Rate Integral Derivative

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R.a. Archer - One of the best experts on this subject based on the ideXlab platform.

  • Diagnosis and Quantification of Stress-Sensitive Reservoir Behaviour from Pressure and Rate Transient Data
    ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, 2012
    Co-Authors: R.a. Archer
    Abstract:

    Classical analytical and numerical techniques for simulation of fluid flow in petroleum reservoirs typically assume permeability is independent of pressure. In naturally fractured and low permeability systems the reservoir permeability may depend on the stress state of the reservoir which means the diffusivity equation that governs single phase flow in the reservoir becomes nonlinear. Stress-sensitive behaviour is particularly relevant to the development of tight gas and other unconventional resources. This work develops a set of tools to diagnose and quantify stress sensitivity through analysis of transient pressure or flow Rate data. The work builds on analytical solutions for radial flow in a stress-sensitive medium presented by Friedel and Voigt (SPE 122768, 2009), and for the linear flow case presented by Archer (AFMC 17, 2010). The radial flow solution uses the Boltzmann transform whereas the linear flow solution is based on the use of the Cole-Hopf transform. High resolution numerical solutions are also used to complement these analytical solutions. Where appropriate pseudo-pressures are used to take account of the pressure dependence of gas properties on pressure. This paper considers both transient pressure and Rate solutions and develops a range of type curve formats to demonstRate how production from stress-sensitive reservoirs differs from conventional reservoirs when plotted in traditional well test format (log-log plot of pressure and pressure Derivative), as a p/z plot (for the gas case), as a Rate versus cumulative plot, and as “Blasingame” type curves in the including the normalised Rate, Rate-Integral, and Rate-Integral-Derivative formats. This suite of tools can be used in a diagnostic manner to identify whether stress-sensitive behaviour is occurring, to quantify the errors that may be made in permeability estimates if stress-sensitive behaviour is ignored, and to estimate the impact of stress-sensitivity on ultimate recovery from a well.

An-zhao Ji - One of the best experts on this subject based on the ideXlab platform.

  • Rate Decline Behavior of Selectively Completed Horizontal Wells in Naturally Fractured Oil Reservoirs
    Mathematical Problems in Engineering, 2019
    Co-Authors: You-jie Xu, Long-xin Li, An-zhao Ji
    Abstract:

    Selectively completed horizontal wells (SCHWs) can significantly reduce cost of completing wells and delay water breakthrough and prevent wellbore collapse in weak formations. Thus, SCHWs have been widely used in petroleum development industry. SCHWs can shorten the effective length of horizontal wells and thus have a vital effect on production. It is significant for SCHWs to study their Rate decline and flux distribution in naturally fractured reservoirs. In this paper, by employing motion equation, state equation, and mass conservation equation, three-dimension seepage differential equation is established and corresponding analytical solution is obtained by Laplace transform and finite cosine Fourier transform. According to the relationship of constant production and wellbore pressure in Laplace domain, dimensionless Rate solution is gotten under constant wellbore pressure in Laplace domain. Dimensionless pressure and pressure derivate curves and Rate decline curves are drawn in log-log plot and seven flow regimes are identified by Stehfest numerical inversion. We compared the simplified results of this paper with the results calculated by Saphir for horizontal wells in naturally fractured reservoirs. The results showed excellent agreement. Some parameters, such as outer boundary radius, storativity ratio, cross-flow coefficient, number and length of open segments, can obviously affect the Rate Integral and Rate Integral Derivative log-log curves of the SCHWs. The proposed model in this paper can help better understand the flow regime characteristics of the SCHWs and provide more accuRate Rate decline analysis of the SCHWs data to evaluate formation.

You-jie Xu - One of the best experts on this subject based on the ideXlab platform.

  • Rate Decline Behavior of Selectively Completed Horizontal Wells in Naturally Fractured Oil Reservoirs
    Mathematical Problems in Engineering, 2019
    Co-Authors: You-jie Xu, Long-xin Li, An-zhao Ji
    Abstract:

    Selectively completed horizontal wells (SCHWs) can significantly reduce cost of completing wells and delay water breakthrough and prevent wellbore collapse in weak formations. Thus, SCHWs have been widely used in petroleum development industry. SCHWs can shorten the effective length of horizontal wells and thus have a vital effect on production. It is significant for SCHWs to study their Rate decline and flux distribution in naturally fractured reservoirs. In this paper, by employing motion equation, state equation, and mass conservation equation, three-dimension seepage differential equation is established and corresponding analytical solution is obtained by Laplace transform and finite cosine Fourier transform. According to the relationship of constant production and wellbore pressure in Laplace domain, dimensionless Rate solution is gotten under constant wellbore pressure in Laplace domain. Dimensionless pressure and pressure derivate curves and Rate decline curves are drawn in log-log plot and seven flow regimes are identified by Stehfest numerical inversion. We compared the simplified results of this paper with the results calculated by Saphir for horizontal wells in naturally fractured reservoirs. The results showed excellent agreement. Some parameters, such as outer boundary radius, storativity ratio, cross-flow coefficient, number and length of open segments, can obviously affect the Rate Integral and Rate Integral Derivative log-log curves of the SCHWs. The proposed model in this paper can help better understand the flow regime characteristics of the SCHWs and provide more accuRate Rate decline analysis of the SCHWs data to evaluate formation.

Long-xin Li - One of the best experts on this subject based on the ideXlab platform.

  • Rate Decline Behavior of Selectively Completed Horizontal Wells in Naturally Fractured Oil Reservoirs
    Mathematical Problems in Engineering, 2019
    Co-Authors: You-jie Xu, Long-xin Li, An-zhao Ji
    Abstract:

    Selectively completed horizontal wells (SCHWs) can significantly reduce cost of completing wells and delay water breakthrough and prevent wellbore collapse in weak formations. Thus, SCHWs have been widely used in petroleum development industry. SCHWs can shorten the effective length of horizontal wells and thus have a vital effect on production. It is significant for SCHWs to study their Rate decline and flux distribution in naturally fractured reservoirs. In this paper, by employing motion equation, state equation, and mass conservation equation, three-dimension seepage differential equation is established and corresponding analytical solution is obtained by Laplace transform and finite cosine Fourier transform. According to the relationship of constant production and wellbore pressure in Laplace domain, dimensionless Rate solution is gotten under constant wellbore pressure in Laplace domain. Dimensionless pressure and pressure derivate curves and Rate decline curves are drawn in log-log plot and seven flow regimes are identified by Stehfest numerical inversion. We compared the simplified results of this paper with the results calculated by Saphir for horizontal wells in naturally fractured reservoirs. The results showed excellent agreement. Some parameters, such as outer boundary radius, storativity ratio, cross-flow coefficient, number and length of open segments, can obviously affect the Rate Integral and Rate Integral Derivative log-log curves of the SCHWs. The proposed model in this paper can help better understand the flow regime characteristics of the SCHWs and provide more accuRate Rate decline analysis of the SCHWs data to evaluate formation.

Craig Emmitt Roco - One of the best experts on this subject based on the ideXlab platform.

  • Reservoir characterization of the Upper and Lower Repetto reservoirs of the Santa Clara field-federal waters, offshore California
    2020
    Co-Authors: Craig Emmitt Roco
    Abstract:

    This thesis presents the characterization of the Upper and Lower Repetto reservoirs of the Santa Clara field, which lies seven miles offshore of Ventura County, California. The approaches that we adopted for this reservoir characterization are based on the analysis of field production data. These reservoir characterization approaches include: The application of the Fetkovich/McCray decline type curve to estimate original oil-in-place, drainage area, flow capacity, and a skin factor for each well. This approach requires converting the field production data for each well to dimensionless decline flowRate, dimensionless Rate Integral, and dimensionless Rate Integral-Derivative functions. These functions are then simultaneously plotted against dimensionless decline time so that a unique match of these plots can be obtained using the Fetkovich/McCray decline type curve (in this research, data conversion and type curve matching are performed using a software package). The analysis of plots of reciprocal production Rate versus material balance time to estimate "movable" or recoverable oil reserves. This new material balance approach is used in conjunction with a semi-analytical method of graphical analysis (pressure drop normalized Rate versus cumulative oil production), which also provides estimates of recoverable oil reserves. Together, these plotting techniques provide good estimates of the estimated ultimate recovery for each well. Our approaches for the analysis of field production data allow us to provide recovery factors for each well (using our estimates of original oil-in-place and estimated ultimate recovery). Furthermore, we were able to geneRate maps of original oil-in-place, estimated ultimate recovery, flow capacity, and permeability for both the Upper and Lower Repetto reservoirs.