Erdal Ozkan

New Solutions for Well-Test-Analysis Problems: Part 1-Analytical Considerations(includes associated papers 28666 and 29213 )

In this paper point-source solutions are derived in the Laplace-transform domain and an extensive library of solutions is documented to obtain pressure distributions and well responses for a wide variety of wellbore configurations: partially penetrating vertical wells, horizontal wells, and fractured wells (complete or limited entry). Wells may be located in infinite or bounded systems (rectangular or circular reservoirs). Several combinations of closed and/or constant-pressure boundary conditions are considered at the vertical and lateral reservoir boundaries. These solutions may be used to examine homogeneous or naturally fractured reservoirs.

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

In this paper 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.

Horizontal Well Pressure Analysis

This paper presents an analysis of the pressure-transient behavior of a horizontal well or a drainhole. The performances of horizontal wells and fully penetrating vertical fractures are compared. Dimensionless wellbore pressures are computed for two classic boundary conditions: infinite conductivity and uniform flux. Results are presented as pseudoskin factors and as type curves. In addition to conventional pressure-vs.-time type curves, derivative type curves from pressure/time predictions are presented. The derivative approach the authors discuss is applicable to a broader range of problems than considered here.

Verification and Proper Use of Water- Oil Transfer Function for Dual-Porosity and Dual-Permeability Reservoirs

Summary Accurate calculation of multiphase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a very crucial issue. In this paper, we will present the viability of the use of a simple transfer function to accurately account for fluid exchange resulting from capillary and gravity forces between fracture and matrix in dual-porosity and dual-permeability numerical models. With this approach, fracture- and matrix-flow calculations can be decoupled and solved sequentially, improving the speed and ease of computation. In fact, the transfer-function equations can be used easily to calculate the expected oil recovery from a matrix block of any dimension without the use of a simulator or oil-recovery correlations. The study was accomplished by conducting a 3-D fine-grid simulation of a typical matrix block and comparing the results with those obtained through the use of a single-node simple transfer function for a water-oil system. This study was similar to a previous study (Alkandari 2002) we had conducted for a 1D gas-oil system. The transfer functions of this paper are specifically for the sugar-cube idealization of a matrix block, which can be extended to simulation of a match-stick idealization in reservoir modeling. The basic data required are: matrix capillary-pressure curves, densities of the flowing fluids, and matrix block dimensions.

Performance of Horizontal Wells Subject to Bottomwater Drive

This paper discusses the performance of a horizontal well subject to bottomwater drive and delineates conditions under which this completion mode is more appropriate. Information presented will enable the engineer to decide what productivity improvements may be expected from horizontal-well completions. The productivities of horizontal wells operating under bottomwater drive are discussed in terms of displacement efficiencies. Results and the discussions are also applicable to oil production by gas-cap drive.

Pilot Testing Issues of Chemical EOR in Large Fractured Carbonate Reservoirs

Many world class large carbonate reservoirs leave behind at least half of the initial oil in place. Typically water injection is used to improve oil recovery while gas injection is used to maintain pressure or to promote oil gravity drainage. Immiscible gas injection, including injection of CO2, has been considered but not implemented on a large scale for economic reasons. Furthermore, interest in using surfactants in large carbonate reservoirs has recently flourished. As a result, we began to investigate the viability of designing and conducting a manageable pilot test program in a large fractured carbonate reservoir using a single-well, dual-completion system to evaluate the efficacy of the surfactant oil mobilization and oil capture. However, pilot testing in large reservoirs is very expensive and requires a long time to complete. These issues are less problematic in pilot testing of small and thin reservoirs in onshore field. In this paper we will present the results of a conceptual model to simulate the performance of surfactant flooding in the above-mentioned pilot test configuration. Three different model formulations, having different approaches to gridding and grid-refinement, were used. These include conventional dual-porosity, dual-permeability, and single-porosity models with variable porosity and permeability to simulate fracture-matrix interactions. Simulation of pilot tests using dual-porosity models shows that gravity is most effective during waterflood but not as effective during the surfactant injection while in the dual-permeability models, the surfactant oil recovery is greater because both gravity and viscous displacement contribute. We will explain the reasons and will indicate which model is more reliable. In general the results of this study give an insight into the viability of using surfactant injection in thick carbonate reservoirs both in the pilot and production stage. Introduction In the U.S, typically about a third of the original oil in place (OOIP) is recovered by primary and secondary recovery processes, leaving two-thirds of the oil behind as remaining oil (NPC, 1984). About 60% of world‟s discovered oil reserves are in carbonate reservoirs, and many of these reservoirs are naturally fractured (Rohel and Choquette, 1985). According to a recent review of 100 fractured reservoirs (Allan and Sun, 2003), fractured carbonate reservoirs with high matrix porosity and low matrix permeability could be good candidates for enhanced oil recovery (EOR) processes. The oil recovery from these reservoirs is typically very low because about 80% of fractured carbonate reservoirs are either oil-wet or mixed-wet. Injected water will not penetrate easily into the oil-wet porous matrix to displace oil. Wettability of carbonate reservoirs probably is the most important oil recovery controlling parameter (Morrow and Mason, 2001; Tong et al., 2002; Hirasaki and Zhang, 2006). Typically water injection is used to improve oil recovery, while gas injection is used to maintain pressure or to promote oil gravity drainage as an IOR process. If gas injection is miscible or near-miscible, oil recovery is enhanced because a fraction of the conventional residual oil is mobilized by miscibility or near-miscibility conditions. Water and gas injection have been used to produce oil from the matrix in naturally fractured reservoirs (NFR) mainly by gravity drainage. Viscous displacement in fracture-dominated NFR generally plays a minor role except for chemical flooding, where surfactants might enter the matrix from fractures with assistance from viscous displacement to mobilize oil. Even this effect appears to be small because of the lack of deep surfactant penetration. In water-wet NFR, water imbibes strongly into the matrix and produces a lot of oil. However, in oil-wet reservoirs, water-flooding is relatively inefficient. This is characterized by the early water breakthrough and rapidly increasing water-oil ratio. The reason is that, for an oil-wet reservoir, the injected water tends to travel only through the fractures and not enter the

Water and Gas Coning toward Finite-Conductivity Horizontal Wells: Cone Buildup and Breakthrough

This study concludes that the shape as well as the time of breakthrough of a water or a gas cone are significantly affected by the pressure drop within the wellbore. An analytical model is used to demonstrate features of the movement of a cone when pressure drops in the wellbore are important. It is shown that wellbore hydraulics produces a self-sharpening feature and this leads to breakthrough at the heel of the well. This behavior may not be demonstrated by assuming an infinite-conductivity wellbore. The model described here may be used to assist simulation studies by providing specifics on the movement of the cone.

Evaluation of inflow performance of multiple horizontal wells in closed systems

This work presents a model to investigate the inflow performance relationships (IPR) of horizontal and vertical wells in a multi-well pattern. The model can be used to compute the overall and individual well performances. It is shown that stabilized IPRs may not be sufficient for the evaluation of horizontal well performances due to prolonged transient flow periods. The results presented in this paper clearly indicate that inflow performance of wells in a multi-well pattern is a dynamic concept; and, especially in the prediction of future performances, dynamic rather than static IPR models should be used. S0195-07380000801-3

Interpretation of horizontal-well production logs : Influence of logging tool

This paper investigates the influence of production-logging tool on wellbore flow-rate and pressure measurements. The focus of the investigation is on the disturbance caused by the production-logging tool and the coiled tubing on the original flow conditions in the wellbore. An analytical model is used in the investigation and single-phase liquid flow is assumed. The influence of the production-logging tool on the measurements is substantiated by the deviation from the original flow-rate and pressure profiles. It is shown that the influence of the production-logging tool manifests itself in low-conductivity wellbores. High production rates further amplify the effect of the production-logging tool. It is concluded that the effect of the production-logging tool may be ignored if dimensionless well conductivity exceeds 500 and the Reynolds number is lower than 100000. Results indicate that a production log run in a low-conductivity horizontal well may not indicate the low-permeability zones along the well.

A Critical Review For Proper Use Of Water-Oil-Gas Transfer Functions In Dual-Porosity Naturally Fractured Reservoirs-Part II

Summary This paper continues the work presented in Ramirez et al. (2009). In Part I, we discussed the viability of the use of simple transfer functions to accurately account for fluid exchange as the result of capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. Here, we show additional information on several relevant topics, which include (1) flow of a low-concentration water-soluble surfactant in the fracture and the extent to which the surfactant is transported into the matrix; (2) an adjustment to the transfer function to account for the early slow mass transfer into the matrix before the invading fluid establishes full connectivity with the matrix; and (3) an analytical approximation to the differential equation of mass transfer from the fracture to the matrix and a method of solution to predict oil-drainage performance. Numerical experiments were performed involving singleporosity, fine-grid simulation of immiscible oil recovery from a typical matrix block by water, gas, or surfactant-augmented water in an adjacent fracture. Results emphasize the viability of the transfer-function formulations and their accuracy in quantifying the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix. For miscible flow, the fracture/matrix mass transfer is less complicated because the interfacial tension (IFT) between solvent and oil is zero; nevertheless, the gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of the oil.