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Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-149

Abstract

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 (G p ) which can be extrapolated to zero p /Z to obtain G . The graphical simplicity of this method makes it very popular. 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. It also does not include other sources of gas storage such as connected reservoirs or adsorption in coal/shale. In the past, researchers have introduced modified gas material balance equations to account for these other sources of energy. However, the simplicity of the p /Z straight line is lost in the resulting complexity of these equations. In this paper, a 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 compressibilities 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. Introduction It has been of great interest to find the original-gas-in-place by using material balance. The conventional gas material balance equation was developed for a "volumetric? gas reservoir. Therefore, the p /Z versus cumulative gas production plot may give misleading results in some situations e.g. when the formation compressibility is of the same order of magnitude as gas compressibility (overpressured reservoirs) or where desorption plays a role (CBM/shale). Figure 1 shows p /Z versus G p for several scenarios with the same original-gas-in-place ( G ). It can be seen from this figure that except for the volumetric reservoir, the plot is not a straight line, because gas expansion is not the only drive mechanism. In fact, water encroachment in water-drive reservoirs, formation and residual fluid expansion in overpressured reservoirs and gas desorption in coalbed methane (CBM) or shale reservoirs can have a significant role as a driving force in these cases. In these situations, where the gas expansion is not the dominant driving force, modified material balance equations have been developed by several researchers. Among them, Ramagost and Farshad [1] modified the conventional material balance equation to account for pore volume shrinkage due to formation and residual fluid expansion and introduced a new plotting function that keeps the material balance as a straight line. So that the modified material balance equation can be used for overpressured reservoirs.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-137

Abstract

Abstract Analysis of production data for characterization of reservoirs is becoming more popular. Sophisticated tools and methodologies exist to extract permeability, completion effectiveness and pore volume from production data (rates and flowing pressures). Often, in practice, these are the only tools available, especially in the case of low permeability reservoirs where it is not practical to conduct buildup tests. Production data, though plentiful, can be of poor quality because of operational problems, or changes in operating conditions, which are usually not documented (re-completions, tubing change-outs, compression, liquid loading, pressure or rate averaging). If this poor quality or inconsistent data is not recognized as such, it can easily be misinterpreted as being a reservoir issue rather than the operating problem that it is. For example, liquid loading, if not recognized, may be misinterpreted as interwell interference or reservoir depletion. In this paper, we review many of the operating problems we have observed in practice, and we discuss ways and patterns for recognizing them as operating issues rather than reservoir phenomena. Diagnosis of production data quality is a critical and necessary step that must precede any interpretation of production data. Recognition of inconsistent data is not always an easy task, and requires a lot of experience. The diagnostics presented in this paper will help the engineer in recognizing these problems, and potentially avoiding misinterpretation of the data. Introduction The analysis of production data to determine reservoir characteristics, completion effectiveness and hydrocarbons-inplace is becoming more and more prevalent. The methods of analysis have been documented and verified in numerous publications [1–7]. The concepts underlying modern production data analysis are the same as pressure transient analysis. Even though both these domains use the same underlying theory of fluid flow through porous media and can determine the same variables (permeability, skin, reservoir size), it should not be assumed that they can replace each other. Pressure transient analysis and production data analysis should be viewed as complimentary and not substitutes for each other. Pressure transient analysis deals mostly with "high frequency/high resolution" shut-in data while production data analysis deals with "low frequency/low resolution" flowing data. This, in itself, presents significant differences in data quality and interpretations. Like all mathematical solutions, the production data analysis methods are subject to numerous assumptions, which often can be justified. In this case, if the data are complete, consistent and of good quality, meaningful results can be obtained. However, if the quality of the data is questionable, then the production data analysis methods should be used with caution. In this case, the analyst's ability to filter out the bad data and extract the true reservoir signal becomes extremely important. As mentioned by Anderson et al. [8], blind application of production data analysis methods without consideration of data quality issues can lead to misinterpretation of the reservoir characteristics. An analyst, who is not experienced in recognizing such inconsistencies, can obtain an answer that appears to be mathematically correct yet be completely wrong because of using "bad data" for analysis.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-124

Abstract

Abstract Hydraulic fracture stimulation is commonly conducted in tight gas reservoirs to improve the deliverability. The typical sequence of events during the initial completion of a tight gas well is to conduct a hydraulic fracture treatment, flow back on clean-up for 2–4 days, shut-in to run pressure gauges and then conduct an extended flow and buildup test. The extended flow period can vary from a few hours to a few days and the subsequent buildup can vary from a day to several weeks. Fracture treatments in the Western Canadian Sedimentary Basin (WCSB) increasingly utilize CO 2 or Nitrogen to assist in the flow-back of these treatments. A CO 2 charged frac can flow back for a day or more, before burnable (reservoir) gas is seen at surface and at this point, there is typically 40+% CO 2 in the total gas. In many cases, this is the first gas rate reported by the testers. When conducting a pressure transient analysis, current industry practice is to ignore the CO 2 volume injected. WCSB operators and regulators continue to push for shorter test durations due to economic and environmental concerns. The objective of this paper is to investigate the impact of ignoring CO 2 injection on post-frac pressure transient analysis, and to provide guidelines on when the pressure transient analyst should take into account the injected CO 2 volumes. Introduction The usage of CO 2 in fracture stimulation has been studied extensively1-4. The practical use of CO 2 in hydraulic fracturing has been available since the 1960's. It was initially pumped with the frac fluids in a ratio adequate to gas lift the liquid back to surface after the treatment. Later, higher CO 2 ratios (50-75%) were used. Recently, liquid CO 2 has been used as the fracturing fluid for proppant transport. A CO 2 -based stimulation can reduce much of the damage related to fracturing fluids. The use of CO 2 can provide a fracture fluid recovery mechanism that is independent of reservoir pressure. It is unique because CO 2 can be pumped as a liquid and then vaporizes to a gas and flows from the reservoir, leaving no liquid or chemical damage. Pressure transient analysis is typically performed on the postfrac buildup to estimate reservoir parameters, such as initial reservoir pressure, permeability, effective fracture length, and deliverability potential etc, based on bottomhole pressure measurements and concurrent surface measurement information, such as wellhead pressure(s), and gas, oil and water rates, etc. Industry Practice in the WCSB A typical tight gas reservoir, vertical well completion in the WCSB commences with a hydraulic fracture treatment. Proppant volumes are rarely below 40 tonnes and frequently exceed 100 tonnes. Fluid volumes are proportionate to the sand volumes and can exceed 200 m 3 . The cleanup flow back times will vary from operator to operator (based on liquid and sand recovery) but are typically 2 to 4 days. Once burnable gas has been reported and liquid and sand volumes (if any) have fallen to acceptable levels, the well is shut-in to run pressure recorders to monitor the extended flow and buildup test.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-198

Abstract

Abstract Traditional decline methods do not work for tight gas wells. A hyperbolic decline is often used for forecasting the production rate and estimating the expected ultimate recovery (EUR) of a gas well. This method is only valid when the well is in the Boundary-Dominated Flow (BDF) regime, and hyperbolic b-values are in the range of 0 to 1. However, most of the production data from tight gas reservoirs is in the transient flow regime and not in the BDF regime. This results in values of b bigger than 1, and a forecast which can significantly over-predict the reserves. The recently developed "power law exponential decline" method seems to be promising in predicting the production rate over both transient and BDF regimes. In this paper, we examine the applicability of the power law exponential decline for different cases. We evaluate its behavior during both the transient and boundary-dominated flow regimes, and specifically for linear and radial transient flow. In the BDF regime, we also study the effect of reservoir size on the decline parameters. We compare the power law exponential decline with the decline from analytical reservoir models, and we modify it accordingly. Furthermore, the sensitivity of the power law equation to any of its parameters is studied. The validity of the power law exponential decline in forecasting production in tight gas wells is tested using synthetic data. Introduction The production of tight gas is becoming commercially significant in North America, and forecasting the future deliverability of tight gas wells is critical to the quantification of reserves. There are two methods of analyzing production data, namely the traditional methods such as exponential or hyperbolic decline [1] , and the modern methods such as Blasingame, Agarwal and the Flowing Material Balance [–6] . The traditional methods are very popular, because they are very easy to use, and only require flow rate and time as inputs. They have served the "reserves evaluation" industry quite well for nearly 100 years. For conventional oil and gas wells, these simple methods are reasonably well behaved and their performance is well understood. However, for tight gas wells, they fail spectacularly, and typically significantly over-predict reserves. The modern methods, on the other hand, are more rigorous, more sophisticated and more reliable. They work well for both conventional and tight gas wells, but they are more complicated to use, and require the availability of bottom-hole flowing pressure in addition to flow rate and time. It is well known that the traditional methods should only be used with production data after Boundary-Dominated Flow (BDF) has been reached [7] . During transient flow, these methods do not apply, and usually result in an "apparent" hyperbolic exponent, b>1. If this value is used to forecast future production, it can significantly over-predict reserves [8] . Not withstanding this serious shortcoming, tight gas wells are commonly forecast using hyperbolic decline with b>1.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 12–14, 2007

Paper Number: PETSOC-2007-011

Abstract

Abstract The purpose of this work is to model the single-phase radial gas flow in coalbed methane including equilibrium sorption phenomena in the coal matrix and Darcy flow in the natural fracture network. Considering a control volume, the gas desorption rate as a function of time and space is incorporated into the radial continuity equation as a source term. Using Langmuir type sorption isotherm, gas desorption rate is determined at any radius of the reservoir. Introducing the definition of pseudo-pressure and pseudo-time, the resulting continuity equation is converted into the linearized diffusivity equation by modification of total gas compressibility. It is shown how the traditional definition of the material balance pseudo-time is modified for dry CBM reservoirs. With the help of these transformations, the traditional (PTA and RTA) type curves can be employed for analysis of production data of dry CBM reservoirs. The model developed here is validated against Fekete's numerical CBM simulator over a wide range of reservoir parameters. In addition, one set of field data from Horseshoe Canyon coals of the Western Canadian Sedimentary Basin is analyzed using the solution procedure presented in this paper. Introduction Coalbed methane (CBM) is a natural gas produced from coal seams. Coal is both the source rock and the reservoir for methane production. The world total CBM resource potential is evaluated at about 143.2 trillion cubic meters. (1) CBM reservoirs are naturally fractured reservoirs that are characterized by two distinct porosity systems including: micropores (matrix) with extremely low permeability and macropores (natural fractures or cleats). Due to the small pore diameter of less than 10 °A, the coal matrix has a large internal surface area of 100 to 300 m 2 g. (2,3) As a result, substantial quantities of gas can be adsorbed on the surface of the coal grains. Micropores are impermeable to gas and inaccessible to water. However, the desorbed gas can transport through the primary porosity system by diffusion. The macropores acts as a sink to the micropores and provide permeability to fluid flow. In porous media with larger pore size distributions, mass transfer is driven by pressure gradients, whereas in coal, mass transfer is driven by concentration gradients. The diffusion through the micropores can be the result of three distinct mechanisms that may act individually or simultaneously (4) : bulk diffusion, where molecule/molecule interactions dominate; Knudsen diffusion, where molecule/surface interaction dominate; and two-dimensional surface diffusion of the adsorbed gas layer. The steady state diffusion coefficient for most coals is on the order of 10 −4 to10 −5 cm 2 s and the transient diffusion coefficient ranges from 0.5 to 10 times the steady-state values. (4) These experimentally determined diffusion coefficient represents averaged values including the contributions of the bulk, Knudsen, and surface diffusion processes. Diffusion effects can be quantified by determining asorption time. The sorption time is equal to the time required to desorb 63.2 percent of the initial gas volume (It is determined from whole core canister desorption test). This time is related to fracture spacing and the diffusion coefficient. (5)

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 12–14, 2007

Paper Number: PETSOC-2007-147

Abstract

Abstract Underbalanced drilling has become increasingly popular as it prevents fluid invasion during drilling operations. Consequently, formation damage may be reduced. This is particularly important in the case of depleted reservoirs or when horizontal and deviated wells are drilled. As a result of the lower pressure in the wellbore there is an inflow from the reservoir into the wellbore, which is continuously measured at the wellhead. This inflow carries information about the reservoir. The objective of this paper is to develop a mathematical model and its associated interpretation methods to estimate reservoir permeability and its variation along the wellbore using the inflow measurements at the wellhead. The traditional methods of pressure and rate transient analysis are not applicable to underbalanced drilling data particularly because the length of the producing interval is continuously increasing with time. In this paper we will develop a mathematical model accounting for this complication. This model calculates inflow rates in the forward mode and the reservoir permeability when used in the backward mode. We have validated our methodology against synthetic data obtained from numerical simulation, and applied it to a number of actual field cases. In field studies, after estimation of the permeability profile along the wellbore, the estimated permeability values were used along with reported bottomhole pressure after end of drilling to calculate gas inflow. This was then compared with the measured total inflow. Good agreement was obtained between the predicted and measured values. Furthermore, a number of sensitivity studies were conducted to examine the sensitivity of the estimated permeability to errors in the reported inflow information and the pressure drop along the wellbore. The results reported in the paper indicate that the estimated permeability profile remained relatively unchanged. Introduction Formation testing during under-balanced (UB) drilling relies on the hypothesis that inflow rate contains enough information from the reservoir to enable determination of some reservoir properties. Acquisition of the flow rate and bottomhole pressure data, and their analysis can offer information about the permeability and its variation along the length of the wellbore. Analyzing the UB drilling data has been the subject of many papers, some of more recent ones are reviewed below. Hunt and Rester [4] modify the standard pressure transient analysis techniques to include time-dependent boundary conditions, which account for the variable well length as the drilling bit progresses in the reservoir. The reservoir parameters are calculated based on a trial and error procedure as part of a history-matching exercise. A more recent paper of the authors [5] extends this to multilayer reservoirs. Kneissl [6] suggests introducing fluctuations to the bottomhole pressure during drilling to calculate both the permeability and the pore pressure during UB drilling. Similarly, Vefring et al [9] show that introducing fluctuations to bottomhole pressure while drilling, can improve the estimation results for calculating both permeability and pore pressure simultaneously. In this paper, as well as their earlier work [8] , the authors tie in a dynamic well-flow model with a simple transient reservoir model.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 12–14, 2007

Paper Number: PETSOC-2007-078

Abstract

Abstract One of the unresolved issues in the evaluation of coalbed methane (CBM) reserves is whether the long term production profile is exponential or hyperbolic. The type of decline used to forecast production can have a significant effect on the remaining reserves; hence, a thorough investigation of CBM decline is warranted. Before investigating the decline behavior of CBM wells, the literature on conventional gas decline analysis is summarized and the factors affecting production performance are discussed. The production performance of CBM is then investigated and compared to conventional gas performance. Simulations were conducted in order to determine the sensitivity of the hyperbolic decline exponent, b, to different reservoir and operating conditions. It was determined that several parameters, including the flowing pressure, affect the decline of conventional gas and CBM wells. Introduction The objective of this study is to review traditional decline analysis and discuss its applicability to CBM. Traditional decline analysis is based on the Arps' (1) equation which was introduced in the 1940's. It is an empirical relation that extrapolates a production forecast based on a curve fit of historical data. The general equation is given by Equation (1) (Available in full paper) The initial decline rate, D i ., and decline exponent, b, are constants used to calculate rate as a function of time. The theoretical limits on the decline exponent are 0 and 1. There are three specialized forms of the equation: exponential, hyperbolic and harmonic. Exponential decline is defined by a b value of 0 and can be recognized in several ways: The decline rate, D,(Available in full paper), is constant at all time A plot of gas rate versus cumulative gas production will be a straight line A plot of the logarithm of gas rate versus time will be a straight line Hyperbolic decline is defined by a b value between 0 and 1 and can be recognized if: The decline rate, D, is decreasing constantly with time. A plot of gas rate versus cumulative gas production has a concave upward appearance. Use of the exponential equation produces a more conservative reserve estimate than the hyperbolic equation, given the same initial decline rate, D i . It is often difficult to distinguish between exponential and hyperbolic decline without a considerable amount of data, so it is up to the judgment of the evaluator to use an appropriate b value. Analogous production history is often used as guidance. The choice of b value no only influences the estimate of reserves, but it also affects how long and at what rates the well will produce, which directly affects the economics of a project. Though Equation 1 is widely used, it does have limitations. It is only valid during boundary-dominated-flow, and when thewell's flowing pressure is constant. Fetkovich (2) created type curves that combine transient solutions with the boundarydominated stems of the Arps' equation. The type curve allows the entire data set to be analyzed, but it is still limited by the constant flowing pressure assumption.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 13–15, 2006

Paper Number: PETSOC-2006-172

Abstract

Abstract Well testing is sometimes reduced to perforating the well, capturing the pressure data and analyzing the data. The primary objective of a Perforation Inflow Test Analysis (PITA) is to estimate the initial reservoir pressure, permeability and skin, for evaluating future development strategy. However, special analytical procedures are required for analyzing the data, because these perforation inflow tests are considerably shorter than conventional well tests, and there is no recorded production. In this study, a systematic analytical procedure for estimating meaningful reservoir parameters from perforation inflow tests will be presented. Two major aspects of data interpretation will be discussed. Diagnostic Analysis and Modeling. A straight-line approach is taken to analyze the early-time and late-time data. A special diagnostic technique is required for detecting and estimating positive or negative skins. A distinctive feature of PITA, is that it does not require calculation of the inflow rates. Note that the same approach can be applied in over-balanced situations, when there is fluid efflux, rather than fluid influx. When employing straight-line analysis techniques, acceptable estimates of initial reservoir pressure, permeability and skin are only obtained if the test duration is sufficient to achieve radial flow. This is usually not a problem in high permeability reservoirs. However, in low permeability reservoirs, the test duration required to reach radial flow canbe prohibitively long. In these cases, the test is often terminated during the transition from wellbore storage to radial flow. Consequently, acceptable estimates of initial reservoir pressure, permeability and skin can only be obtained by extending the analysis into modeling. Field examples will be presented to highlight the methodology. A rigorous technique for estimating the radius of investigation during the test will be discussed. It will be shown that in the presence of measurement errors, radius of investigation will grow to a maximum value. Running the tests for anytime longer will be dominated by the noise. Introduction Well tests have been the primary and most reliable means of characterizing reservoirs for decades. However, there has been a growing trend over the last several years to search for alternatives that could yield the desired information in less time, in a more environmentally-friendly manner, and at a cheaper cost than conventional well tests. The desired change has inevitably been towards tests of shorter duration. 1–4 Although it is accepted that results from short tests with small radii of investigation may not be as reliable as those from conventional well tests, it is reasonable to accept that they could be of value in assisting with strategic decisions about field development, when an increased margin of error can be tolerated. In offshore wells, in addition to the potentially exorbitant cost of testing (several millions of dollars), the drive towards green (shorter) tests is fuelled by environmental considerations, such as requirements for restricted flaring of hydrocarbons. In Alberta and elsewhere in North America, the driving force towards inexpensive tests is the marginal economics of low deliverability wells. Either way, there is an increasing trend towards these green tests to replace conventional well tests.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 7–9, 2005

Paper Number: PETSOC-2005-114

Abstract

Abstract The use of semi-analytic methods for correcting flow equations to accommodate changing gas properties with pressure, has become increasingly common. It is a mainstay of modern production decline analysis as well as gas deliverability forecasting. The use of pseudo-time is one method which enables a time-based correction of gas properties, honoring the gas material balance within the time-based flow equation. By using pseudo-time, the analytical well / reservoir models, derived for the liquid case (slightly compressible fluid) can be modified for gas by re-evaluating the gas properties as the reservoir pressure depletes. These gas correction procedures are well documented in the literature. Also well documented is the iterative nature of the gas properties correction methods, as original gas-in-place is a required input into the equations. The pseudo-time correction is based on the average reservoir pressure and works very well for boundary dominatedflow. However, when transient flow prevails, the pseudo-time concept is not valid and its use can create anomalous responses. This will occur in low permeability systems or in reservoirs with irregular shapes, especially where some of the boundaries are very distant from the well. The semi-analytic gas correction has a "representative pressure" at its root, which, in the existing models, is always the average reservoir pressure. We propose a straight-forward modification to the determination of this pressure as follows. The representative pressure ought to be based on a "radius of investigation" or "region of influence" (in the case of nonradial systems), rather than the average reservoir pressure. Inthe case of a depleting system, the representative pressure would be the same as the average reservoir pressure. The following paper outlines the proposed procedure and illustrates its advantages over the existing method, by using synthetic and field data examples. Introduction Literature on the derivation and usage of pseudo-time is Prevalent (2) (3) . The definition that will be used in this paper is shown below. (Equation) (Available in full paper) The above is used in the pseudo-steady-state equation for gas, which is at the core of most modern production decline analysis methods. It is also used in analytical well / reservoir models, whose conventional formulations are only valid for slightly compressible fluids with constant properties over a given pressure range. These models enjoy widespread usage for both history matching and forecasting, and their inclusion of pseudo-time for gas reservoirs is vital. To illustrate the value of pseudo-time, let us take the simple case of a vertical well in the center of a circular gas reservoir. We will assume constant rate production and pseudo-steady state conditions. Thus, the model that describes the pressure response at the well can be reduced to the pseudo-steady-state equation for gas (5) . (Equation) (Available in full paper) The "f(t)" in equation (2) is the chosen time function. Figure 1 shows the pressure response plotted against time for two cases f(t) = time (t) and f(t) = pseudo-time (ta). Also compared is the numerical solution using the same input parameters.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 7–9, 2005

Paper Number: PETSOC-2005-031

Abstract

Abstract Due to economics or time constraints, well-testing is sometimes reduced to perforating a well under-balanced, andanalyzing the inflow characteristics. The objective of a Perforation Inflow Test Analysis (PITA) is to estimate the initial reservoir pressure, permeability and skin, immediately after perforating the well. This information can be used for evaluating future development strategy. However, special analytical procedures are required for analyzing the data, because these perforation inflow tests are shorter than conventional well tests and the influx rates are not measured. In this study, the working equations for analyzing these short tests are presented, and the procedure required for calculating meaningful estimates of the reservoir parameters is presented. Analyses of early-time and late-time data are the two major components of this approach. The early-time analysis isused for estimating the skin, and the late-time analysis is used for estimating the initial pressure and permeability. A distinctive feature of the PITA is that it does not require calculation of the influx rates, which are generally not available during a perforation test. A special derivative, called the impulse derivative, can be used to determine if the data collected is sufficient to yield meaningful results from a PITA. It is particularly important that the reservoir-dominated flow regime be reached, if the estimates of initial reservoir pressure, permeability and skin are to be acceptable. Good estimates of these parameters from a PITA will minimize the uncertainty associated with non-uniqueness in inverse problems, when modeling the test data. Introduction Conventional well tests have served the petroleum industry faithfully for decades as the primary and most reliable means of: quantifying deliverability, characterizing the reservoir, collecting reservoir fluid samples, and evaluating the condition of the well. However, for the last few years, oil and gas producers have been searching for alternatives that could yield the desired information in less time, in a more environmentally-friendly manner, and at a cheaper cost than from conventional well tests. The trend has inevitably been towards tests of shorter duration. Although it is accepted that results from short tests with small radii of investigation may not be as reliable as those from conventional well tests, it is reasonable to accept that they could be of value in assisting with strategic decisions about field development, when an increased margin of error can be tolerated. In offshore wells, in addition to the potentially exorbitant cost of testing (several millions of dollars), the drive towards green (shorter) tests is fuelled by environmental considerations, such as requirements for restricted flaring of hydrocarbons. InAlberta and elsewhere in North America, the driving force towards inexpensive tests is the marginal economics of low deliverability wells. Either way, there is an increasing trend towards these green tests to replace conventional well tests. One such green test consists of simply allowing the well to flow into the closed wellbore after perforating (closed chamber test). As the fluid from the reservoir enters the wellbore (with a fixed volume), the wellbore pressure builds up.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 7–9, 2005

Paper Number: PETSOC-2005-113

Abstract

Abstract Material Balance calculations for determining oil- or gasin-place are based on obtaining static reservoir pressures as a function of cumulative production. This requires the wells to be shut-in, in order to determine the average reservoir pressure. In a previous publication (1) , it was shown that the material balance calculation could be done without shutting-in the well. The method was called "Flowing Material Balance". While this method has proven to be very good, it is limited to a constant flow rate, and fails when the flow rate varies. The "Dynamic Material Balance" is an extension of the Flowing Material Balance. It is applicable to either constantflow rate or variable flow rate, and can be used for both gas and oil. The "Dynamic Material Balance" is a procedure that converts the flowing pressure at any point in time to the average reservoir pressure that exists in the reservoir at that time. Once that is done, the classical material balance calculations become applicable, and a conventional material balance plot can be generated. The procedure is graphical and very straightforward: knowing the flow rate and flowing sandface pressure at any given point in time, convert the measured flowing pressure to the average pressure that exists in the reservoir at that time; use this calculated average reservoir pressure and the corresponding cumulative production, to calculate the original oil- or gas-in-place by traditional methods. The method isillustrated using data sets. Introduction The material balance method is a fundamental calculation inreservoir engineering, and is considered to yield one of the more reliable estimates of hydrocarbons-in place. In principle, it consists of producing a certain amount of fluids, measuring the average reservoir pressure before and after the production, and with knowledge of the PVT properties of the system, calculating a mass balance as follows: Remaining Hydrocarbons-in-place = Initial Hydrocarbons-inplace- Produced Hydrocarbons At face value, the above equation is simple; however in practice, its implementation can be quite complex, as one must account for such variables as external fluid influx (water drive), compressibility of all the fluids and of the rock, hydrocarbonphase changes, etc. In order to determine the average reservoir pressure, thewell is shut-in, resulting in loss of production. In high permeability reservoirs, this may not be a significant issue, but in medium to low permeability reservoirs, the shut-in durationmay have to last several weeks (and sometimes months) before a reliable reservoir pressure can be estimated. This loss of production opportunity as well as the cost of monitoring the shut-in pressure is often unacceptable. It is clear that the production rate of a well is a function of many factors such as permeability, viscosity, thickness etc… Also, the rate is directly related to the driving force in the reservoir, i.e. the difference between the average reservoir pressure and the sandface flowing pressure. Therefore, it is reasonable to expect that knowledge about the reservoir pressure can be extracted from the sandface flowing pressure if both the flow rate and flowing pressure are measured.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 8–10, 2004

Paper Number: PETSOC-2004-214

Abstract

Abstract There are two commonly used correlations for determining the viscosity of natural gases. These are the Carr, Kobayashi and Burrows (CKB) and the Lee, Gonzalez and Eakin (LGE). The CKB applies to both sweet and sour gas, but the LGE was derived purely for sweet gas. The CKB is a graphical correlation, and consists of two sets of graphs with temperature as the correlating parameter (not easily adaptable for computer applications). On the other hand, the LGE is a set of simple equations, and therefore can be easily programmed in to a computer. The LGE is used in numerous computer programs, with no regard to the fact that it was not derived for sour gas. This study compares the LGE equation to the CKB graphs for both sweet and sour gases. A detailed comparison of the two methods using various gas mixture compositions, temperatures and pressures was conducted. The results illustrate that for sweet gases, the comparison is acceptable, and the LGE equation can be used for most reservoir engineering purposes. However, for sour gases, the differences between the LGE and CKB correlations can be significant. This leads to the conclusion that the LGE correlation, which was derived for sweet gases only, should not be indiscriminately applied to sour gases. Introduction Gas viscosity is used in several calculations dealing with fluid flow and reservoir behavior. Empirical correlations have been developed to estimate values for viscosity over a range of pressures. Most viscosity correlations are either equation based or in a graphical form derived from laboratory measurements. Typically the correlations are functions of temperature, pressure, gas gravity and composition. Often they are paired with various corrections for non-hydrocarbon components. Applying a correlation without corrections to a sour gas case can lead to large errors in predicting viscosity. Carr, Kobayashi and Burrows Correlation The Carr et al correlation (henceforth referred to as CKB) was developed to predict the viscosity of gas hydrocarbon mixtures over a large pressure and temperature range. The limits of the correlation are temperatures between 32 and °400F and reduced pressures up to 20 (which can equate to pressures higher than 12000 psia). It was designed to handle nonhydrocarbon components (CO 2 , N 2 , H 2 S) in concentrations of up to 15 % each. Calculation of viscosity with the CKB method is a three step process based on graphical methods. The first step is to determine the viscosity at atmospheric pressure based on the gas gravity and temperature using figure 1. Next, corrections are added to the viscosity based on the H 2 S, CO 2 and/or N 2 content of the gas. Finally, the viscosity is multiplied by a ratio based on the reduced pressure from figure 2. The only disadvantage of the CKB method is that it is based on several charts, making it difficult to program into a computer. Two methods that have been used to simplify computation have been to generate a series of polynomial curve-fits or to use a table lookup-interpolation scheme (1 ).

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 8–10, 2004

Paper Number: PETSOC-2004-182

Abstract

Abstract Analytical solutions in well-test analysis are oriented towards fluids with a constant viscosity and compressibility in a porous medium with a constant porosity. To use these solutions in gas-flow situations, one needs to apply the pseudo-pressure and pseudo-time transformations. Thus, the non-linear diffusivity equation for gas flow is transformed into a linear one, allowing one to use the solutions for fluids with constant compressibility, viscosity and porosity. Although the computation of pseudo-pressure is reasonably accurate, the conventional computation of pseudo-time by direct integration of the compressibility-viscosity function over time can result in significant errors, when modeling gas reservoirs with residual fluid saturation, rock compressibility and a large degree of depletion. Errors in calculating the pseudo-time result in substantial errors in the material balance, which has an adverse impact on reservoir modeling and production forecasting. In this study, a new method for computing pseudo-time is presented. This method is based on the material balance equation that considers the rock and fluid compressibility. This formulation honors the material balance equation in all situations. Examples are presented to show that the problems with computing pseudo-time, using the traditional definition, can be resolved when the new method is used. Accurate computations of pseudo-time allow one to use the solutions for fluids with constant compressibility and viscosity for modeling and forecasting gas production. Introduction Analytical solutions are generally used to analyze and model well-test and production data. However, these solutions have been developed for fluids with a constant viscosity and compressibility and for formations with a constant porosity. The governing diffusivity equation and its boundary conditions are linear when expressed in terms of pressure, space and time variables. The analytical solutions to these equations are reasonably accurate for the liquid-flow situations. In contrast, the diffusivity equation for gas flow and its boundary conditions are non-linear when expressed in terms of pressure, space and time variables. As no analytical solutions to these non-linear equations are available, one needs to apply pseudo-pressure and pseudo-time transformations in order to use the analytical solutions for liquid flow in gas-flow situations. This approach introduces two variables in the diffusivity equation for gas flow - pseudo-pressure (ψ) as the dependent variable, and pseudotime (ta) as an independent variable. As a result, the diffusivity equation for gas flow is transformed into a linear one, allowing one to use the slightly-compressible-fluid (liquid) solutions. In this study, we are considering a single-phase gas flow situation in the presence of residual fluid saturation and a compressible formation. Here gas is the only mobile phase, while oil and water phases are immobile, if there is any. The pseudo-variables (pseudo-pressure and pseudo-time) can be defined as - Equation (1) (Available in full paper) Equation (2) (Available in full paper) The rationale for defining the above pseudo-variables is demonstrated in Appendix A. Martin3 made the first systematic attempt to define the total system compressibility in multi-phase conditions, neglecting the rock compressibility. Later, Ramey 4 followed Martin's lead and included the formation compressibility in defining the total system compressibility, ct, as Equation (3) (Available in full paper)

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 10–12, 2003

Paper Number: PETSOC-2003-201

Abstract

Abstract Production data generally consists of variable rate and variable flowing pressure. It is convenient to be able to use reservoir models that assume a constant flow rate, since these solutions have been previously derived in the well testing literature. Thus, it is necessary to have a time function capable of converting general production conditions into the equivalent constant rate solution. Blasingame 1 , and later Agarwal et al 2 have shown that Material-Balance-Time provides an exact transformation of constant pressure data to constant rate type curves, during the boundary dominated flow regime. It also yields a reasonable approximation during radial flow, and when rate and/or pressure vary smoothly. Poe 3 has investigated the effectiveness of using material-balancetime for other transient flow regimes using the constant pressure solution, rather than the constant rate solution as a base model. The objectives of this paper are twofold. Firstly, it serves to investigate the applicability of materialbalance- time during the linear flow regime (fracture flow), where the difference between the constant rate and constant pressure solutions is more pronounced. Further to this, material-balance-time correction factors are quantified for both radial and linear transient flow regimes (this has not previously been done using the constant rate solution as the base model). Secondly, it serves to illustrate by synthetic and field examples, a comparison of material-balance-time against the logarithmic superposition time function, to determine under what circumstances material-balance-time errors significantly influence rate transient interpretation, in practice. Introduction In pressure transient tests, the diagnostic plot (log-log plot of pressure and derivative) is an invaluable tool for reservoir characterization. For variable rate drawdown tests and flow and buildup tests, a time superposition function should be used to convert variable rates into an equivalent constant rate solution. Since pressure transient tests are usually dominated by infinite acting flow, the widely accepted time superposition function is one that assumes radial flow (logarithmic superposition time). One of the problems inherent in pressure transient analysis is that radial flow is not always the dominant flow regime. Thus, there is the potential for misinterpretation of the diagnostic plot in certain situations. In recent years, diagnostic plots of various different forms have been used to analyze production data. The nature of production data analysis is different than that of pressure transient analysis, primarily because of the greatly increased time scale, and because production data tends to be much noisier than pressure transient data. Most of the literature agrees that a time superposition function that assumes boundary dominated flow is more appropriate to use on a diagnostic plot of production data, than any transient superposition function, because most production data is under the influence of some sort of reservoir depletion. However, with very low permeability reservoirs, this is not necessarily the case. Material-balance-time is the time superposition function for volumetric depletion. It is rigorous in converting variable rate production into equivalent constant rate production, provided that the flow regime is boundary dominated (volumetric depletion).

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 4–8, 2000

Paper Number: PETSOC-2000-045

Abstract

Abstract In pressure transient analysis, often the geological model is not known, or is ambiguous. Many well tests can be analyzed using a composite reservoir model which assumes that the flow capacity (k*h) near the wellbore is different from that away from the wellbore. There are many naturally occurring reservoirs that can legitimately be modeled this way because the transmissivity is indeed varying laterally. However there are many more reservoirs which have a different flow capacity near the well as compared to the bulk of the formation, not because of lateral permeability changes but because of layering. In these situations, it is the net pay and reserves, not the necessary the permeability, that is changing. This paper compares the pressure transient behavior of a multi-layer system with that of a composite system, and illustrates the similarities and the differences in their respective Derivative signatures. It also investigates the extension of these two different models to pseudo-steady state forecasting. Even though the behavior of these two systems may be similar during transient flow (this is the time domain of most well tests), the long-term performance is significantly different if the improper model is used (this is the time domain of many engineering and economic decisions). The role of the geological model in well testing and deliverability forecasting is discussed, as it can have a significant effect on some parts of the analysis and an insignificant effect on other parts. Introduction Multi-Layer System It is commonly known that if two or more layers of a reservoir are open to a wellbore, and are initially at a common pressure and constant drawdown, the general characteristics of the drawdown response is similar to that of a well producing from a single layer reservoir(1,2). Specifically, each layer will contribute production which is proportional to its transmissibility (kh/ µ). Therefore, the semi-log slope (m) calculated from the infinite acting flow 1 data will be nearly proportional to the sum of the individual layers transmissibilities (any modification of this slope would be due to unequal diffusivities or skin factors). For example, if a well is producing commingled at the wellbore from a layer of 2m and a layer of 3 m net pay (both with a permeability of 20 mD), the semi-log analysis of the radial flow data (refer to Figure #1) will show a flow capacity of 100 mD.m If one layer of a two-layer model is limited in drainage area, a depletion of the limited layer will eventually occur. Upon depletion of this layer, a semilog straight line with a slope "m" that is inversely proportional to the transmissibility of the more extensive layer may be observed. On the derivative nalysis, after the initial radial flow, a unit slope develops followed by a transition to a second radial flow characterized by the typical zero slope. Figure #2 shows the semi-log plot for a two-layer reservoir where the extensive layer has a net pay of 2 m and a permeability of 20 mD (the corresponding dimensionless typecurve is embedded within the figure).

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 4–8, 2000

Paper Number: PETSOC-2000-046

Abstract

Abstract In a gas reservoir, because of the assumptions inherent in the constant rate solution, it is not possible to accurately forecast deliverability during pseudo-steady state (after the reservoir has shown significant depletion). More specifically, the constant rate equation is not consistent with the tank model (material balance). The cause of the inconsistencies lies in the assumption of constant gas properties (ie. compressibility and viscosity). This paper deals with different attempts at modifying the constant rate solution to provide an approximate solution that is consistent with tank type depletion. If possible, it is preferable to approach this type of solution by trying to avoid an iterative approach or a solution that requires the tank model (material balance). Once one begins to incorporate the tank model for pseudo steady state calculation, the calculation of the constant rate solution becomes redundant. Therefore, various procedures were attempted to develop a process that does not require a material balance calculation explicitly, and preferably no iterations. This work also demonstrates that the constant rate solution and the constant pressure solutions are essentially equivalent during transient flow. However, there is a significant difference between them when boundary dominated flow is reached. Introduction Although the quantity of reserves are obviously a very important part of determining the value of a new well, the length of time to produce these reserves is equally important. There is obviously much more value in reserves, if the reserves can be produced over a shorter period of time. Therefore, there is obvious value in preparing accurate gas deliverability forecasts. Currently, the following two methods are used to forecast gas deliverability: Pseudo-steady state equation, and Tank model approach (p/z material balance and Deliverability forecasting) PSEUDO-STEADY STATE SOLUTION The pseudo-steady state solution is based on the "constant rate equation". For a given constant rate, the well's flowing pressure can be calculated as a function of time using the equation shown below. Equation (Available in full paper) In practice, it is often more useful to forecast the rate at a fixed flowing pressure than to forecast the flowing pressure at a fixed gas rate (which is the basis of the pseudo-steady state solution). Since the gas rate will usually vary with time, the correct procedure is to use the equation below in conjunction with the principle of superposition to account for the rate variations. This can be a laborious procedure, and in many instances, a shortcut is taken to simplify the process. This simplification consists of "ignoring" the fact that the pseudo-steady state equation is a "constant rate" solution, and to simply invert the equation and use it to calculate the rate at a constant pressure. While there is some basis for this simplifying assumption (1,2) it can also lead to some erroneous answers. Equation (Available in full paper) Figure 1 shows a comparison of the forecasts obtained by using the principle of superposition and that obtained by using the simplified procedure.