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Djebbar Tiab

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–26, 2013

Paper Number: SPE-164481-MS

Abstract

Interwell connectivity, an important element in reservoir characterization, especially for secondary recovery such as waterflooding, is essential when making decisions on well patterns, infill wells, and injection rates for oil recovery optimization. An existing technique uses multivariate linear regression analysis of flow rates in a waterflood to infer interwell connectivity. Advantages of this technique include a simplified one-step calculation and the availability of production data. A capacitance model was introduced as an extension of the technique to account for shut-in periods and changes in bottomhole pressures in the producers; however, this approach is based on trial and error and requires subjective judgment. This paper presents an alternative analytical approach based on analytic concepts, providing an in-depth understanding of the technique and relationships between interwell connectivity coefficients and other reservoir parameters. The analytical approach uses a mathematical model for bottomhole pressure responses of injectors and producers in a waterflood system. The model is based on a solution for fully penetrating vertical wells in a closed rectangular reservoir with an assumption of steady-state flow. This model is then used to calculate relative interwell permeabilities, which represent the connectivity levels of signal response well pairs. Different synthetic reservoir models were analyzed, including homogeneous, anisotropic reservoirs, and reservoirs with high-permeability channels and transmissibility barriers. Comparisons with results obtained from previous studies of production data and bottomhole pressure data are presented. The main findings of this study are: (a) the mathematical model performs well with interwell connectivity coefficients calculated from flow rate data to quantify reservoir parameters; (b) the proposed approach provides a better understanding of interwell connectivity determination from flow rate data;and (c) the results for relative interwell permeability from flow rate data are similar to those obtained from previous studies of bottomhole pressure data.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–26, 2013

Paper Number: SPE-164482-MS

Abstract

A technique using interwell connectivity is proposed to characterize complex reservoir systems and provide highly detailed information about permeability trends, channels, and barriers in a reservoir. The technique, which uses constrained multivariate linear regression analysis and pseudosteady-state solutions of pressure distribution in a closed system, requires a system of signal wells and response wells. Signal wells and response wells can be either producers or injectors. The response well can also be either flowing or shut in. In this study, for consistency, waterflood systems are used in which the signal wells are injectors and the response wells are producers. Different borehole conditions, such as hydraulically fractured vertical wells, horizontal wells, and mixed borehole conditions, are considered. Multivariate linear regression analysis was used to determine interwell connectivity coeffients from bottomhole pressure data. Pseudosteady-state solutions for a vertical well, a well with fully penetrating vertical fractures, and a horizontal well in a closed rectangular reservoir were used to calculate the relative interwell permeability. The results were then used to obtain information on reservoir anisotropy, high-permeability channels, and transmissibility barriers. The following are some conclusions drawn from this study: (a) the interwell connectivity determination technique using bottomhole pressure fluctuations can be applied to waterflooded reservoirs that are being depleted by a combination of wells (e.g., hydraulically fractured vertical wells and horizontal wells); (b) wellbore conditions at the observation wells do not affect interwell connectivity results; (c) the complex pressure distribution caused by a horizontal well or a hydraulically fractured vertical well can be diagnosed using the pseudosteady-state solution and, thus, its connectivity with other wells can be interpreted. Different synthetic reservoir simulation models are analyzed, including homogeneous reservoirs, anisotropic reservoirs, and reservoirs with a high-permeability channel, or a partially sealing barrier, or a sealing barrier.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–26, 2013

Paper Number: SPE-164499-MS

Abstract

Abstract Hydraulic fracturing process is an important stimulation technique that has been widely used in conventional and unconventional oil and gas reservoirs. The technique involves creation of fracture or fracture system in porous medium to overcome wellbore damage, to improve oil and gas productivity in low permeability reservoirs or to increase production in secondary recovery operations. This paper introduces a new technique for interpreting pressures behavior of a horizontal well with multiple hydraulic fractures. The well extends in multi-boundary reservoirs having different configurations. The hydraulic fractures in this model can be longitudinal or transverse, vertical or inclined, symmetrical or asymmetrical. The fractures are propagated in isotropic or anisotropic formations and considered having different dimensions and different spacing. The study has shown that pressure responses and flow regimes are significantly influenced by both reservoir's boundaries and fractures' dimensions. Different flow regimes have been observed for different conditions. New flow regimes have been introduced in this study. The first one is the early radial flow regime which represents the radial flow around each fracture in the vertical plane resulted due to the partial vertical penetration of hydraulic fractures. The second one is the second linear flow regime which represents the linear flow toward each fractures in the vertical plane normal to the wellbore resulted due to the long spacing between fractures. Third one is the third linear flow regime which represents the linear flow in the vertical plane parallel to the wellbore after the pressure pulse reaches the upper and lower impermeable boundaries.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, April 4–8, 2009

Paper Number: SPE-120106-MS

Abstract

Abstract Currently in the oil industry, a field usually contains several wells producing from the same drainage domain, and each well will have an effect on the pressure at other wells. For an infinite-acting multiple wells system, pressure transient analysis is already done by using superposition principle. This paper presents pressure drawdown equations of a multiple wells system in a circular cylinder reservoir with constant pressure outer boundary. The proposed equations provide fast analytical tools to evaluate the performance of multiple wells, which are located arbitrarily in a circular cylinder reservoir, and are producing at different rates. This paper examines the pressure drawdown response of a specific well located in a system of producing wells. The interference effects of nearby producing wells on the pressure drawdown response are investigated. The proposed equations are illustrated by numerical examples. It is concluded that, for a given multiple wells system in a circular cylinder reservoir, well pattern, well spacing, skin factor, flow rates and well off-center distances have significant effects on single well pressure transient behaviour. Because the reservoir is under edge water drive, the outer boundary is at constant pressure, when producing time is sufficiently long, steady-state is definitely reached. Introduction It is rare to find a reservoir being produced from only a single well. A field usually contains several wells producing from the same drainage domain, and each well will have an effect on the pressure at other wells. If we have one well producing at a constant rate, the flowing bottomhole pressure in that well is a function of its own production as well as the production from surrounding wells. For an infinite-acting multiple wells system, pressure transient analysis is already done by using superposition principle (Lee, et al., 2003).

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, April 4–8, 2009

Paper Number: SPE-120545-MS

Abstract

Abstract The purpose of this study is to develop a technique, based on the pressure derivative concept, for interpreting pressure transient tests in wells with an inclined hydraulic fracture. Detailed analysis of unsteady-state pressure behavior of fully penetrating inclined fracture in an infinite slab reservoir was provided. Both uniform flux and infinite conductivity models were considered. The study has shown that inclined fracture pressure data exhibit similar flow regimes as for vertical fracture counterpart. Those flow regimes are linear and pseudo-radial flow for both uniform flux and infinite conductivity models. However, for infinite conductivity model, a bi-radial flow regime is also observed. In the case of high formation thickness to fracture half length ratio and high angle of inclination, both uniform flux and infinite conductivity inclined fracture model exhibit an additional flow regime called early radial flow. Both bi-radial flow and early radial flow regimes for inclined hydraulic fracture have not been mentioned in the literature before. A step by step procedure based on Tiab's Direct Synthesis (TDS) was developed in this study. Fracture properties such as half fracture length, inclination angle, formation permeability and pseudo-skin factor can be obtained from the direct interpretation of the log-log plot of pressure and pressure derivative without the need of any type curve matching. Several unique features of the pressure and pressure derivative plots of both uniform flux and infinite conductivity inclined fracture models were identified including the points of intersection of straight lines for different flow regimes. These points can be used to verify the results or to calculate unknown parameters. Equations associated with these features were derived and their usefulness was demonstrated. Numerical examples with both pressure build-up and drawdown data were also demonstrated for this procedure. Introduction Hydraulic fracturing is an important well stimulation technique that has been widely used in the oil and gas industry. Most of the pressure transient analysis techniques to analyze pressure responses of fractured wells are based on the assumption that the fracture is either vertical or horizontal. However, a hydraulic fracture could be inclined with a non-zero angle with respect to the vertical direction. Field studies have shown that most hydraulic fractures are never perfectly vertical. Thus, for an inclined hydraulic fracture, the vertical orientation assumption may lead to erroneous results in well test analysis especially when the inclination angle is significant. However, there are very few studies concerning pressure transient analysis of inclined hydraulic fracture and there is no applicable well test analysis procedure available for inclined fractures. For this reason, it is important to develop well test analysis procedures for this type of fracture. Hydraulic fracturing technique involves creation of fracture or fracture system in porous medium to overcome wellbore damage, to improve oil and gas productivity in low permeability reservoirs or to increase production in secondary recovery operations. In this study, a new type curve matching procedure, based on the pressure derivative concept, was developed for interpreting pressure transient tests in a well with an inclined hydraulic fracture. A general literature review on inclined hydraulic fracture will be provided. Both uniform flux and infinite conductivity models will be discussed in this paper. Only the case where the fracture is symmetric in both lateral and horizontal directions was considered in this study. Analytical solution for each flow regime is explained in details.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, April 4–8, 2009

Paper Number: SPE-120540-MS

Abstract

Abstract Hydraulic fracturing is an important well stimulation technique that has been widely used in the oil and gas industry. Most of the pressure transient analysis techniques to analyze pressure responses of fractured wells are based on the assumption that the fracture is either vertical or horizontal. However, a hydraulic fracture could be inclined with a non-zero angle with respect to the vertical direction. Field studies have shown that most hydraulic fractures are never perfectly vertical. Thus, for an inclined hydraulic fracture, the vertical orientation assumption may lead to erroneous results in well test analysis especially when the inclination angle is significant. However, there are very few studies concerning pressure transient analysis of inclined hydraulic fracture and there is no applicable well test analysis procedure available for inclined fractures. For this reason, it is important to develop well test analysis procedures for this type of fracture. The purpose of this study is to develop a technique, based on the pressure derivative concept, for interpreting pressure transient tests in wells with an inclined hydraulic fracture. Detailed analysis of unsteady-state pressure behavior of fully penetrating inclined fracture in an infinite slab reservoir was provided. Both uniform flux and infinite conductivity models were considered. The study has shown that inclined fracture pressure data exhibit similar flow regimes as for vertical fracture counterpart. Those flow regimes are linear and pseudo-radial flow for both uniform flux and infinite conductivity models. However, for infinite conductivity model, a bi-radial flow regime is also observed. In the case of high formation thickness to fracture half length ratio and high angle of inclination, both uniform flux and infinite conductivity inclined fracture model exhibit an additional flow regime called early radial flow. Both bi-radial flow and early radial flow regimes for inclined hydraulic fracture have not been mentioned in the literature before. A type curve matching technique was developed in this study using both pressure and pressure derivative curves. This type curve matching procedures can be used to obtain the following parameters: half fracture length, inclination angle, formation permeability and the pseudo-skin factor. The results should be verified with other pressure plots such as semi-log plot of ?P vs. t and ?P vs. t 1/2 plot. A set of type curves with associated data was also provided for uniform flux and infinite conductivity inclined fracture models. Detailed explanations, tables, figures and numerical examples are included in this paper. Introduction Hydraulic fracturing technique involves creation of fracture or fracture system in porous medium to overcome wellbore damage, to improve oil and gas productivity in low permeability reservoirs or to increase production in secondary recovery operations. In this study, a new type curve matching procedure, based on the pressure derivative concept, was developed for interpreting pressure transient tests in a well with an inclined hydraulic fracture. A general literature review on inclined hydraulic fracture will be provided. Both uniform flux and infinite conductivity models will be discussed in this paper. Only the case where the fracture is symmetric in both lateral and horizontal directions was considered in this study. Analytical solution for each flow regime is explained in details. The calculation procedure and analytical model verification are illustrated using numerical examples.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Production and Operations Symposium, March 31–April 3, 2007

Paper Number: SPE-106881-MS

Abstract

Abstract This paper presents a new procedure to determine inter-well connectivity in a reservoir based on fluctuations of bottomhole pressure of both injectors and producers in a waterflood. The method utilizes a constrained multivariate linear regression analysis to obtain information about permeability trends, channels and barriers. Previous authors applied the same analysis to injection and production rates to infer connectivity between wells. However, in order to obtain good results, they applied various diffusivity filters to the flow rate data to account for the time lags and the attenuation. This was a tedious process that requires subjective judgment. Shut-in periods in the data, which were usually unavoidable when a large number of data points were used, created significant errors in the results and were often eliminated from the analysis. This new method yielded better results compared to the results obtained when production data were used. Its advantages include: (1) No diffusivity filters needed for the analysis; (2) Minimal numbers of data points required to obtain good results; and (3) Flexible plan to collect data as all constraints can be controlled at the surface. The new procedure was tested using a numerical reservoir simulator. Thus, different cases were run on two fields, one with five injectors and four producers and the other with 25 injectors and 16 producers. For a large waterflood system, multiple wells are present and most of them are active at the same time. In this case, pulse test or interference test between two wells are difficult to conduct since the signal can be distorted by other active wells in the reservoir. In the proposed method, interwell connectivity can be obtained quantitatively from multi-well pressure fluctuations without running interference tests. Introduction Well testing is a common and important tool of reservoir characterization. Many well testing methods have been developed in order to obtain different reservoir properties. Interference test and pulse test are used to quantify communication between wells. These methods are often applied to two wells as one well sending the signals (by changing flow rates) and the other receiving them1. However, for a large field such as a waterflood system, multiple wells are present and most of them are active at the same time. In this case, pulse test or interference test between two wells are difficult to conduct since the signal can be distorted by other active wells in the reservoir. In this method, data can be obtained from multi-well pressure test that resemble interference test. Thus, we can have several wells sending signals and the others receiving the signals at the same time. However, the wells that are receiving the signal can either be shut-in or kept at constant producing rates. The pressures at all wells are recorded simultaneously within a constant time interval. The length of the test will depend on the length of the time interval and the number of data points. Results of this method can be used to optimize operations and economics and enhance oil recovery of existing waterfloods by changing well patterns, changing injection rates, recompletion of wells, and in-fill drilling. This work is based on previous work conducted by Albertoni and Lake2 using injection and production rates. In their work, Albertoni and Lake developed and tested different approaches using constrained multivariate linear regression analysis with a numerical simulator and then applied to a waterflooded field in Argentina. They used diffusivity filters to account for the time lag and attenuation of the data. In his thesis, Anh Dinh3 verified the method using different reservoir simulator and applied to a waterflood field in Nowata, Oklahoma. He also investigated the effect of shut-in periods and vertical distances on the results. The main objectives of this work are to verify the results obtained from pressure data with results from flow rate data, to propose a new method to determine interwell connectivity and to suggest further research and study on the method.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Production and Operations Symposium, March 31–April 3, 2007

Paper Number: SPE-106997-MS

Abstract

Abstract A new type curve for well test analysis for non-newtonian fluids in petroleum reservoir is developed. The general analytical solution in Laplace variable presented by Ikoku and Ramey Jr.2 forms the mathematical basis of the proposed type-curves. The equation for the type curve was developed, following similar procedure to that of Bourdet e t al 10. The Bessel functions involved in the final solution of the non-newtonian case cannot be approximated by logarithm function as in the Newtonian case. Hence, the dimensionless group of the skin factor and wellbore storage coefficient used in the Bourdet et al's case was not used in this study. Instead, only the skin factor is retained. The dimensionless wellbore storage coefficient is grouped with the dimensionless time as usual. The log-log plot of the pressure derivatives at the infinite acting radial flow lie on a straight line for each flow behavior index. This straight line intersects the Newtonian infinite acting pressure derivative line at tD/CD = 1. In addition to the unit slope line of the wellbore storage region, this point of intersection provides a fulcrum point for proper curve matching. Thus the characteristic mobility can be computed using this intersection point. Apart from the conventional type-curve-matching method of analysis, the Tiab's direct synthesis (TDS) technique is developed for the evaluation of well test data in non-newtonian fluid flow. This is based on the long time solution as in the conventional case and the characteristic line of the type curve. The process does not involve type curve matching, but provides a direct method of evaluating the well test data from the log-log plot of the pressure and pressure derivatives. Two examples from the references 3 and 6 were used to validate the type curves and satisfactory results were obtained. Introduction Several efforts have been made to develop general type curves to analyze pressure transient data for non-newtonian fluid flow in porous media. The problem has been how to combine the skin factor and wellbore storage coefficient into one dimensionless group as in Bourdet et al's type curves. Poollen et al 1 developed a relationship between the flow rate and pressure differential for a steady state flow while they used numerical method to solve the unsteady state flow. Their method lacked analytical methodology for well test analysis. The work of Ikoku et al 2, 3 & 5 presented the analytical solution that is useful for well test analysis. Odeh and Yang 4 presented similar solution to that of Ikoku et al, but their method of analysis involved trial and error. The flow behavior index cannot be determined directly from Odeh and Yang's method. Vongvuthipornchai and Raghavan 6 developed type curves that include skin factor and wellbore storage coefficient in a similar manner to that of Bourdet type curves for Newtonian fluid. The mathematical equation for the type curve was deduced from their early time solution, but not from the general solution. The straight line of the Non-Newtonian pressure derivatives does not intercept the 0.5-line of the Newtonian pressure derivatives at tD/CD = 1. This raised the question of the validity of such type curve. Olarewaju 7 presented a series of type curves on non-newtonian fluid flow in naturally fractured and homogeneous reservoirs. The pressure derivatives on the type curve for the Newtonian fluid in double porosity case fell below the 0.5-line during radial flow regime. No trough or transition flow was observed. In the non-newtonian case, the extrapolation of the straight line of the pressure derivatives during radial flow does not intercept the 0.5-line at tD/CD = 1. We believe that this should be a unique characteristic feature as shown by Katime and Tiab 8. Eventhough Olarewaju combined wellbore storage and skin factors together as in Bourdet's solution for Newtonian case, the validity of his method is questionable. In this study, the only dimensionless group for characterizing the type curve is the skin factor and flow behavior index. The wellbore storage coefficient is grouped along with the time as in the other existing type curves. The Tiab direct synthesis technique (TDS) which provides a method of well test analysis without type curve matching is also developed for the analysis of pressure transient data for non-newtonian fluid. Mathematical Model The following assumptions are made in deriving the mathematical formulae.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Production and Operations Symposium, March 31–April 3, 2007

Paper Number: SPE-106970-MS

Abstract

Abstract This paper presents a simple productivity equation for a horizontal well in pseudo-steady state in a closed anisotropic box-shaped reservoir, using a uniform line sink model. A new equation for calculating pseudo skin factor due to partial penetration is also proposed. Compared with the equations for horizontal wells in pseudo-steady state in the literature, the new equations are more practical and easy to use in the field practice. They are derived by solving analytically the involved three-dimensional partial differential equations and are extracted from a very complex general solution. The effects of the following parameters on productivity have been investigated: well location, pay zone thickness, well producing length, principal permeability, and dimensions of drainage volume. It is concluded that, though each of these parameters has an effect on productivity, the well length and the permeability perpendicular to the well in the horizontal plane have the strongest influence. Introduction To determine the economical feasibility of drilling a horizontal well, the engineers need reliable methods to estimate its expected productivity. There have been several attempts to describe and estimate horizontal well productivity indexes. Lu 1,2,3 presented steady state productivity equations for a horizontal well in an infinite extention, finite thickness reservoir and in a circular cylinder drainage volume reservoir. Babu and Odeh 4 introduced a complex equation to calculate productivity of horizontal wells which required that the drainage volume be approximately box-shaped, and all the boundaries of the drainage volume be sealed. They reduced their original infinite series solution into equations for shape factor and partial penetration skin. Although their expression for the shape factor is quite simple, the expression for the partial penetration skin is very complicated. Thompson et al.5 proposed an algorithm to compute the horizontal well pressure response in bounded reservoirs. Their algorithm switches between two infinite series solutions (with different rate of convergence) to improve the overall convergence rate. Economides et al.6 proposed a pseudo-steady state computer model using the continuous point source solution. Their model also accounts for well orientation. Helmy and Wattenbarger 7 provided corrections to calculate the shape factor and partial penetration skin factor in pseudo-steady state. Their correlations were developed using nonlinear regression of more than 800 numerical simulation runs for different reservoir aspect ratios, well locations and well penetration ratios. All of the above pseudo-steady state equations are either complicated to use or require computer programming, or empirical relationships that lacks in theoretical bases. This paper provides analytical equations to calculate productivity and pseudo skin factor due to partial penetration of a horizontal well in pseudo-steady state in a closed anistropic box-shaped reservoir. Analytical solutions are derived by assuming uniform fluid withdrawal along the portion of the wellbore open to flow.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–25, 2003

Paper Number: SPE-80899-MS

Abstract

Abstract This paper provides an insight into the mechanism of gas injection process in reducing gas-well productivity losses due to condensate blockage in the near wellbore region. A technique is proposed to predict performance of gas-condensate reservoirs where cycling is employed. Toual gas condensate field with its two reservoirs, TAGS & TAGI, was used as a case study in this paper. Comparison between the primary depletion and gas recycling was studied and the economic feasibility of the project was evaluated. An equation of state (EOS) with 6 pseudo components was used to characterize the complexity of the hydrocarbon column. The model used consists of a grid of 2600 and 1875 cells (25´15´07) and (25´15´05) for TAGS & TAGI respectively. After a successful history match, MER (maximum efficiency rate) of 9% and 8% were used to optimise the primary depletion of TAGS & TAGI reservoirs respectively. After running many cases, it was found that the injection of 100% produced gas for 20 years is the optimum case for the development of the Toual Field. It was observed that the condensate recovery increased as the duration and the volume of the injection gas increased. Prediction runs indicated that the injection of 100% of gas, starting in 2005 will result in a total recovery of 973.38 MSTCM and 777.53 MSTCM (22.2%, 30.5%) for both the reservoirs respectively over a life span of 20 years. Introduction A gas condensate reservoir may be produced in one of the following two ways: Producing the reservoir by natural depletion and by injecting all or part of the dry gas produced back into the reservoir, thereby maintaining the reservoir pressure above the dew point, the main cause of the liquid drop out and reduced deliverability. As the dew point pressure is reached, natural depletion usually leads to the accumulation of an increasing liquid saturation in the pores. The percentage of heavy components in the production decreases with the time that the dew point is reached until the retrograde pressure is attained. At this point the percentage increases but only very gradually. Thus the condensate production is a decreasing function of time. This paper represents the results of the simulation study of both reservoirs TAGS and TAGI of Toual field and proposes the following principle phases for the field: A revision of all geological and petrophysical data also all previous interpretations. Development of geological reservoir model. Simulation and matching of physical properties of gas using Peng-Robinson equation of state (PR-EOS). Determination of volume in place at initial conditions. Simulation and history matching of production of the reservoir using a 3D compositional simulator. Revision of performance of the reservoir with different scenarios of development. Evaluation of the Reservoir Fluid Properties 1- TAGS Gas Zone The reservoir pressure draw-down at time of the sampling was 17 Kg/cm 2 . This draw-down is relatively small and it is likely that the separator samples were representative of the reservoir fluids. Although the laboratory study appeared to be a full depletion study, the retrograde liquid data presented in the present evaluation were obtained entirely from a simulated depletion. The maximum volume of retrograde liquid will be about 4.3 percent of the hydrocarbon pore volume. The laboratory relationship between compressibility factor and pressure was very poor. These data were given little weight in this evaluation study. 2- TAGI Gas Zone The reservoir pressure drawdown at time of the sampling was only 4.8 Kg/cm 2 . It is probable that the separator samples are representative because of the favourable down hole conditions. The dew point of the recombined reservoir fluid was 377.0 Kg/cm 2 absolute at 105 °C. It is probable that the reservoir fluid was originally saturated at the initial conditions of 378.6 Kg/cm 2 absolute and 108 °C at the reference level of - 3099 m, and the data in this evaluation study have been adjusted to this pressure.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–25, 2003

Paper Number: SPE-80926-MS

Abstract

Abstract This paper investigates the performance of horizontal wells under the combined influence of wellbore friction, wellbore storage, and formation damage. A new model is proposed wihich couples wellbore, reservoir, and non-uniform skin, and takes into account the change in flow regime from laminar to turbulent along the wellbore. In the conventional perspectives, wellbore damage may be viewed as an additional pressure drop, is correct only for infinite-conductivity wellbore with uniform damage. It is shown in this paper that the wellbore damage may not be viewed merely as an additive pressure drop due to skin in the presence of friction inside the long horizontal section of the well. Wellbore hydraulics change the flux distribution (inflow profile) along the wellbore and, thus, result in additional pressure drop in the reservoir and across the skin zone. Horizontal wells, for a number of reasons, are unlikely to have smooth distributions of damage along their trajectories. Thus, segmented well testing would be ideal tool to estimate the skin, Si, of each segment especially in the zone where more severe damage is expected, because it delivers a detailed picture of the skin distribution along an extended horizontal well. Finite conductivity solution approaches to infinite conductivity solution at high conductivity values and high wellbore radius. The appearance of bi-linear, linear, and radial flow regimes depends upon the length of the well; for long wells, linear and bi-linear flow regimes are observed, and they are masked in the case of short wells. The perforation number effect appears only in the damaged case, when the open-hole scenario deviates from the two other cases. Another important factor, that affects the behavior of the pressure, is the dimensions of altered permeability region; the higher the radius of filtrate penetration, the higher the volume of affected region and therefore, the higher the loss in pressure. The effect of k/k s is more severe in small wells. Another correlation which allows determine k x directly from the intersection point with the half slope is presented using a new method of interference test interpretation of different segments with each other in the same well. Isolated segment testing would lead to the estimate the local skin factor, a possible indication of uneven damage distribution and a necessary variable for the optimization of matrix stimulation. Thus designing of a remedial treatment, both the type and the location of permeability damage must be considered. Several examples are included to illustrate the use of the model developed. Introduction During the last three decades significant advances in drilling technology have made it possible to drill horizontally. Although slow, this technology is being applied worldwide because of its affordable cost. Horizontal well due to its large flow area, may be several times more productive than vertical well. However, intuition tells that this large contact of the horizontal well with the formation will result more formation damage than the vertical well will. The residing mud filtrate and also the mud particulates can cause damage to the zone by reducing the permeability around the wellbore. This in turn results in higher pressure losses in the vicinity of the wellbore and thus reduces the productivity of the well. Any damage around the wellbore is, therefore, never desired. Since repairing the permeability damage is generally difficult and expensive, all studies emphasize the importance of preventing it. It is usually agreed that the uniform skin region is an idealized case particularly for long horizontal wells. Since the duration of the contact of the drilling fluid with the formation decreases from the heel of the well to the toe, at best a conical skin region with the apex at the toe should be expected. Various physical forces such as grinding, crushing, bit vibration, and fluid as well as particulate invasion are at work at the well bore during the drilling of a long horizontal well which cuase the changes in the radius and permeability of the skin zone along the well length. This may even lead to situations where some portions of the well are closed to inflow because of highly damaged areas. The same effect would, of course, result if the well were completed selectively. This paper adresses issues concerning well pressure and flux distribution under the combined influences of mechanical damage and wellbore hydraulics.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–25, 2003

Paper Number: SPE-80915-MS

Abstract

Abstract Pressure-transient analysis for gas wells has a great importance in the oil and gas Industry. Transient pressure responses of unfractured and hydraulically fractured gas wells may be affected by non-Darcy flow near the wellbore, such important effect needs to be taken into account when estimating reservoir and well parameters. An additional problem encountered in gas wells test analysis is the presence of the rate-dependent skin, which requires a search for another parameter (non-Darcy flow coefficient). Several tests are performed in order to measure the deliverability of gas wells and to describe reservoir performance. Such specific tests as flow after flow, isochronal and modified isochronal were initially designed to obtain the absolute open flow potential of a well, however, the use of these tests has been extended to obtain additional information from the reservoir. Drawdown tests are focused in obtaining such data as wellbore storage, reservoir transmissivity, skin factor, flow efficiency and system geometry. Buildup tests lead us to the average pressure of the reservoir, however, proper analysis of buildup test provides values of permeability, wellbore storage and apparent skin factor. Buildup and drawdown tests are currently analyzed using type-curve matching procedures, which involves trial and error and conventional techniques. Pseudopressure concept, which was used in this study, has shown to provide sufficient engineering accuracy in dealing with gas well test data. This study utilizes characteristic points, intersection and lines found on the pseudopressure and pseudopressure derivative plot to obtain fracture length, fracture conductivity, skin factor and reservoir permeability. It was found that changing the non-Darcy factor, D, the shape of the pseudo-pressure curve varies from the original gas curve shape at D=0, which implies that an additional skin effect is added at high rates. On the other hand, the pseudo-pressure derivative curve remains on its original shape, then, in spite of increasing non-Darcy effect factor, D, the pseudo-pressure derivative curve is not affected by this additional skin effect added to the system because of the non-Darcy flow effect. The interpretation technique was successfully tested with simulated and field examples. Introduction In 1999, Tiab et al. 1 extended the Tiab's Direct Synthesis Technique for interpretation of the behavior of the pressure and pressure derivative data of an oil well intersected by a finite-conductivity hydraulic fracture. Now, this study extends the Tiab's Direct Synthesis Technique usage to vertical gas wells, which also closely follows the procedure outlined by Tiab et al. 1 . During a test on a hydraulically fractured well, initially, fracture-linear flow occurs into the fracture, which is characterized by a slope of 0.5 in a log-log plot. During this fluid period, most of the fluid entering the wellbore comes from fluid expansion in the fracture, the occurrence of this flow period is too short and normally is never seen. Bilinear flow 2 , which is characterized by a slope of 0.25 on the log-log plot, takes place in finite-conductivity fractures as fluid in the surrounding formation flows linearly into the fracture, most of the fluid entering the wellbore during this flow period comes from the formation. Fractures are considered to have finite-conductivity when Dimensionless Fracture Conductivity 2 , C fD <100. Fracture conductivity has been described as having values varying typically from 1 to 500. A low value of conductivity indicates low fracture permeability or long fracture lengths, or possibly both. On the other hand, a high value of conductivity implies high fracture permeability, small fracture length, or both. Formation-Linear flow occurs only in high conductivity fractures ( C fD >100), this flow is also identified by a slope of 0.5, once the linear flow in the formation -or the bilinear flow- vanishes, the pseudo-radial flow takes place. In order to define the system, consider a vertically fractured gas well producing from a horizontal, homogeneous and isotropic formation. The permeability is constant, the thickness is uniform, and the fracture is the same length on both sides of the well.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–25, 2003

Paper Number: SPE-80910-MS

Abstract

Abstract To obtain a reliable characterization of complex reservoirs, geoscientists and petroleum engineers commonly build geologic or geostatistical reservoir models which contain more than a million grid cells. However, for flow simulation such a detailed description demands a great deal of information and processing time. Therefore, less complex models are usually preferred where the number of grid cells must be reduced by a factor of 10 or more. Such scaling up necessarily involves the loss of information that must be captured through upscaling porosity, permeability and the use of pseudofunctions. The main objective of this paper is to determine a general method for using pseudofunctions for upscaling multiphase flow in 3D anisotropic heterogeneous reservoirs with different capillary and gravity numbers and applying the method to a real field case "Hassi Messaoud Field - Algeria". The performance of different types of pseudofunctions is evaluated under different capillary and gravity numbers, and upscaling levels. As a part of this research study a software package to calculate pseudofunctions has been developed. It includes: the input option from ECLIPSE restart files generates pseudo curves for three phase three-dimensional problems using Kyte and Berry, Pore Volume, Stone, and Transmissibility Weighted methods, and generates output file format which can be read by ECLIPSE 100ä. A variety of homogeneous fine grid models representing different flow regimes were considered in this study and the performance of several pseudofunction methods was compared. All the pseudo function methods succeeded in reproducing the fine grid watercut and maintained oil production for the capillary dominated, equilibrium, viscous dominated flows, however, for the gravity dominated flow they failed to match the fine grid curve exactly. Although this shortcoming of the pseudofunction curves gives better results than the rock curves. Next in this study, the results of the waterflood of a heterogeneous 3-D model of HMD Zone 17 are presented. This real field model confirmed the homogeneous case results: for high flow rates the pseudofunctions can be applied successfully to upscale from fine to coarse grid simulation. Introduction As the clock is ticking geostatistical model scales are becoming finer and finer. Unfortunately, the development of reservoir flow simulators is not moving at the same pace to handle such a large fine scale model. A revolution in the computational hardware or modification to the way the simulation is done is therefore necessary. A typical grid block size is 100 m areally and 1–10 m vertically. Such a large grid block may include a lot of heterogeneity. If we use rock curves for simulation with such large grid blocks, the important effects of heterogeneity will be omitted. Large simulation grid blocks will also cause large numerical dispersion. So, under such circumstances, dynamic pseudo functions are needed to replace the rock curves. Through the use of dynamic pseudo functions, one attempts to capture the effects of heterogeneity below the scale of a simulation grid block, and reduce the effects of numerical dispersion. One common use of pseudo functions is to reduce the number of grid blocks used in the simulation, and sometimes even reduce the dimension of the problem such as reducing a 3-D field case model to a 2-D cross-sectional model. By doing so, we hope to retain fine grid information while performing coarse grid simulations. Theory Pseudofunctions Methods Full-field models may not use simulation layers that are on the same scale as the core samples. Consequently, scaleup of relative permeability and capillary pressure often is required for coarse-grid reservoir simulation. This scaleup is accomplished with relative permeability and capillary pressure inter-block pseudo functions. Two types of inter-block pseudofunctions are available to the engineer working on a reservoir study: analytical (1) and dynamic pseudo functions. This study is mainly concerned with the use of dynamic pseudo functions. Well Pseudofunctions: Inter-block pseudofunctions describe the flow of fluids form one gridblock to adjacent gridblocks. These pseudofunctions, however, do not necessarily describe flow from the gridblock to the wellbore. Well pseudofunctions are used to describe flow to the wellbore.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Mid-Continent Operations Symposium, March 28–31, 1999

Paper Number: SPE-52201-MS

Abstract

ABSTRACT This paper extends Tiab's Direct Synthesis technique 1,2 for interpreting the behavior of the pressure and pressure derivative data of a well intersected by a finite conductivity hydraulic fracture. In this technique log-log plots of pressure and pressure derivative data of a pressure drawdown or pressure buildup test are analyzed without using the type-curve matching or regression procedures. A log-log plot of pressure and pressure derivative versus test time for a fractured well in a closed system may reveal the presence of several straight lines corresponding to different flow regimes; bilinear flow, linear flow, infinite-acting radial flow, and pseudo-steady state flow. The slopes and points of intersection of these straight lines are unique and therefore can be used to calculate several well, reservoir and fracture parameters: permeability, skin factor, wellbore storage coefficient, fracture conductivity, half-fracture length, and drainage area. It is found that equations corresponding to the points of intersection are very useful in checking on the parameters obtained from the slopes, when the pressure derivative curve is not smooth. A new equation is derived for calculating (a) the half-fracture length in the absence of the linear flow regime straight line of slope 0.5 such as in the case of low conductivity fracture, (b) the fracture conductivity in the absence of the bi-linear flow line of slope 0.25, and (c) the skin factor in the absence of the infinite acting radial flow line such as in the case of a short test.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 2–4, 1995

Paper Number: SPE-29526-MS

Abstract

Abstract A new model is proposed to characterize the variation in skin effect along a horizontal well. Typically, a cylindrical- shaped damaged region is assumed; however, this work describes the damaged region as a combination cylindrical-conical shape. The shape of the damaged region and the severity of the damage is governed by the contact time of the drilling fluid with the formation. This time is a function of the drilling rate penetration (ROP) and the mud filtrate invasion rate. Simple, empirical models are used to provide POP and mud filtrate invasion rate. The effects of anisotropy ratio, penetration rates, and horizontal length are included in the analysis. Anisotropy and increasing penetration rate both will result in a decrease in the skin effect. Any horizontal well length greater than the equivalent horizontal length of the cone-shaped damage region will result in a constant cylindrical-shaped damage region, which can be evaluated using Hawkins' formula. The cone-shaped damage region will exist at the furtherest end of the horizontal length. The time to transform the cone- shaped damage region to a cylinder is the circulation time after drilling to the total length. This circulation time is determined for the various anisotropy ratios and penetration rates. Introduction It is well known mud filtrate invasion into a formation creates a near wellbore damage region, resulting in an additional pressure drop near the wellbore and loss in pressure drawdown. The concept of skin factor was developed to account for the loss in productivity due to the near wellbore formation damage. The damaged region is typically idealized as a uniform, concentric cylinder about the wellbore Figure 1a illustrates the idealized system for both a vertical and horizontal well. However, it is more likely that the damaged zone is conical in shape, due to the time the mud has to circulate and invade a penetrated foot of formation (Fig 1b). Since the horizontal length is greater than the reservoir thickness, a longer contact time per foot of formation thickness will occur in a horizontal well. The additional time will develop a significant variation in the skin damage along the length of the horizontal well. The objective is to quantify the changing skin factor along the horizontal well, and note any differences with the idealized system. Correctly identifying the skin region will impact completion efforts to remove the damage and mud formulation to minimize the invasion and reduce the damage. Further, this work provides evidence of an "effective horizontal length" which contributes to the productivity of the well and not the entire horizontal length. P. 755

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 21–23, 1993

Paper Number: SPE-25426-MS

Abstract

Abstract The current type-curve matching technique is essentially a trial-and-error procedure without any independent and accurate way of checking the validity of the end results. This paper introduces a new technique for interpreting pressure tests. This technique uses log-log plots of the pressure and pressure derivative versus time to calculate reservoir and well parameters WITHOUT type-curve matching. This paper concentrates on the interpretation of pressure tests in which wellbore storage and skin are present. The technique essentially consists of obtaining characteristic points of intersection of various straight line portions of the pressure and pressure derivative curve, slopes and starting times of these straight lines. These points, slopes and times are then used with appropriate equations to solve directly for permeability, wellbore storage and skin. A step-by-step procedure for calculating these parameters without type-curve matching for five different cases is included in the paper. The most important aspect of this new technique is undoubtedly its accuracy because it uses exact analytical solutions to calculate permeability, skin, and wellbore storage. The second most important feature of this new technique is that it is verifiable. Any two parameters calculated from two independent equations corresponding to two different portions of the pressure derivative curve are verified by a third equation which corresponds to a known and unique point relating the two parameters. The proposed technique is applicable to the interpretation of pressure buildup and drawdown tests. This technique is illustrated by several numerical examples. 1. INTRODUCTION AND BASIC EQUATIONS Interpretation of pressure tests for a single well with wellbore storage and skin in a homogeneous reservoir considerably improved when the type-curve matching technique was published in the seventies. Later that decade Tiab introduced the pressure derivative analysis. He showed that a log-log plot of pressure derivative versus time is an important tool in identifying flow regimes and boundary effects. In the eighties type-curves which combine both the pressure and pressure derivative functions for various reservoir systems became an integral part of modern well test analysis. Unless all flow regimes are definitely observed in the pressure derivative curve, type-curve matching is still a risky technique. Also, combinations of various boundary conditions may yield approximately similar pressure behavior. For a well producing from a bounded system, it is possible for inner and outer boundary effects to interact and considerably affect the well pressure behavior such that the infinite acting radial flow line is either too short or non-existent. Horne showed that log-log type curve matching is not as accurate as conventional semilog methods, because log-log axes tend to mask inaccuracies at late time, where 1 mm deviation of a pressure point may mean an actual error of 200 psia. Finally, the noise in the pressure derivative curve can be sever enough to make it impossible to draw the characteristic straight lines corresponding to flow regimes. P. 203^