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Infinite Acting and Boundary Dominated Flow
Flow in a reservoir is often characterized as being one of two types, namely transient or boundary-dominated. Transient flow takes place during the early life of a well, when the reservoir boundaries have not been felt, and the reservoir is said to be infinite-acting. During this period, the size of the reservoir has no effect on the well performance, and from analysis of pressure or production, nothing can be deduced about the reservoir size. (in theory, the size of the reservoir does have an effect even at very early times, but in reality, this effect is so small as to be negligible --and not quantifiable with any kind of confidence). Transient flow forms the basis of a domain of reservoir engineering called Pressure Transient Analysis (P.T.A.), also known as well test interpretation. The field of well testing relies heavily on equations of flow for a well flowing at constant rate. Initially, the flow regime is transient, but eventually when all the reservoir boundaries have been felt, the well will flow at steady state (if a constant pressure boundary exists) or at pseudo-steady state (if all the boundaries are no-flow boundaries). During pseudo-steady state, the pressure throughout the reservoir declines at the same rate, and the reservoir acts like a tank (hence the alternative name, tank-type behaviour). The concept of pseudo-steady state is applicable to a situation where the well is flowing at a constant flow rate.
When a well is flowing at a constant flowing wellbore pressure, as is often the case in production operations, there is a period of time during which boundaries have no influence, and the flow behavior is "transient". However, after a period of time, when the radius of investigation has reached the outer boundary, the boundary starts to influence the well’s performance, and the pressure drops throughout the reservoir. But unlike pseudo-steady state, where the pressure drop is uniform throughout the reservoir, the pressure at the well is kept constant and the pressure at the boundary is dropping due to depletion. This is a case where the
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boundary is affecting the reservoir pressure, and hence the production rate, but it cannot be called pseudo-steady state, because the pressure drop in the reservoir is not uniform, so it is called boundary-dominated flow.
Thus boundary-dominated flow is a generic name for the well performance when the boundaries have a measurable effect. Pseudo-steady state is only one type of boundary-dominated flow, which takes place when the well is flowing at a constant rate.
Equivalence of Constant Rate and Constant Pressure Solutions
A well produced at a constant rate exhibits a varying (declining) bottomhole flowing pressure, whereas a well produced at a constant bottomhole pressure exhibits a varying decline rate. There is a strong symmetry between the two solutions, as both are obtained from the same equation, namely the equation that governs fluid flow in porous media. The symmetry is not exact, however, because the boundary conditions under which the two solutions are obtained are different. The constant rate solution can be converted to a constant bottomhole pressure solution (and vice versa) using the principle of superposition. The constant bottomhole pressure solution would be obtained by superposing a large number of very short constant rate solutions in time. When plotted against superposition time, the superposed constant rate solution is very similar to the constant pressure solution, provided the discretization intervals are sufficiently small. It turns out that the two solutions are quite similar during transient flow anyway, and therefore superposition is not required to make one look like the other. However, they quickly diverge once boundary dominated flow begins. The constant rate solution behaves like the harmonic stem of the Arps type curves, while the constant pressure solution declines exponentially. The figure below compares the two solutions by plotting the dimensionless typecurves of each.
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A method for forcing one solution to look like the other during boundary dominated flow would be useful because the necessity of using superposition in time would be avoided completely. Because of pressure transient analysis, diagnostic tools for analyzing the constant rate solution are widely known and understood. Therefore, there is value in being able to analyze other types of solutions using the same diagnostic tools. The concept of material-balance time provides the normalization necessary to make constant pressure and constant rate solutions equivalent. Material-balance time converts the boundary dominated flow portion of the constant pressure solution into the pseudo-steady state portion of the equivalent constant rate solution. Plotting using materialbalance time also allows solutions with both declining rates and pressures to look like the equivalent constant rate solution.
Single Well Versus Multiple Well Analysis
All of the methods used in RTA apply to single well analysis only. When considering the production of multiple wells in a field and/or reservoir, the available methods are as follows 1. Empirical- Group production decline plots 2. Material Balance Analysis- Shut-in data only 3. Reservoir Simulation 4. Semi-analytic production data analysis methods (Blasingame et al) The first step in analyzing multiple wells is to identify the objective of the analysis. The following is a list of situations where multiple well analysis is required. 1. Situations where high efficiency is required - Scoping studies / A & D - Reserves auditing 2. Single well methods sometimes don’t apply - Interference effects evident in production / pressure data- Wells producing and shutting in at different times - Predictive tool for entire reservoir is required - Complex reservoir behavior in the presence of multiple wells (multi-phase flow, reservoir heterogeneities) The vast majority of production data can be analyzed effectively without using multi-well methods. The following is a list of situations where single well analysis would suffice.
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http://www. but plotted against a material balance time that includes the effect of the offset wells in the reservoir.com/software/rta/media/webhelp/c-te-concepts.Concepts 1. Low permeability reservoirs . Cases where "outer boundary conditions" do not change too much over the production life of the well . al. Single well reservoirs 2.fekete.Wide range of reservoir types Identifying Interference Blasingame et al Interference Analysis Blasingame et.Pressure transients from different wells in reservoir do not interfere over the production life of the well 3. The process involves analysis of the single well normalized rate response (q/Dp). Interference Analysis extends the concept of single well decline analysis using typecurves to a multi-well pool.htm[6/1/2012 10:35:34 AM] .
the material balance time function is adjusted to account for total pool production as follows: Oil Wells Where Qtot = pool cumulative production at time t Gas Wells Where qtot = pool total production rate at time t tce and tcae are refered to as ”total material balance time” (for oil) and ”total material balance pseudo-time” for gas.fekete. except that material balance time is replaced by total material balance time): 1.htm[6/1/2012 10:35:34 AM] .Concepts Blasingame Type Curve Matching: Multiple Well Pools For Blasingame typecurve analysis in multi-well pools. Normalized Rate Oil Wells Gas Wells http://www. The three rate functions are as follows (defined exactly the same as for single well analysis.com/software/rta/media/webhelp/c-te-concepts.
this will vary with time. it can be approximated as: http://www. It is defined as follows: Oil Wells Gas Wells Calculation of Parameters The calculation of parameters for the multi-well pool case is very similar to that of the single well typecurve analysis. Rate Integral Derivative The rate integral derivative is defined as the semi logarithmic derivative of the rate integral function.fekete. Rate Integral The rate integral is defined at any point in the producing life of a well. However. The normalized rate integral is defined as follows: Oil Wells Gas Wells<</h4> 3. The dimensionless group reD/ D replaces reD as the typecurve matching parameter for the multi- well case. D is defined as the ratio of total pool production to individual well production.Concepts 2. total material balance time (and total material balance pseudo-time) is used in place of material balance time.com/software/rta/media/webhelp/c-te-concepts. as the average rate at which the well has produced until that moment in time. with respect to material balance time. However. In addition. Strictly speaking.htm[6/1/2012 10:35:34 AM] . a new variable D is introduced.
xf. Area and GIP(OIP) are calculated in the same manner as in the single well typecurve analysis.fekete.htm[6/1/2012 10:35:34 AM] . however. The parameters GIP(OIP) and Area. apply to the entire pool. tDde is defined as follows: Solve for rwa as follows: Solve for re from the product of qDde and tDde http://www.Concepts The parameters k. not just the individual well. s.com/software/rta/media/webhelp/c-te-concepts. Type Curve Matching Equations: Multi-Well Radial Oil Wells We define qDde as follows (this is the dimensionless decline rate that accounts for total pool production): k is obtained from rearranging the definition of qDde Now.
htm[6/1/2012 10:35:34 AM] .com/software/rta/media/webhelp/c-te-concepts.fekete.Concepts (Acres) (Mbbl) Blasingame Type Curve Matching: Radial Gas Wells k is obtained from rearranging the definition of: Solve for rwa from the definition of: http://www.
com/software/rta/media/webhelp/c-te-concepts.Concepts Solve for re from the product of qDd and tDd (Acres) Type Curve Matching Equations: Multi-Well Fractured Oil Wells k is obtained from rearranging the definition of: Solve for Xf from the definition of: http://www.fekete.htm[6/1/2012 10:35:34 AM] .
fekete.Concepts Solve for re from the product of qDde and tDde.com/software/rta/media/webhelp/c-te-concepts. (Acres) (Mbbl) Gas Wells k is obtained from rearranging the definition of: Solve for Xf from the definition of: http://www.htm[6/1/2012 10:35:34 AM] .
the sum of the flow rates from two wells with exponential decline is not exponential in general. and adjusted by a factor to account for downtime. For example. Another consideration in multi-well pools is to initialise the production rate of each well to a common start time. and that the pool forecast be obtained from the performance of the averagewell combined with a forecast of the number of producing wells. This makes it easier to arrive at the "average well" performance. it is suggested that the decline analysis be performed on an "average well per operating day". Analysis of the aggregate production would result in continuation of the operation of all three wells (because their total flow rate is larger than the aggregate economic abandonment rate).htm[6/1/2012 10:35:34 AM] . The economic abandonment rate for an aggregate of wells can be misleading. this concern is lessened.Concepts Solve for re from the product of qDde and tDde: (Acres) (bcf) Multi-Well Pools It is common practice to apply decline-curve analysis to aggregated production from a lease or pool. The extension of decline analysis from a single well to aggregated production from a number of wells is sometimes difficult to justify theoretically. http://www. Yet analysis of the individual well rates would clearly show that two of the wells should be abandoned.fekete.com/software/rta/media/webhelp/c-te-concepts. unless both wells have the same decline. the case of three producing wells. for example. when there are sufficient wells to result in a statistical distribution. Consider. Purvis has written two papers in which the decline performance of a pool is studied in a statistical manner. If the wells have reasonably similar declines. Most of the difficulty in extending the single well analysis to an aggregate of wells is often due to the inevitable variation in the number of producing wells over time. It is very possible that the total rate of the three wells would be higher than three times the economic limit of any one well. However. two of which are at a rate below the economic limit and one is producing at a high rate.
skin and OGIP.fekete. al.htm[6/1/2012 10:35:34 AM] . there is important diagnostic value in type curve analysis. for field cases.Concepts Practical Diagnostics Using Production Data and Typecurves Type curve analysis is useful for estimating reservoir parameters such as permeability.com/software/rta/media/webhelp/c-te-concepts. Some practical diagnostics include: Identifying skin damage Qualifying fracture effectiveness Identifying transition between transient and boundary dominated flow Identifying liquid loading Identifying pressure support Characterizing overpressured reservoirs Identifying interference See Anderson et. Base Model http://www. Furthermore.
Concepts Material Balance Diagnostics Productivity Diagnostics http://www.htm[6/1/2012 10:35:34 AM] .fekete.com/software/rta/media/webhelp/c-te-concepts.
They.fekete. Conceptually. they came up with a simple function they called "material-balancetime" which works very well when the change in bottomhole pressure is smooth. Palacio) developed a time-function that enables the matching of production rate data on Fetkovich type curves.Concepts "Bad Data" Diagonostics Material Balance Time The Fetkovich type curves are applicable to wells that produce at constant bottom hole pressure.com/software/rta/media/webhelp/c-te-concepts. the material-balance-time is defined as the ratio of cumulative production. particularly gas wells experience a decline in their bottomhole pressure during their life. even when the flowing pressure is varying. which is the solution widely used in the field of well testing. Q . Blasingame and his students/co-workers (McCray. After developing different time-functions. q: tc = Q / q The symbol tc has been adopted as it represents a corrected time based on cumulative production. also demonstrated that using material-balance-time converts the constant pressure solution into the constant rate solution. Many wells.htm[6/1/2012 10:35:34 AM] . and Agarwal-Gardner et al. as is often the case in production operations. to instantaneous rate. It is also similar to the http://www.
because of the varying gas PVT properties. Where Np is the cumulative oil production. Accordingly.com/software/rta/media/webhelp/c-te-concepts. the simple concept of material-balance-time given by http://www. When analyzing oil wells. The definition of material-balance-time is such as to make these areas the same. It is the value of time that a well would have to flow at the current rate in order to produce the same amount of fluid (and hence honour the material balance principle). but is only valid in terms of pseudo-pressure. also known as real gas potential). the cumulative production is represented by the area under the graph. the ratio of (cumulative production.fekete. In the illustration below.G p / instantaneous flow rate. (Gas rate/pressure analysis is not valid in terms of pressure.Concepts corrected "Horner" time that is used in build-up analysis in well testing. for correcting the effect of a varying flow rate. For gas wells. but it does not honour the pressure balance.htm[6/1/2012 10:35:34 AM] . and qo is the instantaneous oil rate.q g ) is still valid and honours the material balance.
Derivation of material-balance-time for slightly compressible systems.fekete. This is shown in the next figure. When the same type curves (in Figure 1) are plotted against dimensionless material balance time. http://www. A disturbance that is large enough to disrupt boundary-dominated flow.Concepts tc = G p / q g has limited application and is considered to be only an approximation of the more rigorous material-balance-time for gas. namely the equivalence of constant pressure and constant rate solutions. Palacio and Blasingame have developed a time function. it would lose its effectiveness if a new transient were introduced. and the harmonic stem of decline curves. so that it appears identical to the constant-rate solution. provided that the material balance time function is used. Since material balance time is designed to normalize boundary-dominated flow only. which normalizes the boundary-dominated portion of the constantpressure solution. which must be defined in terms of pseudo-time. precisely. It is fundamental to two basic ideas. This is an important result because it illustrates that the same diagnostic plots used in pressure transient analysis can be inverted and used for rate transient analysis. Another way to state the functionality of material balance time is to say that it is effective in normalizing any rate / pressure history (so that it looks like the constant rate solution). and does not address the pseudo-time issues for gas reservoirs.com/software/rta/media/webhelp/c-te-concepts. provided that both sets of data decline monotonically. material balance time also normalizes production histories in which both the rate and the pressure decline. focuses on the flow of liquids. Their time function is called material balance time and it is defined as follows (for slightly compressible fluids): As it turns out. the late-time portion of the constant pressure overlays the constant rate solution. Derivation of material-balance pseudo-time for gas accounts for changing PVT properties with reservoir pressure. Constant Compressibility Fluids Consider an oil reservoir. and their divergence during boundary dominated flow. provided that the rate / pressure history does not contain any disturbances large enough to disrupt boundary-dominated flow. would introduce a new transient flow period.htm[6/1/2012 10:35:34 AM] . A comparison of the constant-rate (declining pressure) and constant-pressure (declining rate) type curves obtained when plotting against dimensionless time (based on area) illustrates the equivalence of the two solutions during the transient period. such as a sudden (and significant) decrease in back pressure.
it has a constant value of 2 (1 divided by ½). rather than reservoir area. During transient (radial) flow. in that it exhibits a slope of negative 1 during transient flow.Concepts From the above figure it can be seen that the inverse logarithmic derivative behaves very similarly to the logarithmic derivative on a welltest type-curve. exhibit a fan of transient stems which converge into one harmonic depletion stem. when plotted against dimensionless time based on area. during pseudo-steady state.com/software/rta/media/webhelp/c-te-concepts.fekete. This follows from the fact that the AG type curve normalizes all rate and pressure solutions. the transient stems merge together. If the data are plotted against a dimensionless time based on effective wellbore radius. This follows from the fact that the pressure decline for a well produced at a constant rate has a constant slope on log-log paper. so that they behave like the constant-rate solution for slightly compressible fluids. unfractured well. the inverse logarithmic derivative falls off with a constant slope of 1 on the log-log plot. http://www. Figure 3 shows the AG type curves for a vertical. for different combinations of re/rw. while the depletion stems fan out. The primary pressure derivative has the opposite behavior to the inverse log derivative. The main difference in appearance between AG type-curves and Fetkovich type-curves is that the depletion stems for AG typecurves all collapse to the harmonic case.htm[6/1/2012 10:35:34 AM] . and becomes constant during boundary dominated flow. The 1/pD (qD) data. Upon reaching boundary dominated flow.
The material-balance-time for gas is developed in terms of pseudo-time. http://www. see Palacio and Blasingame. It does not apply to gas because the compressibility of gas is a very strong function of pressure. as follows: (1) Separating the variables and integrating. for example an undersaturated oil reservoir.fekete. Using the definition of compressibility. Material Balance Time for Oil The following development. applies rigorously to a system with constant compressibility. the oil production from a reservoir is related to the drop in average reservoir pressure. in the same way that the logarithmic pressure derivative aids in flow regime identification on welltest type-curves.Concepts The presence of the inverse log derivative and pressure derivative plots on the AG type-curve aids in the identification of transient and boundary dominated flow regimes.htm[6/1/2012 10:35:34 AM] .com/software/rta/media/webhelp/c-te-concepts.
htm[6/1/2012 10:35:34 AM] . namely. so long as the transients caused by the changing inner boundary condition do not obscure the boundary-dominated flow behaviour. Of course. and intercept p i . The second equation to be used is the pseudo-steady state solution to single-phase liquid flow under constant rate. The important characteristic of Equation (3-a) is that it is always valid. p is typically not available in practice. is obtained. time for the constant flow rate problem. the equivalence of the constant pressure and constant rate solutions. N p . to instantaneous rate. so we must use an alternate approach to applying this concept. Equation (5) suggests that a plot of D p/q as a function of material balance-time is a straight line. Combining the material-balance Equation (3-b) and the pseudo-steady state flow Equation (4) gives: (5) where. q: http://www. Material Balance Pseudo-Time for Gas The concept of material-balance-time and the derivation have been previously discussed. Q . In particular.fekete. and the harmonic stem of decline curves.com/software/rta/media/webhelp/c-te-concepts. This is due to the fact that Equation (3-a) is a material-balance equation. Blasingame and Lee state that the importance of Equation (5) is that it is also valid for moderately changing flow rate and bottomhole pressure conditions. very similar to the PSS plot of D p vs. the reservoir pressure. Blansingame and Lee (SPE 15028) showed that it is also valid when the bottomhole pressure is constant (variable rate). Before doing so. Note that if p is plotted vs. N is the original oil-in-place (OOIP). . N p . is called material-balance-time. flow regime or production scenario whether it is constant or variable flow rate. Material-balance-time is defined as the ratio of cumulative production. we recast Equation (3) in the following form: (3-b) The time function. p av. then a straight line of slope 1/ Nct . regardless of time. (4) Although Equation (4) was derived for constant rate (variable p wf).Concepts (2) and recognizing that the left-hand side is the cumulative oil production. Equation (5) is directly related to two concepts. can be calculated from: (3-a) where. and .
htm[6/1/2012 10:35:34 AM] . taking the reciprocal of Equation (3) results in the harmonic decline equation. Accordingly. (which is the gas equivalent of Equation (4).com/software/rta/media/webhelp/c-te-concepts. the simple concept of material-balance-time given by: has limited application and is considered to be only an approximation of the more rigorous material-balance-time for gas. its application to gas is more complex. and can be written as: (1) and: .fekete. p p and pseudo-time. Derivation of Equation (1) can be found at the end of this section. tca. As discussed in harmonic stem of decline curves. in the section derivation of material-balance-time) to give: (2) Addition of Equation of (1) and (2) results in an equation very similar to that for oil (Equation (5) in the section derivation of material-balance-time). which must be defined in terms of pseudo-pressure. Equation (1) can be coupled with the pseudo-steady state flow equation for the flow of single-phase gas. because of the varying PVT properties of gas. (3) where: and: . Gas flow rate data when normalized with respect to change in bottomhole pseudo-pressure should overlay the harmonic http://www.Concepts Application of this concept to oil was very straight-forward. Derivation of Material Balance Pseudo-Time for Gas. However.
htm[6/1/2012 10:35:34 AM] . for gas reservoirs.com/software/rta/media/webhelp/c-te-concepts. Calculation of the time-function however requires knowledge of the original gas in place (OGIP).fekete.Concepts stem of Fetkovich type-curve when plotted vs. DVw = Expansion of initial water volume (reduces HCPV) http://www. material-balance pseudo-time. We start by defining the material-balance equation for gas with non-zero formation and water compressibility terms. assuming a variable formation compressibility and non-zero initial water saturation. This becomes an iterative process Pseudo-Time for Gas Reservoirs with Variable Formation Compressibility The following is a rigorous development for pseudo-time. Material Balance Equation (1) where: DVp = Reduction in Hydrocarbon Pore Volume (HCPV) due to pore compressibility If cf is a function of pressure then.
fekete. equation 1 becomes: Which reduces to: where: http://www. respectively.htm[6/1/2012 10:35:34 AM] .Concepts Assuming that water compressibility is constant with pressure Vwi and Vpi are the initial pore volume and water volume. They are defined as follows: Thus.com/software/rta/media/webhelp/c-te-concepts.
Concepts Derivation of Pseudo-Time The derivation of pseudo-time requires the development of the PSS equation for gas.fekete. we use the definition of pseudo-pressure and the chain rule.htm[6/1/2012 10:35:34 AM] .com/software/rta/media/webhelp/c-te-concepts. The definition of pseudo-pressure is: (6) To derive pseudo-time. This development involves using pseudopressure and the time based derivative of the gas material-balance equation. as follows: (7) The first term in the numerator of (7) is calculated as follows: Where: Recognizing that: http://www.
Concepts (9) Where: (10) from the definition of pseudo-pressure. (13) and (8) into (7). recognizing that: (13) Substituting equation (11) into (8) and equations (12). we get: http://www. Combining equations (9) and (10). and simplifying. collecting like terms. we get Integrating both sides of (14) with respect to dt.htm[6/1/2012 10:35:34 AM] . we get: (16) (17) Where: (18) Expanding 18.com/software/rta/media/webhelp/c-te-concepts. (10). we get (11) The denominator of (7) is calculated as follows: (12) Also.fekete.
The numerical model continually evaluates the pressure or rate solution under conditions of changing PVT properties. and compare against published correlations. it is critical to understand how RTA uses these properties when the various methods are applied. To obtain realistic results. For instance. the user should strive to ensure that consistent gas properties are entered. http://www. and cg tables. Bg and cg are not independent. The analytical methods (advanced typecurves. regardless of whether or not they are input in the Advanced Properties page. will have no impact on any of the analytical methods. pseudo-time is defined as: (19) Now.htm[6/1/2012 10:35:34 AM] . even if a laboratory study exists. In the vast majority of cases. Gas Properties Gas properties (Z. such as very high pressure / high temperature environments or high H2S and/or CO2 content. the analytical and numerical methods for single phase gas analysis will yield nearly identical results. inputting a user defined Bg table The numerical model also uses variable gas properties. The analytical models use pseudo-time and pseudo-pressure to accommodate these changing properties. Gas properties can be predicted very accurately under a wide range of pressures and temperatures. In the majority of cases. it is not necessary to use input tables to define gas PVT properties. would user defined gas properties be required. Bg. both at sandface (pseudo-pressure) and average reservoir conditions (pseudo-time). Only in extreme cases. FMB and analytical models) only use pressure dependent fluid properties under certain conditions. Thus. tables. and cg) vary significantly with pressure. It is clear that gas properties Z.fekete. oil and water. if user definable PVT is desired. However. Rather they are related through the real gas law.Concepts Finally. equation (17) is rewritten as: (20) Effective Use of Advanced Properties in RTA The advanced fluid properties section in FAST RTA allows the user to specify PVT properties for gas. the underlying numerical solution uses the Bg and Thus. the Z and cg tables have no impact on the numerical solutions. It is important to note that the analytical methods focus on the Z.com/software/rta/media/webhelp/c-te-concepts.
large drawdowns and appreciable reservoir depletion cause inevitable variations in the oil properties (especially compressibility and viscosity).htm[6/1/2012 10:35:34 AM] . Viscosity. co and have values that can be established assuming either saturated or undersaturated condtions.fekete. Again. whereby PVT data is input into RTA. Below the bubble-point pressure. oil properties are usually evaluated at initial conditions and assumed constant throughout the entire analysis. only saturated properties are displayed. the fluid properties listed in the default table are always for gas-saturated conditions (oil compressibility is the only exception). Formation Volume Factor and Solution Gas Ratio When entering laboratory (or simulator) PVT data into the user tables for Bo. The analytical models follow the conventional welltest theory and assume constant values of Bo. Laboratory formation volume factor data is tabulated and graphed as follows: http://www. The graphs that accompany the tables show the undersaturated properties in a different color (usually red). necessary for the efficient solution of the welltest equations. to initial pressure conditions. it is important to use the saturated values only. because oil has very low compressibility. it is critical to understand how the PVT tables are used in the numerical model solution. co. and thus its volume does not change appreciably with pressure and temperature. . and Rs. Gas saturated oil properties are also continued above the initial bubble-point pressure. The properties. a simple example is shown. Saturated vs Undersaturated PVT Properties Oil properties Bo. and require more sophisticated procedures of application. The approximation is considered valid for short flow and buildup tests. down to the user-specified bubble point pressure. Analytical methods are only applicable if there is a single mobile phase in the reservoir. The best course of action is to compliment the analytical methods with numerical reservoir modeling. Extended production scenarios may limit the validity of the approximation for reasons: 1. The RTA properties tables are structured such that the undersaturated properties will be calculated automatically from the saturated data profile.Concepts Oil Properties Oil properties (Bo. the advanced analysis of oil production and pressure data has limited reliability if only the analytical methods are used. than gas . different grid cells may have different bubble-points (oil composition changes as solution gas is produced) at different times during the simulation. The numerical model in RTA is designed to overcome the limitations of oil production analysis and modeling associated with the standard analytical techniques. In other words. 2. Pressures in the well / reservoir system may fall below the bubble-point. In RTA. This is the most accurate and robust way to model variable rate / pressure oil production. In general. this has been considered a reasonable approximation. co and Rs.com/software/rta/media/webhelp/c-te-concepts. The undersaturated properties are displayed on the graph for pressures ranging from initial conditions. This allows the numerical model to function with variable bubble-point conditions. To illustrate the above. However. Traditionally. Rs) are much more complex. The reservoir and flowing pressures may change significantly in a production test: Minor changes in pressures can be ignored in welltest situations. 1. Extended oil production scenarios are frequently associated with free gas (saturated) conditions.
The above process is performed similarly for solution GOR and oil viscosity tables. However.com/software/rta/media/webhelp/c-te-concepts.To enter this into RTA. The undersaturated portion is automatically calculated using the Vasquez and Beggs correlation. we must remove the undersaturated data component: RTA then extrapolates the user defined data above the bubble-point pressure up to initial conditions.htm[6/1/2012 10:35:34 AM] .Concepts 2.fekete. RTA provides an additional http://www.
Oil Compressibility Oil compressibility has limited application in the numerical model and is handled differently than the other properties. water rate. To properly and accurately define the total material balance of an oil or gas reservoir: There may be significant initial water saturation in an oil or gas reservoir. The extrapolation of ratio curves must be done with due regard to the appropriate reservoir mechanism responsible for the observed trend.e. Also. The most notable exception is that the gas solubility in water is assumed to be zero. oil or oil+water). unless the oil is saturated at initial conditions. the numerical model will allow water to be produced and the specified water properties will have an impact on the total solution. An example of a consistent analysis is that of a well producing oil and water. should one extrapolate the rates or the ratios? Because decline curve analysis is an empirical process and is not fully supported in theory. B. the analytical oil methods assume constant PVT properties.fekete. The compressibility of the water may have an impact on the overall solution. co can be calculated using the following formula: Analytical Methods and PVT Properties As stated previously. then these forecasts must also be consistent with an independent analysis and forecast of the water-oil ratio. both the individual rates and their ratios (oil rate. water-oil ratio (WOR). co’s critical component in the numerical model is the undersaturated portion of the data. The viscosity modulus changes the slope and shape of the undersaturated portion of the viscosity correlation. gas-oil or gas-liquid) should be used. which of the ratios (e. especially if the reservoir is over pressured." option is deactivated. Water Properties Water properties may be viewed and manipulated in RTA. gas rate. oil and water. the analytical and numerical methods are nearly identical to those for oil analyses.com/software/rta/media/webhelp/c-te-concepts. water may be a mobile reservoir fluid under two conditions. In RTA. If water is a mobile fluid in the reservoir. there are no simple answers to these http://www. Under these conditions.htm[6/1/2012 10:35:34 AM] . Simultaneous Oil-Gas-Water Flow Decline curves are used for analyzing the production of gas or oil.g. Produced water volumes are recorded and "Water" is selected from the "Current Analysis" pull down menu. The single phase oil compressibility is used to control the mass transfer in the numerical model for all grid cells containing no free gas. Contrary to the other properties. The question often arises as to whether the individual flow rates should be analyzed or the total fluid rates (e. Critical water saturation (Relative Permeability tables) is set to below the initial water saturation value. The values of the properties being used in the analytical methods (always at initial conditions). and the numerical model is used.g. Similarly. this is the red line (Bo. This may be a required step under any of the following conditions: A. i. if a laboratory PVT study is available. If a co table is not included in the laboratory study. the properties are extrapolated to initial conditions using a PVT correlation. water-gas ratio (WGR)). Under these conditions. By simultaneous use of all the data. it is very common for the water-gas ratio to show an increasing trend while the gas rate is showing a decreasing trend. Any user defined PVT data will be honored by the analytical methods in so far as the extrapolated initial values will be used in the analytical solutions. and Rs). In the default graphed data. gas-oil ratio (GOR). are also displayed in the "Quick Properties" page if the "Enable Advanced&hellip. the viscosity modulus . This parameter can be varied to calibrate the oil viscosity correlation to laboratory data. If there are significant produced water volumes in a gas or oil analysis and accurate wellbore modeling of the fluids is required. For example. There are clear inter-relationships that must be honoured between individual flow rates and their ratios. Entering user data in the co table is advisable here. gas-liquid ratio (GLR). it is critical that the oil compressibility be predicted accurately. C. It is not possible to explicitly enter user defined properties at initial conditions in RTA. The trend of ratio curves can be opposite to that of the primary fluid curve. a more consistent analysis can be performed. In all other cases. for accurate history matching in this regime.Concepts calibration parameter for viscosity. Thus. However they can also be used to analyze the performance of wells producing mixtures of gas. If the water rate and the oil rate are analyzed and forecast individually.
total liquids (oil+water) can have an increasing trend while the oil rate has a decreasing trend. qw . Once two variables are fitted to a trend (e. Regardless of the declines being exponential or not. (Total fluid volume will not behave exponentially). WOR or qo+qw) is automatically predetermined. If both the gas rate and the oil rate are exponential. and to extrapolate that trend. the resulting decline analysis should be more reliable because more of the data has been used to arrive at the analysis.g. which displays simultaneously the individual and total flow rates and ratios.htm[6/1/2012 10:35:34 AM] . qo and qw) the third one (e. in some cases.com/software/rta/media/webhelp/c-te-concepts.e. An example of a performance chart is shown below. Some of these inter-relationships are discussed below. If the total fluid (qo + qw) and oil (qo) production rates are linear trends on semi-log co-ordinates (exponential declines). WOR. For example. then the quotient of the water and oil rates (WOR) is linear on a semi-log plot. (qw will NOT behave exponentially). Their interdependence could be controlled by the water-oil ratio trend. then their quotient (qo + qw)/ qo (i. GOR. http://www.Concepts issues. and are displayed in the form of performance charts. plotting the oil rate will give an exponential decline.qo+qw. often in semi-log coordinates (log qo. WOR + 1) will be linear on a semi-log plot. WOR+1. then the gas-oil ratio (GOR) must also be exponential. The product or quotient of two exponentials is another exponential. whereas in other instances. If both qo and qw rates are linear trends on semi-log paper. The most appropriate answer is simply to plot whatever variable in whatever scales that will give a recognizable trend. it is the total liquids (oil+water) that will give an exponential decline. the consistency between different plots needs to be appreciated. However in all cases the inter-relationship between the rates and ratios must be honoured.fekete. Because any analysis must honour all the components and their interdependence.g. Often. WGR versus time). The sum of two exponentials declines is not an exponential unless the individual declines are equal. Performance Charts A performance chart is a graph.
They are usually displayed in performance charts along with the individual rates. http://www. Usually. resulting in a more consistent analysis.fekete.Concepts Ratio Curves The ratio curves are plots of the ratios of oil. CGR (condensate-gas-ratio) : is a measure of the richness of a condensate gas. In this way. WOR+1 is a commonly used ratio. It is equal to the ratio of the total liquids to the oil rate (qo+qw) / qo. A production forecast should be terminated when either the GOR or the WOR become excessive.htm[6/1/2012 10:35:34 AM] . It is used because it often displays an exponential behaviour. the higher the CGR. It is equivalent to 1/(oilcut).com/software/rta/media/webhelp/c-te-concepts. Some of the more commonly used ratios are: GOR (gas-oil-ratio) = qg / qo . An increasing GOR or WOR is usually associated with a decreasing oil rate. however too high a CGR can result in wellbore liquid lifting problems. the interdependence of rates and ratios becomes more evident. WOR (water-oil-ratio) = qw / qo : These reflect the efficiency of the reservoir production mechanism. These various combinations are utilized to reflect different production mechanisms. gas and water rates in various combinations. the more valuable the production.
com/software/rta/media/webhelp/c-te-concepts. Copyright © 2010 Fekete Associates Inc. Water-Cut = qw / (qo+qw) . A production forecast should be terminated when the LGR becomes too high for the production system to handle. http://www. LGR (liquid-gas-ratio) : is a measure of potential production problems associated with lifting of liquids in the wellbore.fekete. is sometimes used instead of WOR for convenience of traditional terminology.htm[6/1/2012 10:35:34 AM] .Concepts WGR (water-gas-ratio) = qw / qg .
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