Boundary-dominated Flow Period Research Articles

Well test analysis of finite-conductivity fractured wells producing at constant bottomhole pressure

Conventional pressure buildup and drawdown tests are generally influenced by wellbore storage effects. These effects may dominate the early well test data prohibiting good formation characterization of the area surrounding the wellbore. One of the advantages of constant bottomhole pressure tests is that they are immune to these adverse effects. Constant pressure test data can be used with confidence to provide good description of the formation around the wellbore in addition to full-scale reservoir interpretation. This paper presents an analysis technique for finite conductivity fractured wells producing at constant bottomhole pressure from closed reservoirs. The reciprocal rate and reciprocal rate derivative data are directly used to determine the fracture and reservoir parameters without recoursing to type curve matching. All the dominant flow regimes such as early time bilinear, pseudo-radial, and boundary-dominated flow are analyzed using log–log plots of the reciprocal rate and reciprocal rate derivative data. The slopes of the straight lines of the different flow regimes are very distinct and are used to determine various reservoir and fracture parameters such as fracture conductivity, reservoir permeability, skin factor, drainage area, and shape factor. Furthermore, a 0.65 slope straight line equation describing the transition between the infinite acting pseudo-radial and the boundary-dominated flow period in rectangular systems is presented. It is shown in the paper that this straight line can be used to either determine the formation permeability in the absence of the pseudo-radial flow, or calculate the drainage area. It is also illustrated that the intersection points of the various straight lines can be used to verify the accuracy of the results obtained from the different flow regimes. A systematic step-by-step procedure illustrating the methodology of the proposed technique for the analysis of bilinear, pseudo-radial, and boundary-dominated flow regimes is described. The applicability of the method is illustrated using two simulated cases.

Decline-Curve Analysis Considering Nonlaminar Flow in Dual-Porosity Systems

Summary Most of the theoretical work on decline-curve analysis with non-laminar flow in the reservoir considers either a dry gas or liquid flow in a homogeneous system. The purpose of this work is to analyze decline curves considering the non-Darcy flow effect in the reservoir for a slightly-compressible-liquid flow in dual-porosity systems at constant wellbore pressure. The transient and boundary-dominated flow periods are examined by means of computer results generated with a finite-difference simulator. Analytical expressions of velocity and wellbore rate are presented for the first time in this paper. These equations contain the laminar-flow solution as a particular case. A method is proposed to identify the presence of inertial effects by plotting d[log(q)]/d[log(t)] against log(t). The method for area calculation under laminar conditions produces a good approximation for a reservoir under nonlaminar flow. However, the presence of inertial effects distorts the shape of decline curves, resulting in erroneous estimates of wellbore and reservoir parameters by type-curve analysis with laminar decline curves. The utility of the methodology presented in this work is illustrated with synthetic examples.

Pressure-Transient and Decline-Curve Behavior in Naturally Fractured Vuggy Carbonate Reservoirs

Summary This study presents a new way to model high secondary porosity, mainly vuggy porosity, in naturally fractured reservoirs. New solutions are presented for two cases, one in which there is no primary flow through the vugs (which is an extension of the Warren and Root model) and one in which the dissolution process of pore throats has created an interconnected system of vugs and caves. In both cases, there is an interaction between matrix, vug, and fracture systems. New insights are provided. Both pressure and production responses during transient and boundary-dominated flow periods are explored. In transient well tests, for the case in which there is no primary flow through the vugs, a change of slope could be present during the transition period. Thus, this study shows that slope ratios of 2:1 of an earlyor late-time segment vs. a transition segment do not necessarily imply transient interaction between matrix and fractures. It is also shown that the presence of vugs and caves may have a definitive influence on decline-curve and cumulative production behaviors; therefore, it is necessary to incorporate vuggy porosity in the process of type-curve match. Finally, the use of the methodology obtained in this work is illustrated with synthetic and field examples.

Automatic Decline-Curve Analysis of Wells in Gas Reservoirs

Summary A method is presented for automatic decline-curve analysis (DCA) of wells in gas reservoirs. It is based on the production behavior of a vertical well in a finite, plane reservoir containing dry gas. The method accounts for pressure-dependent gas properties, covers both transient and boundary-dominated flow, and can accommodate varying wellbore pressures. The physical parameters that govern the production behavior are estimated by nonlinear regression of observed-rate data. Interpretation of the transient flow period yields flow capacity (kh) and skin factor; the boundary-dominated flow period provides well index (WI) and gas initially in place (GIIP). Future production rates can be estimated for operating conditions other than those that prevailed during the historical production period. These estimates also may include upper and lower bounds for a given confidence level. The method is illustrated by a synthetic and a real-life example of a declining production well.

A Semi-Analytic (p/z) Rate-Time Relation for the Analysis and Prediction of Gas Well Performance

Summary In this paper we present a rigorous theoretical development of solutions for boundary-dominated gas flow during reservoir depletion. These solutions were derived by directly coupling the stabilized flow equation with the gas material balance equation. Due to the highly nonlinear nature of the gas flow equation, pseudopressure and pseudotime functions have been used over the years for the analysis of production rate and cumulative production data. While the pseudopressure and pseudotime functions do provide a rigorous linearization of the gas flow equation, these transformations do not provide direct solutions. In addition, the pseudotime function requires the average reservoir pressure history, which in most cases is simply not available. Our approach uses functional models to represent the viscosity-compressibility product as a function of the reservoir pressure/z-factor (p/z) profile. These models provide approximate, but direct, solutions for modeling gas flow during the boundary-dominated flow period. For convenience, the solutions are presented in terms of dimensionless variables and expressed as type curve plots. Other products of this work are explicit relations for p/z and Gp(t). These solutions can be easily adapted for field applications such as the prediction of rate or cumulative production. We also provide verification of our new flow rate and pressure solutions using the results of numerical simulation and we demonstrate the application of these solutions using a field example.

Identification of Minimum Numbers of Layer Required to Model Multilayer Reservoirs

ABSTRACT This paper presents new work to identify the minimum number of layers to model multilayered, commingled reservoirs and show the same well response as the complete systems. The pressure response of a well in a multilayer reservoir may be the same as that from a slightly different reservoir with fewer layers than the original reservoir. We investigated constant rate production and constant bottomhole pressure production in a hydraulically fractured and unfractured wells with varing drainage areas. We also analyzed the behavior during the transient, transition, and boundary-dominated flow periods. We used a commercial finite-difference reservoir simulator to perform the study.

Analyzing Well Production Data Using Combined-Type-Curve and Decline-Curve Analysis Concepts

Summary This paper presents new production decline curves for analyzing well production data from radial and vertically fractured oil and gas wells. These curves have been developed by combining decline-curve and type-curve analysis concepts to result in a practical tool which we feel can more easily estimate the gas (or oil) in place as well as to estimate reservoir permeability, skin effect, fracture length, conductivity, etc. Accuracy of this new method has been verified with numerical simulations and the methods have been used to perform analyses using production data from several different kinds of gas wells. Field and simulated examples are included to demonstrate the applicability and versatility of this technology. These new production decline-type curves represent an advancement over previous work because a clearer distinction can be made between transient- and boundary-dominated flow periods. They also provide a more direct and less ambiguous means of determining reserves. The new curves also contain derivative functions, similar to those used in the pressure transient literature to aid in the matching process. These production decline curves are, to our knowledge, the first to be published in this format specifically for hydraulically fractured wells of both infinite and finite conductivity. Finally, these new curves have been extended to utilize cumulative production data in addition to commonly used rate decline data.

New Results on Decline Curves Considering Non-Darcy Flow Effects

Summary Most theoretical work on decline curves considering nonlaminar flow is related to dry gas systems. The purpose of this study is to analyze decline curves considering non-Darcy flow effects in the reservoir for both slightly compressible liquid flow and solution gas-drive systems, keeping the wellbore pressure constant. The transient and boundary-dominated flow periods are examined by means of a finite difference black-oil reservoir simulator with a variable bubblepoint formulation. The consequences of this formulation under non-Darcy flow are also investigated. The influence of the mechanical skin factor on the rate response is also documented. For the case of liquid flow, presented for the first time, it is an expression to evaluate the total skin factor, which is a function of the mechanical skin and skin caused by inertial forces. This expression is given in terms of physical properties of the system, and it is proportional to the square root of the pressure drop. It also equals the square root of the Reynolds number. This is one of the main findings of this work. The possible presence of a semilogarithmic straight line of reciprocal rate for both liquid and solution gas-drive systems is investigated, and new insights are provided. In general, when inertial effects are important and the bottomhole wellbore pressure is kept constant, a true semilogarithmic straight line of the inverse of oil rate does not develop. This result is valid for both liquid and solution gas-drive systems, and it is an important difference in the case of liquid flow under a constant oil rate production, where a semilog straight line of the pressure drop is evident during the transient period considering a large drainage area. For liquid flow, an apparent straight line may be fitted, and the ordinate to the origin is approximately equal to the value of total skin computed with the expression mentioned previously. The presence of inertial effects distorts the shape of the laminar decline curves for both multiphase and slightly compressible liquid flow, causing type curve analysis to yield wrong estimates of the wellbore and reservoir parameters. Also, to perform a history match with data affected by non-Darcy flow by use of a conventional simulator that uses Darcy's law in its formulation, an alteration of the reservoir properties is necessary.

New Solutions for Well-Test-Analysis Problems: Part 2 — Computational Considerations and Applications

Summary Computational considerations in obtaining well responses and pressure distributions for several problems presented in Part 1 are discussed. In addition, new asymptotic expressions for pressure distributions in closed drainage volumes applicable during the boundary-dominated flow period are derived. Interestingly, these expressions, which are much simpler than those available in the literature, can be used to derive shape factors for a variety of completion conditions (vertical, horizontal, and vertically fractured wells). Application of constant-rate solutions to more complex conditions is also presented.

Boundary-Dominated Flow in Solutions-Gas-Drive Reservoirs

Summary The performance of wells in solution-gas-drive reservoirs during the boundary-dominated flow period is examined. Both constant-wellbore-pressure and constant-oil-rate production modes in closed systems are considered. For the constant-wellbore-pressure production mode, Arps' performance-prediction equations are examined, and predictions of future performance are shown to be strong functions of well spacing, well condition, and fluid properties. The parameters b (the decline exponent) and di (the initial decline rate) in the Arps equations are expressed in terms of physical properties. The conditions under which these equations can be used are specified. An empirical procedure to predict production rates is also presented. In the case of constant-oil-rate production, an expression to correlate the pressure distribution in the reservoir is presented. The correlating function permits us to extend the definition of pseudosteady-state flow to solution-gas-drive systems. Its use also allows the simultaneous computation of average properties (pressure and saturation) during boundary-dominated flow from wellbore information.