A simple and efficient approach has been developed for improving the predictions of gas and liquid phase viscosities of reservoir fluids. The proposed method was based on the Lohrenz-Bray-Clark (LBC) correlation and applied to the Peng-Robinson equation of state (EOS) as all example although it can be applicable to any EOS. It can significantly improve the predictions of gas and liquid phase viscosities of hydrocarbon mixtures, particularly of high viscosity fluids. The approach is quite suitable for equation of state (EOS) based reservoir simulators and can further improve the prediction of reservoir fluid viscosity with appropriate tuning of the EOS.
Accurate predictions of gas and liquid phase viscosities of reservoir fluids are required in reservoir simulators, particularly in equation of state (EOS) based reservoir simulators. Many researchers have focused their attention on improving the prediction of gas and liquid viscosities. However, most of the methods from mathematically rigorous to completely empirical forms are only applicable to either gas phase or liquid phase within a limited range of composition, temperature and pressure. In reservoir simulations related to oil and gas production, viscosity prediction methods are required to be applicable to a wide range of hydrocarbon mixtures at various conditions. The Lohrenz-Bray-Clark (LBC) correlation is probably the most used one in reservoir simulation models. The correlation was based on the Jossi-Stiel-Thodos correlation and modified by Lohrenz et al. The correlation is related to a fourth-degree polynomial in the reduced density. The disadvantage of the correlation is that the predicted viscosity is very sensitive to the density which is normally determined by a cubic EOS and may be very inaccurate for high viscosity fluids. Alternatively Ely and Hanley presented an extended corresponding states model for predicting the viscosity of non-polar pure fluids and their mixtures. Pedersen and Fredenslund studied this method and proposed a new corresponding states method which is based on the principle of corresponding states with methane as the reference component. Later Aasberg-Petersen et al. further improved the model by introducing n-decane as the second reference component. Little and Kennedy used an analogy with the van der Waals EOS to correlate the viscosity of reservoir fluids. Lawal applied the Lawal-Lake-Silberberg EOS to correlate the viscosity as well.
In this study, a simple and efficient approach is proposed to improve the predictions of gas and liquid viscosities of reservoir fluids. The new method is based on the LBC correlation with the introduction of an exponential term and incorporating a cubic EOS. The method has been used to predict the viscosities of pure components, binary mixtures and reservoir fluids over a wide range of pressures and temperatures. The predicted results demonstrate that the new method can significantly improve the accuracy of viscosity predictions when compared with other published methods, particularly for high viscosity fluids. It is shown that the predictions can be further improved by appropriate tuning of the EOS.
As the Lohrenz-Bray-Clark (LBC) correlation is expressed as a function of the reduced density, the calculated viscosity is very sensitive to the density.
Permeability anisotropy in a coal seam in the Bowen Basin has been measured by a multiple well interference test. The degree and orientation of the anisotropy was apparently influenced by coal structural features on various scales. Simulations of the field observations using a two-phase dual porosity model confirmed the single-phase interference test analysis, and also simulated various aspects of the seam response to subsequent stimulation treatments involving two-phase fluid injections. The influences on reservoir response of reservoir heterogeneity, relative permeability and flow localisation are discussed with respect to the application of continuum modelling concepts.
Naturally occurring fracture systems in coal occur on a range of scales. The fractures have much higher fluid conductivities than the coal matrix and generally control the fluid transport properties. The most pervasive natural fracture system is the cleat system, formed mainly in bright coal by orthogonal sets of face and butt cleats, lying in planes normal to bedding. These define a blocky structure within the coal, which because of the more planar and continuous nature of the face cleat relative to the butt cleat, can result in strong permeability anisotropy This is reflected in measured anisotropy ratios as high as 17:1 in the plane of the seams.
Permeability is one of the most important factors controlling the production of coalbed methane (CBM), and efficient stimulation is generally required to obtain adequate gas production rates. Hydraulic fracturing is the commonly applied stimulation method. An alternative technique, openhole cavity completion, may be successful if conditions are suitable. In either case, the presence of horizontal anisotropy in the permeability field can strongly affect the efficiency of the stimulation, and needs to be considered in the stimulation design and the production well layout.
In assessing the likely orientation of permeability anisotropy in a coalbed methane reservoir, it is often assumed that the major permeability axis will parallel the face cleat direction which in turn is assumed to parallel the direction of the major horizontal principal stress. The direction of the major principal stress might be estimated by measurement of hydraulic fracture orientation in a minifrac test in the bounding sediments of the seam, and the major permeability axis inferred from the stress direction. Alternatively, core orientation methods may provide the cleat direction directly. However, these methods may not account for other influences on permeability orientation, such as the effect of broader scale fracture systems, or the coupled effects of the structures with the stress regime and pore fluid pressure gradients.
During an investigation and trial of stimulation by cavity completion carried out in the Bowen Basin, detailed reservoir response to the process was investigated. Reservoir characterisation undertaken before stimulation included direct measurements of permeability anisotropy by interference testing in multiple observation wells. Subsequently, during stimulation operations, both water and air were injected using a range of rates, pressures and durations, including highly dynamic, short duration events. Data from the active wells and the observation wells were continuously recorded throughout the operations. Analysis of permeability anisotropy based on the response of the observation wells was carried out using both standard analytical methods and numerical simulations.
This paper presents the field data in the context of the target seam conditions and compares estimates of permeability anisotropy from the standard analysis of the single-phase interference tests with the values obtained by numerical simulation of the complex two-phase injection history. The limits of continuum analysis in terms of the scale effects of coal structures, mechanical-fluid flow coupling and flow localisation and the implications for coalbed methane reservoir characterisation are discussed.
In the next ten to fifteen years the demand for natural gas in North East Asia is set to double. This paper examines the technical and economic feasibility of transporting natural gas from the gas rich areas of the North West Shelf of Australia and South East Asia via a large diameter pipeline system to the gas markets of North East Asia.
A pipeline from Australia would cross water depths of nearly 2000 metres in the Timor Gap and around the Indonesian archipelago. Whilst advances in new technologies suggest that a pipeline crossing this difficult terrain in very deep water is feasible, economic analysis indicates that such a system is not commercially viable. However, a pipeline from S.E. Asia would offer tariffs similar to those of a LNG transportation system and accordingly it is concluded that such a pipeline can provide a feasible and attractive gas transport system.
Natural gas markets in N.E. Asia, namely Japan, South Korea and Taiwan, are currently serviced by LNG imports from suppliers around the world. In the next ten to fifteen years gas demand in N.E. Asia is set to double, and there exists an opportunity for suppliers in Australia and S.E. Asia to service this demand.
The concept for a pipeline from the North West Shelf of Australia to Japan was publicly mooted in the early 1990's, but has never been considered in any detail. This paper investigates the feasibility of large diameter gas pipeline systems, firstly from Australia to Japan and secondly from S.E. Asia to Japan. Both technical and commercial assessments are made to determine the feasibility of such pipeline systems. For example, a pipeline system from Australia would lie in water depths of up to 2000 metres in the Timor Sea and surrounding southern islands of the Indonesian archipelago. This deepwater section raises many technical challenges which are discussed within the body of the paper.
Supply and Demand of Natural Gas in Asia
Before considering the feasibility of a gas pipeline to Japan, the projected gas demand must be analysed to ensure that a venture of significant magnitude is warranted.
Current forecasts indicate LNG demand in N.E. Asia will increase from 50 to 120 MTPA (68 to 162 BCMPA) in the next fifteen years. Forecasts are based on the increasing energy requirements of the established markets of Japan, Taiwan and South Korea, and emerging markets of Thailand and China, as shown in Fig. 1.
Assuming this demand is realised, by the year 2010 there will be a projected shortfall in supply of approximately 45 MTPA (61 BCMPA). To put these figures in perspective, Australia's current LNG export capacity is 7.5 MTPA. Shortfall in supply is shown on Fig. 1 and defined as gas demand not covered by known contracts, memorandums of understanding or letters of intent, but would be subject to competition from potential LNG projects in USA, South America, Russia and the Middle East. A shortfall in supply of such quantities yield significant opportunities for gas producers to secure market share, and fund developments for gas transport infrastructure.
A Gas Pipeline to Japan
A pipeline system from Western Australia would be approximately 8500 km long and pass up through the Indonesian archipelago, the South China Sea, past China, Taiwan and onto Japan and South Korea. A preliminary pipeline route based on minimising water depths is shown on Fig. 2. The depth profile along the proposed pipeline route is indicated in Fig. 3. The maximum water depth is approximately 1800 metres, located south-west of Timor.
For years the drilling industry has wrestled with the problems associated with well cementing. The introduction of pneumatic bulk systems increased cement slurry mixing rates but accurate density control still eluded the experts. Many companies have introduced process controlled mixing systems but these are both expensive and not totally reliable.
A new cementing system, that does not rely on bulking, has become available to the industry - a storable oilwell cement slurry that can be kept in a liquid state indefinitely and made to set as and when required.
Operators in Indonesia are now benefiting from this new technology. Slurries are mixed and tested to ensure they meet design specifications well before they are required on site. The "Base Slurry" or "Liquid Cement Premix", which typically has a density of 16.0 pounds per gallon (ppg), is transported to the rig, diluted to produce the required density and pumped ensuring a homogeneous slurry from start to finish.
Due to the staggering economic and population growth in Indonesia the government has undertaken an ambitious plan to supply sufficient electricity to support this development. Situated on the "Pacific Rim", in an area renowned for being part of "the Ring of Fire", geothermal electricity generation is an obvious choice and a crucial component to the success of this plan.
A promising geothermal concession earmarked in the plan is situated in a tea plantation on the island of Java. A drilling project was undertaken to evaluate and harness this excellent resource. The evaluation program incorporated the use of two slim hole rigs to drill appraisal wells and establish the full potential of the field.
Companies are being faced with environmental concerns throughout the world. This, and the requirement to reduce the size of drilling sites in environmentally sensitive areas, necessitated a change in the way these operations were serviced (Figure 1). Cementing companies historically have needed a large work area or "foot print" for bulking and mixing equipment.
Geothermal wells arguably present the most severe conditions to which cements are exposed. As a result, the performance requirements are among the most stringent. At present, geothermal cements are usually designed to provide at least 1,000 psi (7.0 Mpa) compressive strength, and no more than 1.0 md water permeability (1). Meeting these requirements was further complicated with the cement slurry for the 4-1/2" casing where, if lost circulation was experienced during drilling and a coring string utilized to reach casing point, the open hole section could have a diameter as small as 5". While casings with tight annular clearances require that "good cementing practices" be observed (i.e. centralization, drilling fluid conditioning etc.) it also creates conditions that demand much greater care and control in slurry and procedure design than "regular" casing cementations. Guidelines, when designing a cement system for slim-holes specify:
1. Keeping the cement slurry density fluctuations to a minimum.
2. Designing the cement slurry to have the lowest practical rheologies while maintaining zero free water breakout.
3. Enhanced slurry rheologies for optimum wellbore flow phenomena.
While free water and thickening time requirements were similar under geothermal and slim-hole conditions, the use of Perlite and silica flour, in large percentages, complicated the rheological limitations. Achieving these prerequisites with less equipment in an environmentally sensitive area posed an interesting problem.
Strategies in Developing Coalbed Methane Prospects in Australia: An Example from the Galilee Basin of Central Queensland M.J. Zebrowitz, SPE, and M.R. Herrington, SPE, Enron Exploration Australia Pty Ltd; M.E. Blauch, SPE, Halliburton Energy Services; and J.M. Coughlin II, SPE, Dominion Energy Inc.
This paper describes Enron Exploration Australia's methodology and strategy for designing hydraulic stimulations used as the completion technique on two pilot coalbed methane wells in the Galilee Basin in central Queensland, Australia. This process involved coal-seam characterization technologies based on the acquisition and petrologic analysis of slim-hole core data. Results to date illustrate the significance of coal-seam characterization, the difficulty in predicting gas/water production behavior based on theoretical modeling, and the stimulation process as a means of gathering critical production data for future development strategies.
Although extensive coalbed methane reserves have been identified in Australia, the primary challenge facing the coalbed methane industry here is to prove the reserves' producibility potential. Enron Exploration Australia is currently facing this challenge in the Galilee Basin in central Queensland. Two areas containing 25 to 35 m of gas-bearing coals and 17 to 23 Bm3 of gas-in-place have been identified as potential gas discoveries.
The strategy for this Galilee Basin development (ATP 529P), an area of approximately 48,000 km2, has evolved since it was leased by Enron in November 1992 (Figure 1). Geological evaluation involved the interpretation and integration of 40,000 km2 of space-borne imagery, 10,000 line kilometers of seismic data, aeromagnetic and gravity surveys, a large vitrinite reflectance database, and stratigraphic cross sections/isopach maps. Wellsites were selected after performing an extensive study of lateral and vertical coal continuity and thickness, modeling lateral and vertical thermal maturity, and implementing a state-of-the-art fracture detection program for locating fracture permeability.
The Galilee Basin consists of two structural regions, the Koburra Trough and the Maneroo Platform ramp. Exploratory wells were strategically placed to evaluate each region (Figure 2). Exploratory drilling was conducted with slim-hole equipment, allowing extensive collection of detailed reservoir data: 1.5 km of core were recovered, 88 gas-content measurements were analyzed, and 34 drill-stem tests (DSTs) were performed.
During the 1993-94 exploration program, the Crossmore and Rodney Creek Anticlines were identified as potential significant gas discoveries. The Crossmore area contains 24 m of fully gas-charged coal and an estimated 17 Bm3 gas-in-place. The Rodney Creek area is underlain by 30 to 35 m of fully gas-charged coal and an estimated 23 Bm3 gas-in-place.
Using the extensive reservoir data set and developing the two structures on 260-ha spacing, engineers conducted a reservoir simulation study to forecast gas rates and cumulative gas recovery. After an accurate conceptual understanding of the coal seams being considered for production was developed, hydraulic stimulation was used as the completion technique on the two pilot wells. Two production wells were drilled and completed in late 1995 to establish baseline gas production rates. The results demonstrate the difficulty in predicting gas/water production behavior based on theoretical modeling.
Exploration Activities and Results
All available geological and geophysical data were used to adapt a comprehensive exploration approach to locate the areas that would be underlain with a highly fractured, gassy, thick coal section. The fracture-detection program centered on a fracture-kinetics model in which open fractures are most likely to form from the draping and warping of sediments over basement features. This model was developed as an analog to the broad platform of continuous permeability present in the San Juan Basin coalbed methane production "Fairway."
The primary basis for wellsite selection was the interpretation and integration of 40,000 km2 of landsat thematic mapper imagery, aeromagnetic and gravity coverage, and approximately 10,000 line kilometers of seismic data that detect subtle basement features with fracture-related permeability.
Dr. Jack R. Nelson, SPE
Increased recovery from existing, marginal and partially depleted oil fields has been the objective of many operators over the years. Conventional step out drilling, redrilling, and reentering are often options to consider in these cases. Improvement in recoverable production may be obtained, although economics may be questionable in many cases.
Horizontal drilling technology has been widely and successfully applied around the world for the recovery of heavy oil, light oil and gas. Impressive technical successes have been achieved in horizontal technology through a variety of improvements in tools, and experience gained over the past several years.
Utilizing horizontal drilling technology in developing and increasing productivity of marginal fields has improved economics in most instances. Also it has provided solutions to the recovery of oil from inaccessible areas in reservoirs such as undrained fault blocks. After abandoning old wells, the existing wellbores are re-entered and horizontally redrilled through the pay zone.
The primary objective of a horizontal well is to increase the wellbore contact with one or more reservoirs. Often this contact will be limited to a specific interval in the reservoir. There are factors and limitations that determine the success of horizontal wells.
This paper will discuss the selection of reservoir candidates, planning options, re-entry drilling, and well completion of the horizontal candidates.
In recent years, horizontal drilling techniques have been successfully used worldwide in a variety of situations. The impressive technological and economic success achieved has resulted from new and improved tools, better methodology, and a wide background of experience that has been developed over time.
Horizontal drilling is being commonly used today as a technique for improving recovery and productivity from marginal or partially depleted fields because it offers the benefit of greatly improved drainage patterns from a minimum of well bores. This application may take the form of re-entering existing well bores and drilling a horizontal hole through a window milled in the casing or new wells may be drilled as necessary. Variations in application are many. The horizontal well bores may be used to improve existing well patterns or, to reach inaccessible areas of the fields or, to permit economic production levels from reservoirs in advance stages of depletion which are subject to water or gas coning.
Benefits of Horizontal "Re-Entry" Drilling
Horizontal wells must be considered today as an attractive way of developing reserves. Drilling horizontally is not an objective itself, the objective is increased production and reserves. A comparison can be made between the productivity of a horizontal vs. a vertical well using different parameters such as spacing, permeability and length of horizontal sections to more easily visualize the capability of horizontal wells for improving production and increasing reserves. These comparisons are based on ideal considerations seldom encountered in real reservoirs but they serve to illustrate the advantages of horizontal drilling.
The comparison will start with spacing (Fig. 1) which is based on the calculation formula of Dr. Joshi. Assuming that the net pay is 50 ft., the horizontal permeability is equal to the vertical permeability, the wellbores have radii of 3.5 in., and that the horizontal sections are 1600 ft., the productivity of each horizontal well is almost 10 times higher than the vertical well for a vertical-well-drainage area of 40 acres.
A new technique has been developed that allows determination of the resistivity of a pristine sample of irreducible water trapped during oil accumulation, This fluid inclusion technique, termed ROI, is directly applicable to the evaluation of oil accumulations where the salinity of present day formation waters below the OWC differs from that of irreducible water trapped during oil accumulation.
Determination of oil saturation for calculation of oil reserves is critically dependent on the resistivity of formation water (Rw). Water saturations calculated from logs require an Rw value for irreducible water in the oil zone. In conventional log analysis the formation water salinity in the oil zone and therefore the Rw is assumed to be the same as that below the OWC. This relies on the assumption that the water below the OWC has not changed following oil charge.
Irreducible water is trapped with oil in microscopic fluid inclusions within reservoir grains. Resistivity of this water can be derived from an ice melting temperature using the correlation between colligative and transport properties of aqueous solutions. Measurements are made on core or cuttings samples from the oil zone and exclude contamination from mud filtrate invasion.
Water below the OWC may change after oil charge in basins which are exposed at the land surface. This may allow recharge of meteoric water, potentially resulting in lower salinity water below the OWC than in the oil zone e.g. in more shoreward oil filled reservoirs underlain by freshwater aquifers in the Gippsland Basin, calculated water saturations using the salinities from water below the OWC are inconsistent with RFT, capillary pressure and production test data. The opposite situation can also occur where tectonic movements cause relatively deep saline water to flow into reservoir rocks below the OWC.
In these situations the water below the OWC will differ in salinity and Rw from irreducible water in the oil zone which is shielded from later flow of formation water by high oil saturation.
The timing of changes in hydrology relative to oil charge has major implications because use of an inappropriate formation water resistivity value can result in incorrect reserves estimation. Decisions regarding field development are linked to reserves estimates and accurate Rw values are essential.
Current Methods for Determination of Rw
The most direct way of finding water resistivity (Rw) is to obtain a sample of formation water and measure its resistivity. However, this is seldom possible, as formation water samples are usually contaminated by mud filtrate. Rw is therefore usually calculated by one of two methods:
1. SP method
2. Archie equation
Reliable determination of oil saturation from logs requires a determination of Rw from a measurement directly on a sample of the irreducible water.
Calculated Rw relies on a number of assumptions which may result in erroneous values - the SP method does not work for oil based muds and does not give correct estimations of Rw in hydrocarbon bearing zones while the Archie equation method only works in clean, water-bearing reservoirs and is typically unreliable in highly fractured or vuggy reservoirs.
Capillary Pressure and Relative Permeability
For practical purposes, the value of the irreducible or minimum water saturation in the oil zone is usually assumed to represent the interstitial water content of the pay section of the reservoir. Interstitial water in this zone is held in place by capillary forces, and flow differentials will not remove it. P. 137
A number of tools are available for production improvements for wells where the cost of workover rigs cannot be justified or where workover rigs are unavailable. Recent literature has described some through tubing and rigless type workover innovations. This paper presents case histories explaining the use of production logging, coiled tubing, small bridge plugs, cement packers, acidizing and oriented perforating methods that resulted in excellent gas and oil production increases. Significant savings were experienced when compared to more conventional rig supported workovers.
Cement packers placed by coiled tubing and oriented through tubing perforating have been used in several cases to restore inactive wells to commercial production rates. This paper describes two such attempts. In another case, extraneous water production was identified with a production log and shut off with a simple bridge plug setting. This was followed by acid stimulation of the gravel pack to restore the damaged interval to good gas rates. A third case is also presented to show several problems that were encountered in an older well.
In order to select the appropriate technique and achieve the best results, a clear understanding of the problems, the objectives, and the available tools is needed for each case. This was accomplished by use of a multi-disciplinary team of various operating company and service company professionals involved in, the design and field operations to thoroughly review each proposal.
VICO Indonesia operates several oil and gas fields in an area of East Kalimantan approximately 140 kilometers north of the city of Balikpapan (Fig. 1). These fields are operated under a production sharing contract with Pertamina, the Indonesian national oil company. VICO is the operator of a joint venture that began in the late 1960's and discovered commercial oil and gas in early 1972.
Today the production rates are approximately 1.7 billion cubic feet (Bcf) gas, 40,000 bbl of condensate and 30,000 bbl of oil per day from VICO's four major fields. Gas is transported and sold through the liquification (LNG) plant at Bontang, and the liquids are blended and sold via the tanker terminal at Santan.
Badak, the largest and oldest field, has now been completely developed by drilling. Because of the large number of reservoirs penetrated by wells in this field, workover operations will continue for many years to recomplete into shallower zones and repair existing completions.
Now, in efforts to maximize the use of all wellbores and considering cost containment issues, production engineers at VICO have designed and performed several unique work programs that utilize rigless methods at a cost of about one-third the cost of similar rig supported workovers. These programs involve the use of production logs, coiled tubing, special cementing techniques, oriented perforating, inflatable packers, acidizing cement packers, computer modelling, small diameter tools, etc.
Generally, very good success has resulted from the overall program. Gas production was increased by 130 million cubic feet per day (MMcf/D) and oil rates improved significantly in 1995. A few unexpected problems were encountered and these are also discussed.
TDT Log, Coiled Tubing cement Packer, Oriented Perforating - Badak Well number 121
The original completion for Badak well number 121 was a dual gas well. By 1993 both zones had watered out, but interest in a zone behind casing led to a thermal decay time (TDT) log survey (Fig. 2). This survey showed that the three zones in the B-12 reservoir were not uniformly depleted since the middle interval was wet while the upper and lower sections contained gas.
This paper discusses a methodology for estimating permeability from well logs, based on conventional core and log data. The work was done on a small set of wells containing a glauconitic sandstone reservoir in the Barrow Sub-basin offshore, Western Australia. Core porosity and permeability data were used to determine porosity-permeability transforms and to subdivide the "greensand" into various groups within two sub-units. Electrofacies patterns and decision functions were determined to establish a link to permeability transforms in order to identify sandstone groups and to obtain porosity and permeability from well logs where cores were not available. Estimates of permeability were found to be more accurate than using other methods. In this technique, permeability transforms were obtained not only by considering unique relationships between porosity and permeability but also grain size and sorting et al. The results of this work have been encouraging and the study is now being extended on a regional basis.
In formation evaluation, it is generally essential to obtain realistic values of permeabilities from well logs because core-based permeability data are often not available either because of bore hole conditions or due to the high cost of coring. For many years, attempts have been made to estimate permeability from well logs. Much literature has been published on the subject and a number of methods and models are being used to achieve this goal. Two categories of equations are generally available. One category contains the so-called 'standard methods' such as Wyllie and Rose (1950), Timur (1968), Coates and Dumanoir (1973) and some modified forms of these. They are based on establishing empirical relationship (formulas or models) which are functions mainly of porosity, permeability, irreducible water saturation or clay content. However, none of these is generally applicable from field to field, well to well or even zone to zone without making adjustments to constants or exponents, or introducing compensations. Moreover, the accurate determination of irreducible water saturation and clay content from well logs is not an easy task. Alternatively, there are 'statistical methods' such as are described by Nicolaysen (1991), Sinha (1994), Johnson (1994) and others. They attempt to establish a direct statistical relationship between log responses and permeability, or use a data base to relate permeability to log responses on a field wide basis. The methods utilise relationships which are implicit in the data to arrive at results. No predetermined equations are required, and results are obtained by statistical inference.
The subject reservoir of this study is an extensive, marine transgressive, and glauconite-rich formation. It was deposited during a southward-progressing marine transgression over deltaic topset sands during the Early Cretaceous. The glauconitic sandstone is mineralogically complex. The main mineral components include quartz, glauconite, siderite, dolomite, calcite, feldspar, kaolinite, pyrite, and their alternation products. Quartz, glauconite, feldspar and siderite generally are the most abundant minerals and occur together in most of the Mardie lithofacies Porosity (helium injection) and permeability were determined on 139 core plugs on 4 wells cored in this area. They indicate that porosities are medium to high (from 13.9% to 29.7%), that permeability ranges from 0.01 md to 47 md throughout the sandstone in the two main sub-units and that there is poor correlation between porosity and permeability. Traditional methods for estimating permeability from log responses are not applicable in the Mardie Greensand.
The effect of reservoir heterogeneity on the productivity of wells in closed depletion reservoirs is investigated. A direct pseudosteady-state equation solution, derived using the divergence theorem, is used to conduct an extensive stochastic simulation study at greatly increased computational efficiency. Dozens of permeability fields corresponding to various Dykstra-Parsons coefficients and correlation lengths are generated using geostatistical simulation techniques. The pseudosteady-state equation is solved by a finite-element method in 2D heterogeneous reservoirs. Pressure drawdown is calculated from the solution. Results are analyzed statistically to examine the effects of geostatistical parameters of reservoir heterogeneity on well productivity during pseudo steady-state.
Analysis of the results show that the properties of the pressure drawdown frequency distribution function are sensitive to structure (well-block permeability) and intensity (Dykstra-Parsons coefficient), but weakly to connectivity (correlation length). Bivariate analysis indicates that the logarithm of pressure drawdown is linearly correlated with the logarithm of the well-block permeability, and that spatial connectivity of permeabilities affects the correlation. Comparison with the behavior of equivalent homogeneous systems provides quantification of an additional pressure loss due to reservoir heterogeneity as a function of Dykstra-Parsons coefficient and correlation length.
The influence of reservoir heterogeneity and geostatistical properties on long-term well productivity in depletion reservoirs has not been addressed in detail. A major purpose of this study is to demonstrate how this issue may be addressed statistically using a simple method for a direct pseudosteady-state solution developed at the University of Texas at Austin (Lee et al., 1996).
Earlier studies obtained the average permeability (and thus well productivity) of heterogeneous reservoirs under global-average parallel flow conditions. It is known that the average permeability is usually near or equal to the geometric mean of the local permeability in 2D uniform flow, if the probability density function of permeability is log-normal (De Marsily, 1991). Bakr et al. (1978) and Gutjahr et al. (1978) have also presented linearized approximations of the average permeability for a log-normal probability distribution function. Lachassagne et al. (1990) suggested the use of power averaging for macroscopically uniform flow to minimize the discrepancy between effective permeability and theoretical results for globally-parallel flow. Holden et al. (1990) also presented an estimator for the effective permeability. None of these studies, however, looked at the problem of converging flow toward a wellbore in heterogenous permeability fields.
Taking advantage of the computational efficiency of a method for directly calculating pseudosteady-state pressure response (Lee et al., 1996) we conducted an investigation of flow into a single well in a square drainage area with stochastically-generated, heterogeneous permeability field. Repeated generation of permeability images allows a stochastic assessment of the impact of geological heterogeneities. The results of pseudopressure drawdown are used to statistically examine the effects of reservoir heterogeneity on long-time well productivity.
Stochastic Model and Simulation Procedure
As a first simplifying assumption, the spatial variability of reservoir properties is limited to that of permeability because the effects of porosity on subsurface fluid flow have been shown to be small (Lake, 1989). P. 251