SUMMARY This paper presents a method of determining kg/ko, oil relative permeability, kro, and gas relative permeability krg, using oil and gas rate-time performance data from individual wells and from a total field. Advanced decline curve analysis is used to obtain original oil in place, N, and thus saturation; the Δp2 form of an oil inflow performance equation is used to determine kro below the bubble point pressure. The procedure was used on production data from several wells in a North Sea naturally fractured limestone volatile oil field. Results indicate the calculated oil and gas relative permeabi1ity curves differ from laboratory and correlation calculated curves. By analyzing the oil and gas relative permeability curves of each of the seven wells in the field, it was found that the degree of natural fracturing of a specific well influences the position of the oil and gas relative permeability curves. The results expressed as kg/ko curves appear to be consistent with the field case history findings of Arps for limestone reservoirs – i.e., as the degree of fracturing increases, the kg/ko curves become more unfavorable with respect to oil recovery. Initial pressure surveys on-each well determine its degree of fracturing while a later field-wide pressure survey confirms the oil-in-place calculated for each well using rate-time decline curve analysis. Pressure-time data to make these calculations is seldom available for all wells in a field or, when available, is much less frequent than rate-time data. In contrast, the principal calculation methods shown in this paper use rate-time data, thus taking advantage of the most frequently collected and the most widely available information.

This paper examines the behavior of heavy oil reservoirs developed with horizontal and multilateral wells. Advanced decline curve analyses were used to characterize flow regimes and estimate the time to pseudosteady-state. Reservoir and well parameters such as the OOIP, Arps "b" exponent, decline rate, reserves, permeability and well productivity indices were also determined. Example analyses are presented for single, dual and triple lateral wells from heavy oil fields located in Venezuela and Canada. All wells exhibit a characteristic extended transient linear flow regime followed by an exponential decline. Similar results were obtained whether the analyses were performed on single, dual or triple lateral wells. Interference between laterals was not observed. Introduction The application of horizontal and multilateral wells is gaining momentum worldwide due to their ability to drain reservoirs more effectively. This advantage is even more pronounced in tight gas or heavy oil reservoirs where low mobility is responsible for long transient flow periods. The relatively new application of these exotic well geometries to such reservoirs provides a challenge in the area of production forecasting because traditional methods and equations were developed based on flow to a vertical well. This paper demonstrates the use of rate-time performance analyses on heavy oil reservoirs developed with horizontal and multilateral wells. Well productivity indices (PI) were calculated from the transient production period by matching the rate-time data to type curves. Permeability-thickness or the equivalent skin factor was calculated based on this PI. Hydrocarbon volume connected to the well, the Arps "b" exponent and the decline rate were calculated from the pseudosteady-state producing period. The decline curve results were also verified using a reservoir simulation flow model. Decline curve analysis was performed on the rate versus time values generated by the flow model to confirm that the model had similar transient and depletion behavior as the actual performance data. Decline Curve Analysis Concepts When a well is first opened to flow, it produces under transient flow conditions. It will remain under this condition until the production from the well affects the entire drainage area. This flow condition is referred to as pseudosteady-state or boundary dominated flow. Transient rate and pressure data are used to calculate permeability-thickness and skin, whereas pseudosteady-state data are used to determine connected OOIP. Constant well pressure solutions used to predict declining production rates as a function of time were first published in 1933 by Moore, Schilthius, and Hurst.[1] Results were presented for infinite, slightly compressible, single phase plane radial systems. The results were presented in graphical form in terms of dimensionless flow rate and dimensionless time as shown in Figure 1.

The overall structure of the PL19–3 field, which is located in Bohai Bay, is an asymmetrical wrench anticline that formed by a combination of differential subsidence, strike-slip faulting, and normal faulting. Faults form the main trapping components for the individual hydrocarbon-bearing fault blocks. The reservoir sands of the deeper Guantao formation are dominantly braided fluvial sandstones, while the shallower Minghuazhen formations are dominantly meandering fluvial sands. Fault blocks penetrated by appraisal or development wells tested oil with viscosities ranging from 10 to 380 cp. Multiple vertically separate pressure systems exist in each fault block. The purpose of this paper is to present a case history that demonstrates multiple methods used to calculate permeability for input into a fine grid geologic model and ultimately a flow simulation model. Special core analysis and facies description was used to generate facies-based permeability versus porosity relationships that can be used with log-calculated variables. Permeability log curves were calculated for each well in the field, and then input them into a geologic flow model. Pressure transient analysis was used to condition the facies based porosity versus permeability relationships to ensure that they matched actual well performance. The permeability logs for all of the producing and injection wells were input into a flow simulation model. Comparisons of model predicted versus actual performance show close agreement. A good permeability estimate ultimately results in reasonable values of transmissibility, original oil in place, and sand connectivity. Advanced decline curve analysis was used as an additional method for calculation of kh, skin, and original oil in place (OOIP) and to validate model predicted performance matched actual transient, depletion, and waterflood performance behavior. In addition because this field contains reservoirs with unconsolidated sands the effect of stress dependent permeability was studied. Introduction The purpose of this paper was to show how all data including core, PVT, well logs, pressure transient tests, and well performance can be used to obtain a valid well log derived porosity-permeability relationship. That relationship then can be used to provide sand sequence variograms of permeability from well logs. If the relationship is valid then the model transmissibility and volumes should give forecasts that match actual performance within an acceptable range. An accurate estimate of permeability is one of the most important requirements for reservoir characterization. Permeability has a large influence on reservoir connectivity, recoverable reserves, decline behavior, individual well productivities, and waterflood behavior. To generate reliable production forecasts for reserves, budgets, well location placement, and development strategies, valid values of permeability are input into a reservoir flow model. The three methods used to ensure valid flow model permeability input are core analysis, Pressure Transient (PT) analysis, and Advanced Decline Curve (ADC) analysis. All three methods should give similar values of permeability. In the following sections, the methods used to determine permeability and the engineering evaluation of determined permeability are presented in detail. First, the procedure employed for establishing the relationship between core-based porosity and permeability was described. Second, the effect of stress dependency in permeability on well production behavior was evaluated. If the impact of stress dependency in permeability on well production behavior is insignificant, then there is no need to consider the influence of stress on permeability determination in PT, ADC analyses, and reservoir flow simulation. Third, the method and results of pressure transient analysis for determining permeability are described. Fourth, the detailed description and results of ADC analysis to determine permeability are presented. Fifth, verification of permeability determined by the methods presented in the paper was performed by full-field reservoir flow simulation. Finally, conclusions from this study are provided. Results and Discussion Core Based Porosity-Permeability Relationship. Conventional cores were cut from three appraisal wells. In addition, percussion sidewall cores were taken in each of the eight wells drilled during field discovery and appraisal.