Schlumberger (Canada)

The Yen–Mullins model, also known as the modified Yen model, specifies the predominant molecular and colloidal structure of asphaltenes in crude oils and laboratory solvents and consists of the following: The most probable asphaltene molecular weight is ∼750 g/mol, with the island molecular architecture dominant. At sufficient concentration, asphaltene molecules form nanoaggregates with an aggregation number less than 10. At higher concentrations, nanoaggregates form clusters again with small aggregation numbers. The Yen–Mullins model is consistent with numerous molecular and colloidal studies employing a broad array of methodologies. Moreover, the Yen–Mullins model provides a foundation for the development of the first asphaltene equation of state for predicting asphaltene gradients in oil reservoirs, the Flory–Huggins–Zuo equation of state (FHZ EoS). In turn, the FHZ EoS has proven applicability in oil reservoirs containing condensates, black oils, and heavy oils. While the development of the Yen–Mullins model was founded on a very large number of studies, it nevertheless remains essential to validate consistency of this model with important new data streams in asphaltene science. In this paper, we review recent advances in asphaltene science that address all critical aspects of the Yen–Mullins model, especially molecular architecture and characteristics of asphaltene nanoaggregates and clusters. Important new studies are shown to be consistent with the Yen–Mullins model. Wide ranging studies with direct interrogation of the Yen–Mullins model include detailed molecular decomposition analyses, optical measurements coupled with molecular orbital calculations, nuclear magnetic resonance (NMR) spectroscopy, centrifugation, direct-current (DC) conductivity, interfacial studies, small-angle neutron scattering (SANS), and small-angle X-ray scattering (SAXS), as well as oilfield studies. In all cases, the Yen–Mullins model is proven to be at least consistent if not valid. In addition, several studies previously viewed as potentially inconsistent with the Yen–Mullins model are now largely resolved. Moreover, oilfield studies using the Yen–Mullins model in the FHZ EoS are greatly improving the understanding of many reservoir concerns, such as reservoir connectivity, heavy oil gradients, tar mat formation, and disequilibrium. The simple yet powerful advances codified in the Yen–Mullins model especially with the FHZ EoS provide a framework for future studies in asphaltene science, petroleum science, and reservoir studies.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> It is well known that inertial navigation systems can provide high-accuracy position, velocity, and attitude information over short time periods. However, their accuracy rapidly degrades with time. The requirements for an accurate estimation of navigation information necessitate the modeling of the sensors' error components. Several variance techniques have been devised for stochastic modeling of the error of inertial sensors. They are basically very similar and primarily differ in that various signal processings, by way of weighting functions, window functions, etc., are incorporated into the analysis algorithms in order to achieve a particular desired result for improving the model characterizations. The simplest is the Allan variance. The Allan variance is a method of representing the root means square (RMS) random-drift error as a function of averaging time. It is simple to compute and relatively simple to interpret and understand. The Allan variance method can be used to determine the characteristics of the underlying random processes that give rise to the data noise. This technique can be used to characterize various types of error terms in the inertial-sensor data by performing certain operations on the entire length of data. In this paper, the Allan variance technique will be used in analyzing and modeling the error of the inertial sensors used in different grades of the inertial measurement units. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data. Being a directly measurable quantity, the Allan variance can provide information on the types and magnitude of the various error terms. This paper covers both the theoretical basis for the Allan variance for modeling the inertial sensors' error terms and its implementation in modeling different grades of inertial sensors. </para>

This paper presents a ray tracing algorithm for rendering 3D scalar fields. An illumination model is developed in which the field is characterized as a varying density emittter with a single level of scattering. This model is equivalent to a particle system in which the particles are sufficiently small. Along each ray cast from the eye, the field is expressed as a function of the ray parameter. The algorithm computes properties of the field along the ray such as the attenuated intensity, the peak density, and the center of gravity, etc., These are mapped into HSV color space to produce an image for visualization.Images produced in this manner are perceived as a varying density 'cloud' where color highlights the computed attributes. The application of this technique is demonstrated for visualizing a three dimensional seismic data set.

Abstract Imaging of microseismic data is the process by which we use information about the source locations, timing, and mechanisms of the induced seismic events to make inferences about the structure of a petroleum reservoir or the changes that accompany injections into or production from the reservoir. A few key projects were instrumental in the development of downhole microseismic imaging. Most recent microseismic projects involve imaging hydraulic-fracture stimulations, which has grown into a widespread fracture diagnostic technology. This growth in the application of the technology is attributed to the success of imaging the fracture complexity of the Barnett Shale in the Fort Worth basin, Texas, and the commercial value of the information obtained to improvecompletions and ultimately production in the field. The use of commercial imaging in the Barnett is traced back to earlier investigations to prove the technology with the Cotton Valley imaging project and earlier experiments at the M-Site in the Piceance basin, Colorado. Perhaps the earliest example of microseismic imaging using data from downhole recording was a hydraulic fracture monitored in 1974, also in the Piceance basin. However, early work is also documented where investigators focused on identifying microseismic trace characteristics without attempting to locate the microseismic sources. Applications of microseismic reservoir monitoring can be tracked from current steam-injection imaging, deformation associated with reservoir compaction in the Yibal field in Oman and the Ekofisk and Valhall fields in the North Sea, and production-induced activity in Kentucky, U.S.A.

Summary This paper presents screening criteria for vertical and horizontal wells with or without induced fractures. The parametric basis of such screening makes the decision on either type of well more objective. A simple procedure to calculate the optimum number of orthogonal transverse fractures in horizontal wells and their sizes is also presented. Two important comparisons have not appeared in the literature: (1) the performance of a fully completed horizontal well with that of a hydraulically fractured well and (2) the performance of a hydraulically fractured horizontal well with that of a hydraulically fractured vertical well. In addition, previous work does not take into account the effect of the plumbing system on well performance. This paper is intended to fill these gaps.

Microseismic Imaging of Hydraulic Fracturing: Improved Engineering of Unconventional Shale Reservoirs (SEG Distinguished Instructor Series No. 17) covers the use of microseismic data to enhance engineering design of hydraulic fracturing and well completion. The book, which accompanies the 2014 SEG Distinguished Instructor Short Course, describes the design, acquisition, processing, and interpretation of an effective microseismic project. The text includes a tutorial of the basics of hydraulic fracturing, including the geologic and geomechanical factors that control fracture growth. In addition to practical issues associated with collecting and interpreting microseismic data, potential pitfalls and quality-control steps are discussed. Actual case studies are used to demonstrate engineering benefits and improved production through the use of microseismic monitoring. Providing a practical user guide for survey design, quality control, interpretation, and application of microseismic hydraulic fracture monitoring, this book will be of interest to geoscientists and engineers involved in development of unconventional reservoirs.

Summary We present the first quantitative study and complete model of the wormholing phenomenon, leading to a means of predicting and optimizing carbonate acidizing treatments. Laboratory experiments on a gypsum model system and computer simulations show that for a given geometry, wormholes can be quantified by a unique parameter, their equivalent hydraulic length. The behavior of this quantifying parameter vs. all the system parameters is studied and allows the quantitative prediction of the efficiency of an acidizing treatment. This study highlights the fractal nature of the phenomenon, which is accounted for in the equations, and the strong effect of the sample geometry. Three types of etching can be obtained: compact, wormhole type, or homogeneous. The optimum conditions for achieving die best skin decrease correspond to the creation of wormholes and can then be defined in terms of fluid reactivity and injection rate.

ABSTRACT A new technique to determine excessive water and gas production mechanisms as seen in petroleum production wells has been developed and verified. Based on systematic numerical simulation studies on reservoir water coning and channeling, it was discovered that log-log plots of WOR (Water/Oil Ratio) vs time or GOR (Gas/Oil Ratio) vs time show different characteristic trends for different mechanisms. The time derivatives of WOR and GOR were found to be capable of differentiating whether the well is experiencing water and gas coning, high-permeability layer breakthrough or near wellbore channeling. This technique was applied on wells in several fields in Texas, California, the Gulf Coast and Alaska. Plots using the actual production history data determined the production problem mechanisms. Together with well tests and logs, the technique was used to select well treatment candidates and to optimize treatments to enhance the return of investment.

Summary A large-scale study of cuttings transport in directional wells is discussed in this paper. Previous investigators used unrealistically high fluid velocities and/or short test sections where steady-state conditions had not been established. This study used a 40-ft [12.2-m] test section. Pipe rotation and eccentricity, as well as several types of drilling muds and flow regimes, were studied. Annulus angles varied from 0 to 90°, and actual drilled cuttings were used. The major factors affecting cuttings transport are drilling fluid velocity, hole inclination, and fluid rheological properties. Much higher annular velocities are required for effective hole cleaning in directional wells than in vertical wells. An increase in hole angle and/or drilling rate reduces the transport performance of drilling fluids. Hole angles of 40 to 50° are critical because of cuttings buildup and downward sliding of the bed of cuttings. High-viscosity muds were observed to provide better transport than low-viscosity muds.

Abstract The effects of natural fissure opening, or pressure dependent leakoff, on the pressure behavior observed during fracturing are significant. Previous work has suggested that this behavior can be identified from pressure diagnostic plots during pumping, or from pressure falloff analysis. However, these techniques lead to ambiguous conclusions regarding the magnitude, and even existence, of pressure dependent leakoff. This paper presents a method of pressure falloff analysis which removes this ambiguity and allows an accurate determination of the magnitude of pressure dependent leakoff. The effects of fracture tip extension and recession, height recession, and transient flow in the fracture are also identified. The effect of pressure dependent fracture compliance, which has not been previously published, is also described.

ABSTRACT This paper presents the results obtained in the study of the transient behavior of a well intersected by a finite conductivity vertical fracture in a double porosity reservoir. Two models are considered to take into account the fluid transfer between matrix blocks and fractures: the pseudo-steady-state matrix flow model and the transient matrix flow model. A general semianalytical model and simplified fully analytical models are presented. It is demonstrated that these systems exhibit the basic behavior of a well with a finite conductivity fracture: that is bilinear flow, pseudolinear flow and pseudoradial flow in addition to the transition flow periods. Each of these flow periods is under the influence of the different states of the fluid transfer between matrix and fractures; that is fracture dominated period, transition period and total system dominated period. It is shown that correlating parameters are the dimension-less fracture conductivity (kfbf)D, the fracture storativity coefficient ω and the interporosity flow parameter λf(or the dimension-less matrix hydraulic diffusivity ηmaD). It was found, for the transient matrix flow model, that the pressure behavior exhibits 1/8 slope in a log-log graph during the bilinear flow dominated by the transition period of the fluid transfer. Hence a graph of pressure versus t1/8 yields a straight line passing through the origin. During the pseudolinear flow, and if the fluid transfer is in the transition period, a log-log graph of the prerssure versus time exhibits 1/4 slope straight line. This means that a graph of p versus t1/4 yields a straight line. Hence it is concluded that bilinear flow is not the only type of flow that exhibits the one quarter slope type of behavior. Type curves are presented to analyze data falling in the bilinear – pseudolinear flow regions. The effect of wellbore storage are also included. The general semianalytical models yields simultaneous the constant flow rate and the constant pressure solutions as well as the pressure derivative function for the constant rate case.

Summary. This paper describesperforation/fracture tests performed perforation/fracture tests performed in large sandstone blocks in a triaxialstress cell to determine perforatinggeometry and perforating-fractureprocedures for optimal fracture procedures for optimal fracture initiation. Four-shot, 1800 phasedperforating guns, steel casing, and perforating guns, steel casing, and oilfield cement were used. In oneseries of experiments, the casing wascemented and cured while undertriaxial stress. Most tests were madewith pore pressure, and vertical andhorizontal wells were simulated. Ingeneral, the tests showed that(1) fractures initiate either at the baseof perforations or at the intersectionof the plane normal to the minimumhorizontal stress that passes throughthe axis of the wellbore and thewellbore surface and (2) fracture initiationdepended on perforation orientationwith respect to the plane normal tothe minimum horizontal stress andthe properties and injection rate ofthe fracture fluid. All fracturesreoriented into the plane normal to theminimum horizontal stress within onewellbore diameter; although multiplefractures were initiated, only primarysingle fractures propagated beyondone wellbore diameter. Introduction Laboratory simulation of fracturing throughcased and perforated wellbores generally hasbeen performed with one or more of thefollowing limiting conditions:scaled tests(rate effects ignored),artificial rock(cement, plaster of Paris, or hydrostone),isolation of the perforations from thewellbore (no pressurization between thescaled casing and the rock),noporoelastic effects (impermeable rock or poroelastic effects (impermeable rock or high-viscosity fracturing fluid),artificially scaled perforations(no perforation damage), andno pore pressure (impermeable ordry rock). Extrapolation of laboratory results todownhole situations must proceed withcaution whenever any of these conditions arepart of the laboratory experiment. For part of the laboratory experiment. For example, Condition 3 is unrealistic downholeand Condition 5 may apply only in specialsituations of high underbalance perforating. Conditions 4 and 6, however, may simulatea well with extensive wellbore andperforation damage. To the best of our knowledge, perforation damage. To the best of our knowledge, Warpinski's mineback experiments, inwhich annulus fractures were observed, were the only experiments conducted in theabsence of these conditions. The experiments discussed in this paperwere planned to evaluate the effect ofperformations on fracture initiation. Because of performations on fracture initiation. Because of the limiting-condition issues discussedabove, fill-scale experiments wereconducted in sandstone rock in a large triaxial stressframe that simulated downhole conditions. Test Fixture The fracture-initiation experiments wereperformed in 27×27×32-in. sandstone performed in 27×27×32-in. sandstone blocks in Terra Tek's 8, psitriaxial stress frame. The circular frame andits top and bottom platens surround the rockand provide reactions for three independentpairs of flat jacks. Flat-jack efficiency was pairs of flat jacks. Flat-jack efficiency was measured at 91 %; all applied stress datause this correction. Access to the centralwellbore is provided through the top loadingplate. Pore pressure was applied by placing plate. Pore pressure was applied by placing the rock in a stainless-steel can with rubberseals on the top and bottom faces. The canallowed the placement of about 0.25 in. ofbauxite beads around the four faces. Theborehole was cored to 4% in., and 3-in. OD × 2 1/2 -in. ID) steel tubing was cementedin place. Through-tubing, 1 11/16-in. orin., 4-shot/ft (SPF), 180 degs phased guns withthree or four shots were used. Table 1 givesthe rock properties. Experimental Procedure Three sets of tests were conducted (Table2). Experimental techniques were enhancedwith each additional set. Rock saturation andpore pressure were added to Set 2. An in-situ pore pressure were added to Set 2. An in-situ pore pressure gauge, a large 2.38-gal pore pressure gauge, a large 2.38-gal intensifier, and casing cemented and cured understress were added to Set 3. The general test procedure was as follows.1. Vacuum saturate the rocks with 3%brine, flowing brine from the uncasedwellbore to the rock sides (Sets 2 and 3 only).2. Cement casing into rock and allow tocure (Sets 1 and 2 only).3. Place rock into test frame. For Set 3, casing was cemented in place before theframe was closed and cured while understress.4. Place perforating gun in wellbore.5. Close frame, apply desired flat-jackand pore pressures; the wellbore is ventedto atmosphere.6. Fire gun. For Set 3, the casing cementcured for a minimum of 24 hours before thegun was fired.7. Flow brine at 2,000 psi from the beadpack through perforations; measure flow pack through perforations; measure flow rate8. Perform various prefractureprocedures depending on test set. procedures depending on test set. 9. Fracture rock with red dye used infracture fluids.10. Remove, cut open, and examine rock. Experimental Results Set 1, Torrey Buff Sandstone. Equipmentfailure prevented on of the specimensin this set. After perforation, the wellborewas flushed with brine, and on Tests 2 and4, brine was injected at low pressure throughthe perforations to saturate the rock locallynear the wellbore. JPT P. 608

The colloidal structure of asphaltenes impacts various physical properties and is important to characterize. Previously, in both laboratory and oilfield studies, asphaltenes have been shown to form nanoaggregates. In addition, previous work has shown that asphaltenes exhibit a critical nanoaggregate concentration (CNAC) in toluene in the range of 50−150 mg/L. In this study, centrifugation is used to prove a major change of asphaltene aggregation at the CNAC concentration, thereby corroborating previous results. Collection of these nanoaggregates by centrifugation validates there existence. The nanoaggregate size is found to be ∼2.5 nm, which is compatible with corresponding previous determinations from gravitational gradients. Asphaltene monomers are seen to be small (<1.5 nm), confirming previous diffusion measurements and corroborating the now common view that asphaltene molecular size is rather small. A two-component, monomer and nanoaggregate, phase equilibrium model is shown to treat the primary features of the data; nevertheless, shortcomings of this model are discussed. These centrifugation experiments are simple and we believe compelling confirmation of the asphaltene CNAC in toluene.

Abstract Asphaltene deposition is one of the important problems of oil production that requires an accurate predictive modelling. We developed an asphaltene deposition model in a pipeline. The model is based on data, which are obtained by experiments performed in a Couette device, where the inner cylinder rotates, and deposition on the outer wall is studied. A detailed theoretical analysis of an applicability of a Couette device for imitation of the asphaltene deposition in a pipe flow is presented. The model developed is based on first principles and consists of the two major modules: (1) a sub‐model describing the particle size distribution evolution in time in a Couette device, and along a pipe; (2) a sub‐model for calculating the particle transport to the wall. A population balance model is employed for modelling the particle size evolution. A concept of the critical particle size is introduced; only particles that are smaller than the critical size can deposit. The model developed contains only three parameters that are determined experimentally using a Couette device. The model of asphaltene deposition in a Couette device allows accurate describing the deposit mass growth in time. Performance of the deposition model for a pipeline with the coefficients obtained by a laboratory Couette device is also illustrated. Le dépôt d'asphaltènes est un des problèmes majeurs de l'industrie pétrolière et nécessite des modèles prédictifs fiables. Nous avons développé un modèle de dépôt d'asphaltènes en conduite pétrolière. Le modèle est basé sur des données obtenues expérimentalement par un système Couette avec cylindre intérieur tournant. Le dépôt sur les parois extérieures, fixes, est alors étudié. Une analyse théorique détaillée de l'applicabilité d'un système Couette à l'étude du dépôt d'asphaltènes en écoulement dans une conduite pétrolière est présentée. Le modèle développé est basé sur des principes fondamentaux et consiste en deux principaux modules: (1) un premier module décrivant l'évolution de la distribution de taille des particules avec le temps dans un système Couette et le long d'une conduite, (2) un deuxième module pour le calcul du transport des particules vers la paroi. Un modèle d'équilibre de population ( population balance model ) est utilisé pour modéliser l'évolution de la taille des particules. Un concept de « taille critique » est alors défini: seules les particules plus petites que cette taille peuvent se déposer. La modélisation contient seulement trois paramètres qui sont déterminés expérimentalement sur un appareil de type Couette. Le modèle permet une description fiable de l'augmentation de la masse de dépôt avec le temps. Les résultats de ce modèle appliqués à une conduite pétrolière avec les paramètres obtenus en laboratoire sur un système Couette sont également démontrés. © 2011 Canadian Society for Chemical Engineering

ABSTRACT Nolte developed an analysis of the pressure decline following a fracturing treatment to provide an estimate of fluid efficiency, fluid loss coefficient, and fracture geometry. This analysis has become an industry standard for evaluating and improving the design of fracturing treatments. The derivations by Nolte assume the leakoff coefficient is a pressure-independent constant. This assumption is valid when leakoff is controlled by a compressible filter cake. In cases where leakoff is primarily controlled by filtrate viscosity, by an incompressible filter cake, or by reservoir permeability and compressibility, the leakoff coefficient is pressure dependent, and, therefore, declines during the closure period. Under these circumstances, direct application of the Nolte technique may not be appropriate, and could cause an optimistic estimate of fluid efficiency and leakoff coefficient. This paper introduces a new plot for fracture pressure decline analysis that determines the pressure parameters (ISIP, Pc, P*) required in the Nolte leakoff calculations. The derivative of this plot may be used to identify the extension period, the closure period, and to assess the influence of pressure dependent leakoff on fracture pressure decline. In order to account for pressure dependent leakoff, equations are presented where the leakoff coefficient is treated as a mathematical variable. The equations describe simple linear relations applicable to the fracture closure period. When these relations are plotted on Cartesian coordinates, the closure period is recognized by a straight line with slope proportional to the leakoff coefficient. As shown in the examples, this modified approach is easily applied and provides new insight to the fracture closure period.

Singly substituted derivatives of cinnamaldehyde were tested as corrosion inhibitors for API J55 steel in static experiments conducted in 75% HCI at 65°C for 24 h. Four substituent sites were examined. Corrosion rates measured with added surfactants were correlated with physicochemical properties of the inhibitors, including electronic, steric, and solubility parameters. The best-fitting simple relations were three- or four-term power-law expressions that incorporate a solvent interaction parameter and, to a lesser extent, a parameter related to electron affinity or electronegativity. These expressions are consistent with a proposed corrosion inhibition model and with the quantitative structure-activity relationship (OSAR) proposed by Hansch. However, no single OSAR was found that would satisfactorily accommodate the data from all four substituent groups, a result attributable to site-specific variability in the nature of the π-electron system and in the molecular geometry.

Abstract The use of polymer solutions to enhance oil-displacement efficiency by seawater injection in North Sea oil reservoirs has been investigated. We have evaluated over 140 polymers for viscosity retention and porous media flow performance under high temperature (90°C), high salinity, and high pressure. Scleroglucan polymers give the best performance in our tests. Polyacrylamides (PAAm's) are particularly unsuitable for mobility control. Using polymers to enhance seawater injection and waterflooding processes is not practical in North Sea reservoirs, but selective injection may improve local sweep efficiencies.

Fracturing-Pressure Analysis for . Non ideal Behavior Summary. The analyses of fracturing pressure, during injection and after shut-in, provide powerful tools for understanding and improving the fracturing process. The current framework of analyses is based on several idealized assumptions. This paper assesses these assumptions paper assesses these assumptions and quantifies the effect of the deviations. The deviations are investigated by numerical simulation, and the results are presented in terms of pressure/time plots, with dimensionless pressure/time plots, with dimensionless parameters used when appropriate. parameters used when appropriate. These plots, with the associated derivatives (slopes), provide diagnostics for interpreting the pressure responses and identifying deviations from assumptions. The focus is for vertical fractures with large horizontal penetrations relative to the vertical height penetrations relative to the vertical height -i.e., the Perkins-Kern assumption. Introduction The important of the analysis of fracturing pressure was recognized in 1958, and the pressure was recognized in 1958, and the current application was reviewed in Refs. 2 and 3. This section provides an introductory perspective, required for subsequent sections of this paper. Fig. 1 illustrates the evolution of the geometry and pressure during injection. The initial stage consists of expanding radial shapes (point source) or elliptical shapes (line source) with decreasing pressure. This stage ends when vertical growth is restricted, from above and below, by competent stress barriers. During the second stage, growth is primary horizontal with increasing pressure. As the net pressure approaches the stress difference, of either barrier formation, the vertical height increases significantly and the net pressure asymptotically approaches the stress differences. The diagnostic log-log plot of net pressure vs.time indicates essentially pressure vs.time indicates essentially straight lines for these three stages. The case of initial radial growth was investigated and characterized into periods dominated by either fluid viscosity or rock toughness. An analysis of elliptical growth showed that, for the limiting case of small aspect ratios (small penetration relative to height), the Khristianovich-Geertsma-de Klerk. (KGD) geometry assumption was valid. The second stage, with increasing horizontal propagation and very limited vertical propagation and very limited vertical growth, follows the Perkins-Kem-Nord-gmn (PKN) assumptions. The pressure, Perkins-Kem-Nord-gmn (PKN) assumptions. The pressure, response for this case and subsequent deviations are characterized by the slopes of the diagnostic log-log plot, as Fig. 2 illustrates. For this figure, Conditions I and II-a correspond to Stages 2 and 3 of Fig. 1. The zeroslope Condition B of Fig. 2 results from inefficient extension when the formation pressure capacity, defined by the in-situ stress pressure capacity, defined by the in-situ stress state (Fig. 14.14 of Ref. 2), is reached. The approximate unit slope (Condition III-a) results from proppant at the fracture extremities, restricting extension. The negative slope, Condition TV, results from penetrating a sum barrier with the subsequent penetrating a sum barrier with the subsequent unrestricted vertical growth into a lower-stress formation. The ideal assumptions for Stage 2 (Fig. 1) and deviations (Conditions II-a and III-a, Fig. 2) are addressed in the following section. After injection, the fluid remaining in the fracture is lost to the formation. From the material balance and negligible fluid compressibility, the fracture volume, Vf, at shut-in is related to the injected volume, Vi, by Vf=n Vi. The proportionality parameter, n, is called the fluid efficiency. After parameter, n, is called the fluid efficiency. After shut-in, the volume lost, VLs, equals the decrease in fracture volume, Vf. For the case without proppant, as, for a calibration treatment, the volume lost between shut-in and closure, VLs (tc), equals the fracture volume at shut-in. A convenient ratio is the volume to volume lost during pumping, VLp, or pumping, VLp, or (1) Also, (2) (3) (4) and (5) where . The expression on the right side of Eq.1 is for no proppant and is the time to close. Eq. 4 expresses the change in fracture volume in terms of the change in average width and fracture area; Eq. 5 expresses the average width in terms of the net pressure at the well (is the fracture closure pressure). Eq 5 results from the elastic behavior of the fracture, to the net pressure, and the pressum gradient in the fracture from the fluid pressum gradient in the fracture from the fluid flow and rheology, characterized by . The fracture compliance, depends on the elastic moduli of the formation and a characteristic dimension. Both and can be defined for the idealized models appplicable to Stages I and 2 of Fig. 1. Combining Eqs. 3 through 5 provides (6) Eq. 6 identifies ideal assumptions required for a direct inference of the fluid loss (volume per unit fracture area,) from the change in wellbore pressure, . JPT P. 210

Abstract The disappearance of cement bond log response as a result of variations of downhole conditions has been observed in numerous wells. This observation has led to concern about the loss of proper zonal isolation. Stresses induced in the cement, through deformation of the cemented casing resulting from the variation of downhole conditions, are the cause of this damage. This paper presents an analysis of the mechanical response of set cement in a cased wellbore to quantify this damage and determine the key controlling parameters. The results show that the thermo-elastic properties of the casing, the cement and formation play a significant role. The type of failure, either cement debonding or cement cracking, is a function of the nature of the downhole condition variations. Such an analysis allows us to propose appropriate cement mechanical properties to avoid cement failure and debonding. We show that the use of high compressive strength cement is not always the best solution and, in some cases, flexible cements are preferred. Introduction The prime objective of cementing the annulus which is present between the casing and the formation is to provide zonal isolation of the formations which have been penetrated by the wellbore No fluid communication should develop during the life of the well between these various formations, whether they are saturated with water, oil or gas. and with the surface. However, even in situations where the cement was properly placed and initially provided a good hydraulic seal, the disappearance of zonal isolation with time is often observed. This disappearance is revealed, for example, by a gas migration problem which was not initially detected, or by the fracturation of a wrong zone during a stimulation treatment. The loss of the cement bond log response with time also creates some concern about the quality of the isolation. Laboratory studies have shown that stresses induced in the cement from the variation of downhole conditions, are the cause of this damage. Various processes can result in a variation of downhole conditions in a cased section of a wellbore These processes include the drilling of the wellbore, the perforation of the casing, and the stimulation and production of the reservoir. Drilling involves a variation of pressure, if the mud weight has been changed to drill the next section, and a temperature increase of the cased sections when the mud, which has been heated by the formation being drilled, returns to the surface via the annulus. Associated to the drilling process are the various pressure increases which result from integrity and leak off tests. Pressure increase during perforation follows the firing of the guns, and, although it is applied dynamically to the casing (cement is more resistant to dynamic loading than to static loading), can lead to cement damage. The amount of pressure increase during perforation is significant since values in excess of 6000 psi have been measured in laboratory experiments The increase of wellbore pressure during hydraulic fracture stimulation is more damaging to the cement sheath as the fluid injection lasts from minutes to hours. Increase of pressure and temperature during production concerns mainly the near surface casing sections, where surface pressure is increased from about atmospheric pressure to production pressure, and temperature is increased to about, in some cases, downhole temperature. The pressure variation usually only concerns the production tubing and therefore does not affect the cemented sections, unless a gas migration problem results in an annulus pressure increase. A temperature increase can also lead to pressure increase in the annuli following gas expansion, if the annuli are saturated with gas. Pressure decrease during production mainly affects the bottom of the hole where downhole pressure, which is controlled by the production rate, decreases from formation pore pressure to downhole production pressure. Finally loadings other than changes of wellbore pressure and temperature can be applied to the cement sheath during the life of the well. For example, an increase of the pressure on the external surface of the cement represents a situation where the formation loads the wellbore due to creep. P. 337^

Numerical modeling of gas hydrates can provide an integrated understanding of the various process mechanisms controlling methane (CH4) production from hydrates and carbon dioxide (CO2) sequestration as a gas hydrate in geologic reservoirs. This work describes a new unified kinetic model which, when coupled with a compositional thermal reservoir simulator, can simulate the dynamics of CH4 and CO2 hydrate formation and decomposition in a geological formation. The kinetic model contains two mass transfer equations: one equation converts gas and water into hydrate and the other equation decomposes hydrate into gas and water. The model structure and parameters were investigated in comparison with a previously published model. The proposed kinetic model was evaluated in two case studies. Case 1 considers a single well within a natural hydrate reservoir for studying the kinetics of CH4 and CO2 hydrate decomposition and formation. A close agreement was achieved between the present numerical simulations and results reported by Hong and Pooladi-Darvish (2003, “A Numerical Study on Gas Production From Formations Containing Gas Hydrates,” Petroleum Society’s Canadian International Petroleum Conference, Calgary, AB, Jun. 10–12, Paper No. 2003-060). Case 2 considers multiple wells within a natural hydrate reservoir for studying the unified kinetic model to demonstrate the feasibility of CO2 sequestration in a natural hydrate reservoir with potential enhancement of CH4 recovery. The model will be applied in future field-scale simulations to predict the dynamics of gas hydrate formation and decomposition processes in actual geological reservoirs.