Skip Nav Destination
Filter
Filter
Filter
Filter
Filter

Update search

Filter

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

### NARROW

Format

Subjects

Date

Availability

1-20 of 21

Keywords: straight line

Close
**Follow your search**

Access your saved searches in your account

Would you like to receive an alert when new items match your search?

*Close Modal*

Sort by

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Petroleum Technology Conference, April 14–16, 2009

Paper Number: SPE-122768-MS

.../well testing flow rate diffusivity analytical solution boundary condition nonlinearity equation

**straight****line**permeability pressure-dependent permeability reservoir differential equation Abstract The transient pressure response in stress-sensitive formations is derived by solving...
Abstract

Abstract The transient pressure response in stress-sensitive formations is derived by solving analytically the radial flow equation with pressure-dependent rock properties. New solutions are obtained for slightly compressible fluids and real gas flow with constant-rate and constant-pressure wellbore boundary conditions using the Boltzmann transformation. In particular in low-permeability formations, a sensitivity exists to pore pressure changes. Permeability there normally declines with the increase of effective stress. The mathematical model presented here takes into account the reduction in permeability caused by an increase in effective stress for two common parameterized pressure-permeability functions, i.e., a linear and an exponential relationship. The analytical solutions are verified with numerical simulation. They are applicable for well test analysis and prediction of flow rates, as demonstrated in this paper. Introduction Virtually all classical analytical techniques to solve the fluid flow equation are based on the assumption of constant rock permeability. In contradiction to the changes in porosity during production, which are captured in the solutions by introducing a constant compressibility for the porous media, permeability is considered to be independent of the pore pressure. Linearization of the pore volume changes and the assumption of a constant permeability result in a constant diffusivity which has been the basis for a wide range of analytical solutions for the parabolic differential equation in the past. This constant property assumption is justified for many typical reservoir engineering problems, in which both local pressure and permeability changes are small and negligible. However, this is not strictly applicable to all kinds of reservoirs. Certain reservoir rocks exhibit a stronger sensitivity to changes of stress conditions during the depletion of the reservoirs, in particular, naturally fractured reservoirs and low-permeability reservoirs. As a rule of thumb, the impact of stress on property alteration increases with the tightness of the reservoir rock. This makes it particularly important in tight-gas or coalbed methane reservoirs. Stress sensitivity impacts both classical well test analysis and performance predictions. In this paper, new analytical solutions are presented for transient radial flow in stress sensitive reservoirs with constant-rate and constant-pressure boundary conditions. The solutions are simple to use and provide a means to derive the transient response of a radial well in pressure-sensitive environment using a typical engineering application such as spreadsheet programs. The solutions are validated against numerical simulation and applied for well test analysis. Background Theoretical consideration of stress-dependent mechanisms goes back to Tezaghi's work, which was introduced in reservoir engineering in the early 1950's. The first important publications were from Fatt and Davis (1952) and Dobrynin (1962). In their papers, the authors investigated the relation between effective stress and reservoir permeability. They concluded that permeability declines with increasing effective stress. Dobrynin (1962) also introduced a mathematically derived capillary model to describe the change of permeability as a function of the changes in in-situ stresses.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium and Exhibition, March 12–15, 2000

Paper Number: SPE-60291-MS

... reservoirs. drillstem/well testing

**straight****line**injection test closure drillstem testing extension mayerhofer method pressure transient analysis specialized mayerhofer plot permeability pressure transient testing diagnostic fracture injection test flow in porous media pressure dependent...
Abstract

Abstract The modified Mayerhofer method has been proposed for estimating permeability from the pressure falloff data in moderate and high permeability reservoirs before hydraulic fracture closure following a diagnostic fracture injection test. Applying the modified Mayerhofer method in low permeability sands, however, requires understanding of the closure mechanism, which is identified with G-function derivative analysis of the before-closure pressure falloff data. This paper demonstrates how G-function derivative analysis and the modified Mayerhofer method are used in conjunction to estimate reservoir permeability in low permeability reservoirs. Numerous applications of G-function derivative analysis have shown the characteristic closure mechanisms—normal, pressure-dependent leakoff from fissure opening, fracture-height recession, fracture-tip extension, and changing compliance—all result in distinctive specialized plots using the modified Mayerhofer method. When the two methods are used in conjunction, G-function derivative analysis provides a means for identifying the falloff data that can be used to estimate permeability and fracture-face resistance without violating the assumptions of the modified Mayerhofer method. Field cases are included to demonstrate that reasonable estimates of reservoir permeability in low permeability reservoirs often can be obtained from the before-closure pressure falloff following a diagnostic fracture injection test. Introduction Valk and Economides 1 published the modified Mayerhofer method for estimating permeability in moderate and high permeability reservoirs from the before-closure pressure falloff data following a diagnostic fracture injection test. The modified Mayerhofer method is based on the technique proposed by Mayerhofer, et al. , 2 and differs from conventional pressure decline analysis in that the problem is formulated in terms of permeability and fracture face resistance as opposed to leakoff coefficient and spurt loss. Before-closure pressure falloff analysis techniques are beneficial for low permeability reservoirs since the shut-in time requirements are substantially lower than the time required for after-closure pressure falloff analysis. Nolte, Maniere, and Owens, 3 however, have noted that fracture extension and fracture recession during closure limit the applicability of before-closure pressure falloff analysis techniques. Nolte, et al. , 3 suggest that after-closure analysis of pseudolinear and pseudoradial flow regimes are superior methods for estimating reservoir parameters, but in low permeability reservoirs, the time required to achieve pseudolinear and pseudoradial flow following a fracture injection test can be excessive. G-function derivative analysis was recently proposed for identifying the leakoff mechanism—normal, pressure-dependent leakoff from fissure opening, fracture-height recession, fracture-tip extension, and changing compliance—from the pressure falloff following a diagnostic injection test. G-function derivative analysis also provides a method for identifying the falloff data that can be used to estimate permeability and fracture-face resistance without violating assumptions of the modified Mayerhofer method. The objective of this paper is to demonstrate how G-function derivative analysis and the modified Mayerhofer method are used in conjunction to estimate permeability in low-permeability reservoirs. Additionally, field cases are included to demonstrate that reasonable estimates of reservoir permeability can often be obtained from the before-closure pressure falloff data in low permeability reservoirs.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 15–18, 1999

Paper Number: SPE-55605-MS

... This paper was prepared for presentation at the 1999 SPE Rocky Mountain Regional Meeting held in Gillette, Wyoming, 15–18 May 1999. water production reservoir simulation water saturation

**straight****line**calculation coal well gas reservoir mass balance equation king compressibility...
Abstract

This paper was prepared for presentation at the 1999 SPE Rocky Mountain Regional Meeting held in Gillette, Wyoming, 15–18 May 1999.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Low Permeability Reservoirs Symposium, April 26–28, 1993

Paper Number: SPE-25880-MS

...^ system analysis porosity society of petroleum engineers hinchman pressure transient testing drillstem/well testing

**straight****line**estimate fracture porosity injection well intersection time compressibility fracture porosity reservoir mobility polymer injectivity test permeability bank...
Abstract

Abstract A new technique is presented to calculate fracture porosity in naturally fractured reservoirs using composite system analyses. The concept outlined here is to inject a viscous solution (e.g. polymer) which will not invade the matrix rock, but remains in the fractures. Subsequent falloff tests can then be used to determine the bank radius of the polymer in the fractures and thus fracture porosity from material balance. In the early 1980's Marathon Oil Company performed a number of polymer injectivity tests in naturally fractured reservoirs. In several cases, apparent bank radius was much larger than anticipated. This observation lead to the technique proposed in this paper. Introduction A difficult problem in characterizing naturally fractured reservoirs is determining the fraction of the pore volume which can be assigned to the fracture network (i.e. fracture porosity). In tight formations, pressure transient testing can give a measure of the relative fracture storage capacity of the formation providing that wellbore storage is minimized. In order to estimate fracture storage capacity from pressure transient testing at least a portion of the transition from fracture response to total system response must be seen on the pressure transient plot. However, in many naturally fractured reservoirs, the system may begin behaving like a homogeneous, single-porosity system in a very short time as given by the following equation : (1) where (for cubical matrix blocks) (2) For moderate matrix permeability (greater than 10 md) and high fracture intensity (), the end of the transition period may be on the order of several seconds as calculated by Eq. 1 and thus may be masked by wellbore storage. Thus, in many highly fractured oil reservoirs, it is only possible to determine the total system effective permeability from a single-well transient test and total porosity-compressibility product from an interference test. In this paper, we propose the use of injectivity and falloff tests combined with composite system transient analysis to estimate the total porosity of the fracture network. TECHNIQUE AND ASSUMPTIONS The most basic application of this technique consists of injecting a fluid into a naturally fractured reservoir and then performing a falloff test. The injected fluid must have a mobility different than the in-situ fluid and only occupy the fractures. P. 439^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Low Permeability Reservoirs Symposium, April 26–28, 1993

Paper Number: SPE-25876-MS

... to as polynomial flow. A plot of vs. is a

**straight****line**with slope Mn. The constant Rn, represents the intercept with the vertical axis. Such plots are usually referred to as specialized plots. The slope term depends on a permeability and the geometry of the dominant mode of flow. P. 383^ polynomial flow...
Abstract

Abstract A generalized methodology for flow period diagnostics and type curve matching is discussed. The method which is based on the concept of a polynomial derivative function, can be used under a variety of flow conditions. A new methodology to highlight possible constant terms during radial or polynomial flow periods is proposed. The constant term reflects the damage skin factor and the degree of convergence to the well. Introduction Ramey probably presented the first type curve to the petroleum industry. Earlougher and Kersch proposed the tD/CD-type curve. This plotting technique was developed further by Gringarten et al. Log-log plotting of pressure derivatives was proposed by Tiab and Kumar and Bourdet et al. They used pressure derivatives with respect to time and log-time respectively. A square-root and a fourth-root derivative for linear and bilinear flow diagnostics were proposed by Jelmert. The technique has been extended to double porosity reservoirs. It was noted in that the square-root and fourth-root derivatives are special cases of the more general polynomial derivative. The existence of polynomial flow periods are well known. Spherical flow has been discussed by Chatas. Linear flow exists in many cases, for instance the vertical fracture. In the case of a finite conductivity fracture a bilinear flow period may appear. POLYNOMIAL FLOW PERIODS Usually a well test may be broken into specific and transitional periods. The specific ones have simple geometric interpretations like radial, spherical and linear flow etc. During the specific flow periods, the asymptotic behavior of the complex mathematical model will approach simple equations. Some of these will be of the power law type as follows: (1) The values of the constants Mn, and Rn, in eq. (1) depend on the flow period. This dependency is indicated by the index n which corresponds to the flow exponent. Flow exponent n = 1/2 is relevant for linear flow, = 1/4 for bilinear and = -1/2 for spherical flow. Wellbore dominated and pseudo steady periods are characterized by a flow exponent n = 1. In mathematics, the above equation is considered a polynomial function for integer values of the flow exponent n. True polynomial behavior in well test theory is possible when n = 1 only. This case corresponds either to the wellbore storage period or to pseudo-steady flow. In this paper we refer to all periods with integer or fractional flow exponent as polynomial flow periods. The coordinate transformation will transform all the power law relations implied by eq.(1) into a linear equation in, that is a simple polynomial equation. Such flow periods exhibit similar behavior and may be treated as a single class referred to as polynomial flow. A plot of vs. is a straight line with slope Mn. The constant Rn, represents the intercept with the vertical axis. Such plots are usually referred to as specialized plots. The slope term depends on a permeability and the geometry of the dominant mode of flow. P. 383^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Low Permeability Reservoirs Symposium, April 26–28, 1993

Paper Number: SPE-25873-MS

... classical semilog

**straight****lines**. These approximate solutions suggest the appropriate pressure, pressure-derivative, integral-pressure-derivative and time groups necessary to prepare type curves. New type curves are presented for both the pseudosteady-state interporosity flow model of Warren and Root...
Abstract

Abstract This work presents new type curves for the characterization of a naturally- fractured (dual-porosity) reservoir. These type curves were motivated by new approximate solutions for the pressure derivative which apply during the transitional flow period which exists between the two classical semilog straight lines. These approximate solutions suggest the appropriate pressure, pressure-derivative, integral-pressure-derivative and time groups necessary to prepare type curves. New type curves are presented for both the pseudosteady-state interporosity flow model of Warren and Root and the transient interporosity flow model of Kazemi and de Swaan. Introduction Naturally fractured reservoirs are also referred to as double-porosity, dual-porosity or fissured reservoirs. In general, a dual-porosity reservoir is considered to be composed of two systems, a matrix system and a fracture or fissure system. The fracture (fissure) system has a high permeability and a low storage capacity, whereas the matrix system has a low permeability but a high storage capacity. Although the matrix system is considered to be permeable so that fluid can be transferred from the matrix system to the fissures, standard fissured reservoir models used in pressure transient analysis assume that all fluid produced at the wellbore is via the fracture system, i.e., from the viewpoint of production, the total reservoir flow capacity is equal to the fracture flow capacity. In the literature, several models have been presented to describe the double porosity (naturally fractured) reservoir pressure behavior. There are two basic models which differ in terms of the treatment of interporosity flow, i.e., the way that the fluid is transferred from the matrix system into the fissures. The first approach is to assume that the rate of fluid transfer from the matrix system to the fracture system is proportional to the difference between the matrix pressure and the fracture pressure. In this approach, the pressure gradients in the matrix are neglected and the matrix/fracture geometry is treated implicitly by using a lumped parameter or shape factor. In the petroleum literature this model is usually referred to as the Warren and Root model, or the pseudo-steady state (PSS) interporosity flow model. We shall use the preceding terminologies interchangeably, however, as pointed out by the last author in 1981, the terminology pseudosteady state is a misnomer. The second approach assumes that the fluid transfer from matrix to fissures occurs under transient state (TS) conditions. In the TS interporosity flow, the fracture/matrix geometry is treated explicitly for an assumed matrix block shape, for example, slab, sphere, cylinder or cube. Throughout, we refer to the latter model as the transient interporosity flow model, the TS model, or the Kazemi-de Swaan model. From a theoretical view point, the Kazemi-de Swaan appears to be superior in that it allows us to account for pressure gradients in the matrix system. These gradients influence fluid transfer and the wellbore pressure response during the transitional flow period, where, throughout, the transitional flow period refers to the time period subsequent to the end of the early-time Warren and Root semilog straight line and prior to the beginning of the late-time Warren and Root semilog straight line. Field cases, however, more frequently support the Warren and Root model; see, for example, Ref. 6. P. 343^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 18–21, 1992

Paper Number: SPE-24376-MS

... oil permeability can be approximated by a piecewise linear function of pressure. P. 571^ flow rate oil permeability equation pressure buildup data semilog plot oil saturation permeability solution-gas-drive reservoir skin factor semilog

**straight****line**buildup data drillstem/well...
Abstract

SPE Member Abstract This work investigates the effect of wellbore storage on the analysis of pressure buildup data obtained in a solution-gas-drive reservoir. All results assume radial flow to a single well draining a solution-gas-drive reservoir with the initial reservoir pressure equal to the initial bubble-point pressure. Although connate water is present, the water is immobile and therefore during production only oil and gas flow within the reservoir. Wellbore storage effects are incorporated by specifying a sandface oil flow rate which during shut-in decreases exponentially from a stabilized constant value of the surface oil flow rate at the time of shut-in to zero. Based on a superposition equation new computational equations for computing-effective oil and gas permeabilities as pointwise functions of pressure from the measured values of the shut-in wellbore pressure are presented. The computational equations require that the sandface oil flow rate be measured and incorporated into the analysis. By combining the computed effective permeability versus pressure relation with the oil saturation versus pressure results computed from the material balance equation, one can approximately construct the effective oil and gas permeabilities as functions of oil saturation. It is also shown that a semilog plot of shut-in pressure-squared versus Homer time represents a viable method for obtaining estimates of the mechanical skin factor and the effective oil permeability at the final value of shut-in wellbore pressure. Introduction Until recently analysis of multiphase flow well-test pressure data was conducted according to analysis techniques essentially based on single phase flow theory. Specifically, Refs. 1 and 2 suggested that one can apply the single phase flow analysis methods to multiphase flow pressure data to estimate the total mobility of the system. Motivated by the works of Evinger and Muskat and Fetkovich, Raghavan suggested semilog analysis techniques based on pseudopressure. These techniques assume radial flow to a completely-penetrating well producing a solution-gas-drive reservoir and assume relative permeability curves as a function of oil saturation are known a priori. Works presented by B e et al. and Aanonsen provided some theoretical basis for the use of pseudofunctions to approximately correlate multiphase flow solutions with the corresponding single-phase liquid solution and also provided computational equations for computing oil saturation as a function of pressure. Motivated by the theoretical ideas of Refs. 6 and 7, Al-Khalifah et al. and Serra et al., independently and concurrently, achieved two major results on the analysis of well-testing pressure data obtained under multiphase flow conditions. First, Al-Khalifah et al. and Serra et al. showed that one could compute effective permeability. as a function of pressure directly from the measured flowing wellbore pressure. Refs. 8 and 9 also showed that one could estimate effective permeabilities as a function of saturation or, if absolute permeability is either known or estimable, one can construct approximate relative permeability curves directly from drawdown values of the wellbore pressure. Second, Al-Khalifah et al." and Serra et al. showed that one can analyze data by using a semilog plot of the wellbore pressure-squared versus time. The analysis can be used to obtain estimates of the initial value of effective oil permeability, the values of effective permeability at the last measured values of flowing wellbore pressure and the mechanical skin factor. The results of Refs. 8 and 9 consider only drawdown analysis. These results were extended to the analysis of buildup data in Refs. 10 and 12. Serra et al. showed that a generalized form of superposition applies provided that the same pressure saturation relationship is used in all pseudo-pressure functions. The authors extended their drawdown method for estimating oil and gas relative permeabilities to pressure buildup data and showed that the mechanical skin factor can be computed by using the pressure-squared method. Regarding analysis based on a semilog plot of pressure-squared versus time, it should be noted that this analysis is applicable because the effective oil permeability can be approximated by a piecewise linear function of pressure. P. 571^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 18–21, 1992

Paper Number: SPE-24372-MS

... drillstem/well testing drillstem testing

**straight****line**dimensionless pressure drop horizontal well flow period time approximation upstream oil & gas Society of Petrohmn Engineers SPE 24372 Deviation of Horizontal Well Interference Testing From the Exponential Integral Solution Dariush...
Abstract

SPE Member Abstract Interference tests provide valuable information about reservoir characteristics such: areal average transmissivity, storativity, and degree of communication between wells, Due to the larger radius of influence and larger contact area of a horizontal well with the formation than its vertical counterpart, the transmissivity and storativity obtained from interference testing of horizontal wells would be much more representative of the formation than the ones obtained from interference testing of vertical wells. This paper provides the dimensionless pressure drop and dimensionless pressure derivative type curves for interference testing of horizontal wells and the appropriate equations to be used in conjunction with the type curves in order to determine transmissivity and storativity from field data. Solutions were also obtained for interference testing between horizontal and vertical wells. The deviation of this solution from the exponential integral solution is explained. Dimensionless time and dimensionless distance criteria is established for a particular set of dimensionless parameters to explain this deviation. Guidelines - given for interference test design. Introduction During the last 15 years, significant advances in drilling technology have made it possible to drill horizontally. A horizontal well, due to its large flow area, may be several times more productive than a vertical well draining the same volume. In a vertical well fractured by massive hydraulic fracturing, it is difficult to obtain an infinite conductivity fracture. In addition, fracture conductivity decreases with time. One reason is because of the problems associated with the proppant transport. The other reasons are due to the proppant embedment and also proppants not being able to withstand in-situ stresses of the rock; thus they break down, causing fracture conductivity to decrease with time. However, a horizontal wellbore offers a permanent infinite conductivity fluid flow path. Also, in reservoirs where the bottom water or gas cap renders fracturing difficult, a horizontal well offers an alternative to obtain high production rates without gas and water coning. The possibility of drilling horizontal wells should be evaluated for: –– Tight reservoirs, especially if vertical fractures are suspected –– Naturally fractured reservoirs containing vertical fractures. –– Unconventional low permeability gas reservoirs. –– Thin formations. –– Thicker zones of marginal permeability. –– Thin oil columns, especially when bottom water and or gascap is present. –– Chalk formations which contain natural fractures. –– Old reservoirs that no longer have adequate drivmechanisms, –– Producing reservoirs with extremely high dip angles. –– Secondary recovery operations (increased injection areaand improved sweep efficiency). –– Heavy oil reservoirs. –– Reduction of turbulence in gas reservoirs. –– Exploration and development of inaccessible locations. –– Areas where environmental concerns minimize number of surface locations. Western exploration activity in North Dakota has been focused on developing the Bakken shale formation reserves with horizontal drilling. The Bakken shale is estimated to have 10 billion barrels of oil which indicates its enormous economic importance and the role that horizontal drilling can play in exploiting these resources. The objectives behind drilling horizontal wells in the Bakken shale are to increase the effective drainage area and maximize recoverable reserves and to increase productivity by encountering more naturally occurring fractures. It is essential to know that efficient implementation of the horizontal well technology requires further understanding of the fluid flow behavior of these wells. Solution to the problem of interference testing of horizontal wells is a major step forward in achieving this objective. Multiple well interference tests provide information about reservoir characteristics such as areal average transmissivity, storativity, and degree of communication between wells. Due to the larger radius of influence and larger contact area of a horizontal well with the formation than its vertical counterpart, it is very reasonable to expect that the transmissivity and storativity obtained from interference testing of horizontal wells - much more representative of the formation than the ones obtained from interference testing of vertical wells. In this respect, interference testing of horizontal wells can be used as a valuable tool in reservoir characterization. The main objectives of previous researchers in the area of well testing of horizontal wells have been to determine the dimensionless pressure at the wellbore, PWD the existence of various flow regimes, the effect of horizontal well length and location on PWD pseudo skin factor, S, and productivity of horizontal wells. These studies have contributed a great deal to the understanding of the pressure behavior and performance of horizontal wells. However, they did not investigate interference testing of horizontal wells ad the corresponding type curves. This paper presents the interference testing of horizontal-to-horizontal and horizontal-to-vertical wells. P. 527^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 18–21, 1992

Paper Number: SPE-24355-MS

... the MBE with these excellent results on this basis, required Bc factor values were back calculated. These back calculated Bc factor values were then re-introduced into the MBE for all four samples with excellent results. equation machine learning

**straight****line**pvt data pvt measurement dry gas...
Abstract

Abstract A new and improved material balance method by which the original dry gas in place and the original condensate in place can be calculated for a retrograde gas condensate reservoir has been formulated. This new MBE is a result of theoretical research that is validated using experimental data. Ultimate validation of the new MBE can be made with field cases, and after a laboratory Bc procedure is established. The new MBE requires a modified PVT procedure to determine the condensate formation volume factor, Bc as introduced here. This variable is currently not in use in the industry and hence is not being measured in current PVT lab procedures. A basic assumption in the new MBE is that no reservoir condensate is produced. Additionally, the new MBE assumes normal pressure, volumetric conditions, and existence of the reservoir at the dew point, Modifications to accommodate water influx and rock and water compressibility were made to the basic equations after validation. Introduction In the recovery operation of a gas condensate reservoir system, the prediction of in-place resources and long term deliverability is of great importance in order that retrograde gas condensate reservoirs be produced efficiently and economically. It is the intent of this technical paper, therefore, to investigate and determine a method to simultaneously predict in-place dry gas and condensate volumes for gas-condensate reservoir systems. This will provide an alternative to the standard volumetric method used for estimating original gas and condensate in-place. The proposed volumetric energy relationship should then provide reservoir engineers with two independent estimates of original hydrocarbon content as well as allow for improved reliability in reserves estimation of gas condensate reservoirs. Most known gas condensate reservoirs are in the ranges of 3,000 to 6,000 psia and 200 to 400F. These ranges, together with wide variations in composition, provide a great variety of conditions for the physical behavior of condensate deposits, emphasizing the need for very meticulous engineering studies of each case in order to select the best modes of development and operation. One such method would require the independent estimation of original dry gas in place and original condensate in place as accommodated by the new MBE for retrograde gas condensate reservoirs. This new MBE will require a modified PVT procedure to produce experimentally determined values of the condensate formation volume factor, Bc per se as introduced here. This variable is currently not in use in the industry and, hence, is not being measured independently or in conjunction with current PVT lab procedures. Because no Bc measurements are as yet available, the scenario under which all parts of the new MBE were verified was that of using PVT simulated production data from four samples on a STB and SCF basis as a guide. In APPENDIX A is the validation of the new MBE using the PVT data from the four samples. Having satisfied the MBE with these excellent results on this basis, required Bc factor values were back calculated. These back calculated Bc factor values were then re-introduced into the MBE for all four samples with excellent results.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Low Permeability Reservoirs Symposium, April 15–17, 1991

Paper Number: SPE-21808-MS

... application transport equation pressure transient analysis reservoir drillstem testing drillstem/well testing laplacian space equation time constant anbarci specification analysis technique symposium exponential integral solution methane

**straight****line**boundary condition SPE SPE 21808...
Abstract

Abstract A simplified analysis technique to determine the desorption characteristics of coal seams using pressure transient analysis is presented. The proposed technique is based on formulation of presented. The proposed technique is based on formulation of single phase gas flow in coal seams with unsteady state sorption/diffusion phenomena in coal matrix and laminar flow in cleat system, The matrix geometry is represented by using spherical elements. A line source solution which defines the pressure distribution in an infinite-acting radial-cylindrical coal seam is used in the development of the proposed analysis technique. The simplified analysis presented in this paper is first tested against a previously developed closed form solution which describes the pressure transient behavior of coal seams. The proposed solution pressure transient behavior of coal seams. The proposed solution shows excellent agreement with this more rigorous solution, and its versatility is demonstrated through a simple analysis procedure which does not require the use of computationally procedure which does not require the use of computationally laborious functional groups. Furthermore, a pressure transient data generated by a coal seam degasification numerical model is analyzed successfully using the methodology presented here. As an example application of the proposed technique to the analysis of drawdown test data is also included. The proposed inverse solution procedure which is devised as a viable pressure transient analysis technique is applicable to coal seams and other unconventional gas reservoirs where adsorption/desorption phenomena are effective. The methodology introduced in this paper has the potential of providing the necessary tools that can be used in in-situ determination of the transport properties and the sorption characteristics of the coalbed methane reservoirs. Introduction Pressure transient analysis is a powerful tool for in-situ characterization of oil and gas reservoirs, and has similar potentials to be used in in-situ determination of transport and sorption characteristics of coal seams. However, existence of a natural fracture network and presence of time dependent sorption phenomena result in a relatively challenging problem of developing a pressure transient analysis technique specifically applicable to coalbed methane reservoirs. Because of the intricate nature of the flow of methane in coal seams the mathematical description of the phenomena is rather more demanding. Some researchers proposed the use of empirical models which are based on the simple mathematical descriptions of the physical phenomena observed. These empirical models are relatively practical but they lack the theoretical rigor required for accurate predictions. Single-porosity models applied to describe methane flow in coal seams employ partial differential equations valid for conventional reservoirs with some modifications such as inclusion of a pressure dependent source term or the modification of the accumulation term. These single-porosity models utilize equilibrium sorption models which do not account for the time dependence of the sorption/diffusion process in the micropore structure of the coal and this results in process in the micropore structure of the coal and this results in predictions of higher flow rates an/or higher reservoir predictions of higher flow rates an/or higher reservoir pressures. pressures. The time dependence of transport of methane in the micropores is taken into consideration in non-equilibrium sorption/diffusion models which are essentially obtained by modifications implemented to the conventional dual-porosity formulations. In dual-porosity approach the mathematical formulation is constructed by a set of coupled equations representing the two-stage flow of methane in the coal seam. While the pseudosteady-state non-equilibrium models are similar to the Warren and Root model of conventional dual-porosity reservoirs, unsteady-state sorption models are obtained by adaptation of the conventional dual-porosity model of De Swaan. The long term predictions of these two non-equilibrium sorption models do not differ significantly, but as concluded by Spencer et al. the early-time predictions obtained using pseudo-steady-state approach may not be accurate. King and Ertekin stated that the more rigorous unsteady-state approach should be taken into consideration in pressure transient analysis applications. Unlike conventional gas reservoirs coal seams, in addition to the gas stored in the pore volumes, also store methane gas as an adsorbed mon-molecular layer on coal grain surfaces. The volume of gas in adsorbed state is controlled by the sorption isotherm. Two different sorption isotherms that are commonly used in formulating the amount of adsorbed gas are Henry's and Langmuir's isotherms. While Henry's law predicts a linear isotherm, Langmuir's theory constructs a non-linear sorption isotherm which supports the mono-molecular layer adsorption presumption. presumption. P. 43

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Low Permeability Reservoirs Symposium, April 15–17, 1991

Paper Number: SPE-21831-MS

... upstream oil & gas

**straight****line**estimation graph application high-velocity effect drillstem/well testing ramey drillstem testing spe 21831 permeability rate testing procedure transient pressure analysis multiple rate test gas well society of petroleum engineers tech...
Abstract

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented. have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers. or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted loan abstract of not more than words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Publications Manager. SPE. P.O. Box 833836, Richardson, TX 75083-3836 U.S.A. Telex, 730989 SPEDAL. Abstract A method is presented to analyze variable rate tests in gas wells considering the effect of damage and high-velocity flow. This is a direct method that allows an estimation of the turbulent term coefficient D and the skin factor without using a trial and error procedure. The methods are applicable to procedure. The methods are applicable to infinite acting radial flow. The method considers a step-function approximation of the flow rate. It consists of two parts: a graph of is made from which we can estimate the formation conductivity kh and a graph of is made that yields an estimate of the parameter D and of the skin factor s. This parameter D and of the skin factor s. This method can also be applied to continuosly varying rate flow tests. Introduction It is often impractical or impossible to keep a constant rate long enough to complete a drawdown test. This being the case, multiple (variable) rate testing and the corresponding analysis techniques are applicable. A variable-rate test may range from one with an uncontrolled, variable rate, to one with a series of constant rates, to testing at constant bottom-hole pressure with a continuously changing flow rate. The literature presents several papers that deal with the analysis of variable rate tests. Gladfelter et al. discussed a method to handle production rate change effects in general 3 -rather than only production rate changes during pressure buildup. Winestock and Colpitts developed a variable rate test analysis method for the case of changes in rate not excessively rapid. This method essentially consists in a normalization of the drawdown data. plotting P(=Pi Pwr)divided by q(t). Another way to analyze variable rate tests could be to discretize the rate history in a series of constant rates and apply the principle of superposition to derive the principle of superposition to derive the interpretation equation. Other authors have proposed the use of the influence function to analyze variable rate tests. A check of the literature shows several ways to solve the problem of analysis of transient tests under the influence of high-velocity effects. P. 249

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Low Permeability Reservoirs Symposium, March 6–8, 1989

Paper Number: SPE-18992-MS

..., porosity, skin, wellbore permeability, porosity, skin, wellbore storage, half-fracture length, and distance to boundaries, without type curve matching. The method consists of obtaining characteristic points of intersection of

**straight****line**portions of the curves and their slope from a loglog plot...
Abstract

Abstract " Direct Type Curve Synthesis" is a novel, direct, quick and accurate approach for interpreting pressure transient tests. This approach uses loglog plots of the pressure derivative versus time to pressure derivative versus time to calculate reservoir parameters such as permeability, porosity, skin, wellbore permeability, porosity, skin, wellbore storage, half-fracture length, and distance to boundaries, without type curve matching. The method consists of obtaining characteristic points of intersection of straight line portions of the curves and their slope from a loglog plot of the pressure derivative as a function of time. pressure derivative as a function of time. These points and slopes are then used with special equations obtained from type-curve plots (i.e. loglog plots) of the dimensionless plots (i.e. loglog plots) of the dimensionless pressure derivative as a function of the pressure derivative as a function of the dimensionless time for the appropriate reservoir system. The new technique is illustrated in this paper for the case of pressure drawdown of vertically fractured wells. For the infinite-conductivity fracture case, pressure derivative plots reveal a dominant pressure derivative plots reveal a dominant flow regime, called here the "bi-radial" flow. This flow regime, which corresponds to the transient period between the infinite acting radial flow and linear flow regimes, is described by a straight line of slope -2/. Several simple equations, using the time of intersection of the three straight lines of slope -0.5 (linear flow), -2/ (bi-radial flow), and - 1 (finite acting radial flow), and the pressure derivative values at test time of one hour have been derived. These equations can be used to calculate the half-fracture length independently of the permeability. The straight line portion of the bi-radial flow regime can be used to calculate k and × f even if the early-time pressure points, which describe the linear flow regime, were not recorded or discarded because of mechanical problems or too few to draw with confidence problems or too few to draw with confidence the half-slope straight line. Introduction Tiab and Kumar presented a study on the behavior of the first and second time derivatives of the dimensionless pressure of a line source well in an infinite reservoir, and developed a technique for analyzing interference test data based on a loglog plot of the first derivative. In a separate paper they applied this function to generate type curves for detecting and locating two parallel sealing faults. Using the same approach, Tiab and Crichlow generated a large number of type-curves for interpreting the pressure transient behavior of a well located in various multiple-sealing-fault systems and inside closed rectangular reservoirs. Since then, several papers on the application of the P'wD -function to a variety of systems have P'wD -function to a variety of systems have been published. Tiab and Puthigai extended the application of this function to infinite conductivity and uniform-flux vertically fractured wells. Later, Bourdet et al. presented pressure derivative type-curves for presented pressure derivative type-curves for naturally fractured reservoirs. Wong, Harrington and Cinco-Ley investigated the characteristics of the pressure derivative curves for a well with a finite-conductivity fracture, wellbore storage and skin under bilinear flow conditions. P. 595

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 11–13, 1988

Paper Number: SPE-17517-MS

... upstream oil & gas total shale model porosity exponent log-log plot water saturation water resistivity exponent

**straight****line**log analysis arw shale group shale reservoir evaluation crossplot equation shaly formation spe 17517 resistivity porosity well logging SPE Society...
Abstract

Abstract New methods are presented for analyzing (1) laminated, (2) dispersed, and (3) total shale models. The techniques involve the use of log-log crossplots of effective porosity vs. true resistivity as affected by a shale group (Ash). Response equations for the above models have been written in such a way as to allow the generation of log-log plots from which values of water saturation can be readily calculated. Three key advantages of the proposed methods are: the value of m does not have to be assumed equal to 2.0; in fact, it can be determined from this analysis by trial and error, water resistivity does not have to be known in advance provided that the reservoir contains some water-bearing intervals, and all shaly intervals being analyzed can be displayed in a single log-log plot that includes porosity and water saturation even if shale volumes are changing continuously. An application is presented in detail. It is concluded that log-log crossplots provide powerful evaluation techniques for the analysis of laminated, dispersed and total shale models. These methods can be readily extended to the analysis of naturally fractured reservoirs. Introduction Pickett plots have been long recognized as very useful in log interpretation. In Pickett's method, a resistivity index, and water saturation, Sw, are calculated from, log-log plots of true (in some cases apparent) resistivity vs. porosity or the response of a porosity tool as shown on Fig. 1. Throughout the years some log analysts have indicated that one of the weaknesses of the Pickett plot is its inability to handle shaly formations. This paper demonstrates that laminar, dispersed and total shale models can be analyzed using log-log crossplots of porosity vs. true resistivity as affected by a shale group (Ash). This is illustrated in the schematic diagram shown on Fig. 2. Similar principles were discussed by Sanyal and Ellithorpe utilizing a shaly model developed by Patchett and Rausch. Excellent reviews of shaly formations analyses were presented by Worthington and Fertl. P. 365^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 11–13, 1988

Paper Number: SPE-17545-MS

... in a naturally fractured reservoir. In this situation a conventional log-log crossplot of delta p vs. time results in two parallel

**straight****lines**with slopes equal to 0.5. Separation between the two lines allows calculation of the storativity ratio, omega. The case of a well in a layered naturally fractured...
Abstract

Abstract Bottom hole buildup pressures on three Wyoming pumping wells have been determined based on liquid level in the annulus as determined from a computerized acoustic device. These buildup data correspond to a naturally fractured reservoir which produces oil, gas and water. Basic formulations and three case histories are presented: The case of a well with after flow effects where the buildup data are properly matched using type curves for dual-porosity systems with restricted (pseudo steady state) interporosity flow and the pressure derivative. The case of a stimulated well in a naturally fractured reservoir. In this situation a conventional log-log crossplot of delta p vs. time results in two parallel straight lines with slopes equal to 0.5. Separation between the two lines allows calculation of the storativity ratio, omega. The case of a well in a layered naturally fractured reservoir with variable afterflow effects. In this case a log-log plot of delta p vs. time shows two parallel straight lines with slopes equal to 1.0. A good match of the data is obtained with a dual-porosity model and the pressure derivative starting at the second 1.0 slope straight line. Acquisition of the raw data, conversion into bottom hole buildup pressures, and analysis utilizing dual-porosity models are presented in detail. It is concluded that pumping wells in naturally fractured reservoirs can be properly evaluated when all phases flowing are taken into account. The same procedure and formulations presented in this work can be utilized for analysis of conventional single-porosity reservoirs by making Warren and Root's omega equal to 1.0. DESCRIPTION OF EQUIPMENT The Automatic Acoustic Bottomhole Pressure system determines the depth to the liquid level, and measures and records the casinghead pressure in a well, unattended. The frequency of data point collection may be specified by the operator. The equipment consists of an electronic package, a wellhead assembly, interconnecting cables, a 12 volt battery, and a small gas supply container. P. 577^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE/DOE Joint Symposium on Low Permeability Reservoirs, May 18–19, 1987

Paper Number: SPE-16394-MS

... with or without measured wellbore flow rate, taking the additional wellbore volume into account. A diagnostic method is also presented for the determination of the correct logarithmic convolution

**straight****line**. It is shown that a simple deconvolution is possible when the wellbore flow rate increases (drawdown...
Abstract

Abstract The use of simultaneously measured downhole pressure and flow rate may not completely eliminate wellbore storage or afterflow effects when there is considerable additional wellbore volume below the pressure gauge and flowmeter. This paper presents new interpretation methods with or without measured wellbore flow rate, taking the additional wellbore volume into account. A diagnostic method is also presented for the determination of the correct logarithmic convolution straight line. It is shown that a simple deconvolution is possible when the wellbore flow rate increases (drawdown) or decreases (buildup) exponentially. For partially penetrated wells, it is also shown that the vertical permeability can be obtained from either the onset of the semilog straight line if it evolves or the simultaneous use of the deconvolution and the convolution associated with non-linear estimation. New solutions are presented for infinite-conductivity vertically fractured wells with wellbore storage (including the fracture storage, which may be important even if the flow rate is measured at the well bore) and skin effects. Two examples are presented to demonstrate the use of the new interpretation methods for both drawdown and buildup tests. Introduction Analytical solutions with wellbore storage, which includes exponential wellbore flow rate, are important for providing a better understanding of the behavior of wells, particularly at early times even if the downhole flow rate is measured. The combined effects of the volume below the flowmeter including rat holes and the volume of fractures (particularly high volume fractures in tight formations) on the well bore pressure have to be considered in the interpretation of well tests. Moreover, it may not be possible or practical to measure downhole flow rate along with pressure for every well. Thus, obtaining analytical solutions with wellbore storage is still important for well testing. The purpose of this work is to present new techniques for the interpretation of simultaneously measured downhole pressure and flow rate when there is a significant wellbore volume below the tool. It is also the purpose of this work to obtain new solutions with wellbore storage effects and to explore their application to the interpretation of a few well test examples.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, May 19–22, 1985

Paper Number: SPE-13898-MS

... used ratetime decline relationship: (1) Arps treated the equation as empirical, but noted that the exponent can be influenced by the reservoir flow conditions. The value of b determines the degree of curvature of the semi-log decline, from a

**straight****line**(exponential decline) at be = 0.0...
Abstract

SPE Member Abstract Standard decline curve equations can by used outside their normal range of application to give accurate and theoretically valid projections of tight gas well performance. This approach is preferable to the use of the reciprocal square-root of time as a preferable to the use of the reciprocal square-root of time as a tight gas well "type curve". Introduction Low permeability fractured gas wells, when produced without constraint, typically exhibit a characteristic decline curve shape: a steep initial decline followed by a long well life at low producing rates relative to the initial potential. The common producing rates relative to the initial potential. The common methods of forecasting production from these wells vary in complexity and in the amount of detail required. Decline curves and mathematical curve fitting require only monthly production data; no knowledge of reservoir properties is necessary. The problem with these techniques it that, especially at early times, problem with these techniques it that, especially at early times, virtually any curve can give a reasonable fit to monthly data. On the other hand, log-log type curves and mathematical simulation require knowledge of the fracture and reservoir geometries as well as a detailed history of flowing rates and pressures. As a practical matter, this kind of detail is often unavailable practical matter, this kind of detail is often unavailable The utility of decline curves can be enhanced by recognizing the influence of the physics of reservoir fluid flow on the resulting semi-log plot. The characteristic tight gas well decline shape is a predictable result of the flow from a low permeability reservoir into a more conductive fracture. The Arps Equation The Arps equation is the most commonly used ratetime decline relationship: (1) Arps treated the equation as empirical, but noted that the exponent can be influenced by the reservoir flow conditions. The value of b determines the degree of curvature of the semi-log decline, from a straight line (exponential decline) at be = 0.0 to increasing curvature at higher values of b. He stated that the value of b varies between zero and 1.0, with no discussion of the possibility of b greater than 1. There is no theoretical basis for limiting the exponent to values less than 1. Using numerical simulations, Gentry and McCray showed that reservoir heterogeneity (e.g., layered reservoirs) can result in a hyperbolic exponent exceeding 1. A single decline equation with b less than 1 cannot approximate a typical tight gas decline shape as shown in Figure 1. Bailey used mathematical curve fitting to determine the "best fit" hyperbolic equation for wells in three tight has basins. For his representative group of fractured Wattenberg Field wells, the optimized exponent exceeds 1 in all but a few cases, and ranges as high as 3.5 in one case. In practice, many engineers avoid the use of hyperbolic decline curves. Some use a favorite French curve to approximate tight gas well declines. Another common approach is to assume a decline shape composed of a series of straight line segments: for example, 50% exponential decline for two years, then 20% decline for three years, followed by 8% decline to an economic limit. While these methods may give satisfactory results for a group of similar wells, one must ask: Why do these wells follow a decline shape which is apparently arbitrary? The Inverse Square-Root of Time Equation In search of an equation which explains the influence of low permeability and flow geometry on the shape of the decline curve, permeability and flow geometry on the shape of the decline curve, some recent papers and articles have proposed the following equations for use with tight gas well declines: (2) The argument for this equation is based on the physics of linear flow and on observations from log-log type curves for fractured wells. P. 491

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 21–23, 1984

Paper Number: SPE-12916-MS

... calculation spe 12916 condensate system equation example calculation molar distribution mole fraction heptanes-plus fraction fraction upstream oil & gas

**straight****line**SPE Society of Petrolet.m Engineers of AIME SPE 12916 An Accurate Method for Extending the Analysis of C7 + by T.H. Ahmed, G.V...
Abstract

Members SPE-AIME Abstract The main objective of this paper is to present an accurate method for extending the molar distribution of the heptanes-plus fraction. The method originated from studying the extended analysis of ten natural gas-condensate mixtures. A FORTRAN subroutine to perform this computation is presented, along with a graphical form of the proposed method. Introduction Equations of state have generally been recognized by the petroleum industry as important analytic expressions used in describing the thermodynamics and behavior of complex hydrocarbon mixtures. An important consideration in using equations of state (EOS) is the difficulty in characterizing the heavy fractions of hydrocarbon mixtures. These fractions, usually lumped as heptanes-plus (C7+), are difficult to define without an extended molar analysis of the plus-fraction. A conventional laboratory hydrocarbon plus-fraction. A conventional laboratory hydrocarbon analysis of a gas-condensate system usually reports the composition of the system (methane through heptanes-plus), molecular weight and density of the plus fraction. Several authors have indicated the well necessity of splitting the C7+ fraction into a number of components for accurate retrograde calculations. Firoozabadi and Katz demonstrated the use of the extended analysis of C7+ with the Peng-Robinson equation of state to accurately predict the behavior of crude oil and gas condensate mixtures. Whitson, in a pioneering paper, noted that lighter systems such as condensate exhibit exponential molar distributions while heavier systems show a left skewed distribution. The author proposed that a probability function (three parameter gamma distribution) can be used to characterize both types of behavior by adjusting a single parameter in the distribution function. Whitson demonstrates excellent agreement between data and his models calculation of the extended analysis given by Hoffman. This paper presents a simple and practical method for extending the molar distribution of heptanes-plus fraction from the normally available physical measurements of C7+, i.e. molecular weight and physical measurements of C7+, i.e. molecular weight and density. To establish the validity of the procedure two types of comparisons were used through-out this study. One is between two sets of calculated results, obtained from the proposed model and other models. The second comparison is between experimental data with extended analysis of C7+ and predicted molar distribution resulting from the method. The Peng-Robinson Equation of State The details of the development of the Peng-Robinson equation of state are given elsewhere. A Peng-Robinson equation of state are given elsewhere. A summary of the equation is presented here for convenience. The equation has the form .........................(1) p. 223

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 22–25, 1983

Paper Number: SPE-11830-MS

... line source pressure drawdown boundary slanted fault equation thickness

**straight****line**drillstem/well testing different dimensionless distance slanted flow barrier pressure transient testing pressure buildup vertical fault reservoir estimation spe 11830 drillstem testing pressure...
Abstract

Abstract The analytical solution of the wellbore pressure in a reservoir which is located near a slanted fault were derived using the method of images and by applying the principle of superposition to the Kelvin's point source solution. The solutions show that the inclination of the flow barrier causes additional pressure drop beyond what is usually considered in the concept of a single mirror image well. The extra pressure drop causes gradual changes on the slope of semi-log plots of pressure versus time. In many cases the behavior resembles that of wells in completely bounded systems. Using the general solution presented in graphical forms, one may estimate the distance to the fault. Introduction During the past thirty years, in the field of pressure transient analysis, a great deal of effort has been focused on the conditions around or within the wellbore to estimate the effects of wellbore storage 1,2 , skin 1–4 , phase separation in tubing, and other well conditions 5,6 . All of this progress has been gained by interpreting the early transient data. Some investigators have developed methods to analyze the middle time data to obtain reservoir and fluid characteristics, such as: transmissivity 7 , storativity 1,2 , and average reservoir pressure 8,9 . The late data, especially when it reflects the boundary characteristics of a reservoir has not been fully researched. Simple geometrical models have been proposed to handle the late time data and the boundary 8. In all of these models, the reservoir is assumed to be bounded in all directions. For cases where limited boundaries affect the flow, the discussion has been focused on linear single or multiple faults. The effect of linear fluid barriers on pressure transient has been the subject of many studies in the past 12,22 . In all the previous work, the boundaries were assumed to be vertical and perpendicular to top and bottom of the formation. The purpose of this study was to find an analytical solution for the effect of a slanted - linear - no - flow boundary on pressure buildup and pressure drawdown behavior of a single well in an otherwise infinite reservoir. Description of the Problem The general assumptions for the analysis of the pressure transient response of a well near an inclined fault are as follows: The well produces at a constant flows rate in an isotropic, homogeneous reservoir of constant thickness; Porosity and permeability are independent of pressure and temperature; The reservoir contains a slightly compressible fluid of constant viscosity and compressibility; The pressure gradients are assumed to be small and the gravity effects are negligible in the reservoir. It is further assumed that the well may be represented by a line source or sink. 13 The side view of the described system is shown in Fig. 1. The pay zone thickness is â??h w â?¿ the horizontal distance from bottom of fault to the well is â??bâ?¿, and the angle between the fault and the course of the well is assumed to be â??aâ?¿. A cylindrical coordinate system with its origin at the intersection of the extension of the well course and the fault may be used for description of any point in the reservoir. For the development of equations, a more suitable cylindrical coordinate system has been used with its origin located at point â??Bâ?¿. In this new system a point â??Mâ?¿ in the reservoir can be defined by three coordinate of r, Ï?, and Zâ? 2 M .

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Rocky Mountain Regional Meeting, May 22–25, 1983

Paper Number: SPE-11833-MS

... equation type curve

**straight****line**drillstem testing semi log application linear impermeable barrier linear barrier buildup test graph semi log**straight****line**detection pressure data pressure drop semilog**straight****line**reference 12 upstream oil & gas spe 11833 drillstem/well...
Abstract

Abstract This work presents a new simple method to detect a linear impermeable barrier by analysis of transient pressure data. This technique is based on the desuperposition method (negative superposition) discussed by some authors and considers the calculation the pressure change caused by the presence of the barrier. The pressure change is analyzed to estimate the distance between the well and the barrier by using the type curve matching technique. Type curves are provided for both drawdown and build tests. The advantage of the technique presented in this work is that pressure data can be analyzed even if the second semilog straight line, whose slope is twice the slope of the first semilog straight line, is not reached. Examples of application are discussed for illustration. Introduction Detection of linear barriers (sealing faults, discontinuities, etc.) by transient pressure analysis has been discussed by pressure analysis has been discussed by several authors in the literature. Horner was first to point out that pressure buildup analysis can be used to pressure buildup analysis can be used to detect the presence of a noflow boundary; he showed that for this situation pressure build up data exhibit two straight line portions on a graph of p ws versus log (tp + t)/ t, the second straight line portion having a slope twice the slope of the first straight line portion. Further discussion on the use of portion. Further discussion on the use of pressure buildup tests for fluid flow barrier pressure buildup tests for fluid flow barrier detection have been presented by Dolan et al, Davis and Hawkins, Standing, Gray, Matthews and Russell, Earlougher and Earlougher and Kazemi. It has been shown that the time of intersection of the twc semilog straight lines provides information to estimate the distance to the barrier. Gray has also shown that the difference between the pressure data and the extrapolation of the first semilog straight line also provides a mean to determine the distance to the barrier even if the second semilog straight line is not reached in the test. Gray and Earlougher and Kazemi pointed out that producing time before a pressure buildup test plays an important role in detecting a sealing fault. It has been mentioned that a small producing time can caused the pressure to deviate downwards from the first semilog straight line and in some instances the doubling slope behavior is not observed being the method of analysis based on the intersection of the two semilog straight lines not applicable. Russell and Pinson have shown that the doubling semilog slope behavior of a well near a barrier is also observed in two flow rate tests. Unfortunately, this type of behavior can also be exhibited by wells in other situations (i.e. wellbore storage effects, fractured wells and naturally fractured reservoirs. The type curve matching technique has been suggested to determine if the doubling semilog slope behavior is caused by the presence of a barrier. The objective of the present work is to extend the method suggested by Gray to detect and determine the location of a barrier by calculating the pressure change caused by the barrier through the use of desuperposition and then applying the type curve matching method to estimate the distance between the well and the barrier. The technique presented here does not require the second semilog straight line to be reached and yields results with a high confidence level because every single pressure point beyond the first semilog pressure point beyond the first semilog straight line is used. P. 237

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Symposium on Low Permeability Gas Reservoirs, May 20–22, 1979

Paper Number: SPE-7941-MS

... pressure transient data plug buildup test Cotton Valley pressure bomb Upstream Oil & Gas reservoir pressure formation flow capacity determination fracture kh determination Cotton Valley well pressure transient test Drillstem Testing flow rate valley well storage effect

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

Abstract Performance analysis of low permeability gas wells requires an accurate knowledge of formation flow capacity (kh) and initial static reservoir pressure (pi). These parameters are used in calculating original gas-in-place, predicting well rates and reserves, and assessing economics. In addition, they are key design and evaluation work. Formation flow capacity and initial reservoir pressure are best determined from prefracturing pressure transient tests; however, conventional testing techniques have proven inadequate in low-permeability formations. Amoco's experience in prefracturing pressure transient testing of the 0.001 to 0.01 md (0.001 to 0.01 × 10(-3) m) gas sands in the Cotton Valley Formation of East Texas has led to the establishment of the following three-step procedure to enhance accurate prefracturing pressure transient data collection: Preflow test for static pressure determination(pi). Pressure drawdown test to determine producing characteristics Pressure buildup test to determine formation flow capacity (kh). Severe wellbore storage effects, which are characteristic of low-permeability formations, have made it necessary to utilize some method of downhole shutin in Cotton Valley to obtain the required pressure data within a reasonable time. Though methods exist to analyze pressure transient data with storage effects, it has been found that a more accurate analysis is possible when the storage effects have been minimized. possible when the storage effects have been minimized. Increased costs resulting from the use of downhole shutin devices may be partially offset by carefully planning the test procedure. planning the test procedure. Actual field results along with predicted results from a 1-D radial, single phase gas reservoir simulator illustrate the effectiveness of the outlined technique and the need for accurate and reliable data. Introduction Low permeability gas wells must be stimulated with MHF treatments to be commercial. Since it is difficult to determine reservoir parameters after fracturing, reliable "prefracturing" pressure transient data is essential to the evaluation of a low permeability gas reservoir. This testing is needed to determine formation flow capacity (kh) and initial static reservoir pressure (pi) which are required for proper MHF design as well as rate, reserve and gas-in-place determination. One of the low permeability gas plays that Amoco is currently developing is the Cotton Valley Sands of East Texas. Amoco's experience in prefracturing pressure transient testing of these sands has been pressure transient testing of these sands has been generally successful when proper test design has been combined with the necessary mechanical technology. This study presents certain aspects of Amoco's prefracturing pressure transient testing experience prefracturing pressure transient testing experience in the Cotton Valley. It covers the objectives and reasons for testing, test design, mechanical aspects of testing, and data analysis. Computer simulated and actual field examples are included for illustration. An additional purpose of this study is to present a systematic thought process necessary for present a systematic thought process necessary for adequate test design data analysis in other similar plays. NEED FOR PREFRACTURING TESTING The reasons for running prefracturing pressure transient tests in low permeability gas plays are similar to the reasons for running them in any gas reservoir. They include a need for accurate measurements or estimates of initial reservoir pressure, formation flow capacity, and relative condition of the near wellbore area (skin zone). The primary differences between a pressure transient test in a low permeability gas well and a more conventional pressure transient test are the difficulties in pressure transient test are the difficulties in obtaining reliable data and its analysis. p. 289