bluuebunny/crossref_metadata_2025 huggingface dataset:
An Interpretation of the Displacement Behavior of Rich Gas Drives Using an Equation-of-State Compositional Model
Authors: Mansoori J. , Gupta S. P.
Published: December 2007

This paper presents the results of a compositional simulation study to investigate the relationship between the displacement mechanism, the minimum enrichment requirement, and the oil recovery efficiency for a rich gas system. The simulation results indicated that the displacement mechanism over a wide range of solvent enrichment was governed by a condensing/vaporizing process; however, the relative importance of the condensing or vaporizing mass transfer processes, and their impact on the overall displacement efficiency, was a function of the enrichment level. For displacements simulated at or above the slim tube minimum enrichment (ME) level (determined from the recovery breakover point on a recovery versus enrichment plot), recovery was high and the process behaved very similar to a classical condensing mechanism. Displacements simulated below the slim tube ME were less efficient; however, both condensing and vaporizing mass transfer processes contributed to the overall recovery efficiency. At enrichment levels considerably above the slim tube ME, the effect of the condensing mass transfer process on the displacement became less significant and the behavior approached that of a classical vaporizing mechanism.

The slim tube technique for determining the ME requirement based on simulation results was further compared with two other computational methods: one based on Hutchinson and Braun's multiple contact mixing,1 and the other based on displacement behavior at the limit of zero dispersion.2 For this rich gas system, the minimum enrichment level predicted by these methods was significantly higher than the slim tube ME and corresponded to conditions of thermodynamic miscibility development by a classical vaporizing mechanism. Despite such a high enrichment requirement needed to achieve thermodynamic miscibility, the oil recovery did not increase significantly beyond that achieved at the slim tube ME.

Simulation results for the condensing/vaporizing system were also compared with those predicted by a classical condensing mechanism. These comparisons showed that: a) for a classical condensing mechanism, the thermodynamic and the slim tube methods predicted the same minimum enrichment requirement; b) at low dispersion the two mechanisms showed similar displacement behavior; and c) higher values of dispersion had a bigger impact in reducing the displacement efficiency of the condensing/vaporizing mechanism compared with the classical condensing process.
Measurement and Correlation of Miscibility Pressures of Reservoir Oils
Authors: Eakin B. E. , Mitch F. J.
Published: December 2007

Minimum Miscibility Pressures (MMP) for 102 combinations of oils, temperatures, and solvents were observed with a Rising Bubble Apparatus. The data were represented with a 4.5% standard deviation by an equation which needs only the solvent composition, oil C7+ fraction molecular weight, and the pseudoreduced temperature. A slightly better standard deviation of 3.5% was obtained by extending Peng's procedure for critical points of mixtures to calculate MMP.
A Study of Remedial Measures for Water-Coning By Means of a Two-Dimensional Simulator
Authors: Pirson S.J. , Mehta M.M.
Published: December 2007

American Institute of Mining, Metallurgical and Petroleum Engineers, Inc.

This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.

Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

A computer program based on the Welge-Weber mathematical model to simulate water coding is developed. Computational characteristics such as rate of convergence, criteria for convergence, level of material balance error, sensitivity of convergence to iteration parameters, grid size and time step size are discussed.

The simulator is verified by studying the effects of various factors such as vertical to horizontal permeability ratio, mobility ratio between oil and water, specific gravity differential between the two phases and flow rate on the advance of a water-cone. The cone shapes and positions are drawn for each case and the results are found to agree with known phenomena.

The model is applied to the study of a stable cone height with known production rates and the results are compared with Muskat's approximate method. Muskat's prediction gives high values for stablized cone positions for reservoirs having a substantial water-oil transition zone.

The simulator is applied to study the relative effectiveness of remedial measures to water-coding such as injection of oil below the perforations, production of water from the underlying aquifer through a double string and the presence of a horizontal impermeable barrier such as a cement pancake.

A new method to prevent water-coning by circulation of oil as a hydraulic doublet placed at the production interval is investigated. It is found to be an effective remedial measure for water-coning problems. The oil doublet so formed is most efficient when its strength is about 20 per cent of the total fluid production.

Reinjection of oil into the reservoir suppresses cone growth in agreement with the Smith-Pirson conclusions. Selective production of water and oil from their respective zones reduces the cone growth, but it gives the same overall water -oil ratio at all times and large volumes of water need to be reinjected for disposal. However, the oil doublet technique appears to be a more suitable remedial measure.
Discount Rates, Cost of Capital, and Property Acquisition Evaluations
Authors: Miller R. J. , Vasquez R.
Published: December 2007

The purpose of this paper is to examine the role of the discount rate in determining the fair market value of a producing oil and gas property; to assess the validity of a discount rate based on a derived source and on an observed or market source, and to evaluate the relationship between discount rates obtained from these two sources. The derivation of a discount rate based on a Cost of Capital approach is compared to the observed effective rate-of-return obtained from analysis of actual producing property acquisitions to (1) determine if a rational relationship occurs between discount rates obtained from the two methods, and (2) how the discount rates obtained from the two methods may reflect changes in the oil and gas industry. The use of derived and observed discount rates in FMV analysis is examined and discussed, particularly as it applies to property acquisitions.
Restructuring of Natural Gas Markets by Regulations and Legislations
Authors: Kumar J.
Published: December 2007

As the natural gas industry in the United States started expanding, states started imposing regulations on the sale, transportation and distribution of gas. In the 1920's, the U.S. Supreme Court issued three famous decisions which spawned the birth of the federal regulation of interstate sale and transportation of gas. In 1938, the U.S. Congress passed the Natural Gas Act (NGA) which empowered the Federal Power Commission to regulate interstate commerce of gas. In 1954, the Supreme Court, in its Phillips Petroleum decision, imposed federal regulation on the wellhead prices of natural gas sold in the interstate market which eventually resulted in low prices and gas shortages in the 1970's. In 1978, the Congress passed the Natural Gas Policy Act (NGPA) which resulted in increased gas prices. The higher prices increased supplies and decreased demand, thus causing a gas surplus. The unprecedented gas surplus in the 1980's resulted in competition at wellhead but this competition could not be extended to the burnertip due to the monopoly ownership of the gas transportation and distribution facilities. In response to this situation, both federal and state regulatory agencies have issued a number of decisions during the last three to four years which are causing a revolutionary changes in the natural gas industry and it is expected that the competitive forces will play a bigger role than at any time in the past in the restructuring of the gas industry.
The Effects of Noise on Interval Correlation Methods Part I: Accuracy and Precision
Authors: Waid C. C. , Faraguna J. K. , Easton S. B.
Published: December 2007

Highly accurate estimates of displacements between dipmeter button curves are essential for computing dips of bedding surfaces. The Pearson product moment correlation coefficient has long been employed to estimate these displacements because it can reduce the effects of uncorrelated, additive noise. Other types of curve similarity measures, namely the L1 and L2 norms, semblance, and the phase correlation coefficient, have similar noise reduction capabilities. This paper reports the results of a comparative study of the effects of noise on the ability of these techniques to accurately estimate displacements. In addition, the effects of displacement magnitude as well as correlation interval length and search length were studied. These experiments indicate that phase correlation coefficient is by far the most accurate of these similarity measures in the presence of uncorrelated, additive noise.

Noise sequences, whose spectra were shaped to cover the range of noise processes encountered during well logging, were added to both real and artificial button data to achieve a wide range of signal-to-noise ratios. Each correlation method was used to estimate the displacements between the noisy curves. The probability of finding the exact displacement as well as the distribution of displacement error was computed.
Design and Evaluation of Pumpin Temperature Surveys for Detecting Cement Channels above Perforations
Authors: Bergren F. E. , Bradley D. A.
Published: December 2007

Movement of fluids in cement channels outside of well casing is a frequently-occuring problem in the production of hydrocarbons. This may result in cross-flow between formations, or fluids being injected into – or produced from – unintended formations. Although channels above perforations are sometimes suspected, their existence is often difficult to detect. An improved method of detecting channels above perforations was developed by computer simulation and correlation of field data. This method, the pump-in temperature survey (PITS), has been proved reliable with recent usage on producing wells at the Prudhoe Bay Field.

A wellbore simulation computer program was used to determine the thermal state of a well during a PITS assuming various combinations of pumped fluid inlet temperature, flowrate, and volume. An optimum volume of pumped fluid to achieve the required temperature depression at the perforations was thus determined. Also, relationships between easily-calculated and measured parameters and the interpretability of PITS logs have been determined. The most important variable in PITS design was found to be pumped volume. The success of a PITS log is also dependent on the temperature depression experienced at the perforations. These findings have been incorporated into design and logging recommendations.

The results of several successful PITS logs are summarized to illustrate the relationship of PITS log response to the existence of cement channels. This summary of log responses may be used as a guide to interpret future PITS logs.

The PITS logs run recently at Prudhoe Bay have shown that, in most cases, it is possible to determine if a channel above the perforations exists. Although a PITS designed to find a channel above the perforations requires substantial logging finesse, it is more economical than the alternatives (cement quality logs and radioactive-tracer logs).
A Technique for Evaluation of Hydraulic Fractures Using Quantitative Concentrations Derived from the Natural Gamma Ray Spectrum
Authors: Jackson C. E. , Gartner M. L.
Published: December 2007

Logging tools that record the entire natural gamma ray spectrum are designed to measure concentrations of the naturally occurring radioactive elements Potassium (K), Uranium (U), and Thorium (Th). Concentrations are determined by applying a device-dependent algorithm to the counts in three or more energy windows (regions of the spectrum).1 A similar technique is used to evaluate induced fractures where the fracturing fluid and/or the proppant is tagged with radioactive tracers (such as Scandium-46 or Iridium-192). The concentration of each tracer element after fracturing operations is used to determine the extent of the fracture network.

A sophisticated mathematical method is used to compute the calibration spectrum for each of the tracer elements in a range of environments. The Boltzmann transport equation is solved for the gamma ray flux at the detector surface and convolved with a detector response function determined by Monte Carlo simulation to obtain the spectra. Once properly calibrated, a spectral stripping technique computes quantitative concentrations for all radioactive isotopes in the formation.

Techniques for utilization of these concentrations is discussed. Several log interpretation examples illustrate the discussion.
Reservoir Modeling of Marginal Aeolian/Sabkha Sequences, Southern North Sea (U.K. Sector)
Authors: Martin J. H. , Evans P. F.
Published: December 2007

Sedimentological core description, log-facies interpretation and well correlation demonstrates the vertical heterogeneity but lateral homogeneity of Permian Rotliegend gas sands in the North Viking Field area. Here, marginal to the main dune belt, the sequence is strongly layered with a harsh permeability distribution.

Intercalated sabkha facies form potential vertical permeability barriers. It is inferred that these represent lacustrine transgressive horizons passing laterally into major first order bounding surfaces formed by the deflation of dune sands down to the water table. Even beds less than 0.5m thick are laterally extensive: detailed correlation has been achieved over a distance of 35km parallel to depositional strike, and 15km parallel to depositional dip.

These conclusions contrast with those of previous work carried out in this area, and differ from a generalised reservoir model for this environmental setting.
Pressure Transient Analysis of Wells with Finite Conductivity Vertical Fractures in Double Porosity Reservoirs
Authors: Cinco-Ley H. , Meng H. -Z.
Published: December 2007

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.
Well Test Intepretation for Naturally Fractured Reservoirs
Authors: Stewart G. , Ascharsobbi F.
Published: December 2007

An analysis of a large number of well tests in naturally fractured reservoirs has confirmed the validity of the pseudo-semi-steady-state model of matrix block support. This is due to interporosity skin as a result of fracture face alteration. Fracture network theory shows that wells in fractured reservoirs should exhibit a negative skin for an ideal connection to the fracture system. A new dimensionless derivative type curve for estimation of dual porosity parameters has been developed.
Single-Phase Flow Through Natural Fractures
Authors: Jones T. A. , Wooten S. O. , Kaluza T. J.
Published: December 2007

It is well known that for a single-phase fluid flowing between smooth parallel plates, the pressure drop is proportional to the cube of the aperture separating the plates. Some investigators2,3 have looked at the effect of surface roughness on flow using fabricated surfaces, induced fractures, or sawed surfaces and have found deviation from that law at small apertures. This paper presents new laboratory data for single-phase flow through open rough natural fractures.

Two types of petroleum reservoir rocks (sandstones and cherts) were used, each having a different surface roughness. Flow through both open and closed fractures is evaluated with apertures ranging between 0.002 to 0.0253 in. A technique for measuring apertures in-situ has been developed which avoids back-calculating apertures from flow data, as other investigators have had to do. Fluids with viscosities of about 1 and 18 cp were used.

At large apertures (0.0253 in), compared to the surface roughness, the cubic law is followed; at smaller apertures for rough fractures, deviation is seen. Transition from laminar to turbulent flow is smooth but is dependent on surface roughness for smaller fracture apertures. Critical Reynolds Number, the Reynolds Number where laminar flow ends, is seen to decrease with decreasing fracture aperture for rough fractures. Data are correlated using plots of friction factor versus Reynolds Number.
Techniques for Measuring the Electrical Properties of Sandstone Cores
Authors: Lewis M. G. , Sharma M. M. , Dunlap H. F. , Dorfman M. H.
Published: December 2007

Methods currently being used to measure the electrical conductivity of fluid saturated porous media are highly sensitive to various capillary and electrical effects. If these effects are not taken into account when making electrical measurements on cores, large errors in the computed values of the resistivity index (I) and the Archie saturation exponent (n) can occur.

Resistivity was monitored at 1 inch [25.4 mm] and 2 inch [50.8 mm] intervals along 6 inch [152.4 mm] Berea cores in order to observe electrical and capillary end effects. Computerized Axial Tomography (CAT Scan) was utilized to examine fluid distributions within the sandstone cores under water-wet primary drainage conditions. When the CAT Scan data was combined with electrical resistivity data, the magnitude of electrical contact resistances between the current electrodes and the core can be estimated as well as the saturation variation due to the capillary end effect. It was found that the contact resistances are substantial at low water saturations and in oil-wet cores.
Field Evaluation of a New Gelant for Water Control in Production Wells
Authors: Avery M. R. , Wells T. A. , Chang P. W. , Millican J. D.
Published: December 2007

A new chemical process for improving the performance of wells producing at high watercuts has been developed. This process is based on covalently bonding a medium molecular weight, cationic polyacrylamide with an organic crosslinking agent to form a three dimensional gel structure. Because the gel solution is hydrophilic, it is preferentially emplaced in the zones of high water saturation and high water permeability. Gelation rate is controlled by adjusting the pH of the gel solution. Once the gel structure has developed, effective water permeability is reduced with little impact on the effective oil permeability.

This paper reports on the results of over 30 wells treated using the new process. Substantial decreases in water production have been realized and, in some cases, significant amounts of incremental oil recovered. The evaluation of these treatments helps demonstrate the working mechanisms of the gelant and the optimum field application of the process.
A New Approach for Mathematical Modeling of Formation Damage Due to Invasion of Solid Suspensions
Authors: Kumar T. , Todd A. C.
Published: December 2007

Formation damage due to invasion of solid suspensions has been studied by several investigators and some modelling approaches have also been reported in the literature, most notably the application of effective medium theory and percolation theory in two and three dimensional capillary networks.

This paper presents a new mathematical model, which is based on mass balance of particles flowing through the porous media. The linear as well as radial forms of the model are described.

Although the differential equations derived take the general form of diffusion-convection equations, the marked difference is in terms of the suitability of the model to apply for variation of parameters such as particle concentration in the fluid, injection rate, density of solid particles, against the depth and time of invasion.

The results of the simulation run agree reasonably well with the experimental damage data obtained on 80mm sandstone core plugs using a multi-port pressure-tapped core holder.

The radial form of the model can be used to simulate formation damage in water injection wells whereas the linear model can simulate damage in filtration systems involving industrial water purification or oilfield water injection treatment.
The Effects of Fluid Preconditioning and Test Cell Design on the Measurement of Dynamic Fluid Loss Data
Authors: McGowen J. M. , McDaniel B. W.
Published: December 2007

Accurate modeling of dynamic fluid loss in the laboratory has increased in importance as the art of computer simulation of fracturing treatments reaches higher levels of sophistication. Three dimensional (3-D) design simulators often require fluid loss behavior of fracturing fluids to be described more explicitly than is achieved using most previous laboratory testing procedures. Even two dimensional (2-D) simulators can only be as valid as the data used in their calculations, and the prediction of fluid leak-off to the reservoir is one of the most critical calculations. Although the use of dynamic fluid loss equipment is not new, it has been found that often overlooked procedural conditions can alter the results obtained.

Some earlier investigators recognized the need for using representative fracture shear rates within the test cell, but failed to consider the importance of fluid shear history prior to entering the cell. This shear history (termed "fluid preconditioning") can significantly affect fluid loss data, even if other factors are held constant. Also cell entrance effects and flow patterns across the core face may lead to inconsistent results when compared to other cell designs. In the work reported in this paper, both test cell configuration and fluid preconditioning were investigated to determine their influence on fluid loss results. More than 200 dynamic fluid loss experiments using two different test cells and two types of preconditioning flow loops have been conducted to investigate the influence of fluid preconditioning and test cell design. The effect on fluid loss resulting from incorporating sand slurries (up to 5 lb/gal) was also investigated.
Field and Laboratory Experience in Stimulating Ekofisk Area North Sea Chalk Reservoirs
Authors: Snow S. E. , Hough E. V.
Published: December 2007

This paper describes field and laboratory work carried out recently to better understand stimulation behavior in Ekofisk Area North Sea chalks. Laboratory work has been done to study chalk hardness, chalk mechanical properties, and the development and stability of propped and acid fracture conductivity. The laboratory work, combined with a review of available stimulation techniques for these formations, shows that stimulations in most of these reservoirs can be optimized with a pseudo limited entry acid fracture technique. Cased hole logging, pressure transient tests, and other field data have been utilized to optimize the design of these stimulations. The best treatments have resulted when several widely spaced clusters of perforations are treated in stages using ball sealers for diversion.
Use of Low-Density, Gravel-Pack Material Improves Placement Efficiency (Part 2)
Authors: Hudson T. E. , Martin J. W.
Published: December 2007

The success of a gravel-pack completion depends on placement of gravel in the perforation tunnel area and the screen-casing annulus. Wellbore deviation is one of the predominant factors affecting gravel placement. As wellbore deviation increases, the gravitational forces and carrier fluid limitations may result in gravel settling (duning) and an incomplete packing of much of the perforation tunnel area, as well as a premature screenout of the screen-casing annulus.

A completion technique is introduced that eliminates problems associated with gravel settling. The technique uses buoyancy forces to counter the gravitational forces on the gravel particulate. Particulate settling is minimized by decreasing the ratio of the particulate density (Dp) to the base fluid density (Dc). Verification of the concept includes test results from a gravel-pack model. The model is 18 ft long with an inside diameter (ID) of 6.2 in., a screen and blank pipe size of 2-7/8 in., and a working pressure of 1,000 psi. The blank pipe length is 6 ft and the screen length is 12 ft. There are 20 perforations that include a chamber to simulate a void space behind the casing.

Test results include gravel-pack efficiency for variations in base fluid properties, wellbore deviation up to 90° (horizontal) and particulate density/ base fluid density ratios (Dp/Dc) from 2.65:1 to 0.8:1. Recommendations for a treatment technique and low-density particulate specifications also are included.
Effect of Concrete and Berea Strengths on Perforator Performance and Resulting Impact on the NEW API RP-43
Authors: Behrmann L. A. , Halleck P. M.
Published: December 2007

A recent work advanced a simple and economical audit method for controlling the field performance of shaped charge perforators. Fundamental to the method are rigorous specifications which will assure reliable, consistent quality control targets which provide performance data translatable to API RP-43 data. Results of an extensive test program showed decreases in perforator penetration with increasing strength of the target materials. Furthermore, the rate of penetration decrease was observed to be dependent bn charge type, target material, and target boundary conditions. Implementation of the referenced perforator performance audit and proposed changes to API RP-43 have challenged past concepts with respect to Berea target consistency, specifications, and translation factors.

The objective of the proposed API RP-43 is to specify recommended test procedures for evaluating the performance of perforating equipment. The desire of the API is to test gun systems in a consistent surface target with properties similar to a sandstone reservoir rock. It is believed that the use of a Berea sandstone target will ease the translation between surface and downhole performance. Thus, the issue addressed in this paper is the determination of perforator performance versus quality control and API Berea properties, their resulting translation factors, and API target specifications.

The present work expands the earlier investigation and focuses on specific issues of: –Determination of the proper Berea property to correlate with penetration.–Selection procedures and specifications for API RP-43 Berea targets.–Translation of quality control Berea data to proposed API RP-43 Berea slab target data. – Translation of API Section I concrete data to proposed Berea slab target data.
Stability and Failure of Spherical Cavities in Unconsolidated Sand and Weakly Consolidated Rock
Authors: Perkins T. K. , Weingarten J. S.
Published: December 2007

The conditions necessary for stability or failure of a spherical cavity in unconsolidated sand or weakly-cemented rocks have been studied. Experiments using physical models have utilized weakly-cemented synthetic, porous rocks. As external confining pressure was applied to the rock, a shear failure region was induced around the cavity. When fluid flowed through this system at increasing rates, the outer boundary of the shear failure zone was calculated to have increased, and a region of disaggregated solids was created adjacent to the cavity.

Equations for convergent flow of a fluid towards a cavity predict that tensile stresses tend to be induced near the cavity face. These tensile stresses pull the pack of disaggregated solids apart, causing it to dilate. A region of material at the limit of tensile stability will be formed. The radius of this zone will expand until the system becomes stable with no induced tensile stress being greater than the slight adhesion provided by an immobile phase, if present.

As the flow rate is increased, the shear failure zone and the zone of material at the limit of tensile stability propagate farther away from the cavity. To preserve stability, the permeability of the sand at the cavity face must progressively increase by further dilation. When the cavity face porosity has increased to some critical porosity, mechanical interaction of the particles is insufficient to keep the pack from becoming fluid-like and being produced into the cavity.

For low permeability models, pressure drop data indicated that average permeabilities in the shear failure zones were greater than the permeabilities of the cemented rock in the surrounding elastic regions. When flow rates increased sufficiently, the shear failure zones expanded to the outer boundary of the models; total collapse of the models ensued and large quantities of sand were produced.

Some data for cavity failure in unconsolidated sands, which are available in the literature, as well as the experimental data for weakly-cemented synthetic rocks, have been analyzed using the equations and concepts developed in this paper. For mixtures of fracture proppant sand, for some coarse natural sands, and for disaggregated solids created around a cavity in the weakly-cemented rocks, the critical porosities at the cavity face (when the cavities were barely stable) were estimated to be in the range of 40% to 53%. An apparent unit cohesive strength of a few tenths of a psi was manifested, perhaps due to mechanical interlocking of the individual grains.
The Effect of High-Pressure Gradients on Gas Flow
Authors: Temeng K. O. , Home R. N.
Published: December 2007

The flow of gases through homogenous porous media is governed by non-linear differential equations when expressed in squares of pressure. In the usual analysis the equations are linearized by assuming small changes in pressure, and thus in fluid properties. The results thus yield a linear relationship between pressure drop and flow rate.

At high flow rates, experiments and well tests show deviations from the behavior predicted by the linear theory. These deviations are usually attributed turbulence, inertial effects and other factors, all of which are usually thought to render Darcy's law invalid. Quadratic and higher order equations are then used to characterize this type of flow, with the nonlinear coefficients determined empirically. However, this study has found that an alternative to using empirically determined non-Darcy effects is to correctly account for the consequences of the assumptions used to linearize the flow equations.

In this study the flow of real gases through porous media was analyzed by incorporating some of the nonlinearities present in the flow equations. It is shown that deviations from linearity, of the form observed in field tests and in laboratory experiments, can result from the nonlinearities inherent in the basic formulation. Thus, a lack of proportionality between pressure drop and flow rate does not necessarily imply or indicate a deviation from Darcy flow.

In laboratory examples it has been possible to correctly determine the observed Forchheimer coefficients, based on the derivation from first principles. This is achieved with only Darcy's law, without reference to any non-Darcy effects.
A Method for Determination of Permeability, Skin, and Turbulence Factor From an Open-Flow Potential Test
Authors: Beck F. E. , Lee R. L.
Published: December 2007

A method is presented by which permeability, skin, and turbulence can be analyzed by interpretation of an open flow potential test. The method is based on a variation in the method suggested by Odeh and Jones, and allows a direct calculation of the turbulence factor from well test data. The method also utilizes the continuous record of bottom hole pressure now recorded for many well tests.

To facilitate interpretation of high permeability data, an optimization scheme is used to arrive at values of permeability, skin, and turbulence factor. Data from an open flow potential test and subsequent build-up are presented; analysis results in a favorable comparison. The optimized permeability, skin, and turbulence values also predicted, with reasonable accuracy, the measured well performance.
Analysis of the Effect of Pressure Data Frequency and Accuracy on the Calculation of Aquifer Influence Functions
Authors: Eicks T. D. , Wattenbarger R. A. , Startzman R. A.
Published: December 2007

The performance of many Gulf Coast gas reservoirs are influenced by water influx from aquifers of unknown size, shape, and properties. Gajdica, et al. (1987) developed an automatic method for computing the performance of an aquifer by determining an Aquifer Influence Function (AIF). The current work investigates the use of Gajdica's AIF method to analyze the scheduling of pressure buildup tests and the effect of errors in this pressure data.

Test cases were constructed in which the AIF was known. A series of computer runs showed that the AIF is more accurate if more pressure data are available. No conclusions were reached about the spacing of the pressure data, but it seems that evenly spaced pressure data is desirable.

More importantly, a technique for detecting and correcting errors in pressure data was developed with the AIF method. The technique clearly shows where pressure errors occurred. Corrections to these pressure errors can then be made. This technique was applied to an actual field case and shows promise as a method for correcting pressure errors for this type of gas reservoir/aquifer system.
A Complex PVT Modeling Study
Authors: Brakstad F. , Bu T. , Bjørlykke O. P. , Mykkeltvedt K.
Published: December 2007

Oseberg, which is one of the major Norwegian North Sea oil fields, will be produced by injection of associated gas and gas supplied through a pipeline from the Troll field. The two gases have different compositions and neither of them is in thermodynamical equilibrium with the in situ oil. By static multiple contact experiments it has been demonstrated that large component exchanges will occur. Other factors of importance for the reservoir process is a pronounced compositional variation with depth in the oil zone and the existence of a gas cap.

A number of relevant measurements and PVT experiments (constant composition expansions and multiple contacts) have been performed in order to obtain data for tuning a qubic Equation of State (EOS) PVT program which is composed of a PVT model and a set of equations. The PVT model consists of a set of well defined pure and pseudo components. Since the PVT program will form the basis for dynamical compositional simulations all the fluids involved must be characterized within a fixed component system. Various approaches have been tried, among them a multivariate lumping scheme.

After regression upon 49 experimental data from 4 fluid samples, four PVT models were obtained; two with 6 and two with 22 components. The paper will discuss the choice of experiments and the ideas behind the selection of models, including the choice of pseudo components and regression variables.
Simplified Compositional Formulation for Modified Black-Oil Simulators
Authors: Whitson C. H. , da Silva F. , Søreide I.
Published: December 2007

This paper gives an evaluation of simplified compositional PVT formulations presently being used in modified black-oil reservoir simulators. In particular we consider a promising four-component general black-oil (GBO) formulation. This formulation has been successfully used in full-field simulations of several North Sea reservoirs containing near-critical fluids with composition that varies areally and with depth. The four "components" used in the GBO formulation are:

non-volatile surface oil volatile surface oil surface hydrocarbon gas injection gas (e.g., N2)

This formulation also models revaporization in reservoirs undergoing dry gas and/or non-hydrocarbon gas injection.

We first review the standard black-oil (BO) model and the modified black-oil model (MBO) based on solution oil-gas ratio (rs). Next, the GBO is introduced for reservoirs where only depletion is considered and therefore the injection gas component is not present. Finally, the four-component GBO formulation is developed for reservoirs undergoing gas injection and where the initial fluid composition may vary throughout the reservoir.

The GBO model requires PVT properties of hypothetical "binary" mixtures which are used to obtain actual fluid behavior. In the appendices we give methods for calculating these binary PVT properties based on correlations, material balance equations, and non-linear regression.
Laboratory Investigation of Inertial Flow in High-Strength Fracture Proppants
Authors: Pursell D. A. , Holditch S. A. , Blakeley D.
Published: December 2007

High velocity fluid flow down hydraulic fractures will create pressure gradients that are proportional to the square of the velocity. As such, Forchheimer's equation, rather than Darcy's law must be used to correctly' estimate the pressure gradients near the wellbore and, consequently, the flow behavior of the hydraulically fractured well. To properly use the Forchheimer equation, one must know the value of β, which is the inertial flow coefficient. Cooke measured values of β for various sizes of Brady sand at several different closure pressures.

Cooke's correlation has been widely used in the industry but we have found that the correlation did not span the permeability range needed for all situations. Specifically, data are needed to estimate the pressure gradients of gas flowing through high strength, high permeability, man-made proppants. We also need the inertial flow data for sand that has been severely crushed,

A laboratory system has been constructed to investigate high velocity flow through fracture proppants. From test data, both proppant permeability and the inertial flow coefficient can be computed. The proppants tested included 12–20 and 20–40 mesh samples of Brady sand, Interprop Plus, and Carbolite. An improved correlation of inertial flow coefficient as a function of proppant permeability and initial mesh size has been developed using our laboratory system. The results indicate that the inertial flow coefficient depends upon the initial mesh size of the proppant, and is independent of the proppant type.

Grain size distribution was found to be a factor controlling the inertial flow coefficient for a given fracture proppant. It was found that different samples with similar permeabilities and inertial flow coefficients also had similar grain size distributions.

A variation in the pore pressure of the nitrogen used in the experiments was shown to have a significant effect on the inertial flow coefficient. The permeabilities calculated from the Forchheimer equation exhibited the same trend of decreasing permeability with increasing pore pressure as the Klinkenberg relationship for Darcy flow. Slip flow was found to influence the results significantly at Reynolds Numbers below 0.1.
Fatigue Reliability Analyses of Fixed Offshore Structures
Authors: Wouts M. A. , van der Graaf J. G. , Vrouwenvelder A. W. C. M.
Published: December 2007

The results of fatigue analyses of fixed offshore structures are very sensitive to the description of the applied loading and the strength of the structure. Conservative values are commonly incorporated in the analyses on the account of uncertainties in regard to pertinent parameters. Hence, a structure can be designed with an acceptable classical factor of safety having, however an unknown probability of fatigue failure. This paper describes a fatigue damage calculation method which accounts explicitly for the uncertainties of the input parameters and thus provides a measure of the probability of fatigue failure. Results of case studies are presented to demonstrate the rationale of the method.
Horizontal Drilling and Completion: Denmark
Authors: Andersen S. A. , Hansen S. A. , Fjeldgaard K.
Published: December 2007

The application of horizontal drilling technique to improve production performance from selected tight chalk reservoirs in the Danish sector of the North Sea has shown to be technically feasible and economically viable.

Maersk Oil and Gas has drilled and completed three horizontal wells with horizontal drainhole sections ranging from 1000 feet to 3000 feet and with displacement of some 9000 feet from the wellhead platform slot.

The essential early planning aspects leading to evaluation and solution of preferred options are discussed. Modifications to the approach adopted as experience is gained and a generalised overview of problems, solutions and costs is included.
Prediction of Laminar and Turbulent Friction Pressures of Cement Slurries in Pipes and Centered Annuli
Authors: Guillot D. J. , Denis J. H.
Published: December 2007

Friction pressures of different cement slurry formulations with properly characterized rheologyhave been measured in a wide variety of flow situations, including laminar (20 to 1000 s-1) and turbulent (2000 <Re< 10000) flow regimes. Tests were performed in pipe and concentric an- nular geometries, using a pilot-scale rig.

In laminar flow, it was established in a previous publication that pipe flow friction losses of cement slurries can be reliably predicted from rotational viscometer measurements made inthe shear rate range of the actual pipe flow. In this paper it is shown that valuable predictionscan also be obtained for concentric annuli, at least when the radius ratio (inner/outer) is greater than 0.3, if the geometry is approximated by a rectangular slot.

Pipe flow experimental data obtained in the turbulent flow regime are compared to several existing models. A modified Dodge and Metzner approach to the problem was found to give the best agreement with the measurements. For concentric annuli, a similar procedure is shown to be acceptable when used with the rectangular slot approximation. Reasonable agreement is found between model predictions and experimental results.

For both flow regimes, the proposed method is no more complicated and is proved, for most field situations, to be much more accurate than the API procedure in predicting pressure drops.
Efficient Use of Locally Refined Grids for Multiphase Reservoir Simulation
Authors: Ewing R. E. , Boyett B. A. , Babu D. K. , Heinemann R. F.
Published: December 2007

Three-dimensional, multiphase flow problems are solved on static, composite grids. The composite grid consists of a global, rectangular coarse grid and a set of locally refined patches around active wells or other areas with important local flow properties. Curvilinear (locally orthogonal) refinements can be utilized to approximate radial or near-radial flow around wells if such flow is assumed to be appropriate. More general localized refinement can be utilized otherwise. Finite differencing is presented which connects the local and global grid cells in an accurate manner.

Other methods for composite grid applications which have appeared in the SPE literature generate linearizations which have lost their banded structure and must utilize corresponding solution algorithms that are extremely difficult to vectorize for efficient solution. Preconditioned iterative techniques will be discussed which allow easy implementation of the composite grid techniques in existing simulators with full vectorization capabilities.

Pressure calculations in a single-phase flow problem with a distribution of injection and production wells exhibit excellent agreement between numerical calculations on locally radial grids and analytical solutions. Water and gas coning results for a single well also show very good agreement between computations on a hybrid grid and a circular cylindrical grid. This indicates the potential for incorporating coning models around any well in a full field-scale application without destroying the efficiency of the original simulator.
Stability Analysis and Switching Criteria for Adaptive Implicit Methods Based on the CFL Condition
Authors: Russell T. F.
Published: December 2007

Adaptive implicit methods seek an efficient middle ground between IMPES and fully implicit time stepping. The principal issue in implementation of these methods is the switching criterion that determines whether a given unknown is implicit or explicit. We develop and justify a criterion based on the Courant-Friedrichs-Lewy (CFL) stability condition. This could also be used for time-step control in IMPES models by indicating the maximum stable time step.

First, we analyze simple problems theoretically and find that adaptive implicit stability, like fully explicit stability, depends on a CFL condition. Next, we develop a switching criterion for a black-oil model and indicate how it could be extended to compositional simulation. The CFL-based criterion involves quantities that an implicit Jacobian must already compute, so its use costs virtually nothing. Each unknown has its own CFL number at every outer Newton iteration, so any combination of implicit and explicit unknowns is possible and a given unknown may switch back and forth through time.

While discussing the simple problems, we analyze and compare three adaptive implicit methods that have been suggested in the literature. One of the methods yields better answers by reducing numerical dispersion. Also, its CFL restriction for practical calculations is looser than those of the other methods, allowing it to make more unknowns explicit.