Formation Volume Factor Research Articles

Correlating the PVT Properties of Nigerian Crudes

Existing correlations for predicting solution gas oil ratio, Rs, and oil formation volume factor, Bo, gave standard deviations as high as 50 and 12 percent, respectively, for Nigerian crudes. New correlations developed using 503 Pressure-Volume-Temperature (PVT) data points from 100 Nigerian crude oil reservoirs of the Niger Delta Basin are presented. The correlations for Rs and Bo predict values from different reservoirs within 6 and 2 percent standard deviations, respectively, and will apply to crudes of specific gravity range 0.811 to 0.966. These correlations are applicable to other crudes with characteristics similar to those of Nigerian crudes.

Shape Factor, CA, Expressed as Skin, sCA

Summary This work presents the conversion of the shape factor, CA, to a pseudosteady-state skin term, sCA. When the shape factor is expressed as a skin term, it becomes easier to see the effect that a well placement in a given drainage area will have on the wells performance. Skin factors for published drainage shapes and well locations are given. Discussion In attempting to calculate interference effects of well locations on production forecasts, it was found very convenient to express the shape factor, CA, as a pseudosteady-state skin term, sCA. When using pseudosteady-state flow pseudosteady-state skin term, sCA. When using pseudosteady-state flow equations, the effect of a well not located in the center of a radial or square drainage area becomes immediately apparent when the shape factor is expressed as a skin term. The general pseudosteady-state equation in terms of CA for oil, gas, or water can be written as ..........................................(1) By using an effective drainage radius, r,', to maintain an equivalent reservoir volume ..........................................(2) and the shape factor for a well at the center of a circular drainage area (CA =31.62), we can obtain the familiar radial flow pseudosteady-state equation ..........................................(3) Introducing a reference shape factor term, we can write ..........................................(4) ..........................................(5) Defining a pseudosteady-state skin factor, sCA, as ..........................................(6) we have, referencing to the center of a circle (the classic analytical solution) with CA, ref = 31.62, ..........................................(7) or, referencing to the center of a square (field and model situations) with CA, ref = 30.8828, ..........................................(8) Values of scA referenced to the center of a circle or square are tabulated in Table 1. Values of CA in Table 1 were obtained from Ref. 1 Constant wellbore pressure production forecasts for wells not in the center of a circle are made conveniently by using the concept of effective wellbore radius with and from Ref. 2 and . Nomenclature A = drainage area, ft2 [M2] B = formation volume factor CA = shape factor D = nondarcy flow constant JPT February 1985 p. 321

Laboratory Design of a Gravity-Stable Miscible CO2 Process

Summary In dipping reservoirs, such as those of the Louisiana gulf coast area, tertiary oil can be recovered by gravity-stable miscible CO2 solvent floods. Laboratory design of gravity-stable floods requires extensive experimental studies to select the proper composition and size of the injected CO2 solvent slug. In a gravity-stable process the injected CO2 solvent slug must be less dense than the oil and water under reservoir conditions. and the injected drive gas must be less dense than the CO2 solvent slug. Laboratory experiments showed that the CO2 solvent slug can be tailored to achieve the density required for a particular gravity-stable application by the addition of methane. Additional studies demonstrated that, if required, various hydrocarbons can be added to the CO2 solvent slug to ensure miscibility with the reservoir oil. Studies were performed to determine density and viscosity of the oil, CO2 solvent, nitrogen. and CO2 solvent/oil mixtures under reservoir conditions. A number of displacement tests at reservoir conditions were conducted in a 12.19-m [40-ft] slim-tube apparatus to determine the miscibility of various CO2 solvent mixtures with reservoir oil. Further floods were produced under reservoir conditions in a 3.66-m 112-ft] sandpack system. These floods were conducted at velocities less than the critical velocity to prevent growth of viscous fingers. The results show that after miscibility was achieved, the injected CO2 solvent mixture effectively removed all the residual oil left after waterflooding. The 3.66-m [12-ft] sandpack floods also provided data to determine dispersion parameters for the leading and trailing edges of the CO2 solvent slug. This information was used to estimate the CO2 solvent slug size for Texaco's gravity-stable CO2 solvent miscible flood in its Bay St. Elaine field, Terrebonne Parish, LA. Introduction A gravity-stable miscible CO2 process can be established in a dipping reservoir by updip injection of a properly designed CO2 solvent. Gravitational forces will stabilize the flowing front because of the density difference between the less dense injected CO2 solvent and the more dense displaced oil and water. A gravity-stable miscible CO2 process was designed at Texaco's Bellaire (TX) Research Laboratories for use in an EOR project at the Bay St. Elaine field. Terrebonne Parish, LA. The project is being conducted in the Miocene 8000 Foot Reservoir E Sand Unit (RESU). Table 1 presents sonic key reservoir data. Reservoir E is bounded on two sides by faults and is truncated updip by an unconformity. This reservoir, with its 36 degrees dip and confined nature. was determined a good EOR candidate for a gravity- stable CO2 miscible flood. Fig. 1 shows a cross section of Reservoir E between the CO2 Injection Well 22–26 and one of the downdip producers, Well 22–5. From the outset, the oil-recovery process envisioned was an updip injection of a CO2 solvent slug, followed by nitrogen drive gas. Once miscibility is established, an oil bank is formed, followed by an oil/CO2 solvent transition zone, CO2 solvent, the CO2 solvent/drive fluid (nitrogen) transition zone, and finally pure drive fluid. Various laboratory studies were performed to design and implement a gravity-stable process in the Bay St. Elaine field. These studies provided the necessary data to design the field project and to evaluate its feasibility and potential success. The laboratory studies conducted to obtain the design data for this project consisted of (1) a PVT study of the reservoir oil, (2) the CO2 solvent PVT properties at reservoir conditions, (3) the miscibility of the CO 2 solvent with reservoir oil at design conditions in slim-tube displacement tests, (4) the phase behavior of the CO2 solvent/oil mixture, and (5) sandpack floods to determine longitudinal dispersion coefficients and coninn miscible displacement of the reservoir oil by the selected CO2 solvent-that is, to determine linear displacement efficiency. This paper discusses each study. Laboratory Studies Reservoir Oil PVT Study. A PVT study of the Bay St. Elaine reservoir oil was performed to determine solution gas/oil ratio (GOR), bubblepoint pressure, formation volume factor (FVF), density. and viscosity as a function of pressure. For this project, the density and viscosity were the most important properties because of the basic design criteria for a gravity-stable flood. In late 1978, existing wells in the project area and adjacent segments were either off production in the 8000 Foot Sand or were not completed in this sand. Available wells producing from the 8000 Foot Sand in the nearby Segment 850 were on gas lift and could not be used to obtain an uncontaminated reservoir oil sample. JPT P. 111^

Fluid-Bearing Capacity of Strandline Sand Deposits--Implication for Hydrocarbon Exploration: ABSTRACT

The fluid-bearing capacity of the Holocene coastal sand deposits of central South Carolina was determined in order to estimate their potential oil-in-place reservoir capacity. These sand bodies, which vary considerably in size, thickness, shape, and continuity, were deposited in a variety of depositional settings including barrier islands, tidal deltas, exposed sand flats, tidal sand ridges, and tidal point bars. Minimum potential sand thickness and conservative mud cutoff values of 10-15% were used to define each sand body type. Average thickness values ranged from 20 ft (6 m) for barrier islands to 15 ft (4.5 m) for exposed sand flats. Within the study area, barrier islands have average sand volumes of 1.3 × 105 acre-ft (1.6 × 108 m3 /SUP>), and tidal delta sands average 1.0 × 105 acre-ft (1.2 × 108 cm3). Potential oil reserve values averaged 7 million bbl for individual barrier islands and 5 million bbl for individual ebb-tidal deltas. If the Holocene sand deposits of the central 50 mi (80 km) of the South Carolina coast were preserved in place, 150-200 million bbl of oil could be contained within the reservoir-quality sands. Of course, these values represent only one small segment of geologic time, approximately 5,000 years. These calculations were based on typical reservoir characteristics and recovery factors found in Cretaceous sandstones buried at 5,000 ft (1,500 m) in the Rocky Mountain area. Average reservoir values used included porosity of 25%, oil saturation of 65%, formation volume factor of 1.3, and 10% of the sand body occupied by hydrocarbons. A better understanding of these strandline sand deposits could improve exploration and future development of these significant, potentially oil-bearing sands. End_of_Article - Last_Page 485------------

Evaluating Constant-Volume Depletion Data

Abstract This paper presents methods for evaluating constant volume depletion (CVD) data obtained from experimental analyses of gas condensates and volatile oils. Theoretical and practical developments are supported by experimental data from a North Sea gas-condensate fluid. The three major contributions of the work are:presentation of material-balance equations to calculate fluid properties from measured CVD data,a simple method for calculating black-oil formation volume factors and solution GOR's using material-balance results and a separator flash program, andinvestigation of the Peng-Robinson (PR) equation of state (EOS) as a tool for matching measured PVT data and studying vapor/liquid phase behavior during CVD. Introduction CVD experiments are performed on gas condensates and volatile oils to simulate reservoir depletion performance and compositional variation. Measured data can be used in a variety of reservoir engineering calculations, among the most useful being material-balance calculations, generating black-oil PVT properties and, more recently, the tuning of empirical EOS. All these applications are addressed in this paper. Few engineers are aware of useful fluid properties that can be derived from CVD data--e.g., liquid composition (and therefrom K-values), density, and molecular mass of the C7+ fraction, vapor density, and total system molecular mass. Only experimental CVD data and simple material-balance equations are used to calculate these data. A procedure outlining these calculations was first presented by Reudelhuber and Hinds. Their description, however, is somewhat difficult to follow and not extensively known or used by petroleum engineers. The material-balance relations are presented here in equation form using current SPE nomenclature. Based on material-balance-derived properties, a method is proposed for calculating black-oil PVT properties--i.e., FVF's and solution GOR's used in two- phase flow equations and reservoir material balances. The method was first suggested by Dodson et al. in 1953 for solution-gas/crude-oil systems. Their method, however, requires expensive and time-consuming liquid sample removals and experimental flash separations. The proposed method follows the Dodson et al. procedure but uses experimentally determined vapor corp. positions and material-balance-derived liquid compositions together with a multistage separator flash program. PVT properties calculated using this method are compared with those predicted by the PR EOS. Though more complicated, empirical equations of state are also used to evaluate CVD data. Several investigators have used the PR EOS to simulate PVT studies of light gas condensates and crude oils. Unfortunately most studies have emphasized K-value predictions instead of volumetric predictions, and most have avoided systems operating near the critical point. Results have varied considerably, depending on which properties are compared. Conrad and Gravier propose a method to improve liquid-density estimations by adjusting properties of the heaviest-plus fraction (boiling point and methane interaction coefficient). Firoozabadi et al. studied another lean gas condensate and found that by adjusting only the methane-heavy fraction interaction coefficient, the PR EOS highly overestimated liquid volumes. About 30 CVD studies performed by commercial and private laboratories were analyzed using the material- balance approach. JPT P. 610^

The Accuracy of PVT Parameters Calculated From Computer Flash Separation at Pressures Less Than 1,000 psia

Introduction Standing derived a set of equations that fit the equilibrium constant data of Katz and Hachmuth at pressures less than 1,000 psia (6.895 MPa) and pressures less than 1,000 psia (6.895 MPa) and temperatures below 250 degrees F (121 degrees C). A standard deviation (SD) of 3.5% between calculated and chart K values is reported by Standing. Not reported, however, is the accuracy of the Katz and Hachmuth K values applied to reservoir fluids of various paraffinicities and containing significant amounts of nonhydrocarbons. Because the data of Katz and Hachmuth were for an Oklahoma City crude oil containing no nonhydrocarbons, it was necessary to investigate their general applicability. A separator flash program was developed that incorporates the Standing K-value equations. The program was used to analyze 15 crude oils from various regions of the world, some containing substantial amounts of nonhydrocarbons. Flash parameters were calculated and compared with experimental values obtained from a PVT analysis of the fluid samples. GOR, average gas PVT analysis of the fluid samples. GOR, average gas gravity, stock-tank oil gravity, and bubble-point formation volume factor were used in the comparisons. Flash Program Description Our vapor and liquid equilibrium calculations involved use of the Katz and Hachmuth K values fitted by Standing. The algorithm used for calculations is described by Standing. The basic equation for fitting K-value data given by Hoffman et al. was used in this study: .......................(1) where coefficients a and c are functions of separator pressure. Psp is measured in psia, and F is a pressure. Psp is measured in psia, and F is a characterization factor. Equations for constants a and c appear in Ref. 1. The characterization factor, F, as defined by Hoffman et al., is ........................(2) where separator temperature, Tsp, is in R, Tb is the average boiling-point temperature in R, and coefficient b is defined for the pure components C3, iC4, nC4, iC5, nC5, and C6 as ........................(3) All other fractions except C7+ (i.e., C1, C2, CO2, N2, and H2S) have modified values of b and Tb, and these values can be determined by the procedure outlined in Ref. 1. The K value for the C7+ fraction was determined by the equation .............................(4) where KC7 was calculated as a pure component. Ref. 1 provides an alternative method to determine KC7+. This provides an alternative method to determine KC7+. This method was not available to the authors at the time this study was conducted. We recommend that the procedure given in Ref. 1 be used to determine KC7+. A check was made to see what, if any, error resulted from using Eq. 4. It was found that there is no significant loss of accuracy in calculated flash parameters unless the oil contains a large C7+ fraction (greater than 0.70). JPT p. 1811

Carbon Dioxide Flooding-fundamentals

Introduction This is the first of two papers dealing with the fundamentals and application of carbon dioxide flooding. First, the basic mechanism involved is discussed. Then a laboratory experimental program as well as predictive techniques to determine the minimum miscibility pressure, swelling of oil, viscosity reduc tion, PVT properties, solution gas drive effect and increased injectivity are presented. Finally, laboratory tests directed toward the determination of residual oil saturation and the anticipated incremental oil recovery are discussed. Introduction Since 1950, the petroleum industry has been carrying out considerable research into the use of Carbon dioxide to increase the recovery of oil from underground hydrocarbon reservoirs(22). In the last few years, about a dozen new field applications have been initiated and more could come if economically priced CO2 supplies are found. Most petroleum research centers have projects relating to CO2 flooding, indicating the current interest in CO2 flooding and promising further innovations in the process. This paper deals with the fundamentals and the research aspects of carbon dioxide flooding. The basic mechanisms which may lead to an increased oil recovery, the data required to evaluate a potential application in the field, certain basic properties of CO2 and carbonated fluids, and the all-important considerations of residual oil and incremental oil recovery are described and discussed. A second paper covers the reservoir engineering aspects of field applications, such as selecting a reservoir suitable for CO2 flooding, determining the CO2 requirements, injection/production strategies and certain recommendations regarding pilot testing the process in the field. Basic Mechanisms Carbon dioxide flooding may be applied in the field as a secondary or tertiary process and would normally involve the injection of CO2 and some other fluids, either sequentially or in an alternating fashion. Generally, in reservoirs in which the displacement is horizontal or nearly so, the CO2 flooding process would involve alternating injection of CO2 and water to attempt to control the mobility of the fluids, whereas in vertical floods the various fluids would be injected sequentially. For example, in vertical downward displacement, the CO2 may be followed by a lighter gas to maximize the advantage of gravity segregation and minimize -viscous and gravity" fingering; in vertical upward displacement, CO2 would be followed by water, again taking advantage of the gravity segregation. Regardless of how CO2 flooding is applied in the field, the following factors may contribute to increasing the oil recovery:reduction of crude oil viscosity;swelling of crude oil;miscibility effects;increase of injectivity;internal solution gas drive. The effects of the foregoing on oil recovery have been discussed in the literature(12,22). Therefore, only the new and hitherto unrecognized aspects will be discussed here. With regard to swelling of crude oil, the additional oil recovery has generally been considered to be due to an increase in the oil formation volume factor so that the residual oil is smaller in volume at surface separator conditions.

Correlations for Fluid Physical Property Prediction

Introduction The evaluation of physical properties of hydrocarbon mixtures is an important step in the design of various stages of oilfield operations. The fluid properties, which change as pressure and temperature change, must be evaluated for both reservoir engineering and production design operations. For example, the production design operations. For example, the calculation of two-phase flowing pressure gradients occurring in piping systems requires prediction of fluid properties such as dissolved gas, formation volume factor (FVF), oil compressibility, and viscosity at various locations in the pipe, Even though laboratory measurements of these properties may be available as a function of pressure, the measurements usually are made at reservoir temperature only. The behavior of these properties with temperature change usually is predicted empirically. Increasing emphasis is being placed on the necessity of having accurate estimates of fluid physical properties in advance of laboratory PVT physical properties in advance of laboratory PVT analyses of the reservoir fluids. Many times these properties are required at a time when the only properties are required at a time when the only information available consists of oil and gas gravities and reservoir pressure and temperature. The purpose of this study was to utilize a large base of laboratory. measured PVT data to develop improved empirical correlations to replace those commonly in use. Many of the presently used correlations were developed many years ago from limited data and are being used beyond the range for which they were intended. JPT P. 968

Generalized Pressure-Volume-Temperature Correlations

Empirical equations for estimating saturation pressure, oil formation volume factor (FVF) at saturation pressure, and two-phase FVF were derived as a function of reservoir temperature, total surface-gas gravity, producing GOR, and stock-tank oil gravity. These equations should be producing GOR, and stock-tank oil gravity. These equations should be valid for all types of oil/gas mixtures after correcting for nonhydrocarbons in surface gases and paraffinicity of oil. Introduction Pressure-volume-temperature (PVT) correlations are Pressure-volume-temperature (PVT) correlations are important tools in reservoir technology. These measurements form the basis for estimating the amount of oil in the reservoir, production capacity, and variations in produced gas/oil ratios during the reservoir's production life. PVT relations also are a requirement for calculating the recovery efficiency of a reservoir. Especially during the prospection phase, when only produced fluid properties are available from flowing tests, one can resort to empirically derived PVT relations. It is, of course, of great importance PVT relations. It is, of course, of great importance that such estimations be as accurate as possible. From PVT correlations published until now, Standing's work is perhaps the most widely used. His correlations were developed for California oils and make no corrections for oil type or nonhydrocarbon content. Other PVT relations developed for oils from other parts of the world, based on Standing's work, yield "best-fit lines" ordinarily parallel-shifted. Their differences can be understood from two factors not included in Standing's original correlations:crude oils from other regions have different paraffinicity - i.e., they contain varying amounts of paraffinic oil components (saturated hydrocarbons in open chains), andthe surface gases from some reservoirs contain relatively large amounts of nonhydrocarbons (CO2, N2, and H2S). By considering the variation in these parameters, this paper develops generalized PVT correlations: (1) (2) (3) These equations were derived from laboratory data, exclusively sampling North Sea oils. However, they should be valid for all types of gas/oil mixtures after correcting for nonhydrocarbons (CO2, N2, and H2S) in the surface gases and paraffinicity of the oil as defined by the Kuop factor. Procedure Procedure PVT Measurements PVT Measurements Six reservoirs fluid samples were made from two North Sea separator liquid and gas samples. These reservoir samples were labeled A1, B1, and C1 and A2, B2, and C2. Fig. 1 shows the experimental procedure used in the PVT analysis. procedure used in the PVT analysis. JPT P. 785

Pressure Transient Analysis of a Vertically Fractured Well Produced by Solution Gas Drive

Abstract Pressure transient data were investigated in a homogeneous and uniform reservoir containing oil and gas and producing at a constant surface oil rate by solution gas drive by means of a vertically fractured well. The well is assumed to be located at the center of a closed-square drainage area. Gravity effects were not included. To my best knowledge, this is the first study ort the pressure transient behavior of a vertically fractured well producing by solution gas drive. producing by solution gas drive. A recent paper presented a new method for analyzing pressure data in wells producing by solution gas drive. The method incorporates changes in effective permeability and fluid properties (formation volume factor, viscosity, and gas solubility) with pressure by means of a pseudo-pressure function however, it dealt exclusively pseudo-pressure function however, it dealt exclusively with plane radial flow. This paper presents the application of that new technique to vertically fractured wells. Dimensionless groups are used throughout to extend the results to other situations having different permeabilities, spacing, reservoir thickness, porosity, etc, provided the PVT relations and relative-permeability characteristics are identical to those used in this study. The pseudo-pressure function concept used to analyze pseudo-pressure function concept used to analyze drawdown and buildup behavior extends the applicability of the results to a wide range of PVT relations and relative-permeability characteristics. Introduction In recent years, the analysis of pressure data of fractured wells has received considerable attention. However, most of this work is related to single-phase flow. An examination of the literature indicated that no rigorous study has been made regarding the pressure behavior of a vertically fractured well producing by solution gas drive. The first objective of this paper is to discuss the transient floe, behavior of the system described above. The second objective is to demonstrate the applicability of a recent technique for determining absolute formation permeability when two phases (oil and gas) are flowing simultaneously. This technique is based on using a pseudo-pressure function that rigorously incorporates changes in permeability with saturation and fluid properties permeability with saturation and fluid properties with pressure. It will be shown that, by using the procedure suggested here, better estimates of procedure suggested here, better estimates of fracture length also can be obtained. LITERATURE REVIEW General equations of motion describing multiphase flow in porous media are well known and will not be discussed here. A summary of the work in this area as if pertains to well test analysis is presented in Ref. 5. This section briefly reviews only the computation of an integral (henceforth called the pseudo-pressure function), which was used in Ref. pseudo-pressure function), which was used in Ref. 5 to analyze drawdown and buildup. In a recent paper, Fetkovich suggested that if the pseudo-pressure function, m (p), given by: (1) is used, then transient, pseudo-steady-state and steady-state multiphase flow through porous media may be described by simple expressions similar to that for the flow of a slightly compressible fluid. For example, Fetkovich suggested that for transient radial flow one can express the flow rate as (2) where to is the dimensionless time given by (3) In Eq. 2, s' represents the skin effect that, in general, includes the effects of damage in the vicinity of the wellbore, as well as a skin effect caused by the development of a gas saturation. SPEJ P. 369

Determination of Waterflood Residual Oil Saturation From Routine Core Analysis

Proposal Proposal Rathmell et al. proposed a method for estimating water-flood residual oil saturations from core saturations where the cores must he taken with water-base muds having a filtrate loss in excess of 5 cc at bottom-hole conditions. Their equation is (So)res = (So)coreBoE .........................(1) where (So)res = average post-waterflood residual oil saturation in the flooded region of the reservoir (So)core = average oil saturation from cores BO = oil formation volume factor at the time of coring E=bleeding factor- proposed to he 1.11. In my opinion. Eq. 1 must be corrected for waterflood displacement efficiency through multiplication by the reciprocal of the conformance factor. The conformance factor may be obtained from a reservoir simulator that accounts for reservoir heterogeneity, capillary effects, and mobilities of oil and water. in the absence of a reliable reservoir simulator, the conformance factor is estimated by (1 − V2)/M, as reported by Craig. Using this empirical factor, I propose Eq. 2 as the most practical and the most convenient method to calculate waterflood residual oil saturation from the average of the oil saturations obtained from routine core analysis (provided the cores are taken with water-base mud): (So)res = (So)core BoE M .........(2) 1 − V2 where M= mobility ratio, the ratio of the mobility of water at the average water saturation in the reservoir at breakthrough to the mobility of oil in the oil bank ahead of the displacing front. V= permeability variation calculated from reservoir core samples as described in Ref. 2. Example This example applies to the 119-R Project of the Henry reservoir, which has been reported elsewhere. The data are obtained from Marathon Oil Co. files or from Ref. 3. The average core oil saturation was obtained from cores taken at the end of waterflooding and before the application of the Maraflood process. The pertinent data are (So)core = 0.248 SWc = 0.25 M = 1.3 V = 0.325 Using Eq. 2 we get (So)res = (0.248)(1.01)(1.11) 1.3 (So)res 1 − (0.325)−2 The post-waterflood residual oil of 0.404 compares favorably with the results of other methods reported in Ref. 3. In fact, the "best" estimate of post-waterflood residual oil for the 119-R Project, as reported in Refs. 4 and 5, is 0.40.

Well Test Analysis: Wells Producing by Solution Gas Drive

Abstract Drawdown and buildup data in a homogeneous, uniform, closed, cylindrical reservoir containing oil and gas and producing by solution gas drive at a constant surface oil rate were investigated. The well was assumed to be located at the center of the reservoir. Gravity effects were not included. Though the reservoir systems studied were assumed to be homogeneous, the effect of a damaged region in the vicinity of the wellbore was examined. Recently, alternate expressions for describing multiphase flow through porous media have been presented. These expressions incorporate changes presented. These expressions incorporate changes in effective permeability and fluid properties (formation volume factor, viscosity, gas solubility) with pressure by means of a pseudopressure function. The validity of applying the pseudopressure-function concept to drawdown and pseudopressure-function concept to drawdown and buildup testing for multiphase-flow situations was investigated. The pseudopressure function for analyzing drawdown behavior is calculated difrerently from that required to analyze buildup data. Consequently, two pseudopressure functions are required for analysis of well behavior in multiphase-flow systems. Dimensionless groups are used to extend the results to other situations having different permeabilities, spacing, reservoir thickness, well permeabilities, spacing, reservoir thickness, well radii, porosity, etc., provided the PVT relations and relative-permeability characteristics are identical to those used in this study. The pseudopressure-function concept used to analyze pseudopressure-function concept used to analyze drawdown and buildup behavior extends the applicability of the results to a wide range of PVT relations and relative-permeability characteristics. Introduction During the past 30 years, more than 300 publications have considered various problems publications have considered various problems pertaining to well behavior. Except for a few (about pertaining to well behavior. Except for a few (about 10), most papers examining transient pressure behavior assume that the fluids in the reservoir obey the diffusivity equation. This implies the use of a single-phase, slightly compressible fluid. The reason for the popularity of this approach is twofold:(1)the ease with which the diffusivity equation can be solved for a wide variety of problems, and(2)the demonstration by some problems, and(2)the demonstration by some workers that, for some multiphase-flow situations, single-phase flow results may be used provided appropriate modifications are made. The necessary modifications are summarized in Ref. 1. The main objective of this study is to present a method for rigorously incorporating changes in fluid properties and relative-permeability effects in the properties and relative-permeability effects in the analysis of pressure data when two phases of oil and gas are flowing. This should enable the engineer to calculate the absolute formation permeability rather than the effective permeability to each of the flowing phases. This method is based on an idea suggested by Fetkovich, who proposed that if an expression similar to the real gas pseudopressure is defined, then equations describing pseudopressure is defined, then equations describing simultaneous flow of oil and gas through porous media may be simplified considerably. The validity of the equations and methods for calculating the pseudopressure function, however, was not presented pseudopressure function, however, was not presented by Fetkovich. LITERATURE REVIEW AND THEORETICAL CONSIDERATIONS General equations of motion describing multiphase flow in porous media have been known since 1936. These equations, and the assumptions involved in deriving them, are discussed thoroughly in the literature and will not be considered here. Equations for two-phase flow were first solved by Muskat and Meres for a few special cases. Evinger and Muskat studied the effect of multiphase flow on the productivity index of a well and examined the steady radial flow of oil and gas in a porous medium. Under conditions of steady radial porous medium. Under conditions of steady radial flow the oil flow rate is given by (1) SPEJ P. 196

Static Formation Temperature From Well Logs - An Empirical Method

Reliable values of static temperature are important for a number of reasons. For example, they are required in designing deep-well cementing programs and in analyzing reservoir fluid properties. Though many engineers hate discouraged the use of recorded log temperatures, these log temperatures can be used to predict static temperature. Introduction Static formation temperature should be determined as accurately as possible for a number of reasons. In-situ sauration distributions computed from resistivity logs require accurate formation water resistivities that depend on temperature. Reliable estimates of bottom-hole temperatures are important in designing deep-well cementing programs and in evaluating reservoir-fluid formation volume factors. Also, the determination of static temperature is necessary for establishing geothermal gradients that can be used to estimate the temperatures of deeper zones. More recently, new exploration techniques have used temperature as a mappable proximity parameter. proximity parameter.Unfortunately, the temperatures recorded during logging operations frequently are not static temperatures. The recorded values are too low. These low temperatures result because the circulating mud temperature frequently is much less than the formation temperature. Schoeppel and Gilarranz reported that early investigators had discouraged the use of bottom-hole temperatures obtained from logs under the assumption that the temperatures would not be correct because the mud and the formation were not in thermal equilibrium. More recently, however, Timko and Fertl suggested that the temperatures recorded while running a series of logs can be interpreted to estimate static formation temperature. They recommend use of a Horner temperature plot, similar to the conventional pressure buildup method, plot, similar to the conventional pressure buildup method, for estimating static formation temperature. Timko and Fertl demonstrate the apparent applicability of the technique with an example. Significantly, we have been unable to find any theoretical justification for an analysis of this type. However, we have seen field cases where the technique gives satisfactory results. The accuracy of this analysis was especially surprising when it was concluded that the two methods - pressure build-up and temperature buildup - are not completely analogous. Thus, the chief objective of the present study was to determine under what conditions the Horner temperature plot can be used to estimate static temperature. Comparison of Temperature And Pressure Buildup Pressure Buildup Pressure Buildup The equation that describes pressure behavior at each point at any time in the well drainage area is point at any time in the well drainage area is(1)2p 1 p c p----- + ---- ---- = ------ ------r2 r r k t Eq. 1 frequently and referred to as the "diffusivity" equation because of its similarity to the diffusivity equation in the heat-transfer literature. Subject to the constraints of an initial condition and a set of boundary conditions, Eq. 1 can be solved. Consider the case of a well producing at a constant rate and located in an infinitely large reservoir. JPT P. 1326

Estimating the Viscosity of Crude Oil Systems

Viscosity values of crude oils and crude oils containing dissolved natural gas are required in various petroleum engineering calculations. In evaluation of fluid flow in a reservoir, the viscosity of the liquid is required at various values of reservoir pressure and at reservoir temperature. This information can be obtained from a standard laboratory PVT analysis that is run at reservoir temperature. There are cases, however, when the viscosity is needed at other temperatures. The most common situation requiring viscosities at various pressures and temperatures occurs in the calculation of two-phase, gas-liquid flowing pressure traverses. These pressure traverses are required in tubing-string design, gas-lift design, and pipeline design. Calculation of these pressure traverses involves dividing the flow string into a number of length increments and calculating the pressure gradient at average conditions of pressure and temperature in the increment. Calculation of pressure and temperature in the increment. Calculation of pressure gradients requires knowledge of oil viscosity. In pressure gradients requires knowledge of oil viscosity. In many cases, the only information available on the fluid properties are the separator gas gravity and stock-tank oil properties are the separator gas gravity and stock-tank oil gravity; therefore, correlations requiring a knowledge of crude oil composition are not applicable.The most popular methods presently used for predicting oil viscosity are those of Beal for dead oil and Chew and Connally for live or saturated oil. Beal correlated dead oil viscosity as a function of API gravity and temperature. Chew and Connally presented a correlation for the effect of dissolved gas on the oil viscosity. The dead oil viscosity and the amount of dissolved gas at the temperature and pressure of interest must be known. pressure of interest must be known. When these correlations were applied to data collected for a study of dissolved gas and formation volume factor, considerable errors and scatter were observed. These data, therefore, were used to develop new empirical correlations for dead or gas-free crude oil as a function of API gravity and temperature, and for live oil viscosity as a function of dissolved gas and dead oil viscosity. A description of the data used, which were obtained from Core Laboratories, Inc., is given in Table 1.The correlation for dead oil viscosity was developed by plotting log 10 (T) vs log 10 log 10 (mu OD + 1) on cartesian plotting log 10 (T) vs log 10 log 10 (mu OD + 1) on cartesian coordinates. The plots revealed a series of straight lines of constant slope. It was found that each line represented oils of a particular API gravity. The equation developed is =, ........................(1) where X = y = Z = The correction of the dead oil viscosity for dissolved gas was developed by taking advantage of the fact that a linear relationship exists between log 10 mu OD and log 10 mu for a particular value of dissolved gas, Rs. Live oil viscosity may be calculated from = ...........................(2) TABLE 1 - DESCRIPTION OF DATA USED Variable Range Solution GOR, scf/STB 20 to 2,070 Oil gravity, API 16 to 58 Pressure, psig 0 to 5,250 Pressure, psig 0 to 5,250 Temperature, F 70 to 295 Number of oil systems - 600 Number of dead oil observations - 460 Number of live oil observations 2,073 P. 1140

Estimating Maximum Sand-Free Production Rates From Friable Sands for Different Well Completion Geometries

Oil or gas can be produced from a friable sand without benefit of sand control. If we have sonic and density log data and know the permeability of the formation, the fluid viscosity, formation volume factor, and number of perforations, we can estimate with a simple equation the maximum possible sand-free production rate. possible sand-free production rate. Introduction In friable formations where sand production can be a problem, it may be possible to produce oil or gas from an essentially undisturbed formation at high rates without resorting to any form of sand control measure. It has been proposed that formation stability is achieved by the establishment of sand arches around each perforation in the casing. This paper presents a technique for utilizing sonic and paper presents a technique for utilizing sonic and density log data to estimate the maximum sand-free production rate from each arch. Thus, estimates of production rate from each arch. Thus, estimates of maximum sand-free production rates from wells are independent of such completion geometry factors as the location and length of perforated interval. The technique is based on the assumption that the maximum possible pressure gradient at the arch face for possible pressure gradient at the arch face for sand-free production is proportional to the sand strength. Arch faces must remain in place if no sand production is to occur; yet they are subjected to the production is to occur; yet they are subjected to the maximum pressure gradient in the reservoir. A less specific means was previously presented for estimating the maximum sand-free production rate. That procedure contained an assumption that is correct as long as completion geometry is not substantially changed in different wells. The assumption was that the ratio between the total reservoir pressure drawdown and the pressure gradient at the face of individual sand arches was the same for all wells. With the new technique presented here, we have eliminated the necessity for including this assumption in our estimates of maximum sand-free production rates. Thus, the new technique provides an improved estimate that can be used to determine if the economics is promising for completing a well without installing any form of sand control. Theoretical Consideration Consider the system illustrated in Fig. 1 for a hemispherical arch formed around a perforation in the casing. When the stress at the arch face exceeds the strength of the sand, particle movement will begin. Logically, the stress at the arch face is directly related to the fluid pressure gradient, which is a critical factor in maintaining formation stability. Moreover, the maximum stress that may be applied without causing a sand problem should be proportional to the strength of the sand. Let dr be the distance between the sand/fluid interface and the outer boundary of sand layer liable to move (Fig. 1). By Darcy's law, the pressure gradient across dr isdp q B = (1) dr 1,127 x 10 (-3) kA Darcy's law applies to laminar flow. To use Darcy's law for calculating the maximum sand-free production rate, we assume that any effects of turbulence on the maximum pressure gradients in different zones are the same. P. 1156

Evaluation of Three New Methods For Predicting Pressure Losses In Vertical Oilwell Tubing

The reliability and relative merits have been estimated for three recently published multiphase-flow pressure-drop prediction correlations applicable to vertical tubing. Data from 726 tests, embracing broad ranges of flow rate, pipe size, API gravity, gas/liquid ratio, and water/oil ratio were used in the evaluation. It was found that no single correlation consistently performed best in every range. Introduction Six of the several correlations available for predicting pressure losses during simultaneous, predicting pressure losses during simultaneous, continuous, steady-state flow of oil, water, and gas in vertical pipes were evaluated statistically by Lawson and Brill. Three more promising correlations have recently been published - those of Beggs and Brill Aziz et al. and Chierici et al. The purpose of this paper is to extend the work of Lawson and Brill to cover the new correlations.Details of the three new methods can be found in the original sources listed in the references. The same flowing pressure surveys and related data for 726 field and experimental wells were used as were reported by Lawson and Brill. Fluid physical properties were estimated using the same correlations as employed by Lawson and Brill.Although every attempt was made by Lawson and Brill to screen data in the data bank, no doubt some questionable data have been included. In a study such as this, the quality of the data is critical. It has been found, for example, that small errors in measured gas volumes and oil formation volume factors can significantly affect the calculated results. A valid criticism of the bank is that inadequate use was made of what limited measured PVT data were available. Another possible criticism is that many of the data used were gas-water data with low gas/water ratios, a situation seldom found in practice. No claim was made that the gas-water data were meant to represent gas well production. Rather, these data are extremely valuable because of the absence of mass transfer between phases and the resulting improved accuracy of, for phases and the resulting improved accuracy of, for example, predicted in-situ phase velocities.All three of the correlations were developed from two-phase flow data, one of the phases being gas. A third phase (water) can be included if we assume that its presence does not change the physical phenomena of two-phase flow. Possible changes that could invalidate results are slippage between oil and water, formation of emulsions, and the influence of water on gas bubble coalescence and the formation of gas slugs. The degree to which such changes are present in the three-phase data is unknown.We applied the three correlations to all data, knowing full well that many of the data were beyond the range of variables used to develop the correlations. However, correlations are frequently used indiscriminately beyond their stated ranges of validity. Therefore a test of their performance over a broad range of data is of value. Validation of Programming Pressure losses calculated by a computer program of Pressure losses calculated by a computer program of each method were compared with the corresponding pressure losses reported by each author for identical pressure losses reported by each author for identical well cases. This comparision indicated the degree of agreement between the results of the two programs. JPT P. 829

Dimensionless PVT Behavior of Gulf Coast Reservoir Oils

The empirical correlations presented here show that for "typical" Gulf Coast reservoir oil, cumulative gas evolution and oil shrinkage are about proportional to pressure drop below the bubble point. The correlations proportional to pressure drop below the bubble point. The correlations should be useful for the Gulf Coast, and the correlation technique, with modifications, might also serve in other geologic provinces. Introduction Often, for an oil reservoir where a PVT analysis is not available, various aspects of depletion-drive behavior must be estimated. over the years various correlations have been published; and reliable empirical relations between bubble-point pressure, solution GOR, formation volume factor, etc., are available. Thus, for a given oil and reservoir conditions these correlations may be used to estimate the properties of the reservoir oil at initial (bubble point) conditions and at any desired pressure below the bubble point. An alternate approach to the use of empirical correlations is the use of a PVT analysis for an oil with properties and reservoir conditions similar to those properties and reservoir conditions similar to those of the reservoir being investigated. With either approach there usually is the question of whether the data so derived are representative of the oil and reservoir being investigated. The purpose of this paper is to present a method of comparing the PVT behavior of different reservoir oils by reducing the PVT data from a large number of oils to sets of dimensionless plots. The relations so developed, which are somewhat easier to use than previously published correlations, should provide previously published correlations, should provide additional insight into the probable PVT behavior of many Gulf Coast oils. These relations are not intended as a substitute for a PVT analysis, should the latter be available. They are designed to be used with other, previously published correlations and reservoir information for determining bubble-point pressure, initial (bubble point) formation volume factor, pressure, initial (bubble point) formation volume factor, reservoir temperature, and formation volume factor at atmospheric pressure and reservoir temperature. Procedure Procedure Sets of dimensionless ratios were calculated for each PVT analysis. These ratios are "dimensionless PVT analysis. These ratios are "dimensionless pressure," "dimensionless cumulative gas evolution," and pressure," "dimensionless cumulative gas evolution," and "dimensionless shrinkage." Dimensionless pressure is defined as pressure divided by bubble-point pressure. Dimensionless cumulative gas evolution is defined as cumulative gas liberated to a pressure divided by total gas liberated by a pressure drop from the bubble point to atmospheric pressure. Dimensionless point to atmospheric pressure. Dimensionless shrinkage is defined as shrinkage to a pressure below the bubble point divided by total shrinkage from the bubble point to atmospheric pressure. (See Nomenclature.) Some of the PVT analyses did not report a value for the formation volume factor at atmospheric pressure and reservoir temperature (Boa); therefore, pressure and reservoir temperature (Boa); therefore, for these analyses the correlation published by Katz was used to estimate this parameter, An example of the computer output showing the original data and the corresponding dimensionless ratios for one of the PVT analyses is shown in Table 1. PVT analyses is shown in Table 1. Dimensionless ratios were calculated from the PVT data from 80 oils in 31 Gulf Coast fields. The range of oil properties and reservoir temperatures is listed in Table 2. The frequency distribution of each variable is shown by the histograms in Figs. 1 through 5. In these histograms each asterisk denotes one oil sample or PVT analysis. JPT P. 538

A Graph for Determining Reserves and Spacing

The graph (Fig. 1) accompanying this article presents a quick method to determine reserves under presents a quick method to determine reserves under varying conditions. It can also be used to estimate minimum spacing for an economic recovery. Example 1 - Recoverable Reserves Reservoir Data Porosity, percent 20 Water saturation (Sw), percent 40 Formation volume factor (FVF) 1.2 Recovery factor, percent 20 Spacing, acres 20 Net pay, ft 50 The solution route is shown on Fig. 1. Solution Oil originally in place, STB/acre-ft 776 Recovery, STB/acre-ft 155 Recovery, bbl 155,000 Example 2 - Spacing Assumptions A recovery of 400,000 bbl is required for an economic return on your investment. Net pay is 100 ft. 3. Recovery is 270 bbl/acre-ft. Solution Draw line from 270 BPAF recovery through all spacing curves. Start at 400,000 bbl recovery and go up to the 100-ft net pay line. Go left until you intersect the 270 BPAF recovery line. This intersection is the spacing required (15 acres). The chart is a simple solution and it will permit on-site analysis. Additional charts can be developed for gas reserve determinations. P. 1470

Reservoir Simulation by a Mathematical Model

A numerical reservoir model which simulates three dimensional, three phase flow through porous media is presented. The model is based on the numerical solution of the equation of conservation of mass for each phase. The state of phase equilibrium is determined by oil and gas formation volume factors and gas solubility. All the fluid properties are considered to be functions of pressure only. In order to solve the resulting matrix equation, the Alternating-Direction method is used. With this model, a two-dimensional simulation of the depletion drive of an oil reservoir, and a three-dimensional simulation of an oil reservoir with a weak water drive were simulated. The necessary time to calculate one time step-block was arround 0.0216 seconds by IBM 360-75 system.

Combustion as a Primary Recovery Process-Midway Sunset Field

Despite the complicated structure of this reservoir, in-situ combustion has been an effective primary recovery process essentially since the beginning of production more than a decade ago. To date, the recovery is 9 million barrels, or 24 percent of the oil originally in placesubstantially higher than the estimated ultimate recovery of 17 percent. Introduction The Moco zone reservoir, located in Sections 34 and 35-T12N-R24W of the Midway Sunset field, Kern County, Calif., was discovered in 1957 and partially developed. However, because there was no demand for the heavy crude, it was essentially shut in until Nov., 1959. It was expected that without fluid injection of some kind there would be a rapid decline in oil production rate. Although there were multiple sands present, the reservoir properties of the Moco zone appeared favorable for in-situ combustion. The structure appeared to be entirely on Mobil Oil Co. property. Predictions of performance under combustion property. Predictions of performance under combustion were based on the results of the South Belridge Thermal Recovery Experiment and on prior supporting work. Evaluation of several methods of operation indicated that the most desirable economics would be obtained if the combustion process were applied immediately. Accordingly, combustion operations were undertaken as soon as practicable after the reservoir was returned to production and development was resumed (this took place in Nov., 1959). Air injection was started in Jan., 1960, at which time the cumulative oil production from the reservoir was 160,000 bbl, or 0.4 percent of the oil in place, and the reservoir pressure was only slightly below its initial value of 1,000 psi. Case histories of other combustion projects have been reported in the literature. projects have been reported in the literature. Reservoir Characteristics The reservoir is a small anticline with six major sands. Structural contours, a type log, and the areal extent of the six sands are shown on Fig, 1. An east-west cross-section (X-X') along the longitudinal axis is shown in Fig. 2. The sands generally are separated by interbedded shales and to the east become thin and disappear. To the west some of the sands merge. The sands were separately identified, correlated, isopached, and designated M1 through M6. This permitted an appropriate design of air distribution permitted an appropriate design of air distribution in the injection wells, which have various combinations of sands open. There are productive zones above and below the Moco reservoir, and the Moco zone itself merges with the Obispo-Pacific fractured shale zone to the east. The presence of these other zones added to isolation problems and costs during development drilling and problems and costs during development drilling and well repair. A north-south cross-section (E-E') across the structure is shown in Fig. 3. The dip is up to 45 degrees to the north and 20 degrees to the south. General reservoir characteristics are as follows: Productive area, acres 150 Average depth, ft 2,100 to 2,700 Gross formation thickness ft 500 Average net sand thickness, ft 129 Porosity, percent 36 Oil saturation, percent 75 Water saturation, percent 25 Formation volume factor 1.06 Initial oil in place, bbl/acre ft 1,980 Initial oil in place, total bbl (millions) 38 JPT P. 981