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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 18–21, 2019

Paper Number: SPE-195152-MS

..., which determines that a plot of the rate-normalized pressure drop vs the pseudo-time produces a

**straight****line**with the slope of such line yielding the OGIP. The use of the pseudo time concept calls for the estimate of gas properties at the prevailing reservoir pressure which in turn is a function of the...
Abstract

Accurate estimation of the Original Gas in Place (OGIP) early in the reservoir life is fundamental as field development plans and ultimate recovery strongly depend on it. This is particularly relevant when the conventional material balance is not suitable due to the lack of pertinent shut-in pressure measurements. This paper presents a case history of a tight gas field in which we use flowing material balance technique and type curves for decline curve analysis to calculate OGIP by using only flowing pressure and rate data. The method uses fundamental pseudo-steady state theory, which determines that a plot of the rate-normalized pressure drop vs the pseudo-time produces a straight line with the slope of such line yielding the OGIP. The use of the pseudo time concept calls for the estimate of gas properties at the prevailing reservoir pressure which in turn is a function of the OGIP and the cumulative production. We propose an iterative scheme based on the Newton-Raphson method to compute the OGIP using the flowing material balance technique coupled with the conventional P/Z material balance. We illustrate the application of the method with the aid of synthetic examples as well as field cases obtained from low permeability gas reservoirs where no shut-in pressures are available. Results from the technique adequately compare with type-curve matching analysis. Furthermore, we demonstrate the problem can be transformed into an equivalent-liquid system and being analyzed with standard PTA techniques using the constant rate liquid solution. In absence of shut-in pressure information, the PSS analysis offers an attractive alternative to the conventional material balance method. Besides, the method only requires minimal phase behavior data in the case of gases rendering its application practical and convenient. Also, we describe how to transform the constant pressure problem into a constant rate one in order to apply standard PTA techniques. Additionally, this work demonstrates the importance of having automated wells with permanent gauges by enhancing the value of the information provided by them in the framework of an adequate and judicious reservoir management.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 18–21, 2019

Paper Number: SPE-194699-MS

... fluid equation gas oil ratio composition mole fraction

**straight****line**predictor reservoir fluid composition fraction molecular weight The cause of the observed fluid property variations is believed to be a complex filling history in combination with biodegradation. The large lateral...
Abstract

The Bahrain Field is characterized by large lateral and vertical variations in fluid properties, with oil gravity ranging between −9 and 80 °API. The lower API crudes are encountered mostly on the structural flanks and within the upper reservoir units, while the highest API crudes are condensates from deeper formations such as Hith and Arab. The deepest reservoir is the gas-bearing Khuff. It has 50 °API condensate and forms a separate fluid type from the rest of the Bahrain Field. The objective of this paper is to derive a single compositional predictor for the entire range of crude gravities. Excluded from this unified model are bitumens from Aruma and Khuff condensates, which are compositionally different. One outcome of this study was to predict the reservoir fluid as a function of well test Gas Oil Ratio (GOR) and API gravity by mathematical recombination of averaged data from abundant well tests across the Bahrain Field. A strong trend of methane fraction in the reservoir fluid versus saturation pressure has been observed, and thus it has been possible to construct the recombined reservoir fluid and then predict saturation pressures, Formation Volume Fraction (FVF), and viscosity. This fluid model was used to initialize compositional models for gas plant evaluations, miscible flood evaluations, and to determine the maximum GOR at which saturation pressure equals reservoir pressure. Another outcome of the unified fluid model was to construct a reservoir fluid composition given a target saturation pressure and API. This information is used to construct representative fluids for laboratory synthesis of crudes and gas for live oil experiments. As part of the process, a number of quality checks were constructed to determine if the fluid encountered is in range of historic produced crudes (e.g. contamination by air or lift gas) and enable construction of fluids for reservoir simulation.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 10–13, 2013

Paper Number: SPE-164427-MS

... gas material balance equation is the simple

**straight****line**plot of p/Z versus cumulative gas production (Gp) which can be extrapolated to zero p/Z to obtain G. The method was developed for a "volumetric" gas reservoir. It assumes a constant pore volume of gas and accounts for the energy of gas...
Abstract

Material balance has long been used in reservoir engineering practice as a simple yet powerful tool to determine the Original-Gas-In-Place (G). The conventional format of the gas material balance equation is the simple straight line plot of p/Z versus cumulative gas production (Gp) which can be extrapolated to zero p/Z to obtain G. The method was developed for a "volumetric" gas reservoir. It assumes a constant pore volume of gas and accounts for the energy of gas expansion, but it ignores other sources of energy such as the effects of formation compressibility, residual fluids expansion and aquifer support. In this paper, overview will presented on new format of the gas material balance equation is presented which recaptures the simplicity of the straight line while accounting for all the drive mechanisms. It uses a p/Z** instead of p/Z. The effect of each of the mentioned drive mechanisms appears as an effective compressibility term in the new gas material balance equation. Also, the physical meaning of the effective compressibility’s are explained and compared with the concept of drive indices. Furthermore, the gas material balance is used to derive a generalized rigorous total compressibility in the presence of all the above-mentioned drive mechanisms, which is very important in calculating the pseudo-time used in rate transient analysis of production data. This Paper will represent another two method of MBE for unconventional reserve.one is appropriate for estimating OGIP and second is appropriate for making Reservoir prediction. These techniques are differing from MBE of conventional gas reservoir in which effect of absorbed gas are included. For calculating OGIP, the assumption of equilibrium between free gas and absorbed gas phase is required. No additional assumptions are required for reservoir prediction.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, September 25–28, 2011

Paper Number: SPE-139696-MS

... found in West Africa on the continental shelf. This is the oil province from which examples will be presented later in this paper. Lo et al (1990) pointed out that plotting ln(WOR) is more convenient than the "X" referred to above. They showed using a simulator that the

**straight****line**behaviour of...
Abstract

As an increasing percentage of the world’s production comes from mature fields, there is a growing need for production enhancement techniques that are both rapid and easy to use for the practicing production engineers. For mature waterfloods, the ln(WOR) versus N p plot enables rapid well screening on the basis of incremental recovery factor, where WOR is the producing Water Oil Ratio and N p is the cumulative oil production. Published in-depth information on application of this tool is sparse. Yet, this is often the only tool available to the production engineer for evaluating development options, where a history-matched simulation model has not been maintained. In this paper, the theoretical basis for the use of the ln(WOR) versus N p is reviewed and studied, and is used to arrive at practical guidelines for interpreting production data. Its applicability as a forecasting tool to single-layered and multilayered clastic, waterflooded reservoirs of varying heterogeneity is demonstrated. Numerical simulation models then predict the behaviour of this plot for a wide range of heterogeneities. Production data is then analysed to show the applications of the theory for multilayered reservoirs. The ln(WOR) versus N p plots are analysed, and the impact of various factors is observed. The authors also demonstrate that, where applicable, this plot is the preferred decline curve for the following reasons: – Ln(WOR) versus N p does not require any pressure data; only surface well test production history is required. – It can be assumed that the ln(WOR) versus Np function is an approximate function of the reservoir only, and is decoupled from the outflow and facility constraints. This is especially useful when comparing artificial lift and drawdown strategies. – It is a decline curve model that provides a forecast of water cut, which is indispensable on waterflood projects.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, September 25–28, 2011

Paper Number: SPE-141085-MS

...) - - 0.85 0.70 - - Fig. 16 Plot of [m(pi) − m(pwf)]/ q g vs t ca * showing with and without adsorbed gas BDF with slope m BDF used to calculate OGIP, Well 314. Fig. 12 Square root of time Plot to determine end of transient time and slope of

**straight****line**exhibited...
Abstract

Shale gas reservoirs have become a major source of energy in the recent years. Developments in hydraulic fracturing technology have made these reservoirs more accessible and productive. Apart from other dissimilarities from conventional gas reservoirs, one major difference is that a considerable amount of gas produced from these reservoirs comes from desorption. Therefore it is important to understand the adsorption phenomenon and to include desorbed gas and its effect in our analysis. The objective of this work was to imbed the adsorbed gas in the techniques used previously for the analysis of tight gas reservoirs. Most of the desorption from Shale gas reservoirs takes place in later time when there is considerable depletion of free gas and the well is undergoing boundary dominated flow (BDF). For that matter (BDF) methods and utilizing end of transient time, to estimate OGIP, that are presented in previous literature are reviewed to include adsorbed gas in them. (Kings (1990) modified z* and (Bumb and McKee’s (1988) adsorption compressibility factor for adsorbed gas are used in this work to include adsorption in the BDF and end of transient time methods. Employing a mass balance, including adsorbed gas, and the productivity index equation for BDF a procedure is presented to analyze the decline trend when adsorbed gas is included. This procedure was programmed in EXCEL VBA named as Shale gas PSS with adsorption (SGPA). SGPA is used for field data analysis to show the contribution of adsorbed gas during the life of the well and to apply OGIP estimation methods with and without adsorbed gas. The estimated OGIP’s were than used to forecast future performance of wells with and without adsorption. Original gas in place (OGIP) estimation methods when applied on field data from selected wells showed that inclusion of adsorbed gas resulted in approximately 30% increase in OGIP estimates and 17% decrease in recovery factor (RF) estimates. This work also demonstrates that including adsorbed gas results in approximately 5% less stimulated reservoir volume estimate.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 15–18, 2009

Paper Number: SPE-120103-MS

... pressure derivative log-log plot 1 horizontal well reservoir Upstream Oil & Gas reservoir pressure flow regime omega 0 drillstem/well testing permeability fractured reservoir semi-log plot fracture system

**straight****line**log-log plot SPE 120103 Pressure Behavior of Horizontal Wells in...
Abstract

Abstract This paper presents pressure bahavior of horizontal wells in dual-porosity, dual-permeability naturally fractured reservoirs. The proposed equation is obtained by double Fourier transformation and Laplace transformation. The results calculated for combinations of various dimensionless characterizing parameters, including the permeability ratio between matrix and fracture systems, have revealed the unique behavior of naturally fractured reservoirs when the flow state within the matrix blocks is taken into account. It is concluded that, for the flow within matrix blocks will weaken the essential nature of fluid flow through a dual-porosity, single permeability medium revealed by Warren-Root model. This paper also presents the application of "Tiab's Direct Synthesis" to horizontal wells in an infinite acting dual-porosity, dual-permeability naturally fractured reservoirs with pseudo-steady state interporosity flow. Introduction The pressure behavior of naturally fractured reservoirs (NFRs) is usually studied using Warren and Root (1963) simplified model neglecting the flow of fluids in the matrix blocks. This simplification generally yields satisfactory results because the matrix permeability is usually much less than that of the fracture system in a naturally fractured reservoir. However, in order to determine the limits of validity of Warren and Root's solution and to study the behavior of a naturally fractured reservoir in which the contrast between the permeability of matrix system and that of fracture system is not significant, the more general Barenblatt-Zheltov-Kochina (1960) model is typically used in the literature. But the analytical solutions to this model which were obtained by numerical analysis or numerical inversion are very complex and inconvenient to use (Chen and Jiang, 1980). Horizontal wells have been proven to be an effective means of producing hydrocarbons from naturally fractured reservoirs. Extension of horizontal well solutions to naturally fractured reservoirs was originally developed by Rosa and Carvalho(1988) using instantaneous source functions. They developed a relationship to determine the naturally fractured, dual-porosity solution in terms of the pressure derivatives in Laplace space. Aguilera and Ng (1991) applied the transform method developed by Goode and Thambynayagam to drawdown and buildup tests in naturally fractured reservoirs. Their solutions led to the identification of six flow periods, some of which may be dominated by natural fractures. To the best of our knowledge, all pressure drawdown and buildup equations for horizontal wells in NFRs are based on Warren and Root model, which is a dual-porosity, single permeability model (see Figure 1 ). This study presents an analytical solution for horizontal wells pressure transient equation in dual-porosity, dual-permeability NFRs. The proposed equation is obtained by double Fourier transformation and Laplace transformation, the results calculated for combinations of various dimensionless characterizing parameters, including the permeability ratio between matrix and fracture systems, have revealed the unique behavior of naturally fractured reservoirs when the flow state within the matrix blocks is taken into account.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 11–14, 2007

Paper Number: SPE-105025-MS

.... They further argued that non-Darcy effects cause an increase in the slope of the linear flow analysis

**straight****line**resulting in low estimate of fracture half-length. Artificial Intelligence Upstream Oil & Gas compressibility Modeling & Simulation drillstem/well testing fracture...
Abstract

Abstract Non-Darcy flow effects have long been recognized to have serious adverse impact on the performance of high-flow rate gas wells. These effects may mask the presence of fractures around the wellbore of naturally fractured reservoirs and may render the effective fracture conductivity and fracture half-length of hydraulically fractured wells much less than the designed parameters. Proper diagnosis of the post-fracture well test and good estimation of the fracture parameters are crucial for proper MHF treatment assessment and production forecast. Even though the effects of non-Darcy flow have been identified in the field and properly acknowledged in the well testing literature, little has been done to improve the well test analysis results. This paper presents for the first time a semi-analytical equation that incorporates the effects of non-Darcy flow in the fracture. The proposed equation describes the flow of real gas under constant bottomhole-pressure condition which has the advantage of reducing the well test duration and minimizing the wellbore storage effects. A detailed investigation of the various parameters influencing the flow behavior of real gas in the fracture nearby the wellbore is also illustrated. Introduction Massive hydraulic fracturing (MHF) treatments are considered as excellent stimulation means of boosting the productivity of both damaged wells and wells producing from low-permeability reservoirs. The primary goal of MHF is to bypass the damaged zone in the vicinity of the wellbore or to create high-permeability fracture connecting low-permeability reservoirs to the wellbore. The extensive use of MHF has dictated the development of good reservoir characterization tools that allow accurate analysis of the transient pressure behavior in the fracture as well as in the surrounding formation. Since the initiation of early MHF jobs, many methods have been proposed to evaluate the fracture characteristics from transient pressure and flow rate data. Numerous competent numerical, 1–6 semi-analytical, 7–14 and type-curve matching 1,10,15–18 techniques were proposed for the analysis of fractured oil wells. However, well test analysts still face problems when analyzing transient data of gas wells. The major difficulty confronting good well test analysis is the presence of non-Darcy flow in the fracture which deteriorates the well's performance and distorts the well test data. If non-Darcy flow effects are not considered in the analysis, erroneous results delineated by low values of fracture conductivity and fracture half-length are obtained. As a consequence of negligence in accounting for the non-Darcy flow behavior, conflicts between the well test estimates and design values of the fracture parameters continue to cause confusion and debate regarding the success of the stimulation treatment. 19 Umnuayponwiwat et al. 20 used field examples to illustrate that traditional well test analysis neglecting high-velocity flow effects may lead to errors up to 78% and 54% in the estimates of the fracture conductivity and fracture half-length, respectively. Over the years, substantial efforts have been directed toward comprehending the adverse impact of non-Darcy flow on the transient behavior of fractured wells. Millheim and Cichowicz 21 and Wattenbarger and Ramey 22 were among the early pioneers who inspected the non-Darcy effects on the flow performance of vertically fractured gas wells. However, their work aimed at assessing the damage caused by non-Darcy flow in the formation surrounding the fracture. Millheim and Cichowicz 21 used Swift and Kiel's 23 radial flow model to examine the effects of turbulence in the formation at long times. Wattenbarger and Ramey 22 concluded that turbulent flow effects are more detrimental in the fracture than in the reservoir and cause an additional pressure drop which is flow rate dependent. They further argued that non-Darcy effects cause an increase in the slope of the linear flow analysis straight line resulting in low estimate of fracture half-length.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 11–14, 2007

Paper Number: SPE-105046-MS

... derivative data to determine the fracture and reservovir parameters. These plots reveal the presence of

**straight****lines**corresponding to linear and pseuso-radial flow regimes; while the the boundary flow effect is detected by an exponential behavior. A 0.65 slope**straight****line**describing the transition period...
Abstract

Abstract Wellbore storage effect can highly degrade conventional pressure buildup and drawdown tests data disturbing the formation characterization of the wellbore surrounding area. Constant bottomhole pressure tests will eliminate this pitfall and provide good reservoir describtion. This paper applies direct synthesis technique for infinite conductivity fractured wells producing at constant bottomhole pressure from finite reservoirs. Without resolving to type-curve matching or regression procedures, this technique analyzes the log-log plot of the reciprocal rate and reciporocal rate derivative data to determine the fracture and reservovir parameters. These plots reveal the presence of straight lines corresponding to linear and pseuso-radial flow regimes; while the the boundary flow effect is detected by an exponential behavior. A 0.65 slope straight line describing the transition period between the pseudo-radial and the boundary effect flow regimes in rectangular systems is also presented. The distinct features of the straight lines' slopes and intersection points are used to calculate various reservoir and fracture parameters such as fracture half-length, reservoir permeability, skin factor, drainage area and shape factor. Equations corresponding to the points of intersections are very useful to verify the accuracy of the results obtained from the slopes of the different flow regimes. A systematic step-by-step procedure illustrating the methodology of the proposed technique for the analysis of linear, pseudo-radial, pseudosteady state flow regimes is described. Detailed examples using different simulated cases are presented to show the applicability of the proposed method. Introduction Hydraulic Fracturing is a stimulation treatment routinely performed on oil and gas wells in low-permeability reservoirs. Specially engineered fluids are pumped at high pressure and rate into the reservoir interval to be treated, causing a vertical fracture to open. Accurate characterization of the fractured well is needed for performance forecasting and optimal reservoir development. Numerous semi-analytical, asymptotic analytical, numerical models and type curves have been developed thru years to describe the pressure behavior of both finite and infinite vertically fractured wells. Russel and Truitt 1 presented a mathematical model along with a set of simulated pressure buildup curves to predict transient behavior in vertically fractured wells. The results of this study were presented as tables of the dimensionless pressure drop as a function of time and fracture penetration. Studying the effects of infinite capacity vertical fractures on well performance, Prats 2 and Prats et al. 3 examined the flow of incompressible and compressible fluids and presented solutions for wells producing at either constant rate or constant bottomhole pressure. Analysing the pressure data of finite conductivity vertical fractured wells in infinite slab reservoirs, Cinco-Ley et al. 4 further modified the work of Russell and Truitt 1 and developed a semi-analytical model and type curves. In 1977, Cinco-Ley and Samaniego 5 extended their previous work to include the effect of wellbore storage and fracture damage in which the skin was defined as an infinitesimal zone surrounding the fracture. They concluded that it is highly imperative to consider the effect of skin or fracture damage in order to analyze pressure transient data in fractured wells effectively. Hanley and Bandyopadhyay 6 presented a simple semi-analytical model for a well in a square with a fully penetrating fracture of uniform flux and infinite fracture capacity. They investigated the effect of wellbore storage, fracture length, fracture capacity, formation properties, and reservoir boundaries. Moreover, Hanley and Bandyopadhyay 6 suggested that the effect of wellbore storage should be taken into account in the pressure transient response of a fractured well in tight reservoir. Another excellent tool for characterizing fractured well that is widely utilized in the petroleum industry is type-curve matching. Type-curve matching is considered a powerful diagnostic technique because of its ability to span the entire range of flow regimes and even include the intervening transition zones. However, due to the non-uniqueness of the type-curve results, extreme care should be exercised in its application.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 12–15, 2005

Paper Number: SPE-93419-MS

...-back Pump-in/shut-in conductivity soliman geometry formation permeability hydraulic fracturing fracture

**straight****line**drillstem testing permeability example 3 intercept determination after-closure analysis initial reservoir pressure upstream oil & gas spe 93419...
Abstract

Abstract A minifrac test is usually performed before a fracture stimulation treatment to calculate formation and fracture properties. Recently the analysis techniques were extended to the after-closure period. The after-closure data are analyzed to calculate formation permeability and reservoir pressure. Technology developers have hypothesized the existence of either pseudo-radial or linear flow behavior during the after-closure region. Identifying the presence of the flowing regime is an awkward process at best. The roots of the linear flow equations are different from those of the pseudo-radial flow equations. Many tests do not follow either flow regime. In this paper, we have created a general approach for analysis of after-closure pressure decline data. Because the determination of the flow regime and type of fracture depends only on time and monitored pressure, the analysis may even be performed in real time. The technique determines whether sufficient data have been obtained to perform a reliable analysis. The calculated parameters would be used to update the fracture design and, in turn, for performing the fracture treatment. The new technique is simpler and more generalized than what currently exists. The technique initially determines whether analyzable data exist. It shows that three flow regimes may dominate the after-closure region, depending on the reservoir properties and residual fracture conductivity. The technique presented not only determines the type of regime, and consequently, the type of residual fracture, it also determines the formation permeability and reservoir pressure. There is no reason to restrict the application of this test to minifrac test analysis. We believe the approach is also applicable to analysis of data after performing a fracture stimulation treatment. A numerical simulator was used to model the pumping and closure process and to validate the new approach. The paper also presents a detailed discussion and analysis of several field cases, demonstrating the various flow regimes and, ultimately, the validity of the developed technique. Introduction Minifrac analysis has considerably progressed since it was introduced by Nolte.[1] This is especially true during the last few years. The boundaries between conventional fracture diagnostic service and conventional well testing are already blurred. Most of the developed analysis techniques presented so far concentrate on the analysis of the before-closure data.[2–14] Recently, analysis techniques for after-closure data have been introduced.[15] The various diagnostic techniques include the conventional methods whose goal is to determine closure pressure and leakoff coefficient, and the latest development of the area leading to calculation of reservoir properties such as pressure and permeability. These tests are conducted after closure, and their analyses rely heavily on the conventional well-testing technology. This paper includes new technology that has not yet been presented in the literature. In addition to conventional well testing, several other specialized tests are performed before, during, or after a hydraulic-fracturing treatment to determine formation and/or fracture parameters. These fracturing tests are performed for the following reasons: Better understand the formation physical and mechanical properties. Predict formation response during the fracturing process. Optimize the fracturing treatment design. The goal of the tests is to determine many of the various parameters influencing a fracturing treatment such as fracture closure pressure, instantaneous shut-in pressure (ISIP), fracture opening pressure, formation leakoff coefficient during a fracturing treatment, and fracture entry pressure. More modern approaches aim at also obtaining formation permeability and original reservoir pressure. There are three basic fracturing tests: Step-rate Pump-in/flow-back Pump-in/shut-in

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Middle East Oil and Gas Show and Conference, March 12–15, 2005

Paper Number: SPE-93560-MS

... permeability short-term pressure transient testing cct

**straight****line**SPE 93560 Review and Application of Short-Term Pressure Transient Testing of Wells M.Y. Soliman, SPE, M. Azari, SPE, and J. Ansah, SPE, Halliburton, and C.S. Kabir, SPE, ChevronTexaco Copyright 2005, Society of Petroleum Engineers Inc...
Abstract

Abstract Short-term pressure transient testing is gaining increased acceptance as an attractive alternative to conventional transient well testing, since the latter usually requires long flow and shut-in periods in order to meet test objectives. Unfortunately, current industry drivers are focusing on short, cost-effective, and environmentally friendly test procedures _ especially in exploration wells in deepwater and arctic environments where conventional tests may be prohibitively expensive or not feasible logistically. While various short-term tests, test procedures, and interpretation methods are available for conducting successful short-term tests, clarity is lacking for specific applications of these methods. Some of these tests include surge testing, closed-chamber testing, slug testing, underbalanced perforating and testing, and back-surge perforation cleaning. This paper provides comprehensive evaluation of general closed-chamber tests, including general surge tests, and their comparison with special tests such as, FasTest,™ Impulse™ test, and slug tests. For each of these techniques, the review will examine: Test design, testing procedure Theoretical background of each of these techniques Method of data analysis including comparisons based on both theoretical and practical considerations to determine the expected reliability, accuracy, and ease of analysis. A large portion of the paper is devoted to field examples. Several field cases are analyzed using the various techniques, and results are tabulated and presented. Analyses of these examples are presented in significantly more detail to compare the many techniques available to analyze the well-testing data obtained from surge testing, closed-chamber DST, slug testing of oil wells, underbalanced perforating and testing, and back-surge perforation cleaning. Introduction The recent technological advances in pressure and temperature gauges, surface and downhole electronics, downhole tool assembly, and data transmission have collectively paved the way for better design and, more importantly, field execution of short-term tests. Some of these tests may last for time periods as short as a few minutes, however producing very reliable estimates of reservoir properties. Techniques developed for analysis of these tests rely on modem gauge capability for accuracy and quick measurement of pressure change with time as well as accurate compensation for the effect of temperature. These methods have been well documented in the literature and include short-term tests such as: DST Slug test General closed-chamber test (CCT) Surge Test Shoot-and-pull" test, which is similar to the backsurge test FasTest (essentially a surge test/CCT) Impulse Test (also essentially a surge test/CCT). All the above tests with the exception of the slug test are similar in nature in the sense that fluid flows into a limited volume chamber where an increasing back pressure causes the influx from the formation to decline. The rate decline can be very fast and is difficult in many instances to calculate. In many of these tests it is practically imposible to distinguish the flow period from the build up period. This dictates the development of specialized techniques that accounts for this test characteristics. In a slug test, however, the fluid flow is not against atmospheric pressure but against increasing hydrostatic head as fluid accumulation takes place. It is usually possible to calculate the production rate from the reservoir into the wellbore, and hence allows for the use of classical analysis techniques. This paper provides comprehensive evaluation of general closed-chamber tests, including general surge tests, and their comparison with special tests such as FasTest, Impulse and slug tests. It also attempts to provide practical considerations of the various tests and analytical techniques to determine the expected reliability, accuracy, and ease of analysis.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, June 9–12, 2003

Paper Number: SPE-81466-MS

...

**straight****line**reservoir pressure diagnostic plot diversion variation drillstem testing upstream oil & gas bottom hole pressure permeability drillstem/well testing acidizing matrix diagnostic plot bpm stimulation theoretical basis society of petroleum engineers spe 81466 injection rate...
Abstract

Abstract During matrix acidizing operations performed on oil wells, post-treatment analysis is often overlooked due to the lack of a simple, robust tool. Current methods rely on the equations used for well tests analysis, either steady state or transient, and focus on the computation of the skin factor. However this computed skin most often proves unreliable due to the complexity of the treatments, which routinely involve multi-layered reservoirs and advanced diversion techniques, i.e. phenomena that are not handled by the well testing equations. As a result, operators content themselves with providing clients with a plot of pump rate and wellhead pressure versus cumulative volume - or time. Unfortunately, any interpretation performed with this type of plot has more in common with divination than science. In this paper, a new way to plot matrix acidizing treatment data is presented. The inverse injectivity index and its integral are plotted versus time. This is similar to Hall plots, which are used to monitor water injection wells, but it corrects for the rate changes occurring during acidizing treatments. The concavity of the integral then visually indicates whether the treatment is achieving stimulation or diversion, and this behavior can easily be identified despite the noise usually associated with any field measurements. As a side benefit, this technique also provides means to verify the average reservoir pressure value. The theoretical basis of this new plot is discussed and its usefulness assessed using data generated by Pericles, a matrix acidizing numerical simulator. A field case is then analyzed and is used as an opportunity to once again emphasize the need for reliable bottom hole pressure data, whether measured or calculated, without which any analysis is inherently flawed. Introduction Matrix stimulation treatments are performed to remove the near wellbore damage that impairs well productivity. Post-treatment analysis is then essential to assess the effectiveness of the stimulation and therefore gain information that will be valuable to optimize future treatments in the same reservoir. Several techniques have been derived to analyze matrix treatments results, including in real time. These techniques focus on the computation of the skin, and can be gathered in three categories, depending on which flow equation is used for the interpretation of the bottom hole pressure response to the treatment: Steady-state or pseudo-steady state, single phase, radial flow; Transient, single phase, radial flow with time superposition; Continuity and Darcy's law equations, which are partial differential equations and therefore require a numerical simulator to be solved. Among those three groups, the most comprehensive technique is the last, since it is not limited to a single layer and single-phase flow, a situation seldom encountered in reality. Moreover it is the only technique that can encompass models taking into account diverters, which have a pronounced impact on the bottom hole pressure behavior. However it requires a comprehensive knowledge of the well and the rock formation, which is rarely achieved in practice and precludes its application to a wide range of treatments. In addition, a thorough knowledge of the software used for the analysis is also required, and rules out its use by non-experts. The second group of techniques essentially considers the stimulation treatment as a well test transient analysis. Yet the current methodology focuses on the pressure function and does not include the pressure derivative, which is essential to identify the correct flow regime, particularly when the time intervals are very short as with matrix treatments. Even though numerous well test interpretation softwares are available commercially, none is targeted towards matrix treatment interpretation, where a strong emphasis on signal filtering and smoothing would be needed due to the amount of noise, unusual in classical well testing, of the pressure transient. Moreover engineers involved with stimulation are not specialized in well test analysis, which remains an art difficult to master.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, June 9–12, 2003

Paper Number: SPE-81516-MS

... solution-gas-drive reservoirs. drillstem/well testing non-darcy flow coefficient test plot correlation

**straight****line**tech skin factor wellbore high-velocity flow simulated case reservoir coefficient pressure condition drillstem testing formation damage permeability flow effect...
Abstract

Abstract This paper presents an investigation of the validity of applying the constant-pressure liquid solution to transient rate-decline analysis of gas wells. Pseudo-pressure, non-Darcy flow effects, and formation damage are incorporated in the liquid solution to simulate actual real gas flow in the vicinity of the wellbore. The study shows that for constant-bottomhole pressure gas production the conventional semilog plot of the inverse of the dimensionless rate versus the dimensionless time used for liquid solution has to be modified to consider the high-velocity flow effects. This is especially true when the reservoir permeability is higher than 1 md and the well test is affected by non-Darcy flow and formation damage. This paper also presents a novel systematic method to determine the formation permeability, mechanical skin factor, and non-Darcy flow coefficient from a single constant-pressure production test. The working equations are written in such a way that allows a graphical analysis of the variable rate with time that is analogous to the analysis of constant-rate production test. The analysis procedure is simple and straightforward. It does not require type-curve matching or correlations. The applicability of the proposed method is illustrated using several simulated examples. The input formation permeability varies from a low value of 0.1 md to a high value of 5 md. The ratio of the downhole pressure to the initial reservoir pressure ranges from 0.1 to 0.8. Introduction The majority of gas well tests are performed assuming constant-rate production conditions. A close inspection of field practices shows that in many cases constant-bottomhole pressure production is desirable and yields results that are as accurate as those obtained from constant-rate production. Geothermal wells, fluid flow into a constant-pressure separator or pipeline, open wells flowing at atmospheric pressure, declining-rate production during reservoir depletion, and production from low-permeability gas reservoirs are few examples where oil and gas wells can be operated under constant-bottomhole pressure conditions. Most gas reserves around the world are found in tight reservoirs where the formation permeability varies from 0.01 md to 5 md. 1,2 These types of gas reservoirs provide excellent opportunity for constant-pressure production practices. As early as 1949, van Everdingen and Hurst 3 presented analytical constant-pressure radial flow solutions for the diffusivity equation. Jacob and Lohman 4 suggested analytical solution in terms of dimensionless flow rate for wells operating under constant-downhole pressure conditions. Tabulated values of dimensionless flow rate versus dimensionless time were provided by Tsarevich and Kuranov 5 for bounded circular systems and by Ferris et al. 6 for unbounded reservoirs. Different methods for the analysis of liquid well test data with constant-pressure conditions at the wellbore were proposed by van Poollen. 7 As far as we know, the first attempt to use conventional semilog techniques to analyze pressure buildup test for a well produced at constant wellbore pressure was suggested by Clegg 8 who used Laplace transforms to obtain approximate solution at large dimensionless production time. More recently, Samaniego and Cinco-Ley 9 investigated the influence of pressure-dependent fluid and rock properties on well production decline in constant-wellbore pressure tests. Uraiet and Raghavan 10 studied the transient pressure behavior in the drainage area of oil wells at constant wellbore pressure. They illustrated the validity of the "infinitesimally-thin" skin and effective wellbore radius concepts to describe the skin region in the vicinity of a well producing at constant-bottomhole pressure. In a different study, Uraiet and Raghavan 11 followed the constant-rate production approach to present a simple procedure to analyze pressure buildup data of a well producing a slightly compressible liquid at constant-pressure conditions. Ehlig-Economides and Ramey 12 suggested various techniques for the analysis of constant-pressure drawdown test of oil wells that are analogous to the conventional constant-rate test. In a separate study, Ehlig-Economides and Ramey 13 used the principle of superposition of continuously varying flow rates to generate an exact solution for buildup test following constant-pressure flow conditions. Camacho-V 14 presented procedures to determine reservoir parameters from constant-pressure drawdown tests conducted on solution-gas-drive reservoirs.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, March 11–14, 1995

Paper Number: SPE-29893-MS

... injection

**straight****line**pressure falloff behavior injectivity injection profile seawater injection reservoir temperature enhanced recovery permeability lnjectivity decline SPE 29893 Factors Affecting lnjectivity Decline A.M. AI-Hamadah, Saudi Aramco SPE Member Copyright 1995, Society of...
Abstract

SPE Member Abstract Reservoir pressure support for a large portion of a giant field is maintained by peripheral seawater injection. The temperature of the injected sea water is significantly lower than the reservoir temperature and also lower than the previously injected water obtained from aquifers. Therefore, a decline in injectivity is expected as a result of higher water viscosity due to lower injection water temperature. This paper presents actual data collected from power water injection wells in two areas of the field, both before and after the start of seawater injection. This data has shown a significant decline in injectivity after conversion to seawater in only one area. The quality of the injected water and other related factors will be reviewed to determine the reasons for this behavior that apparently contradicts what was expected. The paper also discusses the actual effects that cold seawater injection has on pressure falloff behavior. Introduction In a water injection pressure support program, water temperature plays an important role in the efficiency of the injection process. This is because the viscosity of the injected water is directly related to its temperature. The higher the viscosity, the higher the pressure differential required to achieve the same injection rate. As a result, a decline in injectivity is expected upon conversion to a colder water for the same pressure differential. Water injection in the field was first started using warm temperature (aquifer) water. After several years, injection of colder temperature water (seawater) began. In this paper, data collected before and after seawater injection are reviewed to show the actual effect of cold water on injectivity. Only one of the two areas has shown a clear trend of decline in injectivity. Several other factors such as the quality of the injected water, the static bottom hole reservoir pressures, and temperatures will be reviewed in an attempt to explain the observed behavior of the injectivity. HISTORY OF WATER INJECTION This study will be focused on two of the seven areas that constitute the giant field, Area-i and Area-2 This field was discovered in late 1 940s. Oil production from this field commenced in 1951 while water injection was started in 1966 in Area-i using Aquifer-A water and in 1976 in Area-2 using Aquifer-B water. Later, the injection system was converted to seawater to conserve aquifer water. Area-i was converted in 1978, while Area-2 was converted in 1992. P. 593

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, March 11–14, 1995

Paper Number: SPE-29895-MS

... engineers gas well graph-simulated case permeability sandface flow rate drillstem testing upstream oil & gas flow rate reservoir intercept pseudotime pressure measurement bottomhole pressure simulated case drillstem/well testing

**straight****line**normalized pseudopressure new technique...
Abstract

Abstract Most of the problems associated with conventional gas well tests are related to the nonlinearity of the equations describing real gas flow, the presence of the rate dependent (non-Darcy) skin, and the long shut-in time periods required to collect the data for the analysis in tight reservoirs in which the wellbore storage period can be excessively long. This paper presents a new pressure buildup technique that reduces the wellbore storage effects, eliminates the long shut-in periods experienced with conventional tests by using afterflow rate and pressure data, and most importantly provides a direct method to estimate non-Darcy skin. The proposed technique uses normalized pseudo-functions to avoid the nonlinearities of the governing equations and involves using two different plots. The formation permeability is obtained from the slope of the first plot. The mechanical and non-Darcy skin factors are obtained respectively from the slope and intercept of the second plot. A field example and two simulated cases are presented to illustrate the application of the new technique. INTRODUCTION Transient pressure buildup and drawdown test analyses of gas wells differ from that of oil wells. The major difficulties encountered in gas well testing lie in the long afterflow period required to collect the required data for the analysis, in the nonlinearity of the diffusivity equation describing real gas flow in the reservoir, and in the presence of additional inertial-turbulent pressure drop due to high flow rate of gas in the vicinity of the wellbore. In recent years, a considerable amount of work has been directed toward eliminating or minimizing the effects of such difficulties on gas well test analysis. Many authors 1–10 have successfully used the sandface flow rate and pressure data for both oil and gas wells in order to minimize the wellbore storage effects, thereby, reducing the shut-in time of the well and providing more reliable test results than the results obtained using the pressure-time data alone.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, November 16–19, 1991

Paper Number: SPE-21400-MS

... minifracture analysis method. P. 15 flowback period

**straight****line**closure pressure flowback rate upstream oil & gas microfracture gal mechanism drillstem/well testing fracture spe 21400 fracture closure application leakoff flowback test drillstem testing pressure difference...
Abstract

SPE Members Abstract A technique based on a simple compressibility equation and a mass balance equation has been developed that allows accurate determination of fracture volume and closure pressure. This new technique may help resolve the controversial determination of when a fracture closes. Through the graphical representation of this technique, knowledge of the fracture closure mechanism has been gained and presented in this paper. The presented technique may be applied to either microfracture or minifracture tests. It may be applied to a pumpin/flowback test (microfracture) or be pumpin/flowback test (microfracture) or be coupled with the conventional minifracture analysis technique for application to pumpin/shut-in tests. pumpin/shut-in tests. The new technique is illustrated in this paper through its application to actual field cases. In the first field case, it is applied to a microfracture test (pumpin/flowback) performed on a shale formation. The technique clearly identified the closure pressure of the fracture and the fracture pressure of the fracture and the fracture volume, and fluid efficiency was calculated using an iterative scheme. In the second example, the technique was applied to a minifracture test (pump-in/shut-in). The chief technical contributions of this paper may be summarized as follows: A simple new technique is presented for determining fracture volume and closure pressure. Through the graphical representation and application of the new technique, a better understanding of the closure mechanism has been achieved. This technique determines fractureclosure pressure with a fairly high degree of certainty. Introduction During the last few years, the use of a fracturing test prior to the main fracturing treatment has significantly increased. These two tests are microfrac and minifrac tests. Both of these two tests are designed to give specific information about the fracture and/or fluid performance. A microfrac is a test in which one to two bbls of fluid are injected into the formation at a rate ranging from 2 to 20 gal/min. The rate and volume necessary to initiate and propagate a fracture for 10 to 20 ft depend on formation and fracturing fluid properties. Microfracturing tests were performed using many types of fluid, ranging from drilling fluid to gelled fluid. The main purpose of a microfracture is to measure the minimum principle stress. principle stress. Minifractures, on the other hand, are performed using the same type of fluid and performed using the same type of fluid and injection rate as will be used in the fracture treatment. A minifracture test is performed to determine leakoff coefficient performed to determine leakoff coefficient and fracture geometry. In this paper, application and analysis of microfracture and minifracture tests are discussed. A new and simple technique to analyze data from microfractures and minifractures is presented. This technique uses the existing presented. This technique uses the existing minifracture analysis method. P. 15

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, November 16–19, 1991

Paper Number: SPE-21403-MS

... wellbore storage horner plot

**straight****line**derivative curve spe 21403 flow period regime flow regime boundary permeability log-log plot horizontal well superposition time function radial flow upstream oil & gas drillstem testing linear flow drillstem/well testing type curve early...
Abstract

SPE Member Abstract The paper discusses several issues related to the interpretation of transient pressure tests on horizontal wells. Horizontal well type curves incorporating the effects of wellbore storage and skin are used to aid in the diagnosis of and estimation of parameters from test data. Issues addressed in this study include the identification of flow regimes, validity of Horner graphs. and analysis of multirate tests. An example interpretation is discussed to illustrate concepts. It is shown that for other than the most ideal situation, the early radial flow behavior will not be evident. In tests with short flow or buildup periods, it is possible for wellbore storage and skin effects to mask both the early radial and linear flow periods. Where early radial flow is present, it is shown that periods. Where early radial flow is present, it is shown that as long as flow length is very long compared to shutin time, a Horner plot may be used to compute formation parameters. In the general case. type curve matching procedures provide adequate means for estimating the desired parameters from the well test. Introduction Several authors have presented equations describing the transient pressure behavior of horizontal well. For a well bounded by upper and lower impermeable boundaries. the following flow regimes have been inferred: early radial. linear. and pseudo radial Fig. 1 is a schematic of the sequence of development of the various flow regimes. During the early radial period, pressure behavior is infinite-acting, but not necessarily radial. Actual radial flow will occur when the permeability ratio, kv/kH, equals one. Data acquired during this period may be analyzed to obtain a value of equivalent permeability. keq, given by k eq = kHkV (1) Horizontal permeability, kH, may be computed from pressure data obtained during linear or late radial flow. To obtain reliable values of both kH and kV, it is required that data be available from the early radial flow period and either the linear or the late radial period. Depending on well condition and reservoir thickness. the early radial period may be completely masked by wellbore storage and skin effects. The presence of a gas cap or aquifer may distort the linear flow regime, and except in a case where well length is small (relative to reservoir lateral extent), or where flow time is appreciably long, the late radial period may not be observed. For obvious practical reasons, afterflow in horizontal wells will always be present, corresponding at a minimum, to the lateral section of the well. In the general case type curve matching procedures offer the best means of identifying flow regimes, and obtaining reservoir parameters. It is important to note that from a physical and mathematical viewpoint, the pressure behavior of a horizontal well is equivalent to that of a partially completed vertical well bounded by parallel faults. Where pseudoradial flow effects have not been parallel faults. Where pseudoradial flow effects have not been felt, horizontal well behavior can be shown to be identical to a fully penetrating vertical well bounded by parallel faults. In this rotated point of view the parallel faults represent the upper and lower boundaries of the original reservoir system. P. 577

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, March 11–14, 1989

Paper Number: SPE-17942-MS

... theoretical approach. P. 133 porosity triplet base mud projection

**straight****line**well logging standard deviation spe 17942 water saturation equation log analysis regression factor plane saturation new technique upstream oil & gas contour line resistivity artificial intelligence...
Abstract

SPE Members Abstract A new approach in determining the parameters of the Archie's equation a, m and n is presented in this paper. It is based on the presented in this paper. It is based on the use of water saturation from the core or from an EPT type measurement and the resistivity of the formation where this water saturation is known. The proposed method is an extension to a 3D space of the usual regression technique used in a plane, as in the laboratory determination of m and n. Both a spatial visualization and a regression may be used to obtain the Archie parameters. This method may be applied in differ situations: – in a reservoir at any water saturation in a well drilled with a waterbase mud where both MSFL and EPT type logs have been run. – in a reservoir at irreducible water saturation and in a well drilled with a tagged oil base mud of known water loss where the resistivity of the formation is measured by an induction tool and the water saturation is known from either the core or an EPT type tool. – in a reservoir at residual oil saturation (after a waterflood), in a well drilled with a waterbase mud where the resistivity of the formation is measured by a long spacing resistivity tool and the water saturation is known from either an EPT type log or a core. Examples are given of the use of this technique in a carbonate field of the Middle East from two different reservoirs: The high heterogeneity of the first reservoir makes it necessary to sort the data per lithofacies and therefore reduces the number of data points, whereas in the second, more homogeneous results are fairly straight forward and provide an answer close to the accepted triplet (1,2,2) for (a, m, n). Introduction The determination of water saturation from electric logs has been first tackled by Archie who observed an empirical relationship between porosity, water resistivity, resistivity read by the log and water saturation. Archie's equation was using parameters called 'a', 'm' and 'n'. 'a' is usually referenced as the multiplier or coefficient of the formation resistivity factor 'm' is the cementation factor, formation factor or shape factor 3 and 'n' is the saturation exponent. Further to this work, other equations have been proposed in clay formations and empirical attempts of relating m to the porosity have been made (Humble, Shell, porosity have been made (Humble, Shell, etc) as well as theoretical approach. P. 133

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Show, March 11–14, 1989

Paper Number: SPE-17971-MS

... diagnose the existence of fractures in the reservoir. In many cases presented, 2 parallel

**straight****lines**with presented, 2 parallel**straight****lines**with transition in between were noticed on Horner plot. In some cases, the pressure build-up tests plot. In some cases, the pressure build-up tests conducted in...
Abstract

Abstract Field cases of pressure build-up tests are presented for two reservoirs which showed presented for two reservoirs which showed existence of fractures on cores. The nature of the pressure build-up data on these tests have shown the importance of preparing various cross-plots to diagnose the existence of fractures in the reservoir. In many cases presented, 2 parallel straight lines with presented, 2 parallel straight lines with transition in between were noticed on Horner plot. In some cases, the pressure build-up tests plot. In some cases, the pressure build-up tests conducted in the early life of the well were typical of a homogeneous system with afterflow and skin, although linearity of data points was obvious on delta p vs square root of shut-in time plot. Subsequent pressure build-up tests of the plot. Subsequent pressure build-up tests of the well, however, showed 2 parallel lines with transition in between on Horner plot. The tests with 2 parallel slopes, showed unique trend on Pollard plot since it yielded two intersecting Pollard plot since it yielded two intersecting straight lines after early period, not reported earlier. The storativity ratios are estimated to be rather high in spite of the large matrix block height estimated, perhaps due to high matrix permeability. These facts underscores the permeability. These facts underscores the importance of using all available evidences to derive physically consistent parameters for analysis of naturally fractured reservoirs. Introduction Naturally fractured reservoirs have been studied intensively during the past 10 to 15 years in the geological, geophysical, engineering and petrophysical fields. Transient pressure analysis received special attention as pressure analysis received special attention as pressure build-up tests can be conducted on pressure build-up tests can be conducted on almost all old and new wells with relative ease and less cost on a routine basis. Field engineers are quite familiar with the interpretation technique. The literature, however, contains mainly the theoretical aspect of fractured reservoir system and few actual field cases are published to show the reservoir response to variety of such situations likely to be encountered in the field. Of the published analysis, Pollard's work was one of the earliest on pressure build-up analysis. He considered the reservoir as consisting of three regions : area around wellbore covering skin, fracture system and matrix. By breaking the pressure differential into these three components, it was shown that a plot of the log of pressure differential plot of the log of pressure differential associated with any of the regions against time, would result in a straight line. Pirson extended Pollard's method for evaluating matrix pore volume and partitioning coefficient. pore volume and partitioning coefficient. Although Pollard and Pirson methods have some theoretical limitations, as shown by Warren and Root and Kazemi, yet this method was used for fracture analysis. Warren and Root assuming pseudo-steady state interporosity flow, showed that a conventional Horner semi-log plot of pressure vs Horner time results in two parallel straight lines with a transition period in between. Kazemi used a numerical model of a horizontal fracture in a bounded reservoir with unsteady state interporosity flow. The two parallel slopes on conventional plot was confirmed, however, the transition was different due to unsteady state interporosity flow. De Swaan achieved a breakthrough in analysis of naturally fractured reservoir by developing unsteady state interporosity flow. P. 433

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Technical Conference and Exhibition, March 11–14, 1985

Paper Number: SPE-13733-MS

... differentiated and rearranged in such a way that a

**straight****line**relationship between the variables is obtained. This may be achieved by plotting log (tâ??p/â??t) vs. 1/t. The slope and intercept of the resulting**straight****line**are used to estimate the transmissibility and the storage coefficient respectively...
Abstract

Abstract Interference tests are used to estimate reservoir properties such astransmissibility and storage coefficient. The conventional method of analysis which uses a plot of pressure vs. time on a semi-log graph is only applicableat relatively large times to allow for a logarithmic approximation to the Ei-function in the line source solution. At short times the type curve matching technique may be used but this procedure does not allow a fast systematic analysis using regression analysis subroutines via computer. In this paper the line source solution of the diffusivity equation is differentiated and rearranged in such a way that a straight line relationship between the variables is obtained. This may be achieved by plotting log (tâ??p/â??t) vs. 1/t. The slope and intercept of the resulting straight line are used to estimate the transmissibility and the storage coefficient respectively. The extension of the method to two-rate test analysis and pressure build-up analysis is also outlined. The use of the method is illustrated by examples and the results are compared with those obtained from type curve matching and semi-log plots. It is concluded that this method is of particular significance for the analysis of interference tests with short duration and/or large distance between wells. Introduction Most of well test analysis methods are based on the line-source solution of the diffusivity equation. This solution gives the pressure as function of time and distance for an infinite homogeneous reservoir with a single well producing at a constant rate. The principle of superposition is applied for the analysis of multiple rate cases including pressure buildup tests and to account for the presence of other wells (interference tests). The method of images coupled with the superposition of the line-source solution is used to handle bounded reservoirs with different boundary conditions.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Middle East Oil Technical Conference and Exhibition, March 11–14, 1985

Paper Number: SPE-13732-MS

...

**straight****line**form if pressure versus the inverse of time is plotted on a specially devised exponential integral graph paper. Obtaining a**straight****line**on such a graph paper makes the analysis of interference tests very simple. Introduction Interference well tests are conducted in order to determine...
Abstract

SPE Member Abstract A new mathematical and graphical approach to analyze the interference tests is presented. This is based on a mathematical manipulation of the line source solution to the diffusivity equation. This approach yields the exact exponential integral function solution in a straight line form if pressure versus the inverse of time is plotted on a specially devised exponential integral graph paper. Obtaining a straight line on such a graph paper makes the analysis of interference tests very simple. Introduction Interference well tests are conducted in order to determine whether well pairs are in pressure communication and to provide means to estimate mobility-thickness product (kh/mu) and porosity-compressibility thickness product (phi cth) between the wells. In an interference well test, one of two wells is either injected or produced, and the pressure response on the other (the observation well) is observed. The pressure response at the observation well is felt pressure response at the observation well is felt after a time lag and is essentially dependent on the reservoir properties between the two wells. For a single-phase radial flow in a circular horizontal reservoir, the following diffusivity equation is a highly satisfactory model: (1) With the assumptions of infinite-acting, homogeneous and isotropic reservoir, the above equation yields the simple Ei-function solution which gives the pressure change at the observation well as a-function pressure change at the observation well as a-function of time: (2) Where (3) and is known as the Ei-function or the exponential integral. So far interference tests are mostly analysed by type curve matching. A review of the theory and the development of interference testing is presented by Kamal in 1983. In the present new approach, a straight line is obtained when pressure versus the inverse of time is plotted on a specially devised Ei-graph. The slope plotted on a specially devised Ei-graph. The slope and the intercept of this straight line are determined then permeability and compressibility are calculated by using simple equations. The approach eliminates the need for type curve matching, and gives a simple and straight forward method to determine the required reservoir parameters accurately. TYPE CURVE MATCHING A type curve is the theoretical exponential integral solution of the line source model. It is a plot of the pressure change, in dimensionless form, at an observation well caused by either the injection into or production from another well, versus the change in time on log-log paper. The use of dimensionless variables makes it possible to use one type curve for the analysis of various wells. The exponential integral solution of the line-source flow model for pressure P, at any distance r, and time t, is given by Eq. (2). P. 415