SEMINAR ON WATER INFLUX AND WELL TESTING PRESENTED BY : Rishiraj Phukan Rupam Sarmah Satyajit Chowdhury
ACKNOWLEDGEMENT• We thank our faculty Mr. Prasenjit Talukdar, Asst. Professor of Reservoir Engineering, Petroleum Engineering Department, DUIET, for giving us this opportunity to present ourselves on select topics.
ABSTRACT• There is more overall more water produced in reservoirs worldwide than oil & gas production. Thus it is clear that an understanding of reservoir/aquifer interaction can be an important aspect of reservoir management to optimize recovery of hydrocarbons.
WHAT IS WATER INFLUX• The incursion of water (natural or injected) into oil- or gas-bearing formations.• The replacement of produced fluids by formation water.
Occurrence of Water Influx Most petroleum reservoirs are underlain by water, andwater influx into a reservoir almost always takes placeat some rate when gas or oil is produced. Whetherappreciable ,water is produced along with gas or oil &depends on the proximity of the productive interval tothe oil-water contact or gas-water contact and whetherthe well is coning (vertical well) or cresting (horizontalwell). As explained in Schlumberger Oilfield Glossary
CAUSES OF WATER INFLUX• As reservoir fluids are produced and reservoir pressure declines, a pressure differential develops from the surrounding aquifer into the reservoir.• Following the basic law of fluid flow in porous media, the aquifer reacts by encroaching across the original hydrocarbon-water contact.• In some cases, water encroachment occurs due to hydrodynamic conditions and recharge of the formation by surface waters at an outcrop.
CLASSIFICATION OF AQUIFERS• Reservoir-aquifer systems are commonly classified on the basis of: • Degree of pressure maintenance • Flow regimes • Outer boundary conditions • Flow geometries
Degree of Pressure Maintenance • Active water driveew = Qo Bo + Qg Bg + Qw Bw• Where ew = water influx rate, bbl/day Qo = oil flow rate, STB/day Bo = oil formation volume factor, bbl/STB Qg = free gas flow rate, scf/day Bg = gas formation volume factor, bbl/scf Qw = water flow rate, STB/day Bw = water formation volume factor, bbl/STB • Partial water drive • Limited water drive
Outer Boundary Conditions• A). Infinite system indicates that the effect of the pressure changes at the oil/aquifer boundary can never be felt at the outer boundary. This boundary is for all intents and purposes at a constant pressure equal to initial reservoir pressure.• B). Finite system indicates that the aquifer outer limit is affected by the influx into the oil zone and that the pressure at this outer limit changes with time.
Flow Regimes• There are basically three flow regimes that influence the rate of water influx into the reservoir. a. Steady-state b. Semi steady (Pseudo steady)-state c. Unsteady-state
Flow Geometries• Reservoir-aquifer systems can be classified on the basis of flow geometry as: a. Edge-water drive b. Bottom-water drive c. Linear-water drive
RECOGNITION OF NATURAL WATERINFLUX• Natural water drive may be assumed by analogy with nearby producing reservoirs, but early reservoir performance trends can provide clues.• A comparatively low, and decreasing, rate of reservoir pressure decline with increasing cumulative withdrawals is indicative of fluid influx
CONSTANT CONVINIENTPRESSURE INNER BOUNDARYCONSTANT CONDITIONSFLOW RATE I8 DIFFERENT INFINITE CONVINIENT SOLUTIONS OUTER CLOSED BOUNDARY CONDITIONSCONSTANTPRESSURE GEOMETRIES LINEAR RADIAL SPHERICAL
HISTORICAL WATER INFLUX PROVIDED BY MBE EQUATION PROVIDED OOIP IS RESERVOIR KNOWN FROM POREENGINEERING VOLUME ESTIMATES CONSISTS OFUNCERTAINITIES REQUIRES HISTORICAL RESERVOIR PERFORMANCE DATA WATER INFLUX MODELS
WATER INFLUX MODELS THE MATHEMATICAL WATER INFLUX MODELS Pot aquifer Schilthuis’ steady-state Hurst’s modified steady-state The Van Everdingen-Hurst unsteady-state a) Edge-water drive b) Bottom-water drive The Carter-Tracy unsteady-state Fetkovich’s method a) Radial aquifer b) Linear aquifer
POT AQUIFER MODEL• The simplest model that can be used to estimate the water influx into a gas or oil reservoir is based on the basic definition of compressibility (ΔV = c V Δ p).• A drop in the reservoir pressure, due to the production of fluids, causes the aquifer water to expand and flow into the reservoir.• Applying the above basic compressibility definition to the aquifer gives: Water influx = (aquifer compressibility) (initial volume of water)(pressure drop) OR We = (cw + cf) Wi (pi − p) Based on compressibility equation concept
Schilthuis’ Steady-State Model• Schilthuis (1936) proposed that for an aquifer that is flowing under the steady-state flow regime, the flow behaviour could be described by Darcy’s equation. The rate of water influx ew can then be determined by applying Darcy’s equation:
Contd from previous slide…The above relationship can be more convenientlyexpressed as:where ,ew = rate of water influx, bbl/day k = permeability of the aquifer, md h = thickness of the aquifer, ft ra = radius of the aquifer, ft re = radius of the reservoir t = time, daysThe parameter C is called the water influx constant and is expressed inbbl/day/psi.
Hurst’s Modified Steady-State Model• One of the problems associated with the Schilthuis’ steady-state model is that as the water is drained from the aquifer, the aquifer drainage radius ra will increase as the time increases. Hurst (1943) proposed that the “apparent” aquifer radius ra would increase with time and, therefore the dimensionless radius ra/re may be replaced with a time dependent function, as: ra/re = at Schilthuis’ Steady- Hurst’s Modified State Model Steady-State Model We consider the log of We take ra/re as not as a ra/re constant and take and consider the term as [ra/re = at] constant.
Contd from previous slide…The Hurst modified steady-state equation can bewritten in a more simplified form as:
The Van Everdingen-Hurst Unsteady- State Model• The mathematical formulations that describe the flow of crude oil system into a wellbore are identical in form to those equations that describe the flow of water from an aquifer into a cylindrical reservoir. When an oil well is brought on production at a constant flow rate after a shut-in period, the pressure behaviour is essentially controlled by the transient (unsteady-state) flowing condition. This flowing condition is defined as the time period during which the boundary has no effect on the pressure behaviour. Need superposition theorem here. Based on dimensionless diffusivity equation.
Contd from previous page….• Van Everdingen and Hurst (1949) proposed solutions to the dimensionless diffusivity equationfor the following two reservoir-aquifer boundary conditions: • Constant terminal rate • Constant terminal pressure• For the constant-terminal-rate boundary condition, the rate of water influx is assumed constant for a given period; and the pressure drop at the reservoir-aquifer boundary is calculated.
Contd from previous slide….• Van Everdingen and Hurst solved the diffusivity equation for the aquifer-reservoir system by applying the Laplace transformation to the equation. The authors’ solution can be used to determine the water influx in the following systems: • Edge-water-drive system (radial system) • Bottom-water-drive system • Linear-water-drive system
The Carter-Tracy Water Influx Model• To reduce the complexity of water influx calculations, Carter and Tracy (1960) proposed a calculation technique that does not require superposition and allows direct calculation of water influx. Carter-Tracy Water Van Everdingen-Hurst Influx Model Unsteady-State Model Assumes constant water influx Does not assume constant water rates over each finite time interval influx rates over each finite time interval Does not need superposition concept
Contd from previous slide…..Using the Carter-Tracy technique, the cumulative waterinflux at any time, tn, can be calculated directly from theprevious value obtained at tn − 1, or:
Fetkovich’s Method• Fetkovich (1971) developed a method of describing the approximate water influx behaviour of a finite aquifer for radial and linear geometries. In many cases, the results of this model closely match those determined using the Van Everdingen-Hurst approach.• Fetkovich arrived at the following equation: Based on productivity index concept
Contd from previous slide…• The previous equation has no practical applications since it was derived for a constant inner boundary pressure. To use this solution in the case in which the boundary pressure is varying continuously as a function of time, the superposition technique must be applied. Rather than using superposition, Fetkovich suggested that, if the reservoir-aquifer boundary pressure history is divided into a finite number of time intervals, the incremental water influx during the nth interval is:
Well Testing Objectives• To evaluate well condition and reservoir characterization.• To obtain reservoir parameters for reservoir description.• To determine whether all the drilled length of oil well is also a producing zone
Contd from previous slide…•To estimate skin factor or drilling- andcompletion-related damage to an oilwell. Based upon the magnitude of thedamage, a decision regarding wellstimulation can be made.
Introduction To Well Testing Outline• Applications and objectives of well testing• Development of the diffusivity equation• Definitions and sources for data used in well testing
What Is A Well Test?• A tool for reservoir evaluation and characterization• Investigates a much larger volume of the reservoir than cores or logs• Provides estimate of permeability under in-situ conditions• Provides estimates of near-wellbore condition• Provides estimates of distances to boundaries
How Is A Well Test Conducted?Types of Well Tests q Single-Well Multi-Well
Types of Well TestsSingle-well tests Multi-rate Test • Drawdown (producing a well at constant rate beginning at Multi-well tests time zero and measuring the resulting pressure response) • Interference tests (producing one well at • Buildup (shutting a well that has been producing and constant rate beginning measuring the resulting at time zero and pressure response) measuring the resulting • Injection (Similar to a pressure response at drawdown test. Conducted one or more offset wells) by injecting fluid into a well • Pulse tests (alternately at constant rate beginning at producing and shutting time zero and measuring the in (“pulsing”) one well resulting pressure response) beginning at time zero • Injection-falloff (Similar to a and measuring the buildup test. Conducted by resulting pressure shutting in an injection well and measuring the resulting response at one or more36 pressure response) offset wells)
Information from Well Tests • Reservoir information • Extents and structure • Permeability and skin • Pressure • GOR • Samples for PVT analysis • Production estimation37
Well Test ApplicationsExploration • reservoir size, hydrocarbon volume, hydrocarbon type, productivity • (is this zone economic?, how large is the reservoir?)Reservoir Development • pressure, permeability, connectivity, productivity, formation damage, drive mechanism • (what is the reservoir pressure?, how can we estimate reserves?, forecast future performance, optimize production)Reservoir Management • pressure, permeability, drainage, sweep efficiency, formation damage • (is the well damaged?, stimulation treatment38 efficiency, why is the well not performing as expected?)
REFERENCES• SCHLUMBERGER OILFIELD GLOSSARY• ANSWERS.COM• RESERVOIR ENGINEERING BY TAREK AHMED• PRACTICAL ENHANCED RESERVOIR ENGINEERING• THE WORLD WIDE WEB