fig1 schematically illustrates a horizontal well pair ( i . e ., injector and producer ) in a typical sagd bitumen recovery installation in a bitumen - laden subterranean oil sands formation 30 underlying an overburden layer 20 extending to the ground surface 10 , and overlying an underburden formation 40 , all in accordance with prior art knowledge and well within the understanding of persons of ordinary skill in the art . steam under high pressure is introduced into injector well 50 from a connecting well leg ( not shown ) extending to ground surface 10 . injector 50 has a slotted or orificed liner such that steam exits injector 50 through the liner slots or orifices and permeates oil sands formation 30 to create a steam chamber 70 within formation 30 . in this context , the term “ steam chamber ” may be understood to mean a volume within formation 30 in which steam remains present and mobile , at least for so long as steam injection into formation 30 continues . for analytical purposes , it is assumed that regions of formation 30 outside steam chamber 70 are essentially uninfluenced by the steam injected through injector 50 . the pattern of steam migration within formation 30 , and thus the configuration of steam chamber 70 , will vary with a variety of factors including formation characteristics and steam injection parameters . however , as represented by the idealized configuration shown in fig1 , a typical steam chamber 70 for a sagd well can be considered or modeled as being generally wedge - shaped in cross - section , surrounding injector well 50 , with a “ roofline ” 72 and sloping side boundaries 74 converging downward toward a lower limit 76 . steam migrating to steam chamber side boundaries 74 condenses due to the lower temperature of the surrounding region of formation 30 . as the steam condenses , it transfers energy to the bitumen , increasing its temperature and thus decreasing its viscosity such that it becomes flowable , whereupon the mobile bitumen and condensate flow downward and accumulate as a liquid inventory 80 within a lower region of steam chamber 70 , below injector 50 . a fluid interface 85 is thus formed between liquid inventory 80 and the overlying region of steam chamber 70 . based on theory and field observation , the level of fluid interface 85 is assumed for analytical purposes to be lowest ( i . e ., closest to producer 60 ) at a point 85 x directly above producer 60 . a producer well 60 is installed at a selected depth below and generally parallel to injector 50 , such that it can be expected to lie within the zone of liquid inventory 80 upon formation of steam chamber 70 . producer well 60 has slots or other suitable orifices to allow the bitumen / condensate mix in liquid inventory 80 to enter producer 60 for production to the surface 10 . for this purpose , producer well 60 typically has a liner with narrow slots or other orifices that allow liquid flow into producer 60 while substantially preventing sand or other contaminants from entering producer 60 or clogging the slots or orifices in the liner . fig2 provides an enlarged illustration of liquid inventory 80 and producer well 60 within a lower region of steam chamber 70 . also indicated in fig2 is an analysis boundary 90 surrounding producer well 60 , with analysis boundary 90 being an empirically defined or selected parameter for purposes of predictive methods in accordance with the present disclosure . in accordance with a preferred embodiment of these predictive methods , analysis boundary 90 is assumed to be circular in cross - section and centered around producer well 60 , with a radius corresponding the distance from the center of producer 60 to point 85 x on fluid interface 85 . however , alternative configurations of analysis boundary 90 may be appropriate to satisfy case - specific physical and / or analytical constraints . fig3 schematically illustrates one embodiment of a procedure for developing a “ gravity ipr ” for use in evaluating the stability of liquid inventory 80 . in this context , the stability of liquid inventory 80 relates to the stability of the vertical distance from producer 60 to point 85 x on fluid interface 85 at given points along the horizontal length of producer 60 ( which for purposes of fig2 corresponds to the radius of circular analysis boundary 90 ). procedural and analytical steps shown in fig3 are summarized below : measure temperatures within steam chamber 70 and the vertical temperature gradient in liquid inventory 80 . define the temperature drawdown to be the difference between the steam chamber temperature and the inflow temperature ( i . e ., temperature of produced fluids flowing into producer well 60 ). for this purpose : consider a cross - section of producer wellbore 60 and the surrounding liquid inventory 80 in a plane perpendicular to the axis of the wellbore . define analysis boundary 90 such that it encompasses producer wellbore 60 and contacts fluid interface 85 between liquid inventory 80 and the overlying steam chamber 70 . the distance between producer wellbore 60 and fluid interface 85 ( i . e ., the liquid level ) is given by the temperature drawdown and the vertical temperature gradient . for this purpose : map the measured steam chamber temperature and vertical temperature gradient onto the area enclosed by analysis boundary 90 . for this purpose : the temperature at liquid - vapor interface 85 is assumed to equal the steam temperature . the temperature at locations within analysis boundary 90 is calculated from the vertical temperature gradient and the distance below the liquid - vapor interface 85 . specify the pressure conditions at analysis boundary 90 and producer wellbore 60 . define the pressure drawdown to be the difference between the steam chamber pressure and the wellbore pressure . using numerical or analytical methods known to persons of ordinary skill in the art , determine the relationship between the pressure drawdown and the flow rate into wellbore 60 . for this purpose : the pressure at liquid - vapor interface 85 is assumed to equal the pressure within steam chamber 70 ( which is taken to be the saturation pressure corresponding to the measured steam chamber temperature ). the total head ( i . e ., the sum of the pressure head and the elevation head ) is assumed to be constant along analysis boundary 90 . a skin factor is included to account for near - wellbore pressure losses that are measured in the field but not captured by conventional equations for flow through porous media ( e . g ., darcy &# 39 ; s law ). “ skin factor ” in this context is a term well understood in the field ( see , for example , the definition of skin factor in the schlumberger oilfield glossary : www . glossary . oilfield . slb . com ). flow chart blocks 110 and 120 in fig3 represent additional criteria taken into consideration in the solution stage 104 : block 110 — the analysis boundary represents a uniform head ( i . e ., a flow isobar ), and flow normal to the boundary integrated around the perimeter of the boundary defines the inflow to the wellbore . in its simplest form , it is a cylindrical boundary centered on the producer wellbore and touching the lowest part of the fluid interface . other shapes for the analysis boundary can be incorporated to reflect better conformance to a different fluid level interface , if additional refinement to reflect a changing steam chamber shape with time is desired . block 120 — reservoir and fluid properties are calculated over the range of temperatures considered inside the analysis boundary . relative permeability properties are incorporated and in combination with the temperature field and fluid portions in determining the pressure gradients that are integrated to arrive at the inflow characterization . determine the relationship between the pressure drawdown and inflow rate at various temperature drawdowns . plot inflow rate as a function of inflow temperature for a constant pressure drawdown , as shown in fig4 . the slope of the plotted curve ( s ) is negative in the stable range of inflow temperatures . within the stable range of inflow temperatures , an increase in liquid level ( resulting when the delivery rate into liquid inventory 80 exceeds the inflow rate into producer well 60 ) will cause the inflow rate to increase . the liquid level will rise until it reaches an equilibrium position at which the inflow rate matches the delivery rate . a decrease in liquid level ( resulting when the inflow rate exceeds the delivery rate ) causes the inflow rate to decrease . the liquid level will drop until it reaches an equilibrium position at which the inflow rate matches the delivery rate . outside the stable range of inflow temperatures , an increase in liquid level will cause the inflow rate to decrease , allowing the liquid level to “ run away .” for certain combinations of pressure drawdown , fluid properties , and reservoir properties , the slope of the curve ( s ) will be positive for all inflow temperatures , indicating that there is no stable range of inflow temperatures . a decrease in liquid level will cause the inflow rate to increase , potentially leading to steam breakthrough into producer 60 . when coupled to a wellbore hydraulic model , the gravity ipr enables the performance of a production well to be evaluated by measuring the inflow temperature along the well to determine when the liquid level is reaching critical levels ( i . e ., when fluid level rise in portions of the well compromises production efficiency , or when fluid level drop in portions of the well compromises well integrity ). more specifically , the gravity ipr provides a basis for : configuring producer well completions to deliver a pressure distribution that is within the range of self - balancing performance over the life of the well . evaluating how pump intake subcool should be controlled to maintain hydraulic conditions within the self - balancing range of operation over the entire well . evaluating production rate capacities for specific completion options and field applications . using inflow temperature distributions for evaluating completion configuration changes to match reservoir variations and maintain performance within the self - balancing range over the entire well . using temperature fall - off logs for evaluating completion configuration changes to match reservoir variations and maintain performance within the self - balancing range over the entire well . using temperature measurements to set “ smart well ” controls for production wells and maintain performance within the self - balancing range over the entire well . positioning or repositioning tubing intake points to maintain performance within the self - balancing range over the entire well . adjusting chokes on gas lift tubing based on intake temperature to maintain performance within the self - balancing range over the entire well . determining where fluid conditions approach water saturation , leading to flashing , which in turns chokes flow to automatically regulate inflow . by using flow conditions in the gipr assessment , determining locations where pore throat water flashing may produce scaling and inflow restrictions . the gravity ipr also provides a basis for determining reservoir delivery distribution over the length of the steam chamber : for producer wells operating in the self - balancing range , the delivery distribution can be calculated from temperature fall - off logs and inflow distributions using distributed temperature measurements under static inflow conditions . for wells operating in the dynamic range , the reservoir delivery distribution can be calculated from the inflow rate to the well and the transient behaviour of the fluid level . transient plugging development ( for example , plugging of slots / orifices in the liner , or plugging in the formation itself by way or pore throat plugging ) can be determined using temperature measurements and the gravity ipr . producer well configuration updates can be evaluated to : assess the likelihood of maintaining the well in the self - balancing performance envelope and the reconfiguration requirements to maintain stability . determine a production intervention schedule to maintain an efficient production distribution under dynamic fluid level control . other analytical methods for describing the inflow performance of the sagd or any other gravity process can be calibrated using methods in accordance with the present disclosure . for example a conventional ipr inflow performance relationship can be calibrated by determining the drainage radius in the basic ipr equation as a function of inflow temperature . this can provide an even simpler basis for evaluating sagd inflow performance . one example of such an application would be wellbore hydraulics programs used for analyzing and optimizing completions for sagd production . fig5 schematically illustrates one embodiment of a procedure for developing an axial flow relationship for use in predicting the axial flow rate through liquid inventory 80 . in fig5 , reference numbers 101 - 105 , 110 , and 120 correspond to the same reference numbers in fig3 , specifically in the context of a first location along a producer well . reference numbers 201 - 205 , 210 , and 220 similarly correspond to flow chart blocks 101 - 105 , 110 , and 120 in the context of a second location along the producer well . procedural and analytical steps shown in fig5 are summarized below : characterize the gravity ipr at two axial locations along producer well 60 : measured or estimated conditions at the two locations ( for example , steam chamber temperature , vertical temperature gradient , fluid properties , or reservoir properties ) will be used to approximate conditions in the liquid inventory between the two locations . the greater the distance between the two locations , the greater the uncertainty in this approximation . an analysis boundary suitable for characterization of the gravity ipr may not be appropriate for characterization of the axial flow relationship . when liquid flows radially from fluid interface 85 to producer well 60 , the pressure gradient is largest near producer well 60 , where the flow area is smallest and the fluid viscosity is highest ( because the temperature decreases from fluid interface 85 to producer well 60 ). consequently , conditions in the part of liquid inventory 80 near producer well 60 will have a greater influence on the gravity ipr than conditions in other parts of liquid inventory 80 . by contrast , the axial flow relationship will be most strongly influenced by conditions in the part of liquid inventory 80 near fluid interface 85 , where the temperature is highest and the fluid is most mobile . therefore , for characterization of the axial flow relationship , analysis boundary 90 should be expanded to include the part of liquid inventory 80 near fluid interface 85 . for purposes of characterizing an axial flow relationship , the axial hydraulic conductivity may be calculated at numerous points in liquid inventory 80 and analysis boundary 90 defined according to an axial hydraulic conductivity criterion . for example , the analysis boundary may be drawn along a contour of constant axial hydraulic conductivity to encompass only the part of the liquid inventory where the axial hydraulic conductivity is greater than a specified minimum value . the axial hydraulic conductivity criterion may alternatively be expressed in terms of an axial hydraulic conductivity ratio — for example , the ratio of the local axial hydraulic conductivity to the maximum axial hydraulic conductivity . evaluate the axial hydraulic conductivity of the part of liquid inventory 80 enclosed by analysis boundary 90 at both axial locations , using numerical or analytical methods known to persons of ordinary skill in the art . the axial hydraulic conductivity is the proportionality constant relating the axial flow velocity and the axial hydraulic gradient . interpolate to approximate the axial hydraulic conductivity of liquid inventory 80 between the two axial locations . for this purpose : the axial hydraulic conductivity of liquid inventory 80 between the two axial locations is taken as the average of the axial hydraulic conductivity at the first location and the axial hydraulic conductivity at the second location . when conditions other than the liquid level ( for example , the steam chamber temperature , vertical temperature gradient , fluid properties , and reservoir properties ) are approximately equal at the two locations , the axial hydraulic conductivity of liquid inventory 80 at the first location may be assumed to equal the axial hydraulic conductivity at the second location and , in turn , the axial hydraulic conductivity between the two locations . by extension , when conditions other than the liquid level are approximately uniform along producer well 60 , the axial hydraulic conductivity of liquid inventory 80 need only be evaluated at one axial location . variations in the liquid level will shift the mobile part of liquid inventory 80 vertically but will not significantly affect the axial hydraulic conductivity . calculate the axial flow rate through liquid inventory 80 as the product of the axial hydraulic conductivity , effective axial hydraulic gradient , and mean flow area . for this purpose : the effective axial hydraulic gradient between the two locations is taken as the difference between the liquid level at the first location and the liquid level at the second location , divided by the axial distance between the two locations . the effective axial hydraulic gradient may account for variations in the axial hydraulic gradient with distance from producer well 60 due to radial flow from fluid interface 85 to producer well 60 . the mean flow area is taken as the average of the areas enclosed by analysis boundary 90 at the two locations . the gravity ipr may be characterized at a plurality of axial locations along the producer well and axial flow relationships developed for each pair of adjacent locations to create a system of axial flow relationships , or axial flow “ network ”. when included in a wellbore hydraulic model coupled with the gravity ipr , an axial flow network enables improved estimation of liquid level variations over time , based not only on an imbalance between the inflow distribution and delivery distribution , but also on the axial redistribution of liquid from locations with a higher liquid level to locations with a lower liquid level . estimation of the liquid level above blank ( i . e ., unslotted or unscreened ) sections of the producer liner , where liquid must flow axially through the liquid inventory before flowing radially into a slotted section of the liner ; and estimation of the liquid level above locations of formation damage , where a reduction in the near - wellbore permeability causes liquid to flow preferentially in the axial direction . it will be readily appreciated by those skilled in the art that various modifications of methods in accordance with the present disclosure may be devised without departing from the scope and teaching of the present invention . it is to be especially understood that the subject methods are not intended to be limited to any described or illustrated embodiment , and that the substitution of a variant of a claimed element or feature , without any substantial resultant change in the working of the methods , will not constitute a departure from the scope of the invention . in this patent document , any form of the word “ comprise ” is to be understood in its non - limiting sense to mean that any item following such word is included , but items not specifically mentioned are not excluded . a reference to an element by the indefinite article “ a ” does not exclude the possibility that more than one of the element is present , unless the context clearly requires that there be one and only one such element . relational terms such as “ parallel ”, “ horizontal ”, and “ perpendicular ” are not intended to denote or require absolute mathematical or geometric precision . accordingly , such terms are to be understood in a general rather than precise sense ( e . g ., “ generally parallel ” or “ substantially parallel ”) unless the context clearly requires otherwise . wherever used in this document , the terms “ typical ” and “ typically ” are to be interpreted in the sense of representative or common usage or practice , and are not to be understood as implying invariability or essentiality .