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Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 13–17, 1999

Paper Number: PETSOC-99-39

Abstract

Abstract This paper presents results of an investigation of various criteria that can be used for decisions related to reducing the number of layers needed to represent a reservoir in reservoir simulation. One of the approaches towards reducing the number of grid-blocks needed in simulation study is to combine thinner layers represented by scaled petrophysical properties. The Gypsy formation was used to develop three different geological models based on channel identifiers, lithofacies and flow units, respectively. The effect of the criteria used for combining layers on simulation results was studied by conducting scale-up for three different geological models, three different production scenarios and three different boundary conditions. It is observed from the results that the use of lithofacies as a criterion provided the closest match to fine-scale results. Also, results based on three criteria differed significantly only during the early phase of flow. Strategies of geological modeling have a significant impact on scale-up. The channel model and the lithofacies model produce similar results, but flow unit model provides inferior results. Comparing the scale-up results for nine-spot drive, line-drive, and five-spot drive, the line-drive scenario produced the best matches for both water production and reservoir pressure. Comparing the scale-up results obtained for three different boundary conditions, no-flow boundary condition obtained a better results compared to open boundary conditions. Introduction Various scale-up techniques have been developed in recent years, such as average methods (arithmetic, geometric, harmonic) 1,2 , tensor method 3,4,5,6 , transmissibility scale-up 7,8 , renormalization technique 9,10,11,12 , and pressure-solver method 2,13 . A limitation of these scale-up methods is that they concentrate only on the mathematics of combining petrophysical properties of finer grid-blocks, while giving little consideration to the heterogeneity of geological and structural details. These methods choose coarse-grid cell boundaries independent of the distribution of reservoir properties, i.e., averaging reservoir properties within layers or channels without considering the effect of heterogeneity on fluid flow and scale-up. Such 'layer or channel scale-up' may average out the effects of extreme values of reservoir properties, such as thin continuous communicating layers, large flow barriers, or partially communicating faults. Therefore, in order to obtain reliable results in scale-up for reservoir simulation, not only is it very important to use a reliable mathematical method for the calculation of average value of reservoir properties for the upscaled grid blocks, but also to find an effective method to determine the boundaries of upscaled grid blocks. Successful scale-up result can be obtained with the combination of reliable mathematical scale-up methodology and detailed description of formation heterogeneity. One of the objectives of the study is to study the effects of different modeling strategies on scale-up. In an analytical approach, permeability values are averaged or scaled up by using selected mathematical averaging method. The scale-up results obtained from these methods depend only on the distribution of permeability values in reservoir model. In a numerical approach, the average permeability is obtained by first running reservoir simulation on fine-scale model, and then calculating average permeability using the simulation results. For this approach, scale-up results are sensitive to the flow conditions, such as production scenario and boundary condition.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 13–17, 1999

Paper Number: PETSOC-99-45

Abstract

Abstract In many steam-based heavy oil/bitumen recovery processes, non-condensable or condensable gas is either present in the reservoir or is co-injected with steam. The distribution of non-condensable gas in the oil-depleted region can be very complex and may greatly influence process performance. The mechanisms are not fully understood. The current numerical study attempts to better understand the SAGD process where gas is either present or co-injected. Numerical simulations were based on comparison with published laboratory experiments. A sensitivity study was carried out to examine the effects of gas diffusion, heat loss, spatial aspect ratio, and heterogeneity. The study showed that gas diffusion caused by concentration gradient is minimal, and the gas flow appears to be dominated by forced convection. Noncondensable gas accumulates and concentrates in the region where steam condenses. The gas distribution in the oil-depleted zone is determined by steam/gas injection rate and heat loss rate. Introduction The Steam Assisted Gravity Drainage (SAGD) process 1,2 is regarded as one of the leading in-situ recovery processes for heavy oil and bitumen resources. After the success of the UTF 3,4 field pilot, many SAGD projects are in operation, construction, or planning stages in western Canada. In the SAGD process, as the steam chamber grows, oil is gradually recovered, accompanied by increasing steam-oil ratio. At a certain point, it is no longer economic to continue steam injection; however, the reservoir is still hot, and the energy in place can be used. Non-condensable or condensable gas injection has been proposed as a follow-up process. A less energy-intensive gas injection process can maintain reservoir pressure, utilize energy in place, and prolong oil production. When a new SAGD operation is implemented adjacent to a depleted zone, it is likely that steam may escape to the depleted zone, thereby greatly reducing process efficiency. One of the methods proposed to overcome this problem is to inject non-condensable gas into the depleted zone to increase and maintain reservoir pressure, and to prevent steam from escaping. In order to extend the range over which SAGD can be applied, it has been proposed to coinject steam with non-condensable gas to reduce heat loss to the overburden 5 . In fact, in SAGD operations, the injected steam often contains a considerable amount of noncondensable gas, such as carbon dioxide or nitrogen. When SAGD is applied to a live oil reservoir, the solution gas in the oil may mix with the steam, and hence make the process more complicated. All of the above processes and applications involve the presence of a steam-gas mixture in the reservoir. Gas mixing in porous media is a complex process, involving diffusion and convection. Depending on the operating conditions, the distribution and movement of gas and steam in the reservoir may greatly influence process performance. Unfortunately, our understanding of the mechanisms is incomplete. This is because it is very difficult to measure the distribution of gas concentration directly, even under well-controlled laboratory conditions. It is even harder, if not impossible, to measure gas velocity in the reservoir.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 13–17, 1999

Paper Number: PETSOC-99-34

Abstract

Abstract This paper presents the results of a study on the development of efficient methods for scaling of petrophysical properties from high resolution geological models to the resolution of reservoir simulation. These methods were evaluated using the data for Gypsy field located in northeastern Oklahoma near Lake Keystone. In this study, transmissibility between two grid blocks is the property that is scaled. After conducting the linear flow scale-up of transmissibility between two grid blocks, a scale-up of productivity index (PI) was found to be important and necessary in order to account for the radial flow around the wellbore. Special consideration was also needed for the pinch-out grid blocks in the system. Validity of the proposed approach was evaluated by comparing the performance prediction for various reservoir flow scenarios using finescale and coarse-scale reservoir models. Introduction Numerous methods of scale-up for single phase flow have been developed, including average method (arithmetic/ geometric/ harmonic), 1,2 tensor method, 3,4,5,6 transmissibility scale-up, 7,8 renormalization technique, 9,10,11,12 and pressuresolver method. 2,13 The simplest method for scaling permeability of a reservoir formation is the average method. Begg et al .2 determined that harmonic and arithmetic methods gave the lowest and highest values, respectively, of average permeability and the geometric method provided results between the values from harmonic and arithmetic methods. White and Horne 7 demonstrated that the general tensor scaling procedure can give accurate, efficient production estimate on a coarse grid. Uniform pressures are applied at two opposite faces and no-flow boundary conditions are applied at the other four faces when solving the finitedifference equation. Tensor method is significantly more accurate than other scale-up methods, but it greatly increases the computation time needed for simulation. Therefore, it still cannot be directly incorporated into a commercial reservoir simulator without significantly slowing down computation time. Several authors have proposed methods for scale-up at the wellbore or in the vicinity of wells that consider the characteristics of radial flow. Soeriawinata and Kelkar 16 presented an analytical method in which the wellblock was divided into many sectors. The permeability for each layer was calculated as the weighted arithmetic average and the permeability of the wellblock was determined using a thickness averaging method. Ding 17 proposed a scale-up procedure to calculate the equivalent coarse grid transmissibility for the linear flow region based on the results of simulation on fine grid. For radial flow in the vicinity of a well, the transmissibility, or productivity index (PI), was scaled by using an imposed well condition. The methodology was tested by conducting scale-up including both the standard procedure for linear flow pattern and the procedure for radial flow pattern. The errors between fine scale and coarse scale caused by the new scale-up procedure including a radial flow region are much lower than the error caused by standard procedure. TRANSMISSIBILITY SCALE-UP The purpose of permeability scale-up is to preserve the key features of flow on a coarse grid and to match them to a fine gird in reservoir simulation.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 7–9, 1998

Paper Number: PETSOC-98-65

Abstract

Abstract Horizontal wells have been shown to be successful in improving oil recovery for marginal heavy oil reservoirs in Saskatchewan and Alberta. One commonly encountered problem in recovery operations for these poorly consolidated reservoir is the production of sand and fines into the horizontal wellbore, where they settle and accumulate. This paper reports the numerical modeling of gravitational deposition of sand in a horizontal well in such heavy oil reservoirs. The numerical model described in this work examines the transport process mechanistically, based on the conservation equations for the fluid phase (heavy oil) and the solid phase (sand particles). The interaction between these phases is described by empirical correlations. The equations are solved numerically to determine the concentration of sand particles and oil, and their respective pressure and velocity distributions inside the horizontal well. According to the simulation results, oil viscosity and flow velocity play important roles in the transport process, affecting the gravitational settling tendency of solid particles inside the horizontal wellbore. The results provide insight into the roles different mechanisms affect the transport of sand particles; as such, they provide guidelines for production operations involving horizontal wells in poorly consolidated and unconsolidated reservoirs. Introduction Alberta heavy oil reservoirs underlain with bottom-water, has been found to improve primary recovery performance prior to water coning - recovering up to 15%, in some cases, of the initial oil in place, compared with only 5% for a vertical well [I]. Horizontal wells have also been successfully used for increasing steamflood recovery [2–3]. Due to the unconsolidated or poorly consolidated nature of these reservoirs, solid (sand and fines) production is quite prevalent. The produced solids lead to several production problems, including sand filling up the wellbore, preventing the operation of downhole pumps and surface equipment, etc. [4]. In, horizontal well cases, sand production potentially poses a serious problem, as the sand could settle and accumulate inside the horizontal wellbore. This settlement and accumulation of sand particles could give rise to reduced cross-sectional area of the wellbore open to flow (Figure 1). The study reported in this paper examines, using numerical simulation, the gravitational deposition of sand particles inside a horizontal wellbore. A brief survey of the relevant literature is given in the following. Solid-liquid multiphase flows are usually very complex, due to the large number of variables involved in the transport processes, and typically poorly understood interaction between the variables. There have been many experimental investigations of these (and other) flow processes, particularly focused on the deposition of the solid particles. Many of the earliest investigations of solid-liquid flows focused on the settling tendency of solid particles. Richardson and Zaki [5] experimentally determined that the falling velocity of a suspension relative to a horizontal plane was equal to the upward velocity of the fluid required to maintain a suspension at the same concentration. For different flow regimes (i.e. Reynolds numbers), separate correlations were developed from the slope of log-log plot straight lines between suspension falling velocities and suspension porosities.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 7–9, 1998

Paper Number: PETSOC-98-44

Abstract

Abstract The term "Cold Production" refers to the use of operating techniques and specialized pumping equipment to aggressively produce heavy oil reservoirs. This encourages the associated production of large quantities of the unconsolidated reservoir sand creating a modified wellbore geometry that could include "wormholes ∼, dilated zones, or possibly cavities. As well, produced oil in the form of an oil continuous foam resembling chocolate mousse, suggests a foamy solution gas drive occurs in-situ. This leads to anomalously high oil productivity and recovery because free gas stays entrained in the foam, thereby sustaining reservoir pressure. In a recent paper 1 , the mechanisms that lead to this increased productivity were outlined and the suitable reservoir types conducive to cold production techniques were identified. In this paper, these mechanistic concepts are extended to practical, intuitive modeling techniques that can be applied to existing "black oil"reservoir simulators by appropriate alterations to the input data. Importantly, these techniques have been found to match actual cold production behavior in applicable Western Canadian conventional heavy oil reservoirs. With a history matched model, these techniques can be used to extend the cold production scenario into the future, providing better estimates of ultimate recovery. As well, sensitivities to the process can be investigated, including exploring sensitivities to various reservoir and operating parameters (e.g., reservoir pressure, production rate strategies) and examining the impact of a preceding cold production primary depletion on subsequent secondary and tertiary recovery processes. Introduction In approximately the last ten years, many authors have written about the phenomena involved in producing heavy oil by solution-gas drive. Their work has been inspired by field observations of cold production in some of the heavy oil reservoirs in Canada and Venezuela where unexpectedly high oil rates and recoveries, as well as low gas-oil ratios have been attained. This work has included laboratory investigations of fluid and rock properties (including geomechanical studies of the so-called worm holing effects), conceptual postulation of mechanisms in the context of actual field behavior, as well as some attempt to mathematically capture and numerically model these mechanisms. Perhaps one of the first to set forth the mechanisms and possible mathematics was Smith 2 at Husky, who also appears to be one of the first investigators to note that the anomalous production enhancement must arise from a combination of geomechanical and fluid effects (i.e., results cannot be "excused as high permeability channels resulting from sand production"). These two categories of mechanisms - geomechanical effects and fluid effects - are the subject of the mechanisms proposed in the literature for explaining cold production performance of heavy oil reservoirs. Geomechanical Effects Productivity of heavy oil wells experiencing cold production is typically much higher than would be expected - actual productivity exceeds radial Darcy flow predictions (using typical oil viscosities and air permeabilities) by factors of four to ten. The general observation made by numerous producers, that oil rates seem to correlate with sand production, has led many to infer that the production of sand improves inflow performance by increasing the effective permeability of the formation, via the creation of a system of wormholes.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 7–9, 1998

Paper Number: PETSOC-98-56

Abstract

Abstract The Fault Block Model is an alternative simulation tool, developed with the purpose of forecasting well requirement and reservoir performance in strongly faulted gas and gas condensate reservoirs. This model is particularly designed to handle reservoirs where the uncertainty related to gas communication between the various parts or compartment blocks of the field, is pronounced and thought to be the dominant source of reservoir uncertainty. The model can predict reservoir production behavior with reference to a reservoir data basis, as to display the reservoir uncertainty with respect to business opportunities and risks (upside and downside forecast). Based on geological characterization and fault seal analysis, reservoir compartmentalization is implemented. The model forms drainage volumes based on a statistical evaluation of the communication probability between neighboring compartment blocks. Uncertainty analysis is carried out using error propagation techniques, forming an optimistic and a pessimistic view of the reservoir. Production is simulated by material balance calculation technique, producing the reservoir reserves through wells allocated to different drainage volumes. The Fault Block Model has proven to be an advantageous tool in the early stage field development of a North Sea gas-condensate reservoir where the effect of regional well location, number of wells and the optimum well production sequence have been studied. Production profiles from different well location strategies are investigated and various tests involving uncertainty in inter-block communication and in block volume are presented. Uncertainty analysis also includes suggestions on how to reduce reservoir uncertainty and recommendation for an optimum well location strategy. Introduction A classic dilemma in starting up many petroleum reservoir development projects is the restricted access of good and reliable reservoir information, and concurrently, the demand for strategic, well-based and balanced decisions regarding future optimization and reservoir development. At such an early phase in the development process of a new field, lack of reliable reservoir data makes it difficult to forecast future production scenarios, revealing potential financial risks and/or opportunities for enhanced production from the field. In strongly faulted reservoirs, this dilemma appears to be even more pronounced since communication between reservoir segments in the field are strongly related to the faults effectiveness as barrier for fluid flow. Faults generally reduce the communication in the field and consequently increase compartmentalization of reserves. Reduced communication between reservoir segments and related uncertainty makes it more difficult to assess an optimal drainage strategy, defining well locations and sequence of well production. Alternative Reservoir Models The accumulation of reliable reservoir information is considered to monotonically increase with time, as data from field seismic is processed, new appraisal wells drilled and test well production data is being analyzed. Reservoir information, as depicted in Fig. 1, is further increased as more wells are drilled and set into production. By far the most information is obtained by long time production data analysis. A comfortable level of reservoir knowledge is unfortunately achieved late in the lifetime of field production, when the need of such information is not urgent since practically all reserves have nearly been produced.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 7–9, 1998

Paper Number: PETSOC-98-25

Abstract

Abstract Experiments performed on immiscible displacement of heptanes and mineral oil by water in capillary tubing showed that capillary pressure during drainage and imbibitions were constant over a range of velocity from 10 −4 to 10 −2 m /s. The results obtained were quite different from the equilibrium capillary pressure. The drainage capillary pressure was lower than its equilibrium value by 25% for heptanes, and higher by 10% for mineral oil. In the case of imbibitions the capillary pressure for both oils was lower than their respective equilibrium value. Due to the limitation of the apparatus velocities lower than 10 −4 m/s could not be measured. It is, therefore, not clear if capillary pressure during flow would in fact reduce to its equilibrium value at low enough velocities. While it is quite adequate to describe the capillary behavior of two fluids inside a tubing by a single number, one needs to consider capillary pressure as a function of the wetting fluid saturation in the porous media. The problem of considering the effect of flow to this function is going to be more complicated than the single capillary tubing case. The present result indicates that it is inconsistent to use capillary pressure determined from equilibrium conditions and apply it to flowing conditions. Introduction In the study of fluid flow in porous media one starts with the material balance equation for each of the fluids. If they are immiscible, then one needs to consider the interaction between them across the interfaces. A common approach 1–4 is to define a capillary pressure to be equal to the difference in pressure of the two fluids in the same representative elemental volume. This pressure is also assumed to be dependent on the saturation of one of the fluids there. In terms of mathematics, the use of these assumptions completes the system of partial differential equations governing the flow of two fluids in porous media. In actual practice one needs to provide a physically realistic capillary pressure saturation relation in order to make meaningful predictive calculations. Very often capillary pressure is taken to be zero as in Buckley-Leverett's solution for immiscible displacement 5 , or Muskat's model of water coning 6 . However, in some reservoir engineering applications this may not be feasible. For example, when one needs to build a numerical model with more than one layer in the vertical direction it is necessary to input a non-zero capillary pressure curve to initialize the fluids in the reservoir. A realistic initialization would be to use the drainage portion of the capillary pressure saturation relation. In most commercially available simulators this same curve is being used for the subsequent displacement calculations. As the drainage curve is determined while the fluids are at equilibrium, using it for flow calculation implies that capillary pressure is independent of the dynamics. We are not aware of any theoretical justification given in the literature for using this assumption. In fact there was no discussion given on the physical requirements of the capillary pressure saturation relation given in some of the standard texts on numerical reservoir simulation. 7,8

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 7–10, 1997

Paper Number: PETSOC-97-132

Abstract

Abstract In the present paper 3D analytical simulator for modeling horizontal well (HW) and slanting well (SW) performance is presented. Hydrodynamic characteristics of the development process are treated in terms of Newton's and heat potentials, and the developed simulators provide the ability for modeling both stationary and non-stationary states. The computational experiments allowed to analyze the impact of the geometry of the system «reservoir + HW » on performance indexes and to infer new flow rate formulas for stationary and non-stationary drainage. The proposed method is based on iterative algorithms and domain decomposition principle reducing the drainage problem in domains with complicated structure to problems in standard (simple) domains, such as ball, cylinder, etc. The developed numerical methods and flow rate formulas have been validated and proofed to be highly precise. Introduction The fluids drainage in the neighborhood of one or several HW is still less fully studied than in the case of vertical wells (VW). This default may be accounted for by the essentially 3D nature of the hydrocarbons influx toward the well in a reservoir limited by its top, bottom, and the no flow barrier. The main problem consists in determining the dependency of the well's productivity on the reservoir geometry and on the wells interference. A number of analytical formulas and charts [1–8] linking production rate and differential pressure in relation to geometric and hydrodynamic parameters of the system «reservoir + HW » are available. Analytical formulas are mostly obtained by reduction of the authentic 3D model to 2D flow. Precise solution of essentially 3D drainage problems is, very complicated and can be constructed only for special cases (see e.g., [9–10]). Another efficient approach consists in development of computational models to simulate drainage processes in 3D reservoirs [11–13]. In the present paper an'explicit method [14,16] is presented to solve the problem of one-phase incompressible elastic fluid inflow toward a single HW or a group of HW in a 3D reservoir limited by top, bottom, and no-flow barrier. The wellbore is modeled as a superposition of Source Functions (SF) such that in each inner reservoir point these functions satisfy Laplace equation in case of stationary drainage or heat equation in the non-stationary case; the boundary conditions are satisfied on the reservoir top, bottom, and on the no-flow barrier. The solution is sought in terms of discrete density distribution subject to one of the following conditions: the pressure on the wellbore or the flow rate at discrete points of the well is given. In view of the maximum principle (see [15]) it is easy to check that for the approximate solution the deviation from the precise solution in each inner point of the reservoir doesn't exceed the deviation from the given value on the boundary of the well. Thus, the main issue consists in construction of Green's function possessing the outlined properties. Development of a highly precise algorithm for construction of this function in the stationary case and of a parabolic analogue of Schwarz's algorithm [16], utilizing standard Green's function and introducing image well in the non-stationary case, is the main achievement of the presented work.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 7–10, 1997

Paper Number: PETSOC-97-109

Abstract

Abstract A steam injection reservoir simulator was developed with the objective of improving the resolution of the information concerning the flow around a well and between wells. To accomplish this objective, it was necessary to develop the contiguous hyperhybrid grid refinement method. With better well region representation, it has been shown that hyperhybrid grid refinement is useful in studying well operating changes and well interactions, particularly when the regions are made contiguous. Local well effects, interwell interference, multiwell cyclic steaming and conversion to steamflood were examined using hyperhybrid grid refinement. The results of these studies are presented in a separate paper. It is recommended that contiguous hyperhybrid grid refinement be used for analyzing problems where the local well region behavior is important in the context of a field simulation. Furthermore, it is recommended that this refinement technique be used to study interwell interactions where near-well effects are important and the communication path between the wells requires better representation. Introduction At the present time, there are steam injection simulators that may be satisfactory if there are no sharp fronts for steamflood simulation. When it comes to cyclic steaming, simulators are suited best for single well modeling, but multiwell modeling is possible only with difficulties arising from the necessary adjustments of relative permeability, hysteresis, formation compressibility and grid size. Some adjustments may also be required for single wells; however, a radial grid system is better suited for representing a well. Effective fieldwide cyclic steam stimulation simulation is still in the future, when the next generation computers become available. It is recognized in the industry that computational hardware/software allow for the inclusion of a limited number of wells in a thermal simulator. Recent work 1 illustrates this point well-their study contained 4,500 rectangular grids blocks and up to only eight wells. Even at present, a fieldwide cyclic steam stimulation simulation requires a tremendous amount of computer storage and computation time. Yet, such a simulation customarily employs a rectilinear grid that is inadequate for simulating radial flow-an essential flow feature of cyclic steam stimulation-near the wells. In recognition of the fact that the next generation computers are nearby, the objective of this work is to develop a tool that will provide an effective fieldwide simulation. The existence of the next generation computers will not eliminate the need to have radial geometry around the wells. MODEL DESCRIPTION This is the first model to use hyperhybrid grids in thermal simulation. A hybrid grid is defined as a cylindrical grid system embedded into a single fundamental rectilinear grid block and a hyperhybrid ∗ grid is defined as a cylindrical grid system embedded into several contiguous fundamental rectilinear grid blocks. These grids are illustrated in Figure 1. Regions 1, 3 and 5 are hybrid while Regions 2, 4 and 6 are hyperhybrid grids. In addition, this is the first model, black oil or thermal, to offer hybrid and hyperhybrid grid regions that can be contiguous.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 9–11, 1996

Paper Number: PETSOC-96-57

Abstract

Abstract This paper presents a simulation study of a steam assisted gravity drainage(SAGD) process applied to the Hanging stone tar sands reservoir. Two pairs of500 m long horizontal wells installed from the surface are considered. The study was conducted to forecast recovery performance and to furtherunderstand the oil production mechanism. Results predicted that more than 60%of the oil can be produced in 6 years of operation with a steam-oil ratio ofless than 3.0. The study was extended to provide a visual understanding of theflow behavior of steam, oil and water in the reservoir. The fluid flow diagramsrevealed that oil is displaced mainly by steam condensate and that convectiveenergy carried by steam condensate dominates the heat transfer mechanism. The authors applied this recovery mechanism concept to the study of sub coolingtemperature optimization for the steam trap control. The results of thisreservoir dynamics study are presented. Finally the role of this process's geomechanical effects are brieflydiscussed. INTRODUCTION The Hanging stone oil sands reservoir is located near Fort McMurray. Thereservoir is jointly owned by Petro-Canada, Imperial Oil, Canadian Occidentaland Japan Canada Oil Sands (JACOS). The bitumen viscosity at reservoircondition is over 1,000,000 m Pas and will not flow naturally. JACOS is going to use a Steam Assisted Gravity Drainage (SAGD) process toextract bitumen from the Hangingstone reservoir. A cyclic steam stimulation(CSS) process was extensively tested for the same reservoir over a decade. Through a numerical simulation study of the performance, it was found that thebitumen is difficult to produce at economically feasible rates using the CSSprocess for the subject reservoir (1). JACOS has been participating in the Underground Test Facility (UTF) projectsince 1991 when Phase A of the project was completed. From its participation, JACOS has received all of the field data plus operating and drillingexperience. UTF's field data has been extensively analyzed through numericalsimulation. Based on the analysis of the data, it was decided to drill twopairs of 500 m horizontal wells in 1997 and to start operating the SAGD processin 1998. The expected well performance calculated using a thermal simulator ispresented in the paper. Following the base case run, a series of parametricstudies were conducted. Some interesting results, such as the oil recoverymechanism obtained from the study, are also included. Although many uncertainties still exist in both the recovery concept andoperational procedure for the SAGD process, promising potential for itsapplication has been demonstrated in Phases A and B of the UTF project(2,3). One major uncertainty is whether the geomechanical change Of the formationduring the process is an important aspect or not. The role of geomechanicaleffect in the growth of the steam chamber and well performance is alsopresented. A new oil recovery mechanism is required when the geomechanicalchange of the formation occurs in the reservoir. A brief description of therecovery mechanism under the influence of the geomechanical formation change isalso discussed.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 6–8, 1995

Paper Number: PETSOC-95-63

Abstract

Abstract Field results from many heavy oil reservoirs in the Lindbergh and Frog lake fields in northeastern Alberta suggest that primary recovery is mainly governed by the processes of sand production and foamy oil behaviour Sand production leads to the creation of high porosity zones with increased permeability, while foamy oil generation provides the necessary support mechanism to sustain higher production rates. PanCandian Petroleum Limited and Centre for Frontier Engineering Research (C-FER) conducted experimental And numerical studies to understand the various reservoir mechanisms contributing to the high primary production recovery observed in the Lindbergh and Frog Lake fields. Laboratory tests were conducted to study the foamy oil behaviour and evaluate its contribution to the enhanced primary production observed in the field. The numerical modelling included a series of idealized models developed and analyzed to determine the most probable shape of the sand-producing zones. The evaluation focussed on matching not only the observed oil production but also the observed sand volumes removed from the reservoir. The analysis from vertical well stimulation was also extended to horizontal wells. The evaluation of heavy oil reservoir mechanisms for Lindbergh and Frog Lake fields is reported in two parts. Part I includes field testing and reservoir simulation Based on the production data. Part II includes analytical and numerical studies for the coupling effects of sandand oil production, and laboratory testing ofunconsolidated sand under foamy conditions. Introduction The observed primary oil production of many heavy oil reservoirs In the Lindbergh and Frog Lake fields in northeastern Alberta, Figure I. has been significantly higher than predicted by classical darcy flow models. PanCanadian Petroleum Limited and Centre for Frontier Engineering Research (C-FER) conducted experimental and numerical studies to understand the various reservoir mechanisms contributing to the observed highprimary production recovery. This evaluation was conducted in two parts. This paper summarizes the work conducted for Part I of This evaluation and the results obtained in Part I includes geological descriptions of the Lindbergh and frog Lake heavy oil reservoirs. a summary of various field tests conducted in the area lo evaluate recovery mechanisms. The results of preliminary reservoir simulation based on production data and a review of the various mechanisms contributing lo the improved primary production. Part II of This evaluation is reported by the authors in Ref. (I). IT includes laboratory testing of unconsolidated sand under foamy oil conditions to answer questions related o wellbore stability and analytical and numerical studies for coupling the effects of sand and oil production. Geological And Reservoir Description The Mannville group of the Lower Cretaceous is underlain by the Beaverhill Lake carbonates of the Upper Devonian and are overlain by the Joli Fou shales of the Colorado group. In Twp. 056. Rge. 06 W4M. the average Mannvilleroup thickness is 165 m. Figure 2 shows the geological nomenclature used in the Lindbergh (Twp. 055 056. Rge. 04. 05. 06 W4M) and Frog Lake (Twp 055. 506. Rge. 02. 03) areas.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 11–14, 1994

Paper Number: PETSOC-94-77

Abstract

Abstract The most common centrifuges used in the petroleum industry for capillary pressure measurements are made by Beckman. The Beckman centrifuge has, long been found problematic due to its rotor design. The gravity degradation phenomenon at low speeds has been identified as one of the problems for high permeability and porosity sandstone samples, in which the gravitational acceleration distorts the horizontal centrifugal force distribution inside core plugs and thus leads to inaccurate interpretation of capillary pressure information in the high saturation region. The possible remedial countermeasures to this problem may include developing a rotor head with a new configuration that minimizes the effect while maximizing the quality of row experimental data. This paper presents a theoretical analysis of the centrifugal field of rotor systems with pivoted heads. The analysis from the proposed theory shows that a pivoted rotor head makes the gravitational nd centrifugal fields more closely aligned, thereby greatly educing this effect. The new rotor configuration provides n alternative for the centrifuge experiments. A simple approximation is provided to extend the Hassler-Brunner method for use with a pivoted rotor head. Introduction Two of the most important parameters required by petroleum reservoir engineers in order to calculate the performance of oil and gas reservoirs are capillary pressureand relative permeability. Unfortunately, these are he two most difficult parameters to measure. Since the mid-1940'S, 1,2 centrifuges have been used to collect data from which capillary pressure data can be interpreted. The basis of this method is that if a sample of porous edium contains two components, one of which wets the solid, internal surface of the sample, then capillary pressure tends to hold this wetting component inside the sample. If the sample is spun in a centrifuge, the centrifugal force acts to expel the wetting component from the sample, while the capillary pressure forces act to hold the wetting component in the sample. By measuring the amount of wetting component produced as a function of the speed (RPM) at which the sample is spun, a data set may be obtained from which capillary pressure versus saturation may be interpreted. Such interpretations may be very complicated. 3 . In recent years, there has been increasing interest in using a centrifuge to obtain relative permeability. 4 This is done by measuring the rate at which the wetting component is expelled, and interpreting this rate data, again using a complex procedure. 5 Even though centrifuge techniques have been in use for almost 50 years, they have not yet been perfected. Three basic problems remain: obtaining a complete understanding of the mechanisms that are involved in fluid displacement by centrifugal forces, performing true imbibition experiments, and interpreting the data to obtain capillary pressure and relative permeability curves. Considering the first basic problem in particular, two typical phenomena have held people's attention. One is the radial effect due to core width. 6 . Traditionally people assume either a constant or a linear centrifugal acceleration distribution inside the core plug. Such assumptions will cause errors when a short, large diameter core plug is used (unfortunately this is the case for most commercial Beckman centrifuges).

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 11–14, 1994

Paper Number: PETSOC-94-79

Abstract

Abstract A common question when dealing with tight matrix naturally fracturedreservoirs is - How can we determine if the matrix is contributing tohydrocarbon production? One source of information for helping to answer thisquestion is provided by matrix and fracture permeabilities determined with thePressure-Decay Profile Permeameter (PDPP). The useful range of the tool is from0.001 to 20,0000md. These permeabilities are corrected for overburden conditions and are utilizedto numerically simulate the interaction between matrix and fractures in a core.The procedure involves the following steps: From PDPP measurements create iso-permeability maps of the fracturecore. Discretize the permeabilities using a micro-gridover the core area. Select a ‘production’ cell in the fractures and various observation cellsin the matrix. Simulate the core using reservoir pressure, temperature and fluidproperties. The results indicate if the very low matrix permeability contributes tohydrocarbon production in the naturally fractured reservoir where the core wascut. Introduction There are many naturally fractured reservoir around the world in all kinds oflithologies throughout the various geologic periods. This type of reservoirscontains significant amounts of oil and gas resources. They presents botheconomic opportunities and technical challenges. Inorder to properly exploitnaturally fractured reservoirs, engineers and geologists have developedspecialized techniques and tools to help in their evaluation. The overview of the characteristics of naturally fractured reservoirs andtechniques for their analysis have been the subject of various textbooks 1–5 . In a paper on recent advances in the study of naturallyfractured reservoir, Aguilera 6 summarizes the sources of informationavailable to evaluate naturally fractured reservoirs. In a very simple model, a naturally fractured reservoirs consists of matrixrock with high storage and low permeability. These matrix rock is generally notcapable to sustain commercial production without natural fractures. Thefractures have very low storage capacity but high permeability. Fluid in thematrix can bleed off into the fracture network and then be transported throughthe ractures to the wellbore. An often asked question is whether fluid storedin the tight matrix actually contribute to production. A new technique forpermeabilitymeasurements in cores coupled with numerical microsimulation offerssome answers to this question. This could be combined with a laboratory technique that allows to measureseveral hundred pressure readings in a short span of time to study the responseof cores to pressure disturbances. This laboratory technique allows quick andaccurate determination of matrix and fracture properties as reported by Kamathet al. 7 Fractured core properties A carefully handled core from a naturally fractured reservoir provides valuableinformation on reservoir properties, including whole core porosity andpermeability. From well logs we can estimate porosity in the matrix, andractures. Pressure transient analysis can also add information includingfracture porosity and permeability. All these estimates are related to the bulkproperties of the system. With a new permeability measuring equipment, thepressure-decay profile Permeameter 8–10 , detailed description ofpermeability distribution can be obtained.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 11–14, 1994

Paper Number: PETSOC-94-03

Abstract

Abstract Material balance methods of determining reservoir parameters such as the original oil in place are sensitive to uncertainties in the input data. Traditionally, regression techniques have been used to determine the "best-fit" values of the reservoir parameters and these have been used as a good representation of the "true" values. The effect of errors in the reservoir pressure measurements on the Havlena-Odeh 4 method are examined using a gas cap drive reservoir as an example. The errors in the measured pressures are estimated from the available data. These errors are propagated through the calculations and show that the resulting error bars vary with the size of the relative pressure drop. Weighted linear regression is used to determine both the best fit values and the standard deviation, which serves as a measure of the statistical confidence limits. An alternative approach using the material balance method is to calculate the expected pressures from a model and vary the parameters of the model until the pressures match the observed pressures. Minimization of a suitable objective function by non-linear regression provides the best estimates of the reservoir parameters and the confidence limit contours can be derived. These are then used to draw correct inferences from the results - in the example, the possible communication between two oil pools is investigated. The 95% confidence limits are found to cover a wide range in the OOIP and gas cap fraction, thus the "best fit" has limited usefulness. The confidence limits can be used to compare the results of volumetric calculations and to restrict the range of variables used in subsequent reservoir studies.- e.g., numerical simulation. The methods outlined in this paper are general and are not limited to two parameters thus they can be used for any material balance problem. Introduction Material balance is one of the fundamental tools of reservoir engineering.In essence, measurements of the pressure changes in a reservoir as fluids are withdrawn are used to derive the reservoir parameters such as OOIP, gas cap fraction and the water influx characteristics. The significant effect of errors in the data on the derived parameters, such as the OOIP, gas cap fraction and aquifer characteristics was recognized early in the development of the subject, and the equation has been examined by numerous authors 1,5 . Random errors are present in all the input parameters: the average reservoir pressure at any time, the total withdrawals from the reservoir and the PVT properties of the reservoir fluids. Usually, errors in reservoir pressure are the most significant, and only these will be addressed in this paper. Systematic errors (as opposed to random) are also present. These arise from numerous sources e.g., the PVT data not representing the reservoir fluids accurately, a single pressure not representing the reservoir (due to lack of continuity). These will not be discussed in this work, although corrections applied for reservoir pressures in the field example are an example of reducing a set of systematic errors arising from insufficient shut-in time. In this paper a general method for assessing the uncertainties is described.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 11–14, 1994

Paper Number: PETSOC-94-62

Abstract

Abstract This paper describes the procedures used in a joint venture by two software vendors to combine an existing reservoir simulator and an existing surface facilities model into a single forecasting tool. Relatively small changes were made to each program. In the new model, the black oil reservoir simulator provides the formation pressure and water to gas ratio for each well The surface facilities model then calculates the multiphase flow pressure losses in the wellbore and gathering system, plus the corresponding flow rates for each well. The actual production required from each well to satisfy the pipeline contractual requirements, over each time step, is computed by the surface facilities model and relayed back to the reservoir simulator. The time step is determined dynamically according to the requirement of each program. The performance and results from the coupled model are compared to that of running each model separately for a gas storage field in the U.SA and for a gas production field with bottom-water. It is shown that running each model separately does not account for all the factors affecting the forecast. Introduction To determine if a gas contract can be satisfied now and in the future, it is necessary to forecast the performance of the gas reservoir, the gas inflow into the sandface, the multiphase pressure losses in the wellbore and gathering system and the field facilities. Surface production models which rigorously model from the sandface to the plant gate are available. However, these surface packages model reservoirs simply, in most cases as tank-type reservoirs. Comprehensive 3 dimensional reservoir simulators are available, but typically only include simple surface networks which don't adequately model multiphase flow in complex gathering systems 1,2,3 . A different approach has been taken in this paper. Two existing commercial models, a 3 dimensional black oil simulator and a multiphase surface facilities model, from different vendors were coupled into one comprehensive model. Ihis work required only a small fraction of the development time and cost which would have been equired to "add on " a surface network to a reservoir simulator. No simplifications of either component were required and each component was supported by experts in that field. Existing data files and documentation were used irectly. New developments can be added to either model without adversely affecting the interface. Implementation The black oil simulator, IMEX, from the Computer Modelling Group was chosen as the reservoir simulator. FORGAS, from Neotecnology Consultants Ltd. was selected as the surface model. Both models were linked into one executable to save execution time. Two new subroutines were created to pass data between each model. Each routine is responsible for accessing the required data and then converting the data into the acceptable format (e.g. SI to field units). The other model then calls this subroutine whenever it needs the information. The name of each well is used to link the models. A new mainline routine was created which calls each model (as a subroutine) sequentially in a loop.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 6–9, 1992

Paper Number: PETSOC-92-73

Abstract

Abstract Material balance analysis of production performance data for an abnormally-pressured gas reservoir is complicated because of water and rock compressibility effects in addition to gas compressibility effects. Usually, a p/z vs. G p graph for an abnormally pressured gas reservoir yields a significantly overestimated value of the initial gas-in-place. Several researchers have presented material balance analysis methods to obtain reasonably accurate estimates of the initial gas-in-place for abnormally-pressured gas reservoirs. These methods can be broadly grouped into two sets. The first set of methods requires a knowledge of compressibilities and analyzes production performance data to estimate the initial gas-in-place. The second set of methods attempts to obtain both an effective system compressibility and the initial gas-in-place by analyzing production performance data. This study presents an evaluation of several material balance analysis methods for volumetric, abnormally pressured gas reservoirs. The interrelationship between the initial gas-in-place estimates from the two methods by Hammerlindl (1) has been derived theoretically. Non-uniqueness problem in analyzing production performance data of abnormally-pressured gas reservoirs is emphasized. An example problem demonstrates that a small error in the initial reservoir pressure can account for a typical flat portion corresponding to the early production data on the Roach (2) plot. The preceding observation suggests that a hypothesis of changing formation compressibility with pressure as advanced by Poston and Chen (3) is not necessary to explain the shape of the Roach (2) plot. This paper should enhance an analyst's capabilities to perform meaningful material balance analysis of production performance data from an abnormally-pressured gas reservoir. Introduction Material balance analysis of production performance data for an abnormally-pressured gas reservoir should include water, rock, and gas compressibility effects. For a volumetric, abnormally-pressured gas reservoir, a p/z vs. G p graph shows two straight lines of distinctly differenl slopes. An extrapolation based on an early straight line on a p/z vs. G p graph for an abnormally pressured gas reservoir yields a significantly overestimated value of the initial gas-in-place. This paper discusses and evaluates several material balance analysis methods proposed for volumetric, abnormally- pressured gas reservoirs to obtain reasonably accurate estimates of the initial gas-in-place. Material Balance Analysis Methods All material balance analysis methods proposed for volumetric, abnormally-pressured gas reservoirs are based on a material balance equation of the following general form: Equation (Available In Full Paper) Different authors have used different expressions for effective system compressibility (C e ) depending on the drive mechanisms Incorporated In their analyses. The following discusses the two sets of methods proposed for analyzing production performance data for abnormally-pressured gas reservoirs. Methods Based on a Knowledge of System Compressibility Hammerlindl (1) presented two melhods to correct apparent gas-in-place (G app ) obtained from an extrapolation of early straight line on a p/z vs. Gp graph for an abnormally-pressured gas reservoir. Using two pressures, P i and P 2 , actual gas-in-place (G act ) is computed according to Hammerlindl's (1) method I as: <Equation Available In Full Paper>

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 6–9, 1992

Paper Number: PETSOC-92-17

Abstract

Abstract Numerical simulators are often used to aid the study of the factors influencing the unstable miscible displacement processes. One of the deficiencies of the conventional compositional reservoir simulators for predicting the unstable displacement process is that these simulators all involve the use of the assumption that the fluids in each grid block are in a state of thermodynamic equilibrium. In reality, the different fluid phases coexisting in each grid block may not be in equilibrium with each other because of insufficient contact time. A procedure has been developed to calculate the non-equilibrium phase behaviour of the fluids under displacement process conditions. The procedure is based on the mixing parameter model proposed by Todd and Longstaff (1972) and the concept of Murphree efficiency. Phase behaviour calculations are performed for the fluids over the entire grid block under non-equilibrium conditions. The deviation from equilibrium in respect of each component is considered a function of the equilibrium K-value and the effective mobility ratio of the in-situ fluids. Comparisons of the simulation results based on the proposed model with the experimental data obtained from slim-tube displacement tests for well-defined hydrocarbon systems and with simulation results based on conventional equilibrium phase behaviour model are presented. Introduction The formulations used in conventional compositional reservoir simulators for calculating the distribution of reservoir fluids under stable miscible displacement process conditions are generally based on the assumption that the fluid mixture contained in each grid block is in a state of equilibrium. This assumption is valid if, as a result of Sufficient contact time and suitably specified reservoir parameters, complete mixing takes place everywhere at which the displaced fluid is contacted by the displacing fluid. Unfortunately, not all displacement processes are stable. For example, viscous fingering can develop in the flow path of the fluids if the viscosities of the fluids at a certain point are of such magnitudes that they result in a large value for the viscosity ratio µ o / µ g Where µ o is the viscosity of the oil in place and µ g that of the gas, which is in contact with the oil. In situations like this, there is insufficient time for interphase mass transfer to reach an equil ibriurn rate at that point in the reservoir, and consequently, a state of complete mixing will not be a valid assumption to use in making numerical simulation of an unstable displacement process. It has long been recognized that the major factors that affect the stability of a displacement process are the mobility ratio for the reservoir fluids and the heterogeneity of the reservoir formation, which is essentially a large porous medium. Most of the models that have been proposed for use in numerical simulations of the unstable displacement processes are based on the use of some empirical parameters to account for the effects of mass transfer occurring at the interface on the properties of the adjoining fluids. Some of the theories and models relevant to this study are briefly mentioned in the next section.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, April 20–23, 1991

Paper Number: PETSOC-91-53

Abstract

Abstract An analysis of the response of naturally fractured reservoirs to thermal recovery processes is presented, utilizing a suite of dual continuum reservoir simulation models (dual porosity, multiple interacting continua, vertical matrix refinement and dual permeability). The effects of the different models as well a, many fracture and matrix properties on aspects of stearn cycling, steam drive and gravity drainage processes are discussed in some detail. While some factors are consistent with the isothermal response of naturally fractured reservoirs (in particular fracture spacing and the primary effect of matrix permeability), thermal phase behavior and heat flow effects in these reservoirs impart significantly different more complex behavior. Most of the naturally fractured reservoirs which are produced by using thermal processes contain very low mobility oil and therefore heat conduction plays a very important role at the initial stages of production. With increasing oil mobility, convective gravity and capillary forces lake over if the matrix permeability is fairly high or the reservoir is fractured extensively. During a production cycle in a stearn stimulation process, heal is conducted from matrix rock to fracture fluid which can increase the fluid's energy tremendously. Depending on the fracture fluid (water/oil) volatility, the additional energy can cause different phase behavior responses. Introduction Fractured reservoirs occur worldwide in the Middle East, Iran, Iraq, France, USA, Venezuela, Canada (Saidi (1987), van Golf-Racht, (1982)), and hold extensive hydrocarbon reserves. The presence of a large number of fractures throughout the reservoir provides extended area, of high permeability, where the fluid flows more easily. However, the productivity of these reservoirs depends on the porosity and permeability of the matrix, which stores most of the fluids in place. Production will cease in reservoirs with very Light matrix rock after the fracture network is depleted, because fluids arc not able to flow at reasonable rates from the matrix to the fracture. Reservoirs with fair matrix permeability will sustain production, because fluids from the matrix will flow into and replenish the fractures. Although fractured reservoirs have been known and produced for decades, a wide variety of production levels and reservoir responses have been observed. This, in turn has given impetus to more recent indepth analysis (both experimental and theoretical) of the underlying mechanisms. The utility of reservoir simulation models in decoupling and quantifying contributing factors has been recognized. Initially, the behavior of fractured reservoirs was simulated by "single porosity" models with two different approaches: Fraclure and matrix properties were averaged. With this approach the oil recovery is usually overpredicted, (Chen, et al (1987), Dean and Lo (1986)) especially in situations where the fracture spacing is large. Fracture and matrix were represented by separate grid blocks. This case has two major drawbacks for field simulation studies: a very large number of grid blocks is needed to represent the whole reservoir numerical difficulties arise due to great differences between fracture and matrix properties Later, Barenblalt, et al (1960) and Warren and Root (1963) introduced a simple dual continuum concept (the dual porosity model) for single phase flow.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 9–12, 1990

Paper Number: PETSOC-90-01

Abstract

Abstract An algorithm to compute pressure distributions in commingled reservoirs that are produced via complex completion systems is described. We show that single layer solutions for systems of interest can be readily combined to obtain pressure distributions in commingled reservoirs for combinations of rock type. Completion schemes and outer boundary conditions for each layer may be different. Theoretical claims are substantiated by considering example applications. Introduction This communication presents a stable and robust algorithm to compute responses at wells that produce commingled reservoirs. We take advantage of the unique feature of commingled reservoir production for the constant terminal pressure solution and present an algorithm to determine the well response for constant or variable rate production. Expressions to compute sand-face layer rates are also presented. The advantages of the algorithm we present are: any combinations of wellbore and outer boundary conditions can be incorporated and the combinations can be different in each layer, characteristics of each layer including rock type can be different. existing codes for single layer systems can be used with minor modifications to compute commingled reservoir responses, and approximate solutions for various situations of interest can be derived. Our intent is similar to that in Refs. 1–3, in that this algorithm will enable analysts to obtain commingled reservoir responses for interactive analysis and history matching purposes. The efficacy of the algorithm has been tested by comparing responses with standard solutions. 4–7 In general solutions are in agreement to at least three digits. Theoretical Considerations We consider the flow of a slightly compressible fluid of constant viscosity in a commingled reservoir. Each layer is assumed to be a uniform porous medium. However, the properties, rock type, completion conditions, location of boundaries and the boundary condition (closed, constant pressure) in each layer are entirely arbitrary. The initial pressure in each layer is assumed to be different. Solutions discussed in this work will be presented for convenience in dimensionless form. The Van Everdingen-Hurst 8 definitions will be used in this work. For describing properties of the entire reservoir system we use thickness averaged permeability. kh and thickness averaged porosity compressibility product oc t i.e.: Equation (1) (Available in full paper) and Equation (2) (Available in full paper) Here J is the layer index and n is the total number of layers. To outline the algorithm, we will for simplicity assume that the initial pressure in each layer is identical> It is well-known that if a commingled reservoir is produced at a constant pressure, then the layers are effectively decoupled and production from each layer is independent of the other layer. 9 Thus, if q D (t D ) is the total production rate from the commingled reservoir based on kh and q D is the flow rate from layers J based on k J h J then Equation (3) (Available in full paper) The algorithm takes advantage of Eq. 3 and Dubamel's theorem which is given by Equation (4) (Available in full paper) where Equation (5) (Available in full paper)

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Annual Technical Meeting, June 9–12, 1990

Paper Number: PETSOC-90-36

Abstract

Abstract The performance of a normally-pressured gas reservoir depends on gas compressibility effects and water influx. Generally, a straightforward material balance analysis is possible for a normally-pressured gas reservoir to estimate the initial gas-inplace. However, for an abnormally-pressured (or geo-pressured) gas reservoir, material balance analysis is not as simple. Factors complicating the performance of a geo-pressured gas reservoir are water and rock compressibility effects, and shale water influx. These factors often cause an overestimated value of the initial gas-in-place from a p/z-G p graph of the early production performance. Over the years, several corrections have been proposed to accurately estimate the initial gas-in-place. These corrections are based on different forms of material balance equation. This study shows that a general material balance equation applies to both normally-pressured and geo-pressured gas reservoirs. This general material balance equation demonstrates that the nonlinearity on a p/z-G p graph for a geo-pressured reservoir is due to a term containing p 2 /z . Material balance equations previously used in the literature for geo-pressured reservoirs reduce to this general form by using proper definitions of the coefficients in the general material balance equation. A new type-curve matching procedure has been developed to analyze the production performance of a geo-pressured gas reservoir. An example application for using the new method is presented. Introduction A normally-pressured gas reservoir exhibits an initial pressure gradient close to the pressure gradient for water (generally about 9.7 to 11.3 kPa/m). The production performance of a normally-pressured gas reservoir depends on gas compressibility effects and water influx. The effects of water and rock compressibility's are usually neglected while analyzing the performance of a normally-pressured gas reservoir. However, an abnormally-pressured (super-pressured, over-pressured or geo-pressured) gas reservoir exhibits an initial pressure gradient far in excess of typical water column pressure gradient. Prasad and Rogers (1) report initial pressure gradient as large as 21.7 kPa/m for a geo-pressured gas reservoir. A typical geo-pressured gas reservoir may exhibit an initial pressure gradient between 14.7 to 19.3 kPa/m. Though geo-pressured gas reservoirs may be encountered in all parts of the world, several geo-pressured reservoirs exist in the Gulf Coast area of Louisiana and Texas, (2,3) Andarko Basin Delaware Basin, and the Rocky Mountain area of the United States (1) . For a deep, geo-pressured gas reservoir, water and rock compressibility's may be close to gas compressibility during the initial stages of production. Thus, any material balance analysis of early production data from a geo-pressured gas reservoir must include water and rock compressibility effects. This study is limited to volumetric (no water influx or water production) normally - and/or abnormally-pressured gas reservoirs. This study shows that a general material balance equation applies to both normally-pressured and geo-pressured gas reservoirs. This general material balance equation forms the basis of a new type-curve matching procedure to analyze the production performance of a geo-pressured gas reservoir. General Material Balance Equation Bourgoyne et. al. (4) derived a general material balance equation for a geo-pressured gas reservoir as: Equation (1) (Available In Full Paper) where: Equation (2) (Available In Full Paper)