss and found that frictional pressure loss increase if applying rotation to the inner cylinder in the annulus. In addition, Marken et al. 2 emphasize that the flow regime and pressure losses is affected combinations of pipe motion, eccentricities and temperature along the length of the annulus. McCann et al. 3 pointed out that pipe rotation speed and eccentricity strongly affect the pressure loss in narrow annuli. They observed that for power-law fluids, when the flow regime is turbulent, the pressure loss increases with increasing pipe rotation, and when the flow regime is laminar, pressure drop decreases with increasing pipe rotation. Hansen and Sterri 4 experimentally investigated the effect of rotation on the frictional pressure loss in an annulus.

Abstract The Viking reservoirs of west-central Saskatchewan contain a large number of light oil resources, of which only approximately 10% is considered recoverable. Oil production is hindered by (a) permeability damage due to clay swelling and migration during water injection and (b) organic solid (asphaltenes/wax) precipitation due to pressure and temperature variations. The Saskatchewan Research Council conducted laboratory experiments to evaluate and address these problems. Reservoir cores were tested for permeability damage measurements using both injection and produced brine. Different additives [i.e., potassium chloride (KCl) with/without hydrochloric acid (HCl), commercial clay stabilizers, liquid CO 2 , and isopropyl alcohol] were assessed as permeability remedies. The results showed that injection brine caused greater permeability damage than produced brine. KCl solutions preserved permeability, whereas KCl acidized with HCl appreciably improved it in one core. None of the used commercial additives significantly improved permeability. Injection of liquid CO 2 and isopropyl alcohol caused encouraging permeability improvement in some cores. Wax precipitation tests were carried out on both dead oil and live oil samples. It was found that precipitation occurred in the dead oil even at the reservoir temperature of 22 °C. Filtration tests demonstrated that the live oil was much less sensitive to wax precipitation than the dead oil. Introduction The Viking horizon of the Kindersley area of west-central Saskatchewan contains an estimated 300?10 6 m 3 initial oil in place (IOIP), of which only about 10% is deemed to be recoverable (1) . The Saskatchewan Research Council (SRC) carried out an experimental study aimed at evaluating and solving two major problems that hinder effective oil production in the Viking reservoirs of west-central Saskatchewan: permeability damage due to water sensitivity of the formation and organic solid precipitation due to pressure and temperature change. Most of the Viking oil reservoirs are thin, with net pays from 2.0 to 5.4 m, and produce from depths between 640 and 750 m. The reservoir temperatures are around 23 °C, and the discovery pressures are approximately 6.4 MPa. The oil generally has densities between 840 and 870 m 3 /kg (37- 31 °API) and formation volume factors of about 1.1 m 3 /m 3 . Figure 1 shows a detailed map of well locations in Kindersley area in Saskatchewan. It is seen that most of the wells produce oil at rates below 1 m 3 /d (yellow), whereas a number of wells produce more than 10 m 3 /d (black). The Viking reservoirs are sandstone of Lower Cretaceous age that was deposited in a shallow marine environment (2) . The reservoir rocks have variable lithology, and are from mid- to poorly consolidated and contain movable and swelling clays, such as kaolinite and montmorillonite (3,4) . Due to the presence of these clays, the formation is sensitive to fresh water and this has hampered efforts to improve oil recovery by waterflooding. Organic (waxes and/or asphaltenes) solid precipitation is another major factor hindering oil production. This solid removal is costly because it requires periodic workovers as well as disruption to well flow. Consequently, productivity will be greatly improved if these two problems are alleviated or solved.

Abstract The knowledge of Inflow Performance Relationship is an essential piece of information for well performance evaluation and optimization. For single phase oil flow, production rate is proportional to pressure drawdown and therefore the IPR curve is a straight line. Several empirical relations have been proposed in the literature to predict the performance of oil wells producing with two phase flow conditions. However, these relationships are empirical and limited in application. This paper presents a general approach for determination of IPR curves of oil wells below the bubble point pressure. This approach uses the results of well test analysis along with relative permeability and PVT data in the proper fluid flow equations for generation of IPR curves. The proposed method is also capable of predicting future IPR curves. To show that the presented approach is applicable to a wide variety of cases, it is applied to an example oil well in a naturally fractured reservoir. The new method proposed for fractured reservoirs is then compared with some of the empirical methods. It is shown that the new method can predict well deliverability more accurately than other methods. Among different methods evaluated in this work, although underestimating flow rates, Vogel's relation best matched our work. The approach presented in this paper eliminates the need for multipoint tests, and the required data can be obtained from a buildup test. This approach can be applied to both initial well tests (transient flow) and tests done later during production (pseudo steady state flow). The new analytical method proposed for determination of IPR curve is considered a reliable method since it can closely match the flow tests data. Introduction Inflow Performance Relationship (IPR) of a well is the relation between the production rate and flowing bottom hole pressure. For oil wells, it is frequently assumed that fluid inflow rate is proportional to the difference between reservoir pressure and wellbore pressure. This assumption leads to a straight line relationship that can be derived from Darcy's law for steady state flow of an incompressible, single phase fluid and is called the Productivity Index (PI). However, this assumption is valid only above the bubble point pressure. Evinger and Muskat [1] , based on multi-phase flow equations showed that a curved relationship existed between flow rate and pressure, when two phase flow occurs in the reservoir (i.e. saturated oil). In 1968, Vogel [2] presented an empirical inflow performance relationship for solution-gas drive reservoirs, based on computer simulation results and a wide range of rock and fluid properties. His famous dimensionless IPR was developed for flow of saturated oil from a solution-gas drive reservoir into well ignoring skin effects. After Vogel, several empirical relationships have been developed to predict the performance of oil wells in saturated reservoirs [3–12] . However, these IPRs are empirical and have been developed for homogeneous, solution-gas drive reservoirs and may not be applicable to other cases.

Abstract Non-condensable gases (CH 4 , CO 2 , and H 2 S) are present and play an important role in the thermal efficiency of SAGD. However, the role of these gases is not well understood and it is regarded by some people as beneficial, yet detrimental by others. The characterization of the gas flow in SAGD is crucial to predict its effect on the process performance. One mechanism involved in the flow of gas is the viscous drag due to the falling liquids in the SAGD chamber. In this work, the production of gas in SAGD was studied by deriving flow equations that describe the viscous drag in a gas-water-oil system. Two geometries have been studied; these are flow in a capillary tube and flow of a descending film on a plate. The three-phase flow analysis has been extended to a macroscopic level in order to predict the amount of gas produced due to the viscous drag of the falling phases. The assumption that the reservoir behaves as a bundle of capillaries with a pore size distribution was made. Results from this analytical model indicate that some of the gas in the steam chamber flows downwards and therefore could be produced by viscous drag of the falling liquids. Introduction The necessity and interest to fully understand the effect and behavior of non condensable gases (NCG) in SAGD has increased lately due to their important impact on the efficiency of this process, namely, steam consumption and oil production rates. These NCG's are naturally present in the reservoir generally as solution gas and they can also be added intentionally. Thimm [1 ] discussed on the source of these gases. An additional amount of gas (mostly CO 2 and some H 2 S) can also be generated as the reservoir is heated [2, 3) . A number of simulation and laboratory scale studies have been carried out by several researches [2, 4, 5, 6, 7] to describe the role that these gases play in SAGD. However, as of today there is not a consensus or a unified understanding of the role these gases play in the process [8] . There are also some discrepancies between the results obtained in simulation studies and lab scale or field observations. The verdict about the advantages or detrimental impacts that non condensable gases may have on SAGD is not simple as they depend on reservoir and operating conditions [4, 8] . The intentional addition of non condensable gases to SAGD has as well created some controversy in regard to the benefits or disadvantages this may cause in the bitumen recovery [2, 7, 9] . Butler, for instance, seemed to defend the intentional addition of NCG's in SAGD. He claimed that the disastrous effect of these gases on the steam chamber growth and the oil production rate were noticed mostly in numerical simulations but not so much in the field or scaled model experiments.

Abstract Lot of attention has been placed in the evaluation of fracture height growth during hydraulic fracturing. While there are analytical solutions available to estimate vertical fracture growth, a more comprehensive solution requires the use of coupled geomechanics-reservoir simulators that could also fully incorporate the effects of fluid flow into the analysis. This paper introduces results from a coupled geomechanical/reservoir simulator, GMRS?, to estimate the extent of vertical tensile regions developed in the sand interval that could break into adjacent shales during surfactant-polymer injection for a well located onshore Asia. The reservoir was treated as an elastic material and the injection zone was treated as a zone of higher permeability after the weakly consolidated formation reached a tensile stress state. The geomechanical information for GMRS was obtained from triaxial tests, well logs, and minifracs. Reservoir and fluid data were extracted from the in-house reservoir simulator model available for the field (CHEARS). We evaluated half unit of a seven spot pattern by building an unstructured grid, which provide more flexibility in terms of geometry. The results indicated that injection rates higher than 4000 B/D combined with viscosities greater than 10 cp will cause the fractures to break into the shales, reaching the bottom sand. Additionally, injection rates lower than 2000 B/D were shown to be safe even for the highest viscosity tested, viz 30 cp. Viscosities greater than 20 cp will cause the injection fluid to break into adjacent sands if the flow rates are above 2000 B/D. As expected, the higher the viscosity and the injection rate, the higher the tendency of the fractures to grow out of containment. A chart with safe limits for surfactant-polymer injection was provided to the business unit to guide them in the design of new injectors and conditions for safe surfactant-polymer injection. Introduction Modeling fracture growth is the main goal of fracturing modeling. The growth of fractures in layered reservoirs has been mainly attributed to the minimum in-situ stress contrast; while the Young's modulus contrast has considered only secondary in importance. (Warpinski et al, Hongren and Siebrits, Liu et al., 1998). Some parameters that have been found to play important roles in fracture growth are listed as: Shear stress at the interface (Hanson et al) Elastic properties, in-situ stresses and pressure gradients Joints, faults and bedding planes Intefacial slippage In laminated sand and shale sequences, Miskimins and Barree (2003) indicate slippage at the boundaries, rock mechanics property contrast; in particular contrast in Young's Modulus values for the sand and shales, and contribution of differences in poroelasticity for shale and sand as the most significant parameters in laminated reservoirs. Pump rate and rheologic parameters of the injecting fluid have also been found to affect height propagation (Liu, S. et al., 1998) There are no many tools available to model the mechanics of a plethora of individual fractures in a reservoir condition.

Abstract ZM gas reservoir located in Shanxi province of China is a significant development and evaluation block of PetroChina. It belongs to low porosity and low permeability reservoir. Although most of the wells adopt the technology of layered fracturing and commingled production because of low psotfrac output of individual layer, the production is generally low. This paper systematically evaluates the fracturing data, analyzes fracturing operation curves, optimize the fracture parameters and study the technology for improving fracturing effects. In 2006, 63 wells (101 layers) in ZM gas reservoir adopted hydraulic fracturing including individual layer fracturing in 32 wells and layered fracturing in 31 wells. First, utilize the fracturing data in 2006 to comprehensively analyze the relations between formation parameters and different fracturing data including fracturing scale, fracturing effects and fracturing operation parameters, and simulate the fracture geometry in use of FracproPT software. Moreover, all the fracturing operation curves are analyzed and some useful information was acquired which indicates the formation character and also some operation problems, especially the rapid propagation of fracture height. Considering the thickness and permeability of fracturing formation and the differences of interlayer thickness in ZM gas reservoir, we optimize the fracture parameters and recommend the fracturing operation scale. Finally, the fracturing technology is studied for improving fracturing effects in ZM gas reservoir. Introduction ZM gas reservoir is located in Shanxi province of China, and its buried depth is 2200–2800m. Its producing formations include the second section of Shanxi group, eighth section of Shihezi group and Taiyuan group. The main lithology is silicarenite. In second section of Shanxi group, the average porosity is 4.1%, and the average permeability is 0.33?10 −3 µm 2 . In eighth section of Shihezi group, its average porosity is 5.3%, and average permeability is 0.51?10 −3 µm 2 . The average porosity of Taiyuan group is 6.2%, and permeability is 0.89?10 − 3 µm 2 . The gas pressure of Shanxi group is 22.92–25.43MPa, and pressure coefficient is 0.9–1.02. For Shihezi group, the pressure coefficient is 0.85–0.9, and temperature gradient is 2.99_/100m. Most of the wells adopt the technology of layered fracturing and commingled production because of low psotfrac output of individual layer. Statistic analysis of fracturing data Relationship between fracturing scale and formation parameters Fig 1 and fig 2 are the relation curves of proppant concentration and formation parameters through statistic data. Most of the proppant concentration is between 2–8m 3 /m. With the increase of permeability and formation capacity, the proppant concentration decrease a little. When formation capacity is more than 10mDc.m, the proppant concentration is only about 3m 3 /m which is lower. Fig 3 and fig 4 are the relation curves of proppant concentration and formation thickness through statistic data. With the increase of effective thickness, the proppant concentration decreases a little. When formation thickness is 15m around, the concentration is only 3–4m 3 /m which is lower than 5–10m 3 /m of thin layers less than 5m. High proppant concentration for thin layers increases the treatment risk to some extent. At the same time, low concentration for thick formations will decrease stimulation effects.

Abstract In this paper, a new drilling optimization procedure is presented that is designed to improve the drilling efficiency with positive displacement motors (PDMs) and PDC bits. This developed optimization method is based on predicting rate of penetration (ROP) from PDM outputs for any PDC bit design. More specifically, optimization is done for a hole section and optimum values of weight on bit (WOB) and surface RPM are obtained for the section. For given flowrates, estimated values of optimum WOB and surface RPM are used to calculate the corresponding motor differential pressures and the foot by foot ROP values. Also, the method is used to show how improper operational parameters selection can affect total drilling time. A case study was done to consider different PDMs with different lobe configurations and a set of fixed operational parameters. From the new optimization technique, a pre-estimated motor differential pressure versus depth log can be generated for the optimized operational parameters. This information can further be used in hydraulics optimization and proper selection of bit nozzles. The optimization method can not only be applied to determine optimum operational parameters in drilling for one motor, it is also can be used to select the optimum PDM to drill a section most economically. The presented method is verified by generating a confined rock strength log based on drilling data for a previously drilled well in Alberta. This foot by foot strength log is compared to a confined rock strength log generated as a follow up analysis by a commercially available drilling simulator package. Also, PDM differential pressure log is generated and compared to field recorded on bottom differential pressure values. In this paper, a method to optimize the drilling operation with PDMs is presented with a field sample application. It is concluded that consideration of PDM performance/selection drilling planning phase will help to perform a safe and cost effective operation by preventing motor stalls and maintaining highest average ROP for the section. It also proves that by optimizing WOB and surface RPM values for a constant mud flow rate and pre defined bit wear at total depth, a maximum average ROP for the section can be reached for any PDM. The PDM with the lowest $/ft can then be selected based on the analysis. Introduction Drilling simulation has gained a leading position in the well planning and the follow up process. The capability of applying different drilling scenarios in simulators is a powerful tool for drilling engineer to prepare an optimized drilling plan regarding basic criteria such as cost, time and safety. The rising application of Positive Displacement Motors (PDMs) in recent directional and horizontal drilling operations creates a demand for a tool which enables drilling engineer to simulate these operations in a pre-planning mode. Despite of similarities existing between conventional drilling simulation and PDM drilling simulation, there are some differences which can alterthe approach and goals. These dissimilarities are resultant of inseparable characteristics of PDM which exposes limitation on the drilling system hydraulics.

Abstract The purpose of this study is to investigate of experiments to reactive transport module for handling aquifer sequestration of carbon dioxide and modeling of simultaneous geochemical reactions. Two separate cases of laboratory carbon dioxide sequestration experiments, conducted for different rock systems, are modeled using the fully coupled geochemical compositional simulator and the relevant permeability relationships are compared to determine the best fit with the experimental results. This study determined that simulated changes in porosity and permeability could mimic experimental results to some extent. Increased porosities of 7% were found in the dolomite-calcite models and 20% for quartz-carbonate core flooding simulation systems respectively. This is comparable to published experimental results. The formation rock and brine compositions played a significant role for changes taking place in porosity. This study also compared the relevant permeability correlations for their effectiveness in representing the porosity and permeability changes in the carbon dioxide sequestration process. Civan's Power Law correlated experimental changes significantly better than the Kozeny-Carman, and other empirical equations for the permeability. Therefore it is concluded that Civan's Power Law equation of permeability could be an appropriate model for the carbon dioxide sequestration processes. Introduction Over long time periods geological sequestration in some systems also show mineralization effects or mineral sequestration of carbon dioxide, converting the carbon dioxide to a less mobile form. However, a detailed study of these geological systems in many aspects, like petrophysical and geochemical, is needed before disposing of carbon dioxide into these formations. Depleted oil and gas reservoirs and underground aquifers are proposed candidates for carbon dioxide injection. This study is primarily evaluates the effects of carbon dioxide disposal on the geochemical and petrophysical properties of aquifers. For this purpose, two different experimental cases are modeled. The results of the simulation model are compared with published experimental measurements and the variations in porosity and permeability are evaluated with changes in injection rates, temperatures, brine concentration, formation composition etc. In addition the viability of different permeability-porosity models for the carbon dioxide sequestration process is investigated. Large amounts of carbon dioxide can be injected into deep aquifers. Part of the injected carbon dioxide dissolves into brine which induces chemical imbalances into the system. The in situ pH decreases and the carbonic acid formed in this process react with different rock components to reestablish chemical equilibrium. The typical reactions are dissolution and precipitation reactions of rock matrix and rock components. This results in changes of some petrophysical properties of the formation like porosity and permeability which in turn affect the level of the carbon dioxide sequestration. The rest of the carbon dioxide which does not dissolve in brine and is in a supercritical state at the conditions of most aquifers being considered may travel towards the top of the aquifer due to the buoyancy forces. The changes in the petrophysical properties because of the precipitation and dissolution reactions may help or hinder the mobility of the traveling carbon dioxide.

Abstract In China, natural gas consumption is over 670?10 8 m 3 /year with expected growth rate of 10% per year. Most of the gas is transported from well heads to markets over cross-country gas networks, which requires construction of the West to East Gas Network – one of the largest gas network in the world. Presently, the network comprises four large-diameter pipelines and will include most major gas pipelines in China, in the future. It distributes about 300?10 8 m 3 gas per year of which 3% to 5% is burned to power the gas transportation. At the current gas prices, gas transportation costs roughly 350 million dollars per year ? a considerable cost that could be reduced by improvements in network design and operation. The paper reports on a study aimed at optimizing the network to minimize its energy consumption and cost. Large size and complex geometry of the network required breaking it down into simple components, optimizing operation of the components locally, re-combining the optimized components into the network and optimizing the network globally. This three-step approach employed four different optimization methods: penalty function method, pattern search, enumeration and non-sequential dynamic programming to solve the problem. The results show that cost savings due global optimization can be up to 23% and are inversely related to the network throughput. The increase of throughput from 67 million to 90 million m 3 /d would reduce the savings to a mere 1.2%. The result is explained by analyzing the state and the control variables, individual compressors' rate and compression ratio. It is explained why for compressors running in their designed workload, the optimized operation would approach the standard operation scheme. Introduction Natural gas is considered a clean energy resource alternative to coal and oil. It is expected that global consumption of gas will double by 2030 [1] . With fast developing economy of China, domestic consumption of natural gas is presently over 60 billion m 3 /year, while worldwide consumption is approximately thirty times larger. Much of the gas is transported from well heads to market over cross-country gas networks, which prompts China to construct one of the largest gas transportation network in the world. Figure 1 shows the location of the network and table 1 gives the basic parameters. From 3% to 5% of this gas is burned to power the transportation of the remaining amount [1] . At current prices, this is the equivalent of roughly 800 million dollars per year of wasted gas in China. Also, experts estimate that fuel consumption in gas pipeline can reduce by 20% by carefully optimizing the daily operation [2] . Many gas transportation companies have already managed to reduce costs dramatically by optimizing their gas pipelines [3,4,5, 6,7] , their results also showed large reduction of CO 2 and NO x emissions. Also, there has been considerable research work on the subject [7, 8, 9, 10, 11, 12, 13, 14] . Problem Formulation With development of the gas industry, gas pipeline networks have evolved over decades into very large and complex systems.

Abstract A tight gas reservoir is commonly defined as a reservoir having less than 0.1 millidarcies permeability. There are several basic concepts and field cases of different well tests in tight gas reservoirs in the literature, but not presented as a general guide. In this paper, we gather valuable information and provide a useful guide to the most important well tests in tight gas reservoirs. Generally due to low permeability of these reservoirs, a well will not flow initially at measurable rates and conventional well testing cannot be applied. Therefore, fracture stimulation must be considered. Many authors present procedures for design of pre and post-frac tests. The pre-frac test permits calculating preliminary estimates of reservoir permeability and initial pressure. Because of economic and environmental reasons, short duration procedures are of interest. Hence, prime candidates are pre-frac, short time, small volume, closed chamber tests. These tests have to be analyzed by special methods to provide improved values of reservoir parameters. In this study, we also present a review of some aspects in tight gas well testing like pressure-dependent permeability, estimation of pseudo-time at the average pressure of the region of influence, supercharge effect, the problem of treating the pressure-dependent product µc t during pre-frac test analysis and the concept of instantaneous source response Introduction Large decreases in production and increases in demand for fossil-fuels cause the economic gas production from unconventional resources (tight gas, coal bed methane (CBM), and gas hydrate) to be a great challenge. Huge reserves, longterm potential, low gas prices and some other factors account for the great influence of these resources on the future of energy. There is no formal definition for "Tight gas". Commonly used definition, describes tight gas reservoirs as those having permeabilities less than 0.1 millidarcies. Recently, the German Society for Petroleum and Coal Science and Technology (DGMK) defined tight gas reservoirs as those with average effective gas permeability of less than 0.6 mD. "Ultra tight" gas reservoirs may exhibit permeabilities down to 0.001 mD. To improve the recovery of this resource, GFREE [1] research program has been created at the University of Calgary. GFREE [1] stands for: Geoscience aspects (G) Formation evaluation by petrophysics and well test (F) Reservoir drilling, completion and stimulation (R) Reservoir Engineering (RE) Economics and long run supply curves (E) As a part of the activities of this research program, we have concentrated on Formation evaluation (F) by well testing, and conducted a literature survey which is presented in this paper. Well testing is generally done to estimate hydrocarbon (here gas) in-place and recoverable resources. Initial pressure is a critical parameter not only for estimating gas in-place, but also for determining how much field development is required and whether or not the field is overdeveloped. In addition to p i , well testing provides an estimate of permeability. A problem associated with well testing in tight gas sands is that usually long times are required to reach redial flow, due to their extremely low permeabilities.

Abstract Production rate and volume information are important for many reservoir surveillance and management tasks. For example, many techniques for estimating the remaining producible gas in a reservoir depend on accurately knowing the amount of gas produced from the reservoir in combination with the average reservoir pressure. History-matching gas, and water production data using a reservoir simulator is a common practice in workflows used for making investment decisions such as whether or not to drill more wells. The quality of a history-matched model is limited by the quality of the allocated production data. An additional need for quality rate allocation is that the production volumes for individual wells or reservoirs are often required for regulatory reporting. Production allocation for high temperature and pressure is not easy task as the current orifice plate flow meter is not deigned for high condensate gas ratio (CGR). The error in using current meters could reach up to 60 percent in gas rate due to accumulation for condensate on the orifice plate. In this field, there are only two wells producing from two zones. There is only one production separator in the platform which makes the allocation difficult due to the need for shutting down one well to do multirate test on the other well. One of the wells has a downhole pressure gauge but the other well does not. In this paper, we will present new procedures for using a combination of the downhole pressure and multirate tests to construct the accurate inflow performance curve (IPR) for each well. Then, at each reservoir pressure the relationship between wellhead flowing pressure and flow rate is programmed by Visual Basic program (VBA). This program is used to allocate daily gas rate from the wellhead flowing pressure. This method shows high accuracy for allocating the history and current gas flow rate with high condensate ratio. Also, provide accurate well test analysis and accurate reserve calculation. Introduction The availability of accurate production volumes, at the well level and throughout the production network, is fundamental to the workflows that target the optimization of the economic potential of the reservoir. Without an accurate understanding of production volumes, the company's field development and operational decisions may not support the maximum economic value of the reservoir and can undermine the accuracy of the reserves estimates 1–2 . As mentioned there is only one production separator through which the Well-A & Well-B produced fluids entering for the first separation. Well-A starts to produce in September 2002. The problem started when Well-B was first introduced to the production in May 2005 and the flow meters now measured the total gas and condensate flow rates from both wells instead of one well which makes it difficult to allocate the metered flow rates back to the wells in an accurate method. This problem generally affects the back production allocation for each well showing unreal well performance and inaccurate daily production monitoring and also affects the reserves calculation.

Abstract CO 2 flooding can enhance oil recovery by up to 8–16% of the original oil in place and might be suitable for about 80% of oil reservoirs worldwide. In addition to miscibility, displacement efficiency is another factor that needs to be optimized for achieving high oil recovery. Although many techniques have been made available for production optimization in the upstream oil and gas industry, it is still a challenging task to optimize reservoir performance in the presence of physical and/or financial uncertainties. In this paper, a new technique is developed to optimize the displacement efficiency in a CO 2 flooding reservoir under uncertainty. More specifically, potential uncertainties influencing reservoir performance are analyzed and assessed by using the geostatistical technique. This enables us to integrate the available information within a unified and consistent framework and to generate multiple geological realizations accounting for uncertainty and spatial variability. Subsequently, the net present value (NPV) is selected as the objective function to be optimized by using the genetic algorithm, while well rates of the injectors and the flowing bottomhole pressures for the producers are chosen as the controlling variables. In addition, corresponding modifications have been made to accelerate the convergence speed of the genetic algorithm. A field case is used to demonstrate the successful application of the newly developed technique. It has also been found that the genetic algorithm combined with the geostatistical technique can be used to optimize the displacement efficiency under uncertainty in a CO 2 flooding reservoir. Introduction Enhanced oil recovery (EOR) plays an increasingly important role in the petroleum industry. Among the various EOR processes, CO 2 flooding is considered as the most promising and practical process since it not only significantly increases oil recovery, but also considerably reduces greenhouse gas emissions by sequestrating CO 2 into the depleted reservoirs. In practice, CO 2 flooding performance can be greatly affected by the reservoir heterogeneity, which can severely reduce the displacement efficiency, result in early CO 2 breakthrough at the producers, and thus, leave a large amount of bypassed oil in the reservoir. Thus, it is of fundamental and practical importance to optimize production performance of a CO 2 flooding reservoir. The main objective of production optimization in a CO 2 flooding reservoir is to monitor and control the propagation of the flood front, delay CO 2 breakthrough at the producers, and thus, increase the oil recovery and/or the net present value (NPV). Such optimization is made possible by adjusting a set of controlling variables (e.g., flow rates and/or flowing bottomhole pressures)1. After an oil reservoir is put into production, it will be converted from a static system into a dynamic system. Such a system can be treated as a black box, to which injection fluids including gas and water are considered as the inputs and from which the production fluids are treated as the outputs. Changing flow rate and/or bottomhole pressure of the well in turn changes the dynamic state of the system (i.e., reservoir pressure and fluid saturation distribution). These changes will subsequently affect the cumulative production and then the oil recovery and/or NPV.

Abstract Currently in the oil industry, productivity equations for a single well are erroneously used in all reservoir systems, regardless of the interference effects on flow rates of different wells in the same drainage domain This paper presents steady state and pseudo-steady state productivity equations of a multiple wells system in an anisotropic circular or rectangular reservoir. Taking fully penetrating vertical wells as uniform line sinks, and solving square matrices of dimension n, where n is the number of wells, simple, accurate multiple wells productivity equations are obtained. The proposed equations which relate the production rate vector to the pressure drawdown vector provide fast analytical tools to evaluate the performance of multiple wells, which are located arbitrarily in an anisotropic circular or rectangular reservoir. This paper also gives equations for calculating skin factors of each well. It is concluded that, for a given number of wells, well pattern, reservoir boundary conditions, anisotropic permeabilities and skin factor have significant effects on single well productivity and total productivity of the multiple wells system. For a given multiple wells system, if the reservoir is under edge water drive, when producing time is sufficiently long, productivity equation based on the steady-state is required; for a closed-circular or rectangular reservoir, pseudo-steady-state productivity equation is applicable. Introduction Well productivity is one of primary concerns in field development and provides the basis for field development strategy. To determine the economical feasibility of drilling a well, petroleum engineers need reliable methods to estimate its expected productivity. Well productivity is often evaluated using the productivity index, which is defined as the production rate per unit pressure drawdown. We often relate the productivity evaluation to the long-time performance behavior of a well, that is, the behavior during pseudo-steady state or steady state flow. The steady state and pseudo-steady state productivity equations of a fully penetrating vertical well located at the center of a homogeneous, isotropic permeability circular reservoir are sufficiently familiar to petroleum engineers and can be found in any reservoir engineering book [1] . Lu and Tiab extended these well-known productivity equations for a fully penetrating vertical centered well in an isotropic circular reservoir to an off-center partially penetrating vertical well in an anisotropic circular cylinder reservoir [2] . Lu and Tiab also presented steady state and pseudo-steady state productivity equations for a vertical well in an anisotropic box-shaped reservoir [2,3] . The performance of multiple wells system has received attention in the last decade. Camacho-V, Galindo-N, and Prats gave a buildup solution in a system with multiple wells producing at constant wellbore pressures [4] . Umnuayponwiwat, Ozkan, and Raghavan presented equations of pressure transient behavior and inflow performance of multiple vertical and horizontal wells in closed systems [5] . Marhaendrajana and Blasingame presented a solution and associated analysis methodology to evaluate single well performance behavior in a multiple wells reservoir system [6] . Valko, Doublet and Blasingame presented pseudo-steady state productivity index for multiple wells producing from a closed rectangular reservoir [7] , however their equation is only applicable to isotropic reservoir, and an infinite series summation is included in their equation.

Abstract Asphaltene precipitation and deposition is a serious problem in many Iranian fields. The deposited asphaltene results in partial or total blockage of the wellbore, reducing or completely seizing oil production. This paper presents a new approach, based on PVT data, for thermodynamic modeling of asphaltene precipitation. The developed model has been combined with temperature and pressure modeling of the wellbore. The combined model has been used to predict the depth of asphaltene precipitation in the wellbore in several fields in an Iranian field (Kupal), as case study. The results are compared with the field data of asphaltene problems in various wells in Kupal field, as well as the measured depth of obstruction when applicable. There is a good agreement between the predictions and the field data. Finally, a sensitivity analysis has been conducted to simulate the effect of various operational parameters, including; flow rate, wellhead pressure and tubing diameter. The results provide important guidelines in minimizing the risks associated with asphaltene deposition. Introduction Asphaltenes are the heaviest fraction of crude oils which are polyaromatic structures or molecules, containing heteroatom (i.e. S, O, N) and metals (e.g. Va, Ni) that exist in petroleum fluids in an aggregated state 1 . These aggregates are stabilized in solution by resins and aromatics, which act as peptize agents 2 . Asphaltenes and resins, are in the thermodynamic equilibrium at static reservoir condition. However changes in thermodynamic condition such as pressure, temperature or compositions during oil production may cause stabilized asphaltenes precipitate out of fluid and could deposit in reservoir, wellbore, wellstring, transport pipeline or surface processing facilities. Since pressure and temperature changes extremely through production string, this area is the most susceptible for asphaltene precipitation. Deposition of asphaltene on the wall of production string reduces available diameter to oil flow, subsequently, oil production rate decreases. Gradually, oil flow path is plugged by increasing the thickness of deposited asphaltenes. In addition to economical damages as result of seizing oil production, the costs could increase for removing asphaltene obstruction plug by chemical or mechanical treatments. The mechanical treatment of asphaltene removal do not use practically. Because this process is time consuming and sometimes impractical owing to some parts of production system are not accessible. Therefore the most of asphaltene depositions are removed by chemical treatments. It is essential to know the depth of asphaltene deposition in order to implement a successful asphaltene removal operation. Because by knowing the depth of asphaltene deposition, the amount of chemical could be determined. Also, the risk of stuck reduces for coil tubing tool operation. Therefore, asphaltene removal treatment could be faster. The operational production condition affects on the asphaltene deposition in wellstring. Therefore, operational parameters should be known to prevent or eliminate the asphaltenes deposition damages in well string. Thus damages could be reduced by alerting operating conditions. This paper tries to find an approach that is capable to predict asphaltene deposition in well string and studies the effect of different factors on the process of asphaltene deposition including; flow rate, wellhead pressure and tubing diameter.

Abstract Solvent-based process appears to be an increasingly feasible technology for the extraction of heavy oil reserves. However, there is a lack of fundamental understanding of how fracture geometrical characteristics control the oil recovery efficiency in these types of EOR techniques. In this work a series of experiments were performed whereby the pure and mixed hydrocarbon solvents displaced heavy oil in fractured 5-spot glass micromodels. Successive images of solvent injection process were recorded on PC. The oil recovery factor as a function of injected pore volume of solvents was measured using image analysis of the provided pictures. The concentration calibration curves of solvents in heavy oil were used for evaluating the solvents concentration. It has been observed that the oil recovery decreased when the fractures spacing, discontinuity, overlap, and distribution increased. While the oil recovery increased, the orientation angle, discontinuity-distribution and the number of fractures increased. Also, it has been found that there is an optimum solvent composition which maximizes the oil recovery. This study illustrates the application of the micromodels for fundamental studying of solvent-based process in fractured 5-spot systems which are then used to investigate the effect of fracture geometrical characteristics and how these lead to affect oil recovery. Introduction Heavy oil and bitumen reserves represent a considerable portion of worldwide energy resources. It is estimated that these reservoirs contains six trillion barrels of OOIP which is much further than the total conventional oil reservoirs. Great consumption of light oil reserves and hence their dramatic decline encourages more interest in exploitation of highly viscous oil and bitumen for future energy demands. For the optimum conditions, the primary recovery of these reservoirs would not exceed 10 percent of the OOIP [1] . Variety of thermal methods including cyclic steam stimulation, in-situ combustion, and steam assisted gravity drainage are currently being applied for extraction of these crudes. As far as the reservoir's oil is heated, main fraction of the thermal energy is used up in heating the formation itself. For the reservoirs with very thin pay zone, bottom water zone and/or overlying gas zone, excessive depths, low thermal conductivity of rock matrix, high water saturation etc. the economical applicability of the thermal methods is doubtful. With respect to current available recovery technologies, these reservoirs are categorized as problematic reservoirs [2,3] . Less energy consumption, less environmental pollution, and lower capital cost are the main advantageous of solvent-based process over that of thermal methods. Since the HCS are soluble only in the oil then the possibility of solvent loss to the formation and its confining environment is vanished. Therefore, the solvent-based process appears to be the only EOR technology that can be economically justifiable for problematic Iranian heavy oil reservoirs [4] . On the other hand, immiscible secondary recovery methods, even when successful, may leave significant amounts of oil in the reservoir due to the presence of capillary forces which are responsible for the entrapment of the oil [5,6] .

Abstract Geostatistical models of reservoir properties can be hundreds of millions of cells; it is impractical to use them directly in flow simulation due to computational cost. Upscaling techniques are applied to average fine scale permeability values onto coarser flow simulation blocks. In cases where unstructured grids are used or the geology inside the grid block is not aligned with the block geometry, full permeability tensors arise instead of a diagonal tensor. The focus of this work is on development of a method to characterize the full permeability tensor for an unstructured grid block using fine scale heterogeneity information. A single phase flow-based upscaling is performed and a prototype program called ptensor is developed based on the random boundary conditions and optimization technique. Full, symmetric and diagonal permeability tensors are calculated for 2-D and 3-D blocks and sensitivity analysis is performed. Introduction Geostatistical modeling of petrophysical properties can generate fine scale models with hundreds of millions of cells. Using those fine scale models directly in flow simulation is computationally inefficient. Upscaling techniques scale the fine scale models to coarser scale models while preserving the fine scale heterogeneity. A simple averaging is sufficient and reasonable for variables that average linearly; however, in the case of permeability which does not average linearly, a simple arithmetic averaging is inadequate. For complex cases with heterogeneity, flow-based upscaling techniques yield more accurate results (1) . In this type of upscaling the flow equation is solved for pressure and the results are used to calculate the block permeability. Commonly unstructured grids are used in order to better capture the flow response near complex reservoir features such as faults and wells. Usually cases that involve the use of irregular block or a heterogeneous permeability field at fine scale require calculation of the full permeability tensor. White and Horne (2) and Gomez-Hernandez (3) proposed different methods to calculate permeability tensor for regular coarse blocks. In recent years, some approaches are presented by Durlofsky (4) , Prevost (5) and He (6) to calculate the full permeability tensor for irregular shape grid blocks. This paper introduces a simple, fast and accurate method to calculate full, symmetric or diagonal permeability tensor for any corner point geometry grids. The unstructured grid is surrounded by a bounding box and the geometry is simplified with the fine resolution grid. The steady state flow equation is solved, via finite difference, for the input fine grid cells within a bounding box. The results are used to calculate the permeability tensor of corresponding coarse regular or irregular blocks. Randomly assigned boundary conditions are used and the results are optimized to get the desired full, symmetric or diagonal tensor. Methodology Flow based upscaling is used to calculate effective permeability of coarse block. Consider a single rectangle (2-D) or a cube (3-D) imposed on a fine scale model. The idea here is to calculate the pressure at fine scale with specific boundary conditions applied at the boundary of the coarse block and then use the solution to calculate the full permeability tensor for that coarse block.

Abstract The Vapex analytical model is extended to cover situations when diffusion coefficients are dependent on concentration due to the extreme viscosity contrasts between the solutes and solvents. The new analytical model covers such situations along with the cases in which the diffusion coefficient and viscosity relate to each other under the Stokes-Einstein law. In the process, conceptual inconsistency in the past models is uncovered, and a new concept of the "average flow fraction of bitumen" in the flowing mixtures is introduced. The modelled result on overall functionality of the drainage rate of bitumen shows the square-root relationships to key reservoir parameters; it is unchanged from the past analytical models. These relationships are compared with the observed correlations of the scaled bitumen rates to these parameters in the numerous existing Vapex experimental data which cover a variety of conditions. Introduction Dunn et al 1 Developed the theoretical model of the gravity drainage process for bitumen recovery known as Vapex based on the model of the steam-assisted gravity drainage (SAGD) process by Butler et al 2 . This model assumed that the diffusion coefficients of solvent-bitumen systems are constant similar to the case of thermal diffusivity; thus, the steady-state profiles of solvent concentration ahead of the solvent-bitumen interface is the smooth exponential decay towards an infinite distance. In reality, both the diffusion coefficients of both solvent and bitumen are strongly dependent upon compositions due to the extreme viscosity contrasts between the solutes and solvents. As a result, the observed concentration profiles in diffusion experiments exhibit the abrupt front-end profiles3. The theoretical endeavour here is to understand the impact of the non-exponential concentration profiles on the Vapex drainage and bitmen rates. Governing Mechanisms The most fundamental mechanism of the process is the gravity drainage caused by the density difference between the liquid-bitumen phase and the injected vapour phase. The drainage flow of the bitumen phase occurs only from viscosity reduction due to the impact of the injected solvent (or heat in the case of SAGD) of the otherwise semi-solid bitumen. Therefore, how the injected solvent penetrates into the bitumen phase in the reservoir is of the primary importance to the process. According to Fick's law, a material balance across a differential distance dx in this situation can be expressed as a continuity equation for the change of concentration (volume fraction is chosen), C , with time, t, by using the diffusion coefficient, D : Equation (1) (Available in full paper) If the draining interface with a fixed concentration is moving at a velocity U in a direction normal to the interface, at a steady-state condition, the concentration of invaded solvent, C , does not change with time at a given depth from the interface, ξ (a moving axis with the interface, ξ = x-Ut ); then Equation (2) (Available in full paper)

Abstract Accurate estimation of pressure losses associated with fluid flow in annuli is essential to achieve better bottom hole pressure control in drilling operations. Control of formation pressures and optimization of hydraulic programs can be obtained only if the pressure losses in the circulation system are precisely known. One of the major challenges in determining actual annular pressure losses is that the non-Newtonian fluid flow in annular conduit is much more complex than pipe flow. Many investigators proposed different equivalent diameter concepts to link annular flow to well defined pipe flow. In this study, effect of using various equivalent diameter definitions together with three widely used rheological models is analyzed for different annular conditions. The study is aimed to show how pressure losses vary as rheological model and equivalent diameter definitions are coupled. The effects of the ration between inner and outer radius and the effect of flow rate on the accuracy of equivalent diameters are shown in the study as well. It is important to note that, based on the complexity of wellbore configuration, different equivalent diameter definitions might result in more accurate calculations for different parts of the system. This study provides guidelines to predict frictional losses with higher accuracy. Introduction While drilling fluid is circulated in the annulus, it exerts additional pressure on the wellbore. If frictional pressure losses in the annulus are not determined accurately, the equivalent circulating density (ECD) calculations will also be incorrect increasing the chances of having well control problems. Determination of pressure losses in annulus is harder due to the complexity of the geometry compared to regular circular geometry present in pipe flow. Depending on the clearance between wellbore (or casing inner diameter) and pipe outer diameter, and also on the flow rate required to carry cuttings effectively, flow might be in turbulent or laminar regime. Several authors analyzed the non- Newtonian flow in annular conduits and suggested either empirical or analytical solutions. However, disagreement between calculated and measured pressure losses, due to the complex nature of non-Newtonian fluids, still exists today. Fredrickson and Bird 1 have derived an analytical expression to determine frictional pressure losses in annulus for Power Law rheological model. Their approach gives reasonable results when inner to outer radii ratios are more than 0.5. Kozicki, Chou and Tiu 2 determined a relation between maximum velocity and pressure loss for Power Law fluids flowing in ducts of arbitrary cross-sections under laminar flow conditions. Zamora and Lord 3 proposed a new numerical and graphical technique to determine pressure losses of non-Newtonian fluids in pipes and annuli. The model is valid for Bingham Plastic, Power Law and Yield Power Law rheological models. Langlinais, Bourgoyne and Holden 4 compared actual annular pressure losses obtained from two wells with theoretical calculations. They found out that pressure losses are more sensitive to the definition of annular gap compared to rheological model.

Abstract The in-situ extraction of heavy oil and bitumen requires enhanced oil production techniques to sufficiently reduce the viscosity of the oil to produce it at economical rates. Vapour extraction (VAPEX) and warm VAPEX (where the solvent condenses in-situ) are two possibilities for producing highly viscous in-situ oil from Canada's vast reserves. It has been recognized, by now, that the mass transfer involved in the vapour extraction of heavy oil includes both diffusion and convection mechanisms. However, to date, researchers have not been able yet to quantify the role of diffusion and convection in the VAPEX process. Before accurate field scale predictions can be made, the mass transfer and fluid mechanics aspects need to be understood. Laboratory scale experiments were conducted using systems of different length and permeability as well as different solvents and solvent flow rates to examine the effect on sweep efficiency and production. Using a mass transfer coefficient approach, results from the experiments are presented and the mass transfer coefficients compared for different systems. Introduction Vapour extraction (VAPEX) is an enhanced oil recovery technique for recovering in-situ heavy oil and bitumen from Canada's vast reserves. The governing mechanisms are mass transfer and gravity drainage. Solvent that is injected into a horizontal injection well where it diffuses and mixes into the heavy oil/bitumen phase and exponentially reduces the oil's viscosity. The live oil (reduced viscosity) oil can then drain via gravity to a production well. VAPEX laboratory results look promising. But, oil companies have yet to embrace VAPEX; there is no public field trial data, the mass transfer mechanisms are not quantified and there is no reliable model to predict field scale production rates from laboratory data. The goal of this work is to experimentally investigate the mass transfer involved in the VAPEX process using a mass transfer coefficient approach. Previous VAPEX experiments performed in glass etched micromodels showed bitumen dissolving into the liquid butane phase. This was observed under conditions of warm VAPEX, where the butane condensed inside the glass micromodel. In comparison, bitumen dissolution was not observed (due to the opacity of the live oil) in the normal mode of VAPEX operation when solvent vapour diffuses directly into the bitumen (James, L.A. and Chatzis, I., 2004) and (Chatzis, I., 2002). The dissolution of bitumen into draining live oil would still be valid and thus, the concept of using mass transfer coefficients was formulated. Mass transfer coefficients have been widely used in chemical processes such as absorption towers, strippers, packed columns, etc. More recently, mass transfer coefficients of non-aqueous phase liquid (NAPL) dissolution in groundwater were found and used in contaminant transport models (Kim, T-J et. al., 1999). Mass transfer coefficients are a measure of the amount of mass transferred from one phase to another through an effective area based on the concentration gradient driving force. Equation (1) shows the mass transfer coefficient (k) as a function of mass flux (N A ) and species A mass fraction. In terms of finding the mass transfer coefficient of bitumen (k B ) into solvent, the relationship is given by the rate of mass transferred (mB, g/s).