The seismic reflection method is well established in the exploration end of the petroleum industry but little used in reservoir analysis by petroleum engineers. As the major structures have been discovered in many areas, seismic profiling has been turned more and more toward smaller structures and toward exploration for stratigraphic traps which require a far greater precision and fineness of detail to locate. This redirection has precision and fineness of detail to locate. This redirection has resulted in improved seismic equipment design, field recording techniques and seismic data processing procedures. This means that the petroleum engineer, for the first time, may be able to utilize this technique to assist in delineation of the fine subsurface stratigraphy within individual reservoirs.
The technique used for high resolution reservoir profiling is a greatly scaled-down version of that employed in most exploration operations. Every 5 to 20 meters (16 1/2 to 65 feet), a detector produces a new seismic "pseudo" log trace which will subsequently produces a new seismic "pseudo" log trace which will subsequently be correlated with borehole logs and other seismic log traces. Structural information derivable from the log trace displays includes location of very small faults, sand channels and shale-outs. Shape variations in the log traces can provide the petroleum engineer with valuable reservoir information regarding localized depositional environments, pore fluid characteristics, and even porosity and permeability variations across a given reservoir bed, porosity and permeability variations across a given reservoir bed, once a local reference has been established.
Acoustical amplitude analysis of injected, produced or in situ reservoir gases should be a valuable method of monitoring a variety of enhanced oil recovery techniques. Carbon dioxide or other gas injection projects are ideal for seismic pseudo log monitoring. Combustion products from fire floods or injected steam should also be easily seen with high resolution seismic techniques.
High frequency surface to surface seismic profiling offers great potential as a reservoir analysis tool. This potential will be developed by the petroleum engineer working with seismic log displays and field well logs rather than exploration geophysicists using smoothed structural displays.
Porosity, fluid saturation, rock compressibility, permeability and capillary pressure are all terms familiar to the permeability and capillary pressure are all terms familiar to the reservoir engineer but seldom used by the geophysicist. On the other hand root mean square velocity, predominant reflection frequency, normal moveout , wavelet amplitude, deconvolution and other terms in the geophysicists vocabulary are almost never involved in reservoir analysis.
Until recently, this language problem created no particular difficulty since the geophysicists were almost exclusively involved in exploration activities where the targets were big structures and the geological "details", involving potential reservoir rock type, matrix porosity and permeability as well as pore fluid identification, were considered inconsequential as they routinely fell beyond the resolving power of the seismic reflection method.
This has now changed. As the larger structures have been discovered, exploration activities are being redirected to smaller features and especially to stratigraphic traps which require much greater geophysical precision to locate. Demand for increased fineness of detail is resulting in improved geophysical equipment, field recording techniques and computer processing procedures. These improvements allow one for the first time to look at the individual producing formations of immediate interest to the petroleum engineer. petroleum engineer. The change started a few years ago when seismic "Bright Spots" were heralded as a direct hydrocarbon indicator. The "Bright Spot" is caused by the increased seismic reflection amplitude caused by the relatively lower density and velocity of gas filled reservoirs compared to those filled with water. As many operators discovered somewhat later, coal also has low density and velocity and produced bright spots which were easily mistaken for gas. Also depending on the reservoir material, the "Bright Spot" may in fact be a "Dim Spot" or may have no measurable amplitude effect at all.
The use of tungsten carbide inserted roller cones in core bits has been developed by the Deep Sea Drilling Program. During this extensive coring operation, all types of core bits were tried. Most of the types were very limited in the range of formations that they could core effectively. Formations that were made up of chert stringers or largely chert proved to be the most difficult to obtain core recovery during the earl portions of the ocean bottom coring. portions of the ocean bottom coring. They reasoned that a standard TCI three cutter could successfully core these formations and additionally it would have the advantage of being able to have the newest technological advances in the industry. This type of bit soon became their standard.
Determination of when the life bit was completed was made by measuring the core diameter and when it became much less than design, the bit was pulled. However, at the Hot Rock Project at Los Alamos, New Mexico, bits made to core the granitic formation ran into the problem of oversize core because the abrasive wear on the core trimming inserts was more rapid than bearing wear.
With the advent of G.E.'s monocrystalline diamond stratapax, a highly abrasive resistant element used to trim the core and TCI cones to produce stabilization and control the penetration, a most promising new kind of core bit is being prepared to core these very difficult formations.
Our experience with core bits began in 1969 when representatives of the Deep Sea Drilling Program inquired about the possibility of manufacturing a core bit made from standard 7 7/8 cones with tungsten carbide inserts for evaluation.
Hard formation insert bits had evolved to the point where a small core was allowed to form. The point where a small core was allowed to form. The subsequent core would be so small that it would easily break off. It was reasoned that if the cones for a smaller bit were moved outward, then a large core would be allowed to form and this core could then be retrieved in a conventional core barrel.
The first core bits were then made using standard 7 7/8 hard formation cones and adapting them for a 2 1/2" core. This functioned very successfully except in soft formations and so shortly thereafter cones were designed with chisel crest inserts with greater extension in order to cover a wider range of formation types. The advantage of using basically standard 3-cone bit cutters was to take advantage of the development of bits, first sealed roller and later sealed journal, without requiring an expensive R and D project.
Because of the success of these bits, the Los Alamos Scientific Laboratory requested a 9 7/8 core bit to cut pink granite in the drilling of their Hot Dry Rock hole at Fenton Hill near Los Alamos. This hole was projected to core all the way using air as a circulation medium. A special bit was designed for this project but the bit did not perform as expected as project but the bit did not perform as expected as core recovery was very poor and the footage that could be drilled per bit fell much below the projected. An on-the-site observation showed that the poor core recovery was caused by abrasive wear on the inserts that trimmed the core. This resulted in the core rapidly becoming oversize and therefore not able to enter the core barrel. As a result, the core was fragmented and recovery was poor. This was unexpected for on the Deep Sea Drilling operation oversize cores had not been a problem and in fact the decision as to when to pull the bit was determined by how much the core was undersize. The abrasive wear was somewhat relieved by using a harder grade insert and although the bit was still not capable of drilling continuously, at least reasonably good core recovery resulted.
Aqueous solutions of two synthetic petroleum sulfonates, nonyl and dodecyl orthoxylene sulfonates with tertiary amyl alcohol as cosurfactant, were studied with the polarizing microscope. Surfactant concentrations of 2-10%, the approximate range being considered for injection in surfactant processes, were used, while salinities in each system ranged from well below to well above the optimum salinity for a particular mixture of refined oils. The solutions were also studied as a function of temperature and time.
Both these surfactants showed the same pattern of structure variation with salinity. At low salinities there was a dispersion of liquid crystalline particles in brine. At high salinities a single liquid crystal-line phase was present. over a narrow range of intermediate salinities a mixture of these two structures was seen. The generality of this behavior was confirmed by observation of solutions of two conventional petroleum sulfonates, which also exhibited a transition petroleum sulfonates, which also exhibited a transition between structures over a narrow salinity range.
The mean salinity of the transition region was found to increase as a surfactant's optimum salinity increases for a given oil. Since optimum salinity is associated with the lowest interfacial tensions, this result indicates that structure of an injected surfactant solution is related to its ability to produce low tensions on contacting oil. Solution viscosity should also be affected by the structural changes.
A major portion of current research on enhanced oil recovery deals with chemical flooding processes employing surfactants. In many proposed processes the surfactant is injected as a "slug" which is an aqueous saline solution containing the surfactant and often an alcohol cosurfactant as well. Surfactant concentration in the slug is typically in the range of 2-10% by weight.
Both the slug's flow behavior within the reservoir and its interaction with trapped oil globules, especially its ability to produce ultralow interfacial tensions and mobilize such globules, are very important for process performance. To obtain information which will help in understanding and predicting such aspects of slug behavior, we have used the polarizing microscope to study the macroscopic structure of aqueous saline solutions of some petroleum sulfonate surfactants. As discussed below, we have found that structure variation with composition, especially with salinity, follows a general pattern in these systems. in particular, there exists a narrow salinity range for each surfactant-cosurfactant mixture where a change occurs from one type of structure to another. The salinity where this transformation in structure occurs increases as the optimum salinity of the surfactant-cosurfactant mixture increases for a given oil. Since the lowest interfacial tensions occur at optimum salinity, these results suggest that the structure of the injected surfactant slug is related to its ability to produce low tensions upon contact with oil.
The synthetic petroleum sulfonates used were mono-ethanolamine alkyl orthoxylene sulfonates, which were supplied by Exxon Chemical Company. In PDM-337, which contains 84% active sulfonates, the alkyl chain is predominantly dodecyl. In PDM-484, which is 85% predominantly dodecyl. In PDM-484, which is 85% active, the alkyl chain is mainly nonyl. Conventional petroleum sulfonates used were TRS 10-410, which was petroleum sulfonates used were TRS 10-410, which was supplied by Witco Chemical Corporation, and Mahogany AA, which was supplied by Amoco Production Company. ate former contains 61.5% active sulfonates and has an equivalent weight of 424, while the latter contains about 60% active sulfonates and has an equivalent weight of 430.
Reagent grade isopropanol, isobutanol, and tertiary amyl alcohol were used as cosurfactants. The surfactant-cosurfactant mixtures were added to brines of the appropriate compositions made from distilled water and reagent grade NaCl.
A two-dimensional, single phase mathematical model of the reservoir and surface gathering system was used to evaluate the gas reserves and to determine the most profitable future field development policy. History profitable future field development policy. History matching runs with the model indicated that the performance of the Jurassic reservoir is probably performance of the Jurassic reservoir is probably influenced by limited communication with the underlying Mississippian Pekisko formation. This geologically complex situation was successfully modeled by modifying the initial reservoir description of the Jurassic-Detrital Sand. The resulting modified porosity feet (phi h) and permeability feet (kh) maps described the effective gas reserves and effective flow capacity of the reservoir.
Prediction runs were made to investigate the effects of various combinations of compressors and infill wells on field deliverability and ultimate gas recovery. Economic analyses were made for each of the most promising prediction runs. These runs were compared with the base case and with each other to determine the number and location of wells and compressors for best operating strategy.
The best development scheme consisted of five infill wells and terminal compression. The recommended strategy is currently being implemented. Initial results indicate that reservoir performance is in close agreement with the predicted behavior.
The Paddle River Gas Field in Alberta, Canada, consists of two Units: Paddle River Gas Unit No. I operated by Canada-Cities Service, Ltd., and the North Gas Unit operated by CDC Oil and Gas, Ltd. The field has been producing from the Jurassic-Detrital formation since 1966. Production was from five wells in the Gas Unit No. 1 at an average rate of 25 MMcf/D. Data from periodic pressure surveys was available on the periodic pressure surveys was available on the producing wells; in addition, pressure data was available producing wells; in addition, pressure data was available from twelve wells completed in the formation but not produced because their deliverability was not needed produced because their deliverability was not needed to meet the gas sales contract. Plans for future development of the Unit included an increase in the daily gas production capacity to about 60 MMcf/D.
Material balance calculations using the pressure and production data indicated substantially more gas reserves than had been determined from volumetric estimates based on geological maps. There was some geological evidence suggesting that the Jurassic formation might be in limited communication with the underlying Mississippian Pekisko formation in the central and northern part of the field. The Pekisko formation contains viscous oil with a gas cap.
Development of the Gas Unit No. 1 to obtain the desired gas deliverability required a more accurate reservoir description and a method of predicting the effect on deliverability of options such as connecting the shut-in wells to the gathering system, drilling additional wells, and adding compression. A reservoir study was therefore initiated with the following objectives:
1. define the gas reserves accurately,
2. determine the distribution of pore volume and flow capacity in the reservoir, and
3. forecast future gas deliverability for alternative operating methods and find the best method.
The main tool used in the study was a two-dimensional, single phase reservoir model that includes the effects of flow in both the reservoir and gathering system. The excellent pressure data available was used in history matching runs. The resulting modified porosity-feet and permeability-feet maps described the porosity-feet and permeability-feet maps described the distribution of reserves and flow capacity, including the effects of communication between the Jurassic and Pekisko formations. Using the modified reservoir Pekisko formations. Using the modified reservoir description, the model was used to evaluate the effects of different combinations of infill wells, compression, and gathering system modification on field deliverability and ultimate gas recovery.
An investment risk analysis by the probability distribution technique was proposed and published by Hillier in a 1963 issue of Management Science. His work was quite theoretical. A simplified form of the method was presented in petroleum literature by Davidson and Cooper in 1975. However, their work did not extend to using the method in practical decision making. Both of these works critically discussed why this approach is preferable to earlier methods. In as much as the main value of such an innovation and the ultimate need for its publication is its application, discussion of the practical aspects of the method is important. The purpose of this paper is to fulfill this need.
Regardless of what criterion an investor uses to determine the profitability of his venture, the amount of risk involved must be considered for a sound, final decision. As such, many techniques have evolved over the years for quantifying risk. Among the older techniques which have been used are: 1) Payback Period - The length of time required to Payback Period - The length of time required to recover an investment through the net cash flows from the project. 2) Expected Monetary Value - Sum of the products of investment outcomes and their respective products of investment outcomes and their respective chances of occurrence. 3) The Certainity Equivalent - A method of discounting cash flow by a risk-free interest rate. 4) Sensitivity Analysis - Determining the profitability measure by varying an uncertain parameter. For reasons well discussed in parameter. For reasons well discussed in literature, all of these techniques are weak and are inadequate for proper risk portrayal. The more recent and certainly more sophisticated method of risk analysis is the probability distribution of the profitability index. One form of this is the Monte profitability index. One form of this is the Monte Carlo simulation which uses randomly selected parameters from appropriate ranges of values to generate parameters from appropriate ranges of values to generate a series of possible outcomes. While this technique is a quite reliable tool, it does not lend itself to routine application because of the computer work involved. Another form is the, analytical technique proposed by Fredrick Hillier . This approach adopts proposed by Fredrick Hillier . This approach adopts well know statistical theories and assumes the distribution of the profitability index to derive the probability distribution. Hillier's work, though probability distribution. Hillier's work, though amenable to hand calculators, was quite theoretical. A simplified form of the method was presented in petroleum literature by Davidson and presented in petroleum literature by Davidson and Cooper in 1975. However, their work did not extend to using the method in practical decision making.
This paper discusses the practical aspects of Hillier's approach. Although Davidson and Cooper suggested log-normal distribution assumption for analysis of petroleum investments, this work is based on the validity of normal distribution when the random variable is the cash flow. Both assumptions are compared in the discussion. Arriving at a decision to accept or reject an investment proposal on the basis of the method requires the use of utility theory. Therefore, the concept of the theory is reviewed. Its use in conjunction with the probability distribution of net present value is then shown. Finally, a decision present value is then shown. Finally, a decision concerning two or more risky investments may be influenced by the skewness of normal distribution. Hence, the semi-variance equation for testing the normality or magnitude and direction of skewness is presented and its application discussed.
DERIVATION OF PROBABILITY DISTRIBUTION
In his work, Hillier assumed that under conditions of uncertainity, cash flows from an investment are random variables which can be characterized by their means and variances. Therefore, by the central limit theorem, the distribution of these means will be approximately normal. Moreover, their sum will approach a normal distribution. Based on these, he derived the probability distributions of net present values and internal rate of return for three possible cases of cash flows from an investment. These cases include (1) statistically independent cash flows (2) perfectly correlated cash flows and, (3) combined independent and correlated cash flows. This paper considers the second case only.
A comprehensive numerical model of the under-ground coal gasification process via the stream method was developed for a two-dimensional geometry. Seven reactions, involving carbon, carbon dioxide, carbon monoxide, oxygen, water/steam, hydrogen, and methane are accounted for. Nitrogen is the seventh gas component. As a result of gasification, the channel diameter increases with time, and a combustible gas is produced. The model accounts for all of these factors.
Considering the fact that vast known coal reserves occur in the United States, much research has been directed toward producing synthetic liquids and gases via above ground gasification and liquefaction of coal which lends itself to large scale operations. The current federal and state pollution control regulations and the enormous cost of mining, transporting and processing make this process commercially unfeasible. Furthermore a low quality coal cannot be used in this process. Some of these problems can be avoided if gasification of coal in situ is utilized.
This process, known as underground gasification of coal, is defined as the controlled burning of coal seam in the presence of gas mixture consisting of mainly nitrogen, oxygen and steam, to produce gasification reactions. A combustible gas mixture containing nitrogen, carbon monoxide, steam, hydrogen, methane and carbon dioxide is formed, which can be used in the generation of electricity on a commercial scale.
This method possesses many advantages over conventional mining and synthetic fuel operations in that it minimizes health hazards to miners, improves process safety, provides ecological benefits in that process safety, provides ecological benefits in that the land surface is left intact, and eliminates much of the need for aboveground plant requirements. Furthermore, it offers a technically simple and feasible method for producing the vast bituminous and low rank coal reserves in the United States (much of which can neither be economically mined nor is acceptable in rank for commercial synthetic fuel operations), and if designed properly can be very economical.
In order to increase the understanding of this process, a series of steady state analytical models process, a series of steady state analytical models by the stream methods were developed by Magnani, by Magnani and Farouq Ali, and by Farouq Ali and Pasha. The steady state assumption of the process enabled the extraction of closed form solutions, which, though complex, were useful for carrying out parameter sensitivity studies. Furthermore, these models were of considerable value for carrying out pseudosteady state simulation of unsteady state underground coal gasification process.
The present model is a numerical extension of the previous models, and as a result is considerably more general. A two dimensional axisymmetrical coal seam is assumed to be ignited at one end and thereafter a mixture of air and steam (or a mixture of oxygen enriched air and steam) is injected. As a result, the combustion zone advances in both axial and radial directions and the channel wall recedes resulting in the production of a combustible gas mixture.
It should be mentioned that while this study has been devoted to the stream method of underground coal gasification, a number of other simulation studies has been reported which consider other gasification processes. These include the works of Kotowski and processes. These include the works of Kotowski and Gunn, Gunn and Whiteman, Winslow, Thorsness and Rosza, and Dinsmoor, Galland and Edgar.
1. The coal bed consists of 100% carbon. However, the model allows for source terms in all components considered and thus the influx of any of these as a function of distance and time may be simulated.
2. The gasification channel is initially assumed to be of cylindrical geometry, one extremity of which is ignited.
This study has looked into the feasibility of operating a floating methanol plant in a North Sea environment. The plant was fed with associated gas from an oil field.
Both the technical and economical results are promising. This indicates that such projects might promising. This indicates that such projects might be an alternative solution for otherwise reinjected gas; however, more work needs to be done to evaluate their attractiveness.
By now the floating production facility approach is a well recognized concept. Its major advantages are savings in capital investments, shorter development time, and increased flexibility because parts of the facility can be easily relocated.
So far the interest has focused mostly on floating gas processing plants; however, to the author's knowledge none is planned yet for the North Sea.
The purpose of this study was to do a technical/ economical feasibility study of gas-to-methanol conversion aboard a converted oil tanker in the North Sea.
The methanol plant would be of Imperial Chemical Industries (ICI) design. Close contacts were established with their contractors in order to find what is critical when operating a plant under such adverse conditions.
With few exceptions the contractors outlined the same points as critical. Based on this information and knowledge about the limitations on other parts of the facility, it was possible to arrive at parts of the facility, it was possible to arrive at an expected "on time" plant availability.
The methanol producer was treated as a separate company, buying associated gas from the field operators.
A computer model was written to perform the economic evaluations. Both a base case calculation and a sensitivity analysis were treated in this model.
2. DESCRIPTION OF EQUIPMENT AND PROCESSES
Fig. 1 shows a principle view of the thought facility. The associated gas arrives at the SALM base, rises through it, and feeds into flexible lines to the plant. The 1000 M.T./day methanol plant is ICI's L.P. (low pressure) design.
In the plant the gas is first desulphurized. It is then combined with superheated steam (prepared from seawater) and fed to a reformer. There, synthesis gas, comprising hydrogen and carbon oxides, is formed. This mixture is further compressed and fed to the reactor where the methanol reaction takes place. This methanol is thereafter distilled and place. This methanol is thereafter distilled and stored in the tanker.
The processing tanker, together with the shuttle tanker when loading occurs, is free to weathervane 360 degrees around the SALM. The shuttle tanker then brings the methanol to a shore base for further distillation into grade AA before being stored.
The methanol facility is self-sufficient with energy and has an overall thermodynamic efficiency of approximately 60%. As a rule of thumb, it can be said the production of 1 M.T. of methanol requires approximately 31 MMSCF of natural gas.
3. TECHNICAL FEASIBILITY
The mooring unit is of Exxon's SALM type. It is able to permanently moor a 50-60000 DWT tanker in a northern North Sea environment, and should therefore not represent operating limitations.
The Exxon SALM is built in modules for rapid connections/disconnections when maintenance or repairs are performed at the field site.
Early in 1978, Sandia Labs participated in massive hydraulic fracture mapping experiments with Amoco in the Wattenburg area. On two of these massive hydraulic fractures in the Sussex formation, a downhole, wall clamped, three-axis geophone was tested. On the first experiment, the system was clamped in the open hole section during the breakdown phase. On the second experiment, the system was located in the lubricator during the main fracture and was lowered into place after shut-in.
Breakdown pump of the first experiment was conducted in four phases. The formation was first broken down and shut-in for a quiet period and then three 5000 gallon stages of fluid without proppant were pumped with a quiet period after each one. Following the last quiet period, flow back was started and half way through a shut-in was scheduled for the fifth and last quiet period. During even the smallest flow rates, the noise induced into the geophones was extremely large and masked any other seismic activity. During the quiet periods, several seismic events were observed. These apparently are from two sources: 1) motion associated with permanent movements of the fracture face permanent movements of the fracture face and 2) high frequency impulsive sources possibly associated with thermal possibly associated with thermal fracturing.
Following the 124,000 gallon fracture on the second experiment, the seismic system was lowered into place and clamped into the casing 50 feet above the open hole section that had been fractured. Seismic signals were recorded for approximately six hours after shut-in when the test was terminated. Both types of signals seen on the early experiment also appear to be present after the fracture treatment.
With the increased use of massive hydraulic fracturing, the knowledge of fracturing dimensions and orientation has increased in importance. The efficient and economic placement of wells for the optimum development of a field will require that fracture orientations be known. Fracture detection and orientation techniques received a considerable effort by El Paso Natural Gas in their Pinedale Field in 1974 and 75. The importance of determining fracture orientations was demonstrated by their research program in fracture mapping and the economic implications were described in reference 2.
Seismic detection of fracture signals has been ongoing for several years. In an early attempt to detect fractures at Oak Ridge, surface recording of seismic signals was utilized. The fact that seismic signals are created by hydraulic fracturing and that fracture faces may be mapped by determining the originating point of the signals has been well established. The frequency content of the seismic signals and the attenuation of the earth makes it imperative that seismic recordings be made close to the fracturing if the locations are to be determined. Extensive seismic recordings that were made at the surface during a massive hydraulic fracture in the Wattenburg area by Sandia proved to be incapable of determining fracture orientation. However, seismic signals can be received in the wellbore and these received signals used to map the orientation and plan view of the fracture in the vicinity plan view of the fracture in the vicinity of the wellbore.
Following the Wattenburg experiments in 1976, where surface seismic signals were not detected, Sandia initiated their program to develop a borehole seismic program to develop a borehole seismic recording system.
A finite element model was used to study the behavior of a well intersecting a finite conductivity vertical fracture at the center of a closed square reservoir. The two dimensional flow of single phase fluid was assumed to follow Darcy's law. The fracture and formation were represented by regions of uniform permeability and porosity. The well history prior to the boundary influence was found to be a prior to the boundary influence was found to be a function only of the dimensionless fracture conductivity, (kfw)D= (kf/k) (w/x f).
A period of pseudoradial flow, during which conventional analytic methods may be applied, develops following the early transient period. This period may not develop before the onset of pseudosteady state when xf/xe >1/2 and (kfw)D > . Fracture length and conductivity have little effect on the time of development of pseudosteady state flow. Graphs of log PD vs. log tDf for various values of (kfw)D have few distinguishing characteristics to aid type curve matching of field data. Data from the pseudoradial flow period give a good estimate of formation permeability and wellbore skin effect when matched with any of several curves. Calculations of fracture length are not reliable, however.
Large hydraulic fracturing operations have become commonplace, creating a need for better understanding of the flow near fractured wells. The expense of these operations increases the importance of diagnostic tools for analyzing the resulting fracture. Type curve matching of transient pressure data yields an apparent fracture length, pressure data yields an apparent fracture length, and is most often applied assuming that kf/k is infinite. However, analyses of a number of recent field tests using this technique produced apparent fracture lengths much smaller than were predicted by design calculations and by knowledge of treatment volumes. It has been speculated that this may result from limited fracture conductivity causing a deviation from ideal behavior. The non-ideal nature of both natural and induced fractures has long been recognized. Muskat in 1937 presented an analysis of pressure and fluid entry presented an analysis of pressure and fluid entry distribution along a fracture under steady state conditions. Prats studied steady state flow using conformal mapping of an elliptic fracture and reservoir. The limiting case yielded the solution for a fractured well in a circular reservoir. Prats deduced the effective well radius to be one-fourth the tip-to-tip fracture length when (kfw)D >2/pi.
Because the steady state flow of fluids following Darcy's law is described by La Place's equation, numerous potentiometric model studies have been undertaken. The difficulty of finding appropriate materials has caused discrepancies between results, some of which conflict with analytically derived limits.
These studies of steady and pseudosteady state flow are the basis of fracture design charts. It is important that consistent and correct data be used in these charts and for transient test analysis in order to optimize fracture design and to successfully evaluate the job.
Transient flow to a finite conductivity fracture was modeled by Scotts, who used the analogy between heat and mass flow. He confirmed Prats' results at very high fracture conductivity, but found less agreement when (kfw)D less than 2/pi. Scott attributed this to the scale limitation imposed by his heating and thermo-couple wires.
Pressure test analysis in fractured wells has relied Pressure test analysis in fractured wells has relied primarily on numerical and analytic studies of primarily on numerical and analytic studies of infinitely conducting fractures. The works of Russell and Truitt and Gringarten, et al. have made possible the use of short time transient well test data possible the use of short time transient well test data for evaluation of both reservoir permeability and apparent fracture length. The latter showed that a graph of dimensionless pressure vs. the log of dimensionless time has the slope 1.151 in the absence of a boundary effect.
Past research in miscible flooding has indicated some residual oil may be left in carbon dioxide swept rock as a result of CO2-oil phase behavior, rock pore structure, or mobile water saturation. Determination of the magnitude of this residual oil saturation in the reservoir rock of interest is important when a field is evaluated for CO2 miscible flooding. However, miscible displacements in laboratory outcrop cores sometimes exhibit a length effect, suggesting that reservoir rock samples as long as ten feet or greater may be required for the determination of the true unit displacement efficiency. This paper describes the development of a technique allowing the measurement of CO2 unit displacement efficiency in short core system consisting of either actual reservoir rock or outcrop sandstones.
A number of core floods were performed under varying conditions in which continuously injected CO2 displaced a synthesized reservoir fluid from 15- to 30-cm long Berea sandstone cores and low permeability carbonate cores from a West Texas permeability carbonate cores from a West Texas reservoir. For secondary and tertiary recovery floods in both core types, residual oil saturations comparable to those reported for long sandstone systems were observed when solvent fingering was controlled. Length and rate effects previously observed are demonstrated to depend primarily on solvent sweep efficiency rather than the mechanism for achieving miscibility. The current as well as previous studies show that gravity, transverse dispersion, and viscosity gradation may each be effective stabilizing mechanisms under appropriate conditions. This work allows the relative importance of each to be estimated in a core flood and for the first time their combined influence correlated with the measured overall displacement efficiency. Two methods are described and shown to be effective for generating the viscosity graded CO2-oil transition zone required for flood stabilization when gravity and transverse dispersion are relatively unimportant, as in short, low permeability reservoir core samples. Based on these concepts, laboratory CO2 floods may be designed to prevent viscous fingering now enabling measurement of the true CO2 unit displacement efficiency in short laboratory systems.
Carbon dioxide miscible flooding is one of the more promising processes for enhanced oil recovery. Evaluation of prospects for full-scale CO2 flooding requires a thorough understanding of recovery behavior. Unit displacement efficiency is an important factor in such an evaluation and, because unit displacement efficiency may depend on rock and fluid properties, core displacement tests in actual properties, core displacement tests in actual reservoir rock using realistic reservoir fluids may be necessary for the evaluation of each candidate reservoir. This paper describes a technique for flooding short pieces of reservoir rock containing reservoir fluids at reservoir temperature to determine the residual oil saturation left in the fully-swept rock.
Very few CO2 miscible displacement tests have been performed in the past using actual reservoir rock. Instead, most laboratory studies of CO2 flooding (as well as with LPG and other solvents) have been conducted using outcrop sandstone cores. Berea, Boise and Torpedo sandstones were chosen due to their availability and uniformity. These sandstones can be cut easily into lengths of approximately 10 ft, and much longer systems for displacement studies can be constructed by butting cores together. Reservoir rock, on the other hand, must be obtained from oil-field core samples. Lengths of reservoir rock for laboratory flooding are limited to several feet at most for stacked cores and to considerably less for single cores.
A wide variation in the apparent residual oil saturation left to miscible flooding, Sor, has been observed in laboratory displacements with both CO2 above the multi-contact miscibility pressure and with first-contact miscible fluids even when similar porous media were used. porous media were used.